Subgroups — C₇×#61163 #13238379

Order 1792.

2124 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₇×#3323	C₂	1	2	yes	maximal, complemented
5	C₇×#3317	C₂	1	2	yes	maximal, complemented
6	C₇×#3315	C₂	1	2	yes	maximal, complemented
7	C₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₇×#3310	C₂	1	2	yes	maximal, complemented
9	C₇×#3300	C₂	1	2	yes	maximal, complemented
10	C₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₇×#552	—	2	1	no	—
32	C₇×#552	—	2	1	no	—
33	C₇×#552	—	2	1	no	—
34	C₇×#552	—	2	1	no	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×#552	C₂²	1	2	yes	complemented
38	C₇×#552	C₂²	1	2	yes	complemented
39	C₇×#550	C₂²	1	1	yes	characteristic
40	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
41	C₇×#548	C₂²	1	1	yes	characteristic
42	C₇×#548	C₂²	1	1	yes	characteristic
43	C₇×#547	—	2	1	no	—
44	C₇×#547	C₂²	1	1	yes	characteristic
45	C₇×#546	—	2	1	no	—
46	C₇×#546	—	2	1	no	—
47	C₇×#546	C₂²	1	1	yes	characteristic
48	C₇×#546	C₂²	1	1	yes	characteristic
49	C₇×D₄²	—	2	1	no	—
50	C₇×D₄²	C₂²	1	1	yes	characteristic
51	C₇×#532	—	2	1	no	—
52	C₇×#532	C₂²	1	1	yes	characteristic
53	C₂×C₇×#126	—	2	1	no	—
54	C₂×C₇×#125	—	2	1	no	—
55	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
56	C₇×#525	—	2	1	no	—
57	C₇×#525	—	2	1	no	—
58	C₇×#525	C₂²	1	1	yes	characteristic
59	C₇×#525	C₂²	1	1	yes	characteristic
60	C₂×C₇×#123	—	2	1	no	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₇×#41	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×C₇×D₄	—	2	1	no	—
66	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
67	C₂×C₇×#117	—	2	1	no	—
68	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₇×#491	C₂²	1	2	yes	complemented
71	C₇×#490	C₂²	1	2	yes	complemented
72	C₇×#488	C₂²	1	2	yes	complemented
73	C₇×#488	C₂²	1	2	yes	complemented
74	C₇×#485	C₂²	1	2	yes	complemented
75	C₇×#485	C₂²	1	2	yes	complemented
76	C₇×#484	C₂²	1	2	yes	complemented
77	C₇×#483	C₂²	1	2	yes	complemented
78	C₇×#482	C₂²	1	2	yes	complemented
79	C₇×#482	C₂²	1	2	yes	complemented
80	C₇×#481	C₂²	1	2	yes	complemented
81	C₇×#480	C₂²	1	2	yes	complemented
82	C₇×#479	C₂²	1	2	yes	complemented
83	C₇×#479	C₂²	1	2	yes	complemented
84	C₇×#478	C₂²	1	2	yes	complemented
85	C₇×#478	C₂²	1	2	yes	complemented
86	C₇×#470	C₂²	1	2	yes	complemented
87	C₇×#470	C₂²	1	2	yes	complemented
88	C₇×#468	C₂²	1	2	yes	complemented
89	C₇×#468	C₂²	1	2	yes	complemented
90	C₇×#467	C₂²	1	2	yes	complemented
91	C₇×#467	C₂²	1	2	yes	complemented
92	C₇×#465	C₂²	1	2	yes	complemented
93	C₇×#465	C₂²	1	2	yes	complemented
94	C₇×#464	C₂²	1	2	yes	complemented
95	C₇×#464	C₂²	1	2	yes	complemented
96	C₇×#462	C₂²	1	2	yes	complemented
97	C₇×#460	C₂²	1	2	yes	complemented
98	C₇×#452	C₂²	1	2	yes	complemented
99	C₇×#452	C₂²	1	2	yes	complemented
100	C₇×#452	C₂²	1	2	yes	complemented
101	C₇×#452	C₂²	1	2	yes	complemented
102	C₇×#451	C₂²	1	2	yes	complemented
103	C₇×#451	C₂²	1	2	yes	complemented
104	C₇×#450	C₂²	1	2	yes	complemented
105	C₇×#450	C₂²	1	2	yes	complemented
106	C₇×#441	C₂²	1	2	yes	complemented
107	C₇×#440	C₂²	1	2	yes	complemented
108	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
109	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
110	C₇×#436	C₂²	1	2	yes	complemented
111	C₇×#435	C₂²	1	2	yes	—
112	C₇×#435	C₂²	1	2	yes	complemented
113	C₇×C₈×D₄	C₂²	1	2	yes	complemented
114	C₇×#428	C₂²	1	1	yes	characteristic, complemented
115	C₇×#428	C₂²	1	1	yes	characteristic, complemented
116	C₇×#428	C₂²	1	1	yes	characteristic, complemented
117	C₇×#423	C₂²	1	1	yes	characteristic, complemented
118	C₇×#419	C₂²	1	1	yes	characteristic, complemented
119	C₇×#419	C₂²	1	2	yes	complemented
120	C₇×#418	C₂²	1	2	yes	complemented
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic
123	C₇×#417	C₂²	1	1	yes	characteristic
124	C₇×#417	C₂²	1	1	yes	characteristic, complemented
125	C₇×#417	C₂²	1	1	yes	characteristic, complemented
126	C₇×#417	C₂²	1	1	yes	characteristic, complemented
127	C₇×#417	C₂²	1	1	yes	characteristic, complemented
128	C₇×#417	C₂²	1	1	yes	characteristic, complemented
129	C₇×#417	C₂²	1	1	yes	characteristic, complemented
130	C₇×#417	C₂²	1	2	yes	complemented
131	C₇×#417	C₂²	1	2	yes	complemented
132	C₇×#416	C₂²	1	2	yes	complemented
133	C₇×#416	C₂²	1	2	yes	complemented
134	C₂×C₇×#103	C₂²	1	2	yes	complemented
135	C₂×C₇×#102	C₂²	1	2	yes	complemented
136	C₇×#407	C₂²	1	1	yes	characteristic, complemented
137	C₇×#407	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
139	#61163	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	1	no	—
143	C₂×C₇×#41	—	2	1	no	—
144	C₂×C₇×#41	—	2	4	no	—
145	C₂×C₇×#41	—	2	4	no	—
146	C₂×C₇×#41	—	4	2	no	—
147	C₂×C₇×#41	—	4	2	no	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂×C₇×#41	C₂³	1	1	yes	characteristic
152	C₂×C₇×#41	C₂³	1	1	yes	characteristic
153	C₂×C₇×#41	C₂³	1	1	yes	characteristic
154	C₂×C₇×#41	C₂³	1	1	yes	characteristic
155	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
157	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
158	C₂²×C₇×D₄	—	2	1	no	—
159	C₂²×C₇×D₄	—	2	1	no	—
160	C₂²×C₇×D₄	—	2	1	no	—
161	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
162	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₇	—	2	1	no	—
165	C₂³×C₄×C₇	—	2	1	no	—
166	C₂³×C₄×C₇	—	2	1	no	—
167	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
169	C₇×#137	—	2	4	no	—
170	C₇×#137	—	4	2	no	—
171	C₇×#137	—	4	2	no	—
172	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
173	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
174	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
175	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
176	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
177	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
178	C₂×C₇×M₁₆	—	4	2	no	—
179	C₂×C₇×M₁₆	—	4	2	no	—
180	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
183	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
184	C₂×C₇×M₁₆	C₂³	1	2	yes	—
185	C₂×C₇×M₁₆	C₂³	1	2	yes	—
186	C₂²×C₇×C₈	C₂³	1	2	yes	—
187	C₂²×C₇×C₈	C₂³	1	2	yes	—
188	C₇×C₄⋊Q₈	—	2	1	no	—
189	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
190	C₇×#127	—	2	1	no	—
191	C₇×#127	C₂³	1	1	yes	characteristic
192	C₇×#126	—	2	2	no	—
193	C₇×#126	—	2	2	no	—
194	C₇×#126	—	2	2	no	—
195	C₇×#126	—	2	2	no	—
196	C₇×#125	—	2	2	no	—
197	C₇×#125	—	2	2	no	—
198	C₇×#125	—	2	2	no	—
199	C₇×#125	—	2	2	no	—
200	C₇×#125	—	2	1	no	—
201	C₇×#125	—	2	1	no	—
202	C₇×#125	C₂³	1	2	yes	—
203	C₇×#125	C₂³	1	2	yes	—
204	C₇×#124	—	2	1	no	—
205	C₇×#124	—	2	1	no	—
206	C₇×#124	C₂³	1	1	yes	characteristic
207	C₇×#124	C₂³	1	1	yes	characteristic
208	C₇×#123	—	2	2	no	—
209	C₇×#123	—	2	2	no	—
210	C₇×#123	—	2	2	no	—
211	C₇×#123	—	2	2	no	—
212	C₇×#123	—	2	1	no	—
213	C₇×#123	—	2	1	no	—
214	C₇×#123	—	2	1	no	—
215	C₇×#123	—	2	1	no	—
216	C₇×#123	—	2	1	no	—
217	C₇×#123	—	2	1	no	—
218	C₇×C₂²⋊Q₈	—	2	1	no	—
219	C₇×C₂²⋊Q₈	—	2	1	no	—
220	C₇×C₂²⋊Q₈	—	2	1	no	—
221	C₇×C₂²⋊Q₈	—	2	1	no	—
222	C₇×C₂²⋊Q₈	—	2	1	no	—
223	C₇×C₂²⋊Q₈	—	2	1	no	—
224	C₇×C₂²⋊Q₈	—	2	1	no	—
225	C₇×C₂²⋊Q₈	—	2	1	no	—
226	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₇×#121	—	2	1	no	—
235	C₇×#121	—	2	1	no	—
236	C₇×#121	—	2	1	no	—
237	C₇×#121	—	2	1	no	—
238	C₇×#121	—	2	1	no	—
239	C₇×#121	—	2	1	no	—
240	C₇×#121	—	2	1	no	—
241	C₇×#121	—	2	1	no	—
242	C₇×#121	—	2	1	no	—
243	C₇×#121	—	2	1	no	—
244	C₇×#121	C₂³	1	1	yes	characteristic
245	C₇×#121	C₂³	1	1	yes	characteristic
246	C₇×#121	C₂³	1	1	yes	characteristic
247	C₇×#121	C₂³	1	1	yes	characteristic
248	C₇×#120	—	2	1	no	—
249	C₇×#120	—	2	1	no	—
250	C₇×#120	—	2	1	no	—
251	C₇×#120	—	2	1	no	—
252	C₇×#120	—	2	1	no	—
253	C₇×#120	—	2	1	no	—
254	C₄×C₇×Q₈	—	2	1	no	—
255	C₄×C₇×Q₈	—	2	1	no	—
256	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
257	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
258	C₄×C₇×Q₈	C₂³	1	2	yes	—
259	C₄×C₇×Q₈	C₂³	1	2	yes	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	1	no	—
262	C₄×C₇×D₄	—	2	1	no	—
263	C₄×C₇×D₄	—	2	1	no	—
264	C₄×C₇×D₄	—	2	1	no	—
265	C₄×C₇×D₄	—	2	1	no	—
266	C₄×C₇×D₄	—	2	1	no	—
267	C₄×C₇×D₄	—	2	1	no	—
268	C₄×C₇×D₄	—	2	1	no	—
269	C₄×C₇×D₄	—	2	1	no	—
270	C₄×C₇×D₄	—	2	1	no	—
271	C₄×C₇×D₄	—	2	1	no	—
272	C₄×C₇×D₄	D₄	1	1	yes	characteristic
273	C₄×C₇×D₄	D₄	1	1	yes	characteristic
274	C₄×C₇×D₄	D₄	1	1	yes	characteristic
275	C₄×C₇×D₄	D₄	1	1	yes	characteristic
276	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
277	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
278	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
279	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
280	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
281	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
282	C₇×#117	—	2	1	no	—
283	C₇×#117	—	2	1	no	—
284	C₇×#117	—	2	2	no	—
285	C₇×#117	—	2	2	no	—
286	C₇×#117	—	2	2	no	—
287	C₇×#117	—	2	2	no	—
288	C₇×#117	—	2	1	no	—
289	C₇×#117	C₂³	1	2	yes	—
290	C₇×#117	C₂³	1	2	yes	—
291	C₇×#117	C₂³	1	1	yes	characteristic
292	C₂×C₇×C₄⋊C₄	—	2	1	no	—
293	C₂×C₇×C₄⋊C₄	—	2	1	no	—
294	C₂×C₇×C₄⋊C₄	—	2	1	no	—
295	C₂×C₇×C₄⋊C₄	—	2	1	no	—
296	C₂×C₇×C₄⋊C₄	—	2	1	no	—
297	C₂×C₇×C₄⋊C₄	—	2	1	no	—
298	C₂×C₇×C₄⋊C₄	—	2	1	no	—
299	C₂×C₇×C₄⋊C₄	—	2	1	no	—
300	C₂×C₇×C₄⋊C₄	—	2	1	no	—
301	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
303	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
304	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
313	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
314	C₂×C₄²×C₇	—	2	1	no	—
315	C₂×C₄²×C₇	—	2	1	no	—
316	C₂×C₄²×C₇	—	2	1	no	—
317	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
318	C₇×#107	C₂³	1	2	yes	—
319	C₇×#107	C₂³	1	2	yes	—
320	C₇×#107	C₂³	1	2	yes	—
321	C₇×#106	C₂³	1	2	yes	—
322	C₇×#106	C₂³	1	2	yes	—
323	C₇×#106	C₂³	1	2	yes	—
324	C₇×C₄⋊C₈	C₂³	1	2	yes	—
325	C₇×C₄⋊C₈	C₂³	1	2	yes	—
326	C₇×#103	C₂³	1	2	yes	—
327	C₇×#103	C₂³	1	2	yes	—
328	C₇×#103	C₂³	1	2	yes	—
329	C₇×#103	C₂³	1	2	yes	—
330	C₇×#103	C₂³	1	2	yes	—
331	C₇×#103	C₂³	1	2	yes	—
332	C₇×#103	C₂³	1	2	yes	—
333	C₇×#103	C₂³	1	2	yes	—
334	C₇×#103	C₂³	1	2	yes	—
335	C₇×#103	C₂³	1	2	yes	—
336	C₇×#103	C₂³	1	2	yes	—
337	C₇×#102	C₂³	1	2	yes	—
338	C₇×#102	C₂³	1	2	yes	—
339	C₇×#102	C₂³	1	2	yes	—
340	C₇×#102	C₂³	1	2	yes	—
341	C₇×#102	C₂³	1	2	yes	—
342	C₇×#102	C₂³	1	2	yes	—
343	C₇×#102	C₂³	1	2	yes	—
344	C₇×#102	C₂³	1	2	yes	—
345	C₇×#102	C₂³	1	2	yes	—
346	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
347	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
348	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
349	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
350	C₇×#97	C₂³	1	2	yes	—
351	C₄×C₇×C₈	C₂³	1	2	yes	—
352	C₂×#552	C₂×C₇	1	1	yes	characteristic, complemented
353	D₄×#41	C₂×C₇	1	1	yes	characteristic
354	#3327	C₂×C₇	1	2	yes	complemented
355	#3323	C₂×C₇	1	2	yes	complemented
356	#3317	C₂×C₇	1	2	yes	complemented
357	#3315	C₂×C₇	1	2	yes	complemented
358	#3312	C₂×C₇	1	2	yes	complemented
359	#3310	C₂×C₇	1	2	yes	complemented
360	#3300	C₂×C₇	1	2	yes	complemented
361	#3296	C₂×C₇	1	2	yes	complemented
362	#3142	C₂×C₇	1	1	yes	characteristic, complemented
363	#3093	C₂×C₇	1	1	yes	characteristic, complemented
364	#3092	C₂×C₇	1	1	yes	characteristic, complemented
365	#3080	C₂×C₇	1	1	yes	characteristic, complemented
366	#3056	C₂×C₇	1	1	yes	characteristic, complemented
367	#3056	C₂×C₇	1	1	yes	characteristic, complemented
368	#3037	C₂×C₇	1	1	yes	characteristic, complemented
369	#3007	C₂×C₇	1	1	yes	characteristic, complemented
370	#3007	C₂×C₇	1	1	yes	characteristic, complemented
371	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
372	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
373	#2896	C₂×C₇	1	1	yes	characteristic, complemented
374	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
375	C₂⁴×C₇	—	2	1	no	—
376	C₂⁴×C₇	—	2	1	no	—
377	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
379	C₇×#41	—	2	2	no	—
380	C₇×#41	—	2	2	no	—
381	C₇×#41	—	2	2	no	—
382	C₇×#41	—	2	2	no	—
383	C₇×#41	—	2	2	no	—
384	C₇×#41	—	2	2	no	—
385	C₇×#41	—	2	2	no	—
386	C₇×#41	—	2	2	no	—
387	C₇×#41	—	2	2	no	—
388	C₇×#41	—	4	4	no	—
389	C₇×#41	—	4	4	no	—
390	C₇×#41	—	4	1	no	—
391	C₇×#41	—	4	1	no	—
392	C₇×#41	—	4	1	no	—
393	C₇×#41	—	4	1	no	—
394	C₇×#41	—	4	4	no	—
395	C₇×#41	—	4	4	no	—
396	C₇×#41	#41	1	4	yes	—
397	C₂×C₇×Q₈	—	2	1	no	—
398	C₂×C₇×Q₈	—	2	1	no	—
399	C₂×C₇×Q₈	—	2	1	no	—
400	C₂×C₇×Q₈	—	2	2	no	—
401	C₂×C₇×Q₈	—	2	2	no	—
402	C₂×C₇×Q₈	—	2	2	no	—
403	C₂×C₇×Q₈	—	2	2	no	—
404	C₂×C₇×Q₈	—	4	1	no	—
405	C₂×C₇×Q₈	—	4	1	no	—
406	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
409	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×D₄	—	2	1	no	—
411	C₂×C₇×D₄	—	2	2	no	—
412	C₂×C₇×D₄	—	2	2	no	—
413	C₂×C₇×D₄	—	2	1	no	—
414	C₂×C₇×D₄	—	2	1	no	—
415	C₂×C₇×D₄	—	2	1	no	—
416	C₂×C₇×D₄	—	2	1	no	—
417	C₂×C₇×D₄	—	2	1	no	—
418	C₂×C₇×D₄	—	2	1	no	—
419	C₂×C₇×D₄	—	2	1	no	—
420	C₂×C₇×D₄	—	2	1	no	—
421	C₂×C₇×D₄	—	2	1	no	—
422	C₂×C₇×D₄	—	2	1	no	—
423	C₂×C₇×D₄	—	2	1	no	—
424	C₂×C₇×D₄	—	2	1	no	—
425	C₂×C₇×D₄	—	2	1	no	—
426	C₂×C₇×D₄	—	2	1	no	—
427	C₂×C₇×D₄	—	4	1	no	—
428	C₂×C₇×D₄	—	4	1	no	—
429	C₂×C₇×D₄	—	4	2	no	—
430	C₂×C₇×D₄	—	4	4	no	—
431	C₂×C₇×D₄	—	4	4	no	—
432	C₂×C₇×D₄	—	4	4	no	—
433	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
434	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
435	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
436	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
437	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
438	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
439	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₇	—	2	1	no	—
441	C₂²×C₄×C₇	—	2	2	no	—
442	C₂²×C₄×C₇	—	2	2	no	—
443	C₂²×C₄×C₇	—	2	2	no	—
444	C₂²×C₄×C₇	—	2	2	no	—
445	C₂²×C₄×C₇	—	2	1	no	—
446	C₂²×C₄×C₇	—	2	1	no	—
447	C₂²×C₄×C₇	—	2	1	no	—
448	C₂²×C₄×C₇	—	2	1	no	—
449	C₂²×C₄×C₇	—	2	2	no	—
450	C₂²×C₄×C₇	—	2	2	no	—
451	C₂²×C₄×C₇	—	2	1	no	—
452	C₂²×C₄×C₇	—	2	1	no	—
453	C₂²×C₄×C₇	—	2	1	no	—
454	C₂²×C₄×C₇	—	2	1	no	—
455	C₂²×C₄×C₇	—	2	1	no	—
456	C₂²×C₄×C₇	—	2	1	no	—
457	C₂²×C₄×C₇	—	2	1	no	—
458	C₂²×C₄×C₇	—	2	1	no	—
459	C₂²×C₄×C₇	—	2	1	no	—
460	C₂²×C₄×C₇	—	2	1	no	—
461	C₂²×C₄×C₇	—	4	4	no	—
462	C₂²×C₄×C₇	—	4	4	no	—
463	C₂²×C₄×C₇	—	4	4	no	—
464	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
465	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
466	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
467	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
468	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
469	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
470	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
471	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
472	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
477	C₇×Q₁₆	—	2	4	no	—
478	C₇×Q₁₆	—	4	2	no	—
479	C₇×Q₁₆	—	4	2	no	—
480	C₇×SD₁₆	—	2	4	no	—
481	C₇×SD₁₆	—	4	2	no	—
482	C₇×SD₁₆	—	4	2	no	—
483	C₇×M₁₆	—	2	2	no	—
484	C₇×M₁₆	—	2	2	no	—
485	C₇×M₁₆	—	2	2	no	—
486	C₇×M₁₆	—	2	2	no	—
487	C₇×M₁₆	—	4	2	no	—
488	C₇×M₁₆	—	4	2	no	—
489	C₂×C₇×C₈	—	4	2	no	—
490	C₂×C₇×C₈	—	4	2	no	—
491	C₂×C₇×C₈	C₂⁴	1	2	yes	—
492	C₂×C₇×C₈	C₂⁴	1	2	yes	—
493	C₂×C₇×C₈	C₂⁴	1	2	yes	—
494	C₂×C₇×C₈	C₂⁴	1	2	yes	—
495	C₇×C₄⋊C₄	—	2	1	no	—
496	C₇×C₄⋊C₄	—	2	1	no	—
497	C₇×C₄⋊C₄	—	2	2	no	—
498	C₇×C₄⋊C₄	—	2	2	no	—
499	C₇×C₄⋊C₄	—	2	2	no	—
500	C₇×C₄⋊C₄	—	2	2	no	—
501	C₇×C₄⋊C₄	—	2	2	no	—
502	C₇×C₄⋊C₄	—	2	2	no	—
503	C₇×C₄⋊C₄	—	2	1	no	—
504	C₇×C₄⋊C₄	—	2	1	no	—
505	C₇×C₄⋊C₄	—	2	1	no	—
506	C₇×C₄⋊C₄	—	2	2	no	—
507	C₇×C₄⋊C₄	—	2	2	no	—
508	C₇×C₄⋊C₄	—	2	2	no	—
509	C₇×C₄⋊C₄	—	2	2	no	—
510	C₇×C₄⋊C₄	—	2	2	no	—
511	C₇×C₄⋊C₄	—	2	2	no	—
512	C₇×C₄⋊C₄	—	2	1	no	—
513	C₇×C₄⋊C₄	—	2	1	no	—
514	C₇×C₄⋊C₄	—	2	1	no	—
515	C₇×C₄⋊C₄	—	2	1	no	—
516	C₇×C₄⋊C₄	—	2	1	no	—
517	C₇×C₄⋊C₄	—	2	1	no	—
518	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
519	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
520	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
521	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
522	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
523	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
524	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
525	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
526	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
527	C₇×C₂²⋊C₄	—	2	2	no	—
528	C₇×C₂²⋊C₄	—	2	2	no	—
529	C₇×C₂²⋊C₄	—	2	2	no	—
530	C₇×C₂²⋊C₄	—	2	2	no	—
531	C₇×C₂²⋊C₄	—	2	1	no	—
532	C₇×C₂²⋊C₄	—	2	1	no	—
533	C₇×C₂²⋊C₄	—	2	2	no	—
534	C₇×C₂²⋊C₄	—	2	2	no	—
535	C₇×C₂²⋊C₄	—	2	1	no	—
536	C₇×C₂²⋊C₄	—	2	1	no	—
537	C₇×C₂²⋊C₄	—	2	1	no	—
538	C₇×C₂²⋊C₄	—	2	1	no	—
539	C₇×C₂²⋊C₄	—	2	1	no	—
540	C₇×C₂²⋊C₄	—	2	1	no	—
541	C₇×C₂²⋊C₄	—	2	1	no	—
542	C₇×C₂²⋊C₄	—	2	1	no	—
543	C₇×C₂²⋊C₄	—	2	1	no	—
544	C₇×C₂²⋊C₄	—	2	1	no	—
545	C₇×C₂²⋊C₄	—	2	1	no	—
546	C₇×C₂²⋊C₄	—	2	1	no	—
547	C₇×C₂²⋊C₄	—	2	1	no	—
548	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
549	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
550	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
551	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
552	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
553	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
554	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
555	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
556	C₄²×C₇	—	2	2	no	—
557	C₄²×C₇	—	2	2	no	—
558	C₄²×C₇	—	2	2	no	—
559	C₄²×C₇	—	2	2	no	—
560	C₄²×C₇	—	2	1	no	—
561	C₄²×C₇	—	2	1	no	—
562	C₄²×C₇	—	2	1	no	—
563	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
564	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
565	C₄²×C₇	C₂⁴	1	1	yes	characteristic
566	C₄²×C₇	C₂⁴	1	1	yes	characteristic
567	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
568	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
569	C₂×#137	C₂²×C₇	1	1	yes	characteristic
570	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
571	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
572	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
573	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
574	#552	—	2	1	no	—
575	#552	—	2	1	no	—
576	#552	—	2	1	no	—
577	#552	—	2	1	no	—
578	#552	C₂²×C₇	1	2	yes	—
579	#552	C₂²×C₇	1	2	yes	complemented
580	#552	C₂²×C₇	1	2	yes	complemented
581	#552	C₂²×C₇	1	2	yes	complemented
582	#550	C₂²×C₇	1	1	yes	characteristic
583	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
584	#548	C₂²×C₇	1	1	yes	characteristic
585	#548	C₂²×C₇	1	1	yes	characteristic
586	#547	—	2	1	no	—
587	#547	C₂²×C₇	1	1	yes	characteristic
588	#546	—	2	1	no	—
589	#546	—	2	1	no	—
590	#546	C₂²×C₇	1	1	yes	characteristic
591	#546	C₂²×C₇	1	1	yes	characteristic
592	D₄²	—	2	1	no	—
593	D₄²	C₂²×C₇	1	1	yes	characteristic
594	#532	—	2	1	no	—
595	#532	C₂²×C₇	1	1	yes	characteristic
596	C₂×#126	—	2	1	no	—
597	C₂×#125	—	2	1	no	—
598	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
599	#525	—	2	1	no	—
600	#525	—	2	1	no	—
601	#525	C₂²×C₇	1	1	yes	characteristic
602	#525	C₂²×C₇	1	1	yes	characteristic
603	C₂×#123	—	2	1	no	—
604	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
605	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
606	C₄×#41	C₂²×C₇	1	1	yes	characteristic
607	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
608	C₂×C₄×D₄	—	2	1	no	—
609	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
610	C₂×#117	—	2	1	no	—
611	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
612	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
613	#491	C₂²×C₇	1	2	yes	complemented
614	#490	C₂²×C₇	1	2	yes	complemented
615	#488	C₂²×C₇	1	2	yes	complemented
616	#488	C₂²×C₇	1	2	yes	complemented
617	#485	C₂²×C₇	1	2	yes	complemented
618	#485	C₂²×C₇	1	2	yes	complemented
619	#484	C₂²×C₇	1	2	yes	complemented
620	#483	C₂²×C₇	1	2	yes	complemented
621	#482	C₂²×C₇	1	2	yes	complemented
622	#482	C₂²×C₇	1	2	yes	complemented
623	#481	C₂²×C₇	1	2	yes	complemented
624	#480	C₂²×C₇	1	2	yes	complemented
625	#479	C₂²×C₇	1	2	yes	complemented
626	#479	C₂²×C₇	1	2	yes	complemented
627	#478	C₂²×C₇	1	2	yes	complemented
628	#478	C₂²×C₇	1	2	yes	complemented
629	#470	C₂²×C₇	1	2	yes	complemented
630	#470	C₂²×C₇	1	2	yes	complemented
631	#468	C₂²×C₇	1	2	yes	complemented
632	#468	C₂²×C₇	1	2	yes	complemented
633	#467	C₂²×C₇	1	2	yes	complemented
634	#467	C₂²×C₇	1	2	yes	complemented
635	#465	C₂²×C₇	1	2	yes	complemented
636	#465	C₂²×C₇	1	2	yes	complemented
637	#464	C₂²×C₇	1	2	yes	complemented
638	#464	C₂²×C₇	1	2	yes	complemented
639	#462	C₂²×C₇	1	2	yes	complemented
640	#460	C₂²×C₇	1	2	yes	complemented
641	#452	C₂²×C₇	1	2	yes	complemented
642	#452	C₂²×C₇	1	2	yes	complemented
643	#452	C₂²×C₇	1	2	yes	complemented
644	#452	C₂²×C₇	1	2	yes	complemented
645	#451	C₂²×C₇	1	2	yes	complemented
646	#451	C₂²×C₇	1	2	yes	complemented
647	#450	C₂²×C₇	1	2	yes	complemented
648	#450	C₂²×C₇	1	2	yes	complemented
649	#441	C₂²×C₇	1	2	yes	complemented
650	#440	C₂²×C₇	1	2	yes	complemented
651	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
652	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
653	#436	C₂²×C₇	1	2	yes	complemented
654	#435	C₂²×C₇	1	2	yes	—
655	#435	C₂²×C₇	1	2	yes	complemented
656	C₈×D₄	C₂²×C₇	1	2	yes	complemented
657	#428	C₂²×C₇	1	1	yes	characteristic, complemented
658	#428	C₂²×C₇	1	1	yes	characteristic, complemented
659	#428	C₂²×C₇	1	1	yes	characteristic, complemented
660	#423	C₂²×C₇	1	1	yes	characteristic, complemented
661	#419	C₂²×C₇	1	2	yes	complemented
662	#419	C₂²×C₇	1	1	yes	characteristic, complemented
663	#418	C₂²×C₇	1	2	yes	complemented
664	#417	C₂²×C₇	1	1	yes	characteristic
665	#417	C₂²×C₇	1	1	yes	characteristic
666	#417	C₂²×C₇	1	1	yes	characteristic
667	#417	C₂²×C₇	1	1	yes	characteristic, complemented
668	#417	C₂²×C₇	1	1	yes	characteristic, complemented
669	#417	C₂²×C₇	1	1	yes	characteristic, complemented
670	#417	C₂²×C₇	1	1	yes	characteristic, complemented
671	#417	C₂²×C₇	1	1	yes	characteristic, complemented
672	#417	C₂²×C₇	1	1	yes	characteristic, complemented
673	#417	C₂²×C₇	1	2	yes	complemented
674	#417	C₂²×C₇	1	2	yes	complemented
675	#416	C₂²×C₇	1	2	yes	complemented
676	#416	C₂²×C₇	1	2	yes	complemented
677	C₂×#103	C₂²×C₇	1	2	yes	complemented
678	C₂×#102	C₂²×C₇	1	2	yes	complemented
679	#407	C₂²×C₇	1	1	yes	characteristic, complemented
680	#407	C₂²×C₇	1	1	yes	characteristic, complemented
681	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
682	C₂³×C₇	—	2	2	no	—
683	C₂³×C₇	—	2	2	no	—
684	C₂³×C₇	—	2	1	no	—
685	C₂³×C₇	—	2	2	no	—
686	C₂³×C₇	—	2	1	no	—
687	C₂³×C₇	—	2	1	no	—
688	C₂³×C₇	—	4	1	no	—
689	C₂³×C₇	—	4	1	no	—
690	C₂³×C₇	—	4	1	no	—
691	C₂³×C₇	—	4	2	no	—
692	C₂³×C₇	—	4	2	no	—
693	C₂³×C₇	—	4	2	no	—
694	C₂³×C₇	—	4	2	no	—
695	C₂³×C₇	—	8	1	no	—
696	C₂³×C₇	—	8	1	no	—
697	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
698	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
699	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
700	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
701	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
702	C₇×Q₈	—	2	1	no	—
703	C₇×Q₈	—	2	2	no	—
704	C₇×Q₈	—	2	1	no	—
705	C₇×Q₈	—	2	1	no	—
706	C₇×Q₈	—	2	2	no	—
707	C₇×Q₈	—	2	1	no	—
708	C₇×Q₈	—	2	1	no	—
709	C₇×Q₈	—	4	2	no	—
710	C₇×Q₈	—	4	2	no	—
711	C₇×Q₈	—	4	2	no	—
712	C₇×Q₈	C₂×#41	1	2	yes	—
713	C₇×D₄	—	2	4	no	—
714	C₇×D₄	—	2	2	no	—
715	C₇×D₄	—	2	2	no	—
716	C₇×D₄	—	2	1	no	—
717	C₇×D₄	—	2	1	no	—
718	C₇×D₄	—	2	1	no	—
719	C₇×D₄	—	2	1	no	—
720	C₇×D₄	—	2	1	no	—
721	C₇×D₄	—	4	1	no	—
722	C₇×D₄	—	4	1	no	—
723	C₇×D₄	—	4	2	no	—
724	C₇×D₄	—	4	2	no	—
725	C₇×D₄	—	4	2	no	—
726	C₇×D₄	—	4	2	no	—
727	C₇×D₄	—	4	2	no	—
728	C₇×D₄	—	4	2	no	—
729	C₇×D₄	—	4	2	no	—
730	C₇×D₄	—	4	2	no	—
731	C₇×D₄	—	4	2	no	—
732	C₇×D₄	—	4	2	no	—
733	C₇×D₄	—	4	2	no	—
734	C₇×D₄	—	8	1	no	—
735	C₇×D₄	—	8	1	no	—
736	C₇×D₄	—	8	1	no	—
737	C₇×D₄	C₂×#41	1	2	yes	—
738	C₂×C₄×C₇	—	2	2	no	—
739	C₂×C₄×C₇	—	2	2	no	—
740	C₂×C₄×C₇	—	2	1	no	—
741	C₂×C₄×C₇	—	2	2	no	—
742	C₂×C₄×C₇	—	2	2	no	—
743	C₂×C₄×C₇	—	2	2	no	—
744	C₂×C₄×C₇	—	2	2	no	—
745	C₂×C₄×C₇	—	2	4	no	—
746	C₂×C₄×C₇	—	2	1	no	—
747	C₂×C₄×C₇	—	2	1	no	—
748	C₂×C₄×C₇	—	2	1	no	—
749	C₂×C₄×C₇	—	2	1	no	—
750	C₂×C₄×C₇	—	2	1	no	—
751	C₂×C₄×C₇	—	2	1	no	—
752	C₂×C₄×C₇	—	2	1	no	—
753	C₂×C₄×C₇	—	2	1	no	—
754	C₂×C₄×C₇	—	2	2	no	—
755	C₂×C₄×C₇	—	2	1	no	—
756	C₂×C₄×C₇	—	2	1	no	—
757	C₂×C₄×C₇	—	2	2	no	—
758	C₂×C₄×C₇	—	2	2	no	—
759	C₂×C₄×C₇	—	2	1	no	—
760	C₂×C₄×C₇	—	2	1	no	—
761	C₂×C₄×C₇	—	2	2	no	—
762	C₂×C₄×C₇	—	4	1	no	—
763	C₂×C₄×C₇	—	4	1	no	—
764	C₂×C₄×C₇	—	4	2	no	—
765	C₂×C₄×C₇	—	4	2	no	—
766	C₂×C₄×C₇	—	4	2	no	—
767	C₂×C₄×C₇	—	4	2	no	—
768	C₂×C₄×C₇	—	4	2	no	—
769	C₂×C₄×C₇	—	4	2	no	—
770	C₂×C₄×C₇	—	4	2	no	—
771	C₂×C₄×C₇	—	4	2	no	—
772	C₂×C₄×C₇	—	4	2	no	—
773	C₂×C₄×C₇	—	4	2	no	—
774	C₂×C₄×C₇	—	4	4	no	—
775	C₂×C₄×C₇	—	4	2	no	—
776	C₂×C₄×C₇	—	4	4	no	—
777	C₂×C₄×C₇	—	4	2	no	—
778	C₂×C₄×C₇	—	4	2	no	—
779	C₂×C₄×C₇	—	8	1	no	—
780	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
781	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
788	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄×C₇	C₂×#41	1	2	yes	—
790	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
791	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
792	C₇×C₈	—	2	2	no	—
793	C₇×C₈	—	2	2	no	—
794	C₇×C₈	—	2	2	no	—
795	C₇×C₈	—	2	2	no	—
796	C₂×#41	—	2	1	no	—
797	C₂×#41	—	2	1	no	—
798	C₂×#41	—	2	1	no	—
799	C₂×#41	—	2	1	no	—
800	C₂×#41	—	2	4	no	—
801	C₂×#41	—	2	4	no	—
802	C₂×#41	—	4	2	no	—
803	C₂×#41	—	4	2	no	—
804	C₂×#41	C₂³×C₇	1	1	yes	characteristic
805	C₂×#41	C₂³×C₇	1	1	yes	characteristic
806	C₂×#41	C₂³×C₇	1	1	yes	characteristic
807	C₂×#41	C₂³×C₇	1	1	yes	characteristic
808	C₂×#41	C₂³×C₇	1	1	yes	characteristic
809	C₂×#41	C₂³×C₇	1	1	yes	characteristic
810	C₂×#41	C₂³×C₇	1	1	yes	characteristic
811	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
812	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
813	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
814	C₂²×D₄	—	2	1	no	—
815	C₂²×D₄	—	2	1	no	—
816	C₂²×D₄	—	2	1	no	—
817	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
818	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
819	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
820	C₂³×C₄	—	2	1	no	—
821	C₂³×C₄	—	2	1	no	—
822	C₂³×C₄	—	2	1	no	—
823	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
824	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
825	#137	—	2	4	no	—
826	#137	—	4	2	no	—
827	#137	—	4	2	no	—
828	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
829	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
830	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
831	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
832	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
833	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
834	C₂×M₁₆	—	4	2	no	—
835	C₂×M₁₆	—	4	2	no	—
836	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
837	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
838	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
839	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
840	C₂×M₁₆	C₂³×C₇	1	2	yes	—
841	C₂×M₁₆	C₂³×C₇	1	2	yes	—
842	C₂²×C₈	C₂³×C₇	1	2	yes	—
843	C₂²×C₈	C₂³×C₇	1	2	yes	—
844	C₄⋊Q₈	—	2	1	no	—
845	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
846	#127	—	2	1	no	—
847	#127	C₂³×C₇	1	1	yes	characteristic
848	#126	—	2	2	no	—
849	#126	—	2	2	no	—
850	#126	—	2	2	no	—
851	#126	—	2	2	no	—
852	#125	—	2	2	no	—
853	#125	—	2	2	no	—
854	#125	—	2	2	no	—
855	#125	—	2	2	no	—
856	#125	—	2	1	no	—
857	#125	—	2	1	no	—
858	#125	C₂³×C₇	1	2	yes	—
859	#125	C₂³×C₇	1	2	yes	—
860	#124	—	2	1	no	—
861	#124	—	2	1	no	—
862	#124	C₂³×C₇	1	1	yes	characteristic
863	#124	C₂³×C₇	1	1	yes	characteristic
864	#123	—	2	2	no	—
865	#123	—	2	2	no	—
866	#123	—	2	2	no	—
867	#123	—	2	2	no	—
868	#123	—	2	1	no	—
869	#123	—	2	1	no	—
870	#123	—	2	1	no	—
871	#123	—	2	1	no	—
872	#123	—	2	1	no	—
873	#123	—	2	1	no	—
874	C₂²⋊Q₈	—	2	1	no	—
875	C₂²⋊Q₈	—	2	1	no	—
876	C₂²⋊Q₈	—	2	1	no	—
877	C₂²⋊Q₈	—	2	1	no	—
878	C₂²⋊Q₈	—	2	1	no	—
879	C₂²⋊Q₈	—	2	1	no	—
880	C₂²⋊Q₈	—	2	1	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
883	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
884	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
885	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
886	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
887	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
888	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
889	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	—	2	1	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	C₂³×C₇	1	1	yes	characteristic
901	#121	C₂³×C₇	1	1	yes	characteristic
902	#121	C₂³×C₇	1	1	yes	characteristic
903	#121	C₂³×C₇	1	1	yes	characteristic
904	#120	—	2	1	no	—
905	#120	—	2	1	no	—
906	#120	—	2	1	no	—
907	#120	—	2	1	no	—
908	#120	—	2	1	no	—
909	#120	—	2	1	no	—
910	C₄×Q₈	—	2	1	no	—
911	C₄×Q₈	—	2	1	no	—
912	C₄×Q₈	C₂³×C₇	1	2	yes	—
913	C₄×Q₈	C₂³×C₇	1	2	yes	—
914	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
915	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	C₇×D₄	1	1	yes	characteristic
929	C₄×D₄	C₇×D₄	1	1	yes	characteristic
930	C₄×D₄	C₇×D₄	1	1	yes	characteristic
931	C₄×D₄	C₇×D₄	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
933	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
934	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
935	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
936	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
937	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	—	2	2	no	—
941	#117	—	2	2	no	—
942	#117	—	2	2	no	—
943	#117	—	2	2	no	—
944	#117	—	2	1	no	—
945	#117	C₂³×C₇	1	2	yes	—
946	#117	C₂³×C₇	1	2	yes	—
947	#117	C₂³×C₇	1	1	yes	characteristic
948	C₂×C₄⋊C₄	—	2	1	no	—
949	C₂×C₄⋊C₄	—	2	1	no	—
950	C₂×C₄⋊C₄	—	2	1	no	—
951	C₂×C₄⋊C₄	—	2	1	no	—
952	C₂×C₄⋊C₄	—	2	1	no	—
953	C₂×C₄⋊C₄	—	2	1	no	—
954	C₂×C₄⋊C₄	—	2	1	no	—
955	C₂×C₄⋊C₄	—	2	1	no	—
956	C₂×C₄⋊C₄	—	2	1	no	—
957	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
961	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
962	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
963	C₂×C₂²⋊C₄	—	2	1	no	—
964	C₂×C₂²⋊C₄	—	2	1	no	—
965	C₂×C₂²⋊C₄	—	2	1	no	—
966	C₂×C₂²⋊C₄	—	2	1	no	—
967	C₂×C₂²⋊C₄	—	2	1	no	—
968	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
970	C₂×C₄²	—	2	1	no	—
971	C₂×C₄²	—	2	1	no	—
972	C₂×C₄²	—	2	1	no	—
973	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
974	#107	C₂³×C₇	1	2	yes	—
975	#107	C₂³×C₇	1	2	yes	—
976	#107	C₂³×C₇	1	2	yes	—
977	#106	C₂³×C₇	1	2	yes	—
978	#106	C₂³×C₇	1	2	yes	—
979	#106	C₂³×C₇	1	2	yes	—
980	C₄⋊C₈	C₂³×C₇	1	2	yes	—
981	C₄⋊C₈	C₂³×C₇	1	2	yes	—
982	#103	C₂³×C₇	1	2	yes	—
983	#103	C₂³×C₇	1	2	yes	—
984	#103	C₂³×C₇	1	2	yes	—
985	#103	C₂³×C₇	1	2	yes	—
986	#103	C₂³×C₇	1	2	yes	—
987	#103	C₂³×C₇	1	2	yes	—
988	#103	C₂³×C₇	1	2	yes	—
989	#103	C₂³×C₇	1	2	yes	—
990	#103	C₂³×C₇	1	2	yes	—
991	#103	C₂³×C₇	1	2	yes	—
992	#103	C₂³×C₇	1	2	yes	—
993	#102	C₂³×C₇	1	2	yes	—
994	#102	C₂³×C₇	1	2	yes	—
995	#102	C₂³×C₇	1	2	yes	—
996	#102	C₂³×C₇	1	2	yes	—
997	#102	C₂³×C₇	1	2	yes	—
998	#102	C₂³×C₇	1	2	yes	—
999	#102	C₂³×C₇	1	2	yes	—
1000	#102	C₂³×C₇	1	2	yes	—
1001	#102	C₂³×C₇	1	2	yes	—
1002	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
1003	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
1004	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
1005	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
1006	#97	C₂³×C₇	1	2	yes	—
1007	C₄×C₈	C₂³×C₇	1	2	yes	—
1008	C₂²×C₇	—	2	1	no	—
1009	C₂²×C₇	—	2	1	no	—
1010	C₂²×C₇	—	2	1	no	—
1011	C₂²×C₇	—	2	1	no	—
1012	C₂²×C₇	—	2	1	no	—
1013	C₂²×C₇	—	2	1	no	—
1014	C₂²×C₇	—	2	1	no	—
1015	C₂²×C₇	—	2	1	no	—
1016	C₂²×C₇	—	2	1	no	—
1017	C₂²×C₇	—	2	1	no	—
1018	C₂²×C₇	—	2	2	no	—
1019	C₂²×C₇	—	2	1	no	—
1020	C₂²×C₇	—	2	1	no	—
1021	C₂²×C₇	—	2	1	no	—
1022	C₂²×C₇	—	4	4	no	—
1023	C₂²×C₇	—	4	1	no	—
1024	C₂²×C₇	—	4	1	no	—
1025	C₂²×C₇	—	4	1	no	—
1026	C₂²×C₇	—	4	1	no	—
1027	C₂²×C₇	—	4	1	no	—
1028	C₂²×C₇	—	4	1	no	—
1029	C₂²×C₇	—	4	1	no	—
1030	C₂²×C₇	—	4	1	no	—
1031	C₂²×C₇	—	8	2	no	—
1032	C₂²×C₇	—	8	4	no	—
1033	C₂²×C₇	—	8	4	no	—
1034	C₂²×C₇	#546	1	2	yes	—
1035	C₂²×C₇	#575	1	2	yes	—
1036	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
1037	C₄×C₇	—	2	1	no	—
1038	C₄×C₇	—	2	1	no	—
1039	C₄×C₇	—	2	1	no	—
1040	C₄×C₇	—	2	1	no	—
1041	C₄×C₇	—	2	1	no	—
1042	C₄×C₇	—	2	1	no	—
1043	C₄×C₇	—	2	2	no	—
1044	C₄×C₇	—	2	1	no	—
1045	C₄×C₇	—	2	1	no	—
1046	C₄×C₇	—	4	2	no	—
1047	C₄×C₇	—	4	1	no	—
1048	C₄×C₇	—	4	1	no	—
1049	C₄×C₇	—	4	1	no	—
1050	C₄×C₇	—	4	2	no	—
1051	C₄×C₇	—	4	2	no	—
1052	C₄×C₇	—	4	2	no	—
1053	C₄×C₇	—	4	1	no	—
1054	C₄×C₇	#546	1	2	yes	—
1055	C₄×C₇	C₂²×#41	1	1	yes	characteristic
1056	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1057	C₂⁴	—	2	1	no	—
1058	C₂⁴	—	2	1	no	—
1059	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
1060	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
1061	#41	—	2	2	no	—
1062	#41	—	2	2	no	—
1063	#41	—	2	2	no	—
1064	#41	—	2	2	no	—
1065	#41	—	2	2	no	—
1066	#41	—	2	2	no	—
1067	#41	—	2	2	no	—
1068	#41	—	2	2	no	—
1069	#41	—	2	2	no	—
1070	#41	—	4	4	no	—
1071	#41	—	4	4	no	—
1072	#41	—	4	1	no	—
1073	#41	—	4	1	no	—
1074	#41	—	4	1	no	—
1075	#41	—	4	1	no	—
1076	#41	—	4	4	no	—
1077	#41	—	4	4	no	—
1078	#41	C₇×#41	1	4	yes	—
1079	C₂×Q₈	—	2	1	no	—
1080	C₂×Q₈	—	2	1	no	—
1081	C₂×Q₈	—	2	1	no	—
1082	C₂×Q₈	—	2	2	no	—
1083	C₂×Q₈	—	2	2	no	—
1084	C₂×Q₈	—	2	2	no	—
1085	C₂×Q₈	—	2	2	no	—
1086	C₂×Q₈	—	4	1	no	—
1087	C₂×Q₈	—	4	1	no	—
1088	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1089	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1090	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
1091	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	1	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	1	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	4	1	no	—
1110	C₂×D₄	—	4	1	no	—
1111	C₂×D₄	—	4	2	no	—
1112	C₂×D₄	—	4	4	no	—
1113	C₂×D₄	—	4	4	no	—
1114	C₂×D₄	—	4	4	no	—
1115	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1116	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1117	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1118	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1119	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1120	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1121	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1122	C₂²×C₄	—	2	1	no	—
1123	C₂²×C₄	—	2	2	no	—
1124	C₂²×C₄	—	2	2	no	—
1125	C₂²×C₄	—	2	2	no	—
1126	C₂²×C₄	—	2	2	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	1	no	—
1131	C₂²×C₄	—	2	2	no	—
1132	C₂²×C₄	—	2	2	no	—
1133	C₂²×C₄	—	2	1	no	—
1134	C₂²×C₄	—	2	1	no	—
1135	C₂²×C₄	—	2	1	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	1	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	1	no	—
1142	C₂²×C₄	—	2	1	no	—
1143	C₂²×C₄	—	4	4	no	—
1144	C₂²×C₄	—	4	4	no	—
1145	C₂²×C₄	—	4	4	no	—
1146	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1147	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1148	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1149	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1150	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1151	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1152	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1153	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1154	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1155	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1156	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1157	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1158	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1159	Q₁₆	—	2	4	no	—
1160	Q₁₆	—	4	2	no	—
1161	Q₁₆	—	4	2	no	—
1162	SD₁₆	—	2	4	no	—
1163	SD₁₆	—	4	2	no	—
1164	SD₁₆	—	4	2	no	—
1165	M₁₆	—	2	2	no	—
1166	M₁₆	—	2	2	no	—
1167	M₁₆	—	2	2	no	—
1168	M₁₆	—	2	2	no	—
1169	M₁₆	—	4	2	no	—
1170	M₁₆	—	4	2	no	—
1171	C₂×C₈	—	4	2	no	—
1172	C₂×C₈	—	4	2	no	—
1173	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1174	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1175	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1176	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1177	C₄⋊C₄	—	2	1	no	—
1178	C₄⋊C₄	—	2	1	no	—
1179	C₄⋊C₄	—	2	2	no	—
1180	C₄⋊C₄	—	2	2	no	—
1181	C₄⋊C₄	—	2	2	no	—
1182	C₄⋊C₄	—	2	2	no	—
1183	C₄⋊C₄	—	2	2	no	—
1184	C₄⋊C₄	—	2	2	no	—
1185	C₄⋊C₄	—	2	1	no	—
1186	C₄⋊C₄	—	2	1	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	2	2	no	—
1189	C₄⋊C₄	—	2	2	no	—
1190	C₄⋊C₄	—	2	2	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	2	no	—
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	2	1	no	—
1195	C₄⋊C₄	—	2	1	no	—
1196	C₄⋊C₄	—	2	1	no	—
1197	C₄⋊C₄	—	2	1	no	—
1198	C₄⋊C₄	—	2	1	no	—
1199	C₄⋊C₄	—	2	1	no	—
1200	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1201	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1202	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1203	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1204	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1205	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1206	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1207	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1208	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	—	2	2	no	—
1216	C₂²⋊C₄	—	2	2	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	—	2	1	no	—
1220	C₂²⋊C₄	—	2	1	no	—
1221	C₂²⋊C₄	—	2	1	no	—
1222	C₂²⋊C₄	—	2	1	no	—
1223	C₂²⋊C₄	—	2	1	no	—
1224	C₂²⋊C₄	—	2	1	no	—
1225	C₂²⋊C₄	—	2	1	no	—
1226	C₂²⋊C₄	—	2	1	no	—
1227	C₂²⋊C₄	—	2	1	no	—
1228	C₂²⋊C₄	—	2	1	no	—
1229	C₂²⋊C₄	—	2	1	no	—
1230	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1231	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1232	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1233	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1234	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1235	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1236	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1237	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1238	C₄²	—	2	2	no	—
1239	C₄²	—	2	2	no	—
1240	C₄²	—	2	2	no	—
1241	C₄²	—	2	2	no	—
1242	C₄²	—	2	1	no	—
1243	C₄²	—	2	1	no	—
1244	C₄²	—	2	1	no	—
1245	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1246	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1247	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1248	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1249	C₂×C₇	—	2	2	no	—
1250	C₂×C₇	—	2	2	no	—
1251	C₂×C₇	—	4	1	no	—
1252	C₂×C₇	—	4	1	no	—
1253	C₂×C₇	—	4	1	no	—
1254	C₂×C₇	—	4	2	no	—
1255	C₂×C₇	—	8	1	no	—
1256	C₂×C₇	—	8	1	no	—
1257	C₂×C₇	C₂×#546	1	1	yes	characteristic
1258	C₂×C₇	C₂×#575	1	1	yes	characteristic
1259	C₂×C₇	#3586	1	1	yes	characteristic
1260	C₂³	—	2	1	no	—
1261	C₂³	—	2	2	no	—
1262	C₂³	—	2	2	no	—
1263	C₂³	—	2	2	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	4	1	no	—
1267	C₂³	—	4	1	no	—
1268	C₂³	—	4	1	no	—
1269	C₂³	—	4	2	no	—
1270	C₂³	—	4	2	no	—
1271	C₂³	—	4	2	no	—
1272	C₂³	—	4	2	no	—
1273	C₂³	—	8	1	no	—
1274	C₂³	—	8	1	no	—
1275	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1276	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1277	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1278	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1279	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1280	Q₈	—	2	1	no	—
1281	Q₈	—	2	2	no	—
1282	Q₈	—	2	1	no	—
1283	Q₈	—	2	1	no	—
1284	Q₈	—	2	2	no	—
1285	Q₈	—	2	1	no	—
1286	Q₈	—	2	1	no	—
1287	Q₈	—	4	2	no	—
1288	Q₈	—	4	2	no	—
1289	Q₈	—	4	2	no	—
1290	Q₈	C₂×C₇×#41	1	2	yes	—
1291	D₄	—	2	4	no	—
1292	D₄	—	2	2	no	—
1293	D₄	—	2	2	no	—
1294	D₄	—	2	1	no	—
1295	D₄	—	2	1	no	—
1296	D₄	—	2	1	no	—
1297	D₄	—	2	1	no	—
1298	D₄	—	2	1	no	—
1299	D₄	—	4	1	no	—
1300	D₄	—	4	1	no	—
1301	D₄	—	4	2	no	—
1302	D₄	—	4	2	no	—
1303	D₄	—	4	2	no	—
1304	D₄	—	4	2	no	—
1305	D₄	—	4	2	no	—
1306	D₄	—	4	2	no	—
1307	D₄	—	4	2	no	—
1308	D₄	—	4	2	no	—
1309	D₄	—	4	2	no	—
1310	D₄	—	4	2	no	—
1311	D₄	—	4	2	no	—
1312	D₄	—	8	1	no	—
1313	D₄	—	8	1	no	—
1314	D₄	—	8	1	no	—
1315	D₄	C₂×C₇×#41	1	2	yes	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	2	no	—
1318	C₂×C₄	—	2	2	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	2	no	—
1328	C₂×C₄	—	2	2	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	2	2	no	—
1331	C₂×C₄	—	2	4	no	—
1332	C₂×C₄	—	2	2	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	2	no	—
1336	C₂×C₄	—	2	2	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	4	1	no	—
1341	C₂×C₄	—	4	1	no	—
1342	C₂×C₄	—	4	2	no	—
1343	C₂×C₄	—	4	2	no	—
1344	C₂×C₄	—	4	2	no	—
1345	C₂×C₄	—	4	2	no	—
1346	C₂×C₄	—	4	2	no	—
1347	C₂×C₄	—	4	2	no	—
1348	C₂×C₄	—	4	2	no	—
1349	C₂×C₄	—	4	2	no	—
1350	C₂×C₄	—	4	2	no	—
1351	C₂×C₄	—	4	2	no	—
1352	C₂×C₄	—	4	4	no	—
1353	C₂×C₄	—	4	2	no	—
1354	C₂×C₄	—	4	4	no	—
1355	C₂×C₄	—	4	2	no	—
1356	C₂×C₄	—	4	2	no	—
1357	C₂×C₄	—	8	1	no	—
1358	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1359	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1360	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1361	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1362	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1363	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1364	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1365	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1366	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1367	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1368	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1369	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1370	C₈	—	2	2	no	—
1371	C₈	—	2	2	no	—
1372	C₈	—	2	2	no	—
1373	C₈	—	2	2	no	—
1374	C₇	#61163	1	1	yes	characteristic, direct product factor, Sylow
1375	C₂²	—	2	1	no	—
1376	C₂²	—	2	1	no	—
1377	C₂²	—	2	1	no	—
1378	C₂²	—	2	1	no	—
1379	C₂²	—	2	1	no	—
1380	C₂²	—	2	1	no	—
1381	C₂²	—	2	1	no	—
1382	C₂²	—	2	1	no	—
1383	C₂²	—	2	1	no	—
1384	C₂²	—	2	1	no	—
1385	C₂²	—	2	1	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	1	no	—
1388	C₂²	—	2	2	no	—
1389	C₂²	—	4	4	no	—
1390	C₂²	—	4	1	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	1	no	—
1396	C₂²	—	4	1	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	8	2	no	—
1399	C₂²	—	8	4	no	—
1400	C₂²	—	8	4	no	—
1401	C₂²	C₇×#546	1	2	yes	—
1402	C₂²	C₇×#575	1	2	yes	—
1403	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1404	C₄	—	2	1	no	—
1405	C₄	—	2	1	no	—
1406	C₄	—	2	1	no	—
1407	C₄	—	2	1	no	—
1408	C₄	—	2	1	no	—
1409	C₄	—	2	1	no	—
1410	C₄	—	2	1	no	—
1411	C₄	—	2	1	no	—
1412	C₄	—	2	2	no	—
1413	C₄	—	4	2	no	—
1414	C₄	—	4	2	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	2	no	—
1417	C₄	—	4	1	no	—
1418	C₄	—	4	1	no	—
1419	C₄	—	4	1	no	—
1420	C₄	—	4	2	no	—
1421	C₄	C₇×#546	1	2	yes	—
1422	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1423	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1424	C₂	—	2	2	no	—
1425	C₂	—	2	2	no	—
1426	C₂	—	4	1	no	—
1427	C₂	—	4	1	no	—
1428	C₂	—	4	1	no	—
1429	C₂	—	4	2	no	—
1430	C₂	—	8	1	no	—
1431	C₂	—	8	1	no	—
1432	C₂	C₂×C₇×#546	1	1	yes	characteristic
1433	C₂	C₂×C₇×#575	1	1	yes	characteristic
1434	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×D₄×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#552	C₂	semidirect
3. C₇×#3327	C₂	semidirect
4. C₇×#3323	C₂	semidirect
5. C₇×#3317	C₂	semidirect
6. C₇×#3315	C₂	semidirect
7. C₇×#3312	C₂	semidirect
8. C₇×#3310	C₂	semidirect
9. C₇×#3300	C₂	semidirect
10. C₇×#3296	C₂	semidirect
11. C₇×#3142	C₂	semidirect
12. C₇×#3093	C₂	semidirect
13. C₇×#3092	C₂	semidirect
14. C₇×#3080	C₂	semidirect
15. C₇×#3056	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3037	C₂	semidirect
18. C₇×#3007	C₂	semidirect
19. C₇×#3007	C₂	semidirect
20. C₄×C₇×#137	C₂	semidirect
21. C₇×D₄×M₁₆	C₂	semidirect
22. C₇×#2896	C₂	semidirect
23. C₂×C₇×#417	C₂	semidirect
27. C₂×C₇×#137	C₂²	semidirect
28. C₂×C₇×#137	C₂²	semidirect
29. C₂²×C₇×M₁₆	C₂²	semidirect
30. C₂²×C₇×M₁₆	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
37. C₇×#552	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
55. C₂×C₇×#125	C₂²	semidirect
61. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₄×C₇×Q₈	C₂²	semidirect
68. C₂×C₇×#117	C₂²	semidirect
69. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
70. C₇×#491	C₂²	semidirect
71. C₇×#490	C₂²	semidirect
72. C₇×#488	C₂²	semidirect
73. C₇×#488	C₂²	semidirect
74. C₇×#485	C₂²	semidirect
75. C₇×#485	C₂²	semidirect
76. C₇×#484	C₂²	semidirect
77. C₇×#483	C₂²	semidirect
78. C₇×#482	C₂²	semidirect
79. C₇×#482	C₂²	semidirect
80. C₇×#481	C₂²	semidirect
81. C₇×#480	C₂²	semidirect
82. C₇×#479	C₂²	semidirect
83. C₇×#479	C₂²	semidirect
84. C₇×#478	C₂²	semidirect
85. C₇×#478	C₂²	semidirect
86. C₇×#470	C₂²	semidirect
87. C₇×#470	C₂²	semidirect
88. C₇×#468	C₂²	semidirect
89. C₇×#468	C₂²	semidirect
90. C₇×#467	C₂²	semidirect
91. C₇×#467	C₂²	semidirect
92. C₇×#465	C₂²	semidirect
93. C₇×#465	C₂²	semidirect
94. C₇×#464	C₂²	semidirect
95. C₇×#464	C₂²	semidirect
96. C₇×#462	C₂²	semidirect
97. C₇×#460	C₂²	semidirect
98. C₇×#452	C₂²	semidirect
99. C₇×#452	C₂²	semidirect
100. C₇×#452	C₂²	semidirect
101. C₇×#452	C₂²	semidirect
102. C₇×#451	C₂²	semidirect
103. C₇×#451	C₂²	semidirect
104. C₇×#450	C₂²	semidirect
105. C₇×#450	C₂²	semidirect
106. C₇×#441	C₂²	semidirect
107. C₇×#440	C₂²	semidirect
108. C₄×C₇×Q₁₆	C₂²	semidirect
109. C₄×C₇×SD₁₆	C₂²	semidirect
110. C₇×#436	C₂²	semidirect
112. C₇×#435	C₂²	semidirect
113. C₇×C₈×D₄	C₂²	semidirect
114. C₇×#428	C₂²	semidirect
115. C₇×#428	C₂²	semidirect
116. C₇×#428	C₂²	semidirect
117. C₇×#423	C₂²	semidirect
118. C₇×#419	C₂²	semidirect
119. C₇×#419	C₂²	semidirect
120. C₇×#418	C₂²	semidirect
124. C₇×#417	C₂²	semidirect
125. C₇×#417	C₂²	semidirect
126. C₇×#417	C₂²	semidirect
127. C₇×#417	C₂²	semidirect
128. C₇×#417	C₂²	semidirect
129. C₇×#417	C₂²	semidirect
130. C₇×#417	C₂²	semidirect
131. C₇×#417	C₂²	semidirect
132. C₇×#416	C₂²	semidirect
133. C₇×#416	C₂²	semidirect
134. C₂×C₇×#103	C₂²	semidirect
135. C₂×C₇×#102	C₂²	semidirect
136. C₇×#407	C₂²	semidirect
137. C₇×#407	C₂²	semidirect
138. C₄×C₇×M₁₆	C₂²	semidirect
139. #61163	C₇	direct (N × H)
352. C₂×#552	C₂×C₇	semidirect
354. #3327	C₂×C₇	semidirect
355. #3323	C₂×C₇	semidirect
356. #3317	C₂×C₇	semidirect
357. #3315	C₂×C₇	semidirect
358. #3312	C₂×C₇	semidirect
359. #3310	C₂×C₇	semidirect
360. #3300	C₂×C₇	semidirect
361. #3296	C₂×C₇	semidirect
362. #3142	C₂×C₇	semidirect
363. #3093	C₂×C₇	semidirect
364. #3092	C₂×C₇	semidirect
365. #3080	C₂×C₇	semidirect
366. #3056	C₂×C₇	semidirect
367. #3056	C₂×C₇	semidirect
368. #3037	C₂×C₇	semidirect
369. #3007	C₂×C₇	semidirect
370. #3007	C₂×C₇	semidirect
371. C₄×#137	C₂×C₇	semidirect
372. D₄×M₁₆	C₂×C₇	semidirect
373. #2896	C₂×C₇	semidirect
374. C₂×#417	C₂×C₇	semidirect
570. C₂×#137	C₂²×C₇	semidirect
571. C₂×#137	C₂²×C₇	semidirect
572. C₂²×M₁₆	C₂²×C₇	semidirect
573. C₂²×M₁₆	C₂²×C₇	semidirect
579. #552	C₂²×C₇	semidirect
580. #552	C₂²×C₇	semidirect
581. #552	C₂²×C₇	semidirect
598. C₂×#125	C₂²×C₇	semidirect
604. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
605. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
607. C₂×C₄×Q₈	C₂²×C₇	semidirect
611. C₂×#117	C₂²×C₇	semidirect
612. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
613. #491	C₂²×C₇	semidirect
614. #490	C₂²×C₇	semidirect
615. #488	C₂²×C₇	semidirect
616. #488	C₂²×C₇	semidirect
617. #485	C₂²×C₇	semidirect
618. #485	C₂²×C₇	semidirect
619. #484	C₂²×C₇	semidirect
620. #483	C₂²×C₇	semidirect
621. #482	C₂²×C₇	semidirect
622. #482	C₂²×C₇	semidirect
623. #481	C₂²×C₇	semidirect
624. #480	C₂²×C₇	semidirect
625. #479	C₂²×C₇	semidirect
626. #479	C₂²×C₇	semidirect
627. #478	C₂²×C₇	semidirect
628. #478	C₂²×C₇	semidirect
629. #470	C₂²×C₇	semidirect
630. #470	C₂²×C₇	semidirect
631. #468	C₂²×C₇	semidirect
632. #468	C₂²×C₇	semidirect
633. #467	C₂²×C₇	semidirect
634. #467	C₂²×C₇	semidirect
635. #465	C₂²×C₇	semidirect
636. #465	C₂²×C₇	semidirect
637. #464	C₂²×C₇	semidirect
638. #464	C₂²×C₇	semidirect
639. #462	C₂²×C₇	semidirect
640. #460	C₂²×C₇	semidirect
641. #452	C₂²×C₇	semidirect
642. #452	C₂²×C₇	semidirect
643. #452	C₂²×C₇	semidirect
644. #452	C₂²×C₇	semidirect
645. #451	C₂²×C₇	semidirect
646. #451	C₂²×C₇	semidirect
647. #450	C₂²×C₇	semidirect
648. #450	C₂²×C₇	semidirect
649. #441	C₂²×C₇	semidirect
650. #440	C₂²×C₇	semidirect
651. C₄×Q₁₆	C₂²×C₇	semidirect
652. C₄×SD₁₆	C₂²×C₇	semidirect
653. #436	C₂²×C₇	semidirect
655. #435	C₂²×C₇	semidirect
656. C₈×D₄	C₂²×C₇	semidirect
657. #428	C₂²×C₇	semidirect
658. #428	C₂²×C₇	semidirect
659. #428	C₂²×C₇	semidirect
660. #423	C₂²×C₇	semidirect
661. #419	C₂²×C₇	semidirect
662. #419	C₂²×C₇	semidirect
663. #418	C₂²×C₇	semidirect
667. #417	C₂²×C₇	semidirect
668. #417	C₂²×C₇	semidirect
669. #417	C₂²×C₇	semidirect
670. #417	C₂²×C₇	semidirect
671. #417	C₂²×C₇	semidirect
672. #417	C₂²×C₇	semidirect
673. #417	C₂²×C₇	semidirect
674. #417	C₂²×C₇	semidirect
675. #416	C₂²×C₇	semidirect
676. #416	C₂²×C₇	semidirect
677. C₂×#103	C₂²×C₇	semidirect
678. C₂×#102	C₂²×C₇	semidirect
679. #407	C₂²×C₇	semidirect
680. #407	C₂²×C₇	semidirect
681. C₄×M₁₆	C₂²×C₇	semidirect
1374. C₇	#61163	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#552	2
C₇×D₄×#41	2
C₇×#3327	2
C₇×#3323	2
C₇×#3317	2
C₇×#3315	2
C₇×#3312	2
C₇×#3310	2
C₇×#3300	2
C₇×#3296	2
C₇×#3142	2
C₇×#3093	2
C₇×#3092	2
C₇×#3080	2
C₇×#3056	2
C₇×#3037	2
C₇×#3007	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₇×#2896	2
C₂×C₇×#417	2
#61163	7

Subgroups — C7×#61163 #13238379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61163 #13238379