Subgroups — C₇×#60982 #13238198

Order 1792.

1728 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3260	C₂	1	2	yes	maximal, complemented
4	C₇×#3258	C₂	1	2	yes	maximal, complemented
5	C₇×#3242	C₂	1	2	yes	maximal, complemented
6	C₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3222	C₂	1	2	yes	maximal, complemented
9	C₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₇×#3174	C₂	1	2	yes	maximal, complemented
17	C₇×#3123	C₂	1	2	yes	maximal, complemented
18	C₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#555	—	2	1	no	—
25	C₇×#553	—	2	1	no	—
26	C₇×#553	—	2	1	no	—
27	C₇×#551	—	2	1	no	—
28	C₇×#551	—	2	1	no	—
29	C₇×#547	—	2	1	no	—
30	C₇×#546	—	2	1	no	—
31	C₇×#546	—	2	1	no	—
32	C₇×#544	C₂²	1	1	yes	characteristic
33	C₇×#542	C₂²	1	1	yes	characteristic
34	C₇×#542	C₂²	1	1	yes	characteristic
35	C₇×#541	—	2	1	no	—
36	C₇×#541	—	2	1	no	—
37	C₇×#541	—	2	1	no	—
38	C₇×#541	—	2	1	no	—
39	C₇×#541	C₂²	1	2	yes	—
40	C₇×#541	C₂²	1	2	yes	—
41	C₇×#541	C₂²	1	2	yes	complemented
42	C₇×#541	C₂²	1	2	yes	complemented
43	C₇×#540	C₂²	1	1	yes	characteristic
44	C₇×#540	C₂²	1	1	yes	characteristic
45	C₇×#535	C₂²	1	1	yes	characteristic
46	C₇×#532	C₂²	1	1	yes	characteristic
47	C₇×#532	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#529	C₂²	1	1	yes	characteristic
50	C₇×#529	C₂²	1	1	yes	characteristic
51	C₂×C₇×#126	—	2	1	no	—
52	C₂×C₇×#126	—	2	1	no	—
53	C₂×C₇×#125	—	2	1	no	—
54	C₂×C₇×#125	—	2	1	no	—
55	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
56	C₇×#525	C₂²	1	1	yes	characteristic
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₇×#121	C₂²	1	1	yes	characteristic
60	C₇×#520	C₂²	1	1	yes	characteristic
61	C₇×#518	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×#117	C₂²	1	1	yes	characteristic
65	C₇×#501	C₂²	1	2	yes	complemented
66	C₇×#499	C₂²	1	2	yes	complemented
67	C₇×#497	C₂²	1	2	yes	complemented
68	C₇×#492	C₂²	1	2	yes	complemented
69	C₇×#491	C₂²	1	2	yes	complemented
70	C₇×#490	C₂²	1	2	yes	complemented
71	C₇×#488	C₂²	1	2	yes	complemented
72	C₇×#487	C₂²	1	2	yes	complemented
73	C₇×#485	C₂²	1	2	yes	—
74	C₇×#485	C₂²	1	2	yes	—
75	C₇×#484	C₂²	1	2	yes	—
76	C₇×#484	C₂²	1	1	yes	characteristic, complemented
77	C₇×#483	C₂²	1	2	yes	—
78	C₇×#483	C₂²	1	1	yes	characteristic, complemented
79	C₇×#481	C₂²	1	1	yes	characteristic
80	C₇×#481	C₂²	1	1	yes	characteristic
81	C₇×#481	C₂²	1	1	yes	characteristic, complemented
82	C₇×#480	C₂²	1	1	yes	characteristic
83	C₇×#480	C₂²	1	1	yes	characteristic
84	C₇×#480	C₂²	1	1	yes	characteristic, complemented
85	C₇×#479	C₂²	1	2	yes	complemented
86	C₇×#479	C₂²	1	2	yes	complemented
87	C₇×#479	C₂²	1	2	yes	complemented
88	C₇×#478	C₂²	1	2	yes	complemented
89	C₇×#478	C₂²	1	2	yes	complemented
90	C₇×#478	C₂²	1	2	yes	complemented
91	C₇×#477	C₂²	1	2	yes	complemented
92	C₇×#475	C₂²	1	2	yes	complemented
93	C₇×#470	C₂²	1	2	yes	complemented
94	C₇×#468	C₂²	1	2	yes	—
95	C₇×#468	C₂²	1	2	yes	—
96	C₇×#468	C₂²	1	2	yes	complemented
97	C₇×#467	C₂²	1	2	yes	complemented
98	C₇×#465	C₂²	1	2	yes	—
99	C₇×#465	C₂²	1	2	yes	—
100	C₇×#465	C₂²	1	2	yes	complemented
101	C₇×#464	C₂²	1	2	yes	complemented
102	C₇×#464	C₂²	1	2	yes	complemented
103	C₇×#462	C₂²	1	2	yes	complemented
104	C₇×#461	C₂²	1	2	yes	complemented
105	C₇×#461	C₂²	1	2	yes	complemented
106	C₇×#461	C₂²	1	2	yes	complemented
107	C₇×#460	C₂²	1	2	yes	complemented
108	C₇×#460	C₂²	1	2	yes	complemented
109	C₇×#452	C₂²	1	2	yes	—
110	C₇×#452	C₂²	1	2	yes	—
111	C₇×#451	C₂²	1	1	yes	characteristic, complemented
112	C₇×#451	C₂²	1	1	yes	characteristic, complemented
113	C₇×#450	C₂²	1	2	yes	—
114	C₇×#450	C₂²	1	2	yes	—
115	C₇×#448	C₂²	1	1	yes	characteristic
116	C₇×#448	C₂²	1	1	yes	characteristic
117	C₇×#448	C₂²	1	1	yes	characteristic
118	C₇×#448	C₂²	1	1	yes	characteristic
119	C₇×#448	C₂²	1	1	yes	characteristic, complemented
120	C₇×#448	C₂²	1	1	yes	characteristic, complemented
121	C₇×#441	C₂²	1	2	yes	complemented
122	C₇×#440	C₂²	1	2	yes	complemented
123	C₇×#440	C₂²	1	2	yes	complemented
124	C₇×#440	C₂²	1	2	yes	complemented
125	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
126	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
129	C₇×#433	C₂²	1	2	yes	—
130	C₇×#433	C₂²	1	2	yes	—
131	C₇×#432	C₂²	1	1	yes	characteristic, complemented
132	C₇×#432	C₂²	1	1	yes	characteristic, complemented
133	C₇×#431	C₂²	1	1	yes	characteristic, complemented
134	C₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₇×#424	C₂²	1	2	yes	complemented
136	C₇×#407	C₂²	1	1	yes	characteristic
137	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₇×#405	C₂²	1	2	yes	complemented
139	#60982	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	C₂³	1	1	yes	characteristic
143	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×D₄	—	2	1	no	—
146	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×M₁₆	C₂³	1	2	yes	—
157	C₂²×C₇×C₈	C₂³	1	2	yes	—
158	C₇×C₄⋊Q₈	—	2	1	no	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×#127	C₂³	1	1	yes	characteristic
166	C₇×#127	C₂³	1	1	yes	characteristic
167	C₇×#126	—	2	1	no	—
168	C₇×#126	—	2	1	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#126	—	2	2	no	—
174	C₇×#126	—	2	2	no	—
175	C₇×#126	—	2	2	no	—
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	1	no	—
178	C₇×#126	—	2	1	no	—
179	C₇×#125	—	2	2	no	—
180	C₇×#125	—	2	2	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	1	no	—
189	C₇×#125	—	2	1	no	—
190	C₇×#125	C₂³	1	2	yes	—
191	C₇×#125	C₂³	1	1	yes	characteristic
192	C₇×#125	C₂³	1	2	yes	—
193	C₇×#125	C₂³	1	1	yes	characteristic
194	C₇×#124	—	2	1	no	—
195	C₇×#124	—	2	1	no	—
196	C₇×#124	—	2	1	no	—
197	C₇×#124	—	2	1	no	—
198	C₇×#124	C₂³	1	1	yes	characteristic
199	C₇×#124	C₂³	1	1	yes	characteristic
200	C₇×#123	—	2	1	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	1	no	—
204	C₇×#123	—	2	1	no	—
205	C₇×#123	—	2	1	no	—
206	C₇×#123	—	2	1	no	—
207	C₇×#123	—	2	1	no	—
208	C₇×#123	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	1	no	—
212	C₇×C₂²⋊Q₈	—	2	1	no	—
213	C₇×C₂²⋊Q₈	—	2	1	no	—
214	C₇×C₂²⋊Q₈	—	2	1	no	—
215	C₇×C₂²⋊Q₈	—	2	1	no	—
216	C₇×C₂²⋊Q₈	—	2	1	no	—
217	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	1	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	1	no	—
231	C₇×#121	—	2	1	no	—
232	C₇×#121	—	2	1	no	—
233	C₇×#121	C₂³	1	1	yes	characteristic
234	C₇×#121	C₂³	1	1	yes	characteristic
235	C₇×#121	C₂³	1	1	yes	characteristic
236	C₇×#121	C₂³	1	1	yes	characteristic
237	C₇×#121	C₂³	1	1	yes	characteristic
238	C₇×#121	C₂³	1	1	yes	characteristic
239	C₇×#120	—	2	1	no	—
240	C₇×#120	—	2	1	no	—
241	C₇×#120	—	2	1	no	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	1	no	—
246	C₄×C₇×Q₈	C₂³	1	2	yes	—
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
249	C₄×C₇×Q₈	C₂³	1	2	yes	—
250	C₄×C₇×Q₈	C₂³	1	2	yes	—
251	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	1	no	—
258	C₄×C₇×D₄	—	2	1	no	—
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	1	no	—
262	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
263	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
264	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
265	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
266	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
267	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
268	C₇×#117	—	2	1	no	—
269	C₇×#117	—	2	1	no	—
270	C₇×#117	—	2	1	no	—
271	C₇×#117	D₄	1	1	yes	characteristic
272	C₇×#117	D₄	1	1	yes	characteristic
273	C₇×#117	D₄	1	1	yes	characteristic
274	C₇×#117	D₄	1	1	yes	characteristic
275	C₇×#117	C₂³	1	1	yes	characteristic
276	C₇×#117	C₂³	1	1	yes	characteristic
277	C₇×#117	C₂³	1	1	yes	characteristic
278	C₇×#117	C₂³	1	1	yes	characteristic
279	C₇×#117	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₄⋊C₄	—	2	1	no	—
281	C₂×C₇×C₄⋊C₄	—	2	1	no	—
282	C₂×C₇×C₄⋊C₄	—	2	1	no	—
283	C₂×C₇×C₄⋊C₄	—	2	1	no	—
284	C₂×C₇×C₄⋊C₄	—	2	1	no	—
285	C₂×C₇×C₄⋊C₄	—	2	1	no	—
286	C₂×C₇×C₄⋊C₄	—	2	1	no	—
287	C₂×C₇×C₄⋊C₄	—	2	1	no	—
288	C₂×C₇×C₄⋊C₄	—	2	1	no	—
289	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
290	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
291	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
300	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₇	—	2	1	no	—
302	C₂×C₄²×C₇	—	2	1	no	—
303	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
305	C₇×#107	C₂³	1	2	yes	—
306	C₇×#107	C₂³	1	2	yes	—
307	C₇×#107	C₂³	1	2	yes	—
308	C₇×#107	C₂³	1	2	yes	—
309	C₇×#106	C₂³	1	2	yes	—
310	C₇×#106	C₂³	1	2	yes	—
311	C₇×#106	C₂³	1	2	yes	—
312	C₇×#106	C₂³	1	2	yes	—
313	C₇×C₄⋊C₈	C₂³	1	2	yes	—
314	C₇×C₄⋊C₈	C₂³	1	2	yes	—
315	C₇×C₄⋊C₈	C₂³	1	2	yes	—
316	C₇×C₄⋊C₈	C₂³	1	2	yes	—
317	C₇×#103	C₂³	1	2	yes	—
318	C₇×#103	C₂³	1	2	yes	—
319	C₇×#103	C₂³	1	2	yes	—
320	C₇×#103	C₂³	1	2	yes	—
321	C₇×#103	C₂³	1	2	yes	—
322	C₇×#103	C₂³	1	2	yes	—
323	C₇×#103	C₂³	1	2	yes	—
324	C₇×#103	C₂³	1	2	yes	—
325	C₇×#103	C₂³	1	2	yes	—
326	C₇×#103	C₂³	1	2	yes	—
327	C₇×#102	C₂³	1	2	yes	—
328	C₇×#102	C₂³	1	2	yes	—
329	C₇×#102	C₂³	1	2	yes	—
330	C₇×#102	C₂³	1	2	yes	—
331	C₇×#102	C₂³	1	2	yes	—
332	C₇×#102	C₂³	1	2	yes	—
333	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₇×#97	C₂³	1	2	yes	—
340	C₇×#97	C₂³	1	2	yes	—
341	C₄×C₇×C₈	C₂³	1	2	yes	—
342	C₄×C₇×C₈	C₂³	1	2	yes	—
343	#3494	C₂×C₇	1	1	yes	characteristic
344	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
345	#3260	C₂×C₇	1	2	yes	complemented
346	#3258	C₂×C₇	1	2	yes	complemented
347	#3242	C₂×C₇	1	2	yes	complemented
348	#3234	C₂×C₇	1	1	yes	characteristic, complemented
349	#3232	C₂×C₇	1	1	yes	characteristic, complemented
350	#3222	C₂×C₇	1	2	yes	complemented
351	#3218	C₂×C₇	1	1	yes	characteristic, complemented
352	#3206	C₂×C₇	1	1	yes	characteristic, complemented
353	#3196	C₂×C₇	1	1	yes	characteristic, complemented
354	#3193	C₂×C₇	1	1	yes	characteristic, complemented
355	#3190	C₂×C₇	1	1	yes	characteristic, complemented
356	#3187	C₂×C₇	1	1	yes	characteristic, complemented
357	#3178	C₂×C₇	1	2	yes	complemented
358	#3174	C₂×C₇	1	2	yes	complemented
359	#3123	C₂×C₇	1	2	yes	complemented
360	#3120	C₂×C₇	1	2	yes	complemented
361	#3117	C₂×C₇	1	1	yes	characteristic, complemented
362	#3112	C₂×C₇	1	1	yes	characteristic, complemented
363	#3108	C₂×C₇	1	1	yes	characteristic, complemented
364	#3103	C₂×C₇	1	1	yes	characteristic, complemented
365	#2924	C₂×C₇	1	1	yes	characteristic, complemented
366	C₂⁴×C₇	—	2	1	no	—
367	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
368	C₇×#41	—	4	2	no	—
369	C₇×#41	—	8	2	no	—
370	C₇×#41	—	8	2	no	—
371	C₂×C₇×Q₈	—	2	1	no	—
372	C₂×C₇×Q₈	—	2	1	no	—
373	C₂×C₇×Q₈	—	2	1	no	—
374	C₂×C₇×Q₈	—	2	1	no	—
375	C₂×C₇×Q₈	—	4	2	no	—
376	C₂×C₇×Q₈	—	4	2	no	—
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
379	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	—	2	1	no	—
392	C₂×C₇×D₄	—	4	2	no	—
393	C₂×C₇×D₄	—	8	2	no	—
394	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
395	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
396	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₇	—	2	1	no	—
398	C₂²×C₄×C₇	—	2	1	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	1	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	4	2	no	—
410	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₇×Q₁₆	—	4	2	no	—
421	C₇×Q₁₆	—	4	2	no	—
422	C₇×SD₁₆	—	4	2	no	—
423	C₇×SD₁₆	—	4	2	no	—
424	C₇×SD₁₆	—	4	2	no	—
425	C₇×SD₁₆	—	4	2	no	—
426	C₇×SD₁₆	—	4	2	no	—
427	C₇×SD₁₆	—	4	2	no	—
428	C₇×M₁₆	—	4	2	no	—
429	C₂×C₇×C₈	—	4	2	no	—
430	C₂×C₇×C₈	C₂⁴	1	2	yes	—
431	C₂×C₇×C₈	C₂⁴	1	2	yes	—
432	C₂×C₇×C₈	C₂⁴	1	2	yes	—
433	C₂×C₇×C₈	C₂⁴	1	2	yes	—
434	C₇×C₄⋊C₄	—	2	1	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	2	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	1	no	—
454	C₇×C₄⋊C₄	—	2	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	1	no	—
458	C₇×C₄⋊C₄	—	2	1	no	—
459	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	1	no	—
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	—	2	1	no	—
463	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
467	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
469	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
470	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
471	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
472	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
477	C₇×C₂²⋊C₄	—	2	1	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	2	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	2	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	1	no	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	1	no	—
486	C₇×C₂²⋊C₄	—	2	1	no	—
487	C₇×C₂²⋊C₄	—	2	1	no	—
488	C₇×C₂²⋊C₄	—	2	1	no	—
489	C₇×C₂²⋊C₄	—	2	1	no	—
490	C₇×C₂²⋊C₄	—	2	1	no	—
491	C₇×C₂²⋊C₄	—	2	1	no	—
492	C₇×C₂²⋊C₄	—	2	1	no	—
493	C₇×C₂²⋊C₄	—	2	1	no	—
494	C₇×C₂²⋊C₄	—	2	1	no	—
495	C₇×C₂²⋊C₄	—	2	1	no	—
496	C₇×C₂²⋊C₄	—	2	1	no	—
497	C₇×C₂²⋊C₄	—	2	1	no	—
498	C₇×C₂²⋊C₄	—	2	1	no	—
499	C₇×C₂²⋊C₄	—	2	1	no	—
500	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
501	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
502	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
503	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
504	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
505	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
506	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
507	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₇	—	2	2	no	—
509	C₄²×C₇	—	2	2	no	—
510	C₄²×C₇	—	2	2	no	—
511	C₄²×C₇	—	2	2	no	—
512	C₄²×C₇	—	2	1	no	—
513	C₄²×C₇	—	2	1	no	—
514	C₄²×C₇	—	2	1	no	—
515	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
516	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
517	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
518	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
519	C₄²×C₇	C₂⁴	1	1	yes	characteristic
520	C₄²×C₇	C₂⁴	1	1	yes	characteristic
521	C₄²×C₇	C₂⁴	1	1	yes	characteristic
522	C₄²×C₇	C₂⁴	1	1	yes	characteristic
523	#555	—	2	1	no	—
524	#553	—	2	1	no	—
525	#553	—	2	1	no	—
526	#551	—	2	1	no	—
527	#551	—	2	1	no	—
528	#547	—	2	1	no	—
529	#546	—	2	1	no	—
530	#546	—	2	1	no	—
531	#544	C₂²×C₇	1	1	yes	characteristic
532	#542	C₂²×C₇	1	1	yes	characteristic
533	#542	C₂²×C₇	1	1	yes	characteristic
534	#541	—	2	1	no	—
535	#541	—	2	1	no	—
536	#541	—	2	1	no	—
537	#541	—	2	1	no	—
538	#541	C₂²×C₇	1	2	yes	—
539	#541	C₂²×C₇	1	2	yes	—
540	#541	C₂²×C₇	1	2	yes	complemented
541	#541	C₂²×C₇	1	2	yes	complemented
542	#540	C₂²×C₇	1	1	yes	characteristic
543	#540	C₂²×C₇	1	1	yes	characteristic
544	#535	C₂²×C₇	1	1	yes	characteristic
545	#532	C₂²×C₇	1	1	yes	characteristic
546	#532	C₂²×C₇	1	1	yes	characteristic
547	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
548	#529	C₂²×C₇	1	1	yes	characteristic
549	#529	C₂²×C₇	1	1	yes	characteristic
550	C₂×#126	—	2	1	no	—
551	C₂×#126	—	2	1	no	—
552	C₂×#125	—	2	1	no	—
553	C₂×#125	—	2	1	no	—
554	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
555	#525	C₂²×C₇	1	1	yes	characteristic
556	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
557	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
558	C₂×#121	C₂²×C₇	1	1	yes	characteristic
559	#520	C₂²×C₇	1	1	yes	characteristic
560	#518	C₂²×C₇	1	1	yes	characteristic
561	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
562	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
563	C₂×#117	C₂²×C₇	1	1	yes	characteristic
564	#501	C₂²×C₇	1	2	yes	complemented
565	#499	C₂²×C₇	1	2	yes	complemented
566	#497	C₂²×C₇	1	2	yes	complemented
567	#492	C₂²×C₇	1	2	yes	complemented
568	#491	C₂²×C₇	1	2	yes	complemented
569	#490	C₂²×C₇	1	2	yes	complemented
570	#488	C₂²×C₇	1	2	yes	complemented
571	#487	C₂²×C₇	1	2	yes	complemented
572	#485	C₂²×C₇	1	2	yes	—
573	#485	C₂²×C₇	1	2	yes	—
574	#484	C₂²×C₇	1	2	yes	—
575	#484	C₂²×C₇	1	1	yes	characteristic, complemented
576	#483	C₂²×C₇	1	2	yes	—
577	#483	C₂²×C₇	1	1	yes	characteristic, complemented
578	#481	C₂²×C₇	1	1	yes	characteristic
579	#481	C₂²×C₇	1	1	yes	characteristic
580	#481	C₂²×C₇	1	1	yes	characteristic, complemented
581	#480	C₂²×C₇	1	1	yes	characteristic
582	#480	C₂²×C₇	1	1	yes	characteristic
583	#480	C₂²×C₇	1	1	yes	characteristic, complemented
584	#479	C₂²×C₇	1	2	yes	complemented
585	#479	C₂²×C₇	1	2	yes	complemented
586	#479	C₂²×C₇	1	2	yes	complemented
587	#478	C₂²×C₇	1	2	yes	complemented
588	#478	C₂²×C₇	1	2	yes	complemented
589	#478	C₂²×C₇	1	2	yes	complemented
590	#477	C₂²×C₇	1	2	yes	complemented
591	#475	C₂²×C₇	1	2	yes	complemented
592	#470	C₂²×C₇	1	2	yes	complemented
593	#468	C₂²×C₇	1	2	yes	—
594	#468	C₂²×C₇	1	2	yes	—
595	#468	C₂²×C₇	1	2	yes	complemented
596	#467	C₂²×C₇	1	2	yes	complemented
597	#465	C₂²×C₇	1	2	yes	—
598	#465	C₂²×C₇	1	2	yes	—
599	#465	C₂²×C₇	1	2	yes	complemented
600	#464	C₂²×C₇	1	2	yes	complemented
601	#464	C₂²×C₇	1	2	yes	complemented
602	#462	C₂²×C₇	1	2	yes	complemented
603	#461	C₂²×C₇	1	2	yes	complemented
604	#461	C₂²×C₇	1	2	yes	complemented
605	#461	C₂²×C₇	1	2	yes	complemented
606	#460	C₂²×C₇	1	2	yes	complemented
607	#460	C₂²×C₇	1	2	yes	complemented
608	#452	C₂²×C₇	1	2	yes	—
609	#452	C₂²×C₇	1	2	yes	—
610	#451	C₂²×C₇	1	1	yes	characteristic, complemented
611	#451	C₂²×C₇	1	1	yes	characteristic, complemented
612	#450	C₂²×C₇	1	2	yes	—
613	#450	C₂²×C₇	1	2	yes	—
614	#448	C₂²×C₇	1	1	yes	characteristic
615	#448	C₂²×C₇	1	1	yes	characteristic
616	#448	C₂²×C₇	1	1	yes	characteristic
617	#448	C₂²×C₇	1	1	yes	characteristic
618	#448	C₂²×C₇	1	1	yes	characteristic, complemented
619	#448	C₂²×C₇	1	1	yes	characteristic, complemented
620	#441	C₂²×C₇	1	2	yes	complemented
621	#440	C₂²×C₇	1	2	yes	complemented
622	#440	C₂²×C₇	1	2	yes	complemented
623	#440	C₂²×C₇	1	2	yes	complemented
624	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
625	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
626	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
627	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
628	#433	C₂²×C₇	1	2	yes	—
629	#433	C₂²×C₇	1	2	yes	—
630	#432	C₂²×C₇	1	1	yes	characteristic, complemented
631	#432	C₂²×C₇	1	1	yes	characteristic, complemented
632	#431	C₂²×C₇	1	1	yes	characteristic, complemented
633	#431	C₂²×C₇	1	1	yes	characteristic, complemented
634	#424	C₂²×C₇	1	2	yes	complemented
635	#407	C₂²×C₇	1	1	yes	characteristic
636	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
637	#405	C₂²×C₇	1	2	yes	complemented
638	C₂³×C₇	—	2	2	no	—
639	C₂³×C₇	—	2	1	no	—
640	C₂³×C₇	—	2	1	no	—
641	C₂³×C₇	—	2	1	no	—
642	C₂³×C₇	—	4	1	no	—
643	C₂³×C₇	—	4	1	no	—
644	C₂³×C₇	—	4	2	no	—
645	C₂³×C₇	—	8	1	no	—
646	C₂³×C₇	—	8	1	no	—
647	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
648	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
649	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
650	C₇×Q₈	—	2	2	no	—
651	C₇×Q₈	—	2	2	no	—
652	C₇×Q₈	—	2	2	no	—
653	C₇×Q₈	—	2	2	no	—
654	C₇×Q₈	—	2	2	no	—
655	C₇×Q₈	—	4	2	no	—
656	C₇×Q₈	—	4	2	no	—
657	C₇×Q₈	—	8	1	no	—
658	C₇×Q₈	—	8	1	no	—
659	C₇×D₄	—	2	2	no	—
660	C₇×D₄	—	2	2	no	—
661	C₇×D₄	—	2	2	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	2	no	—
664	C₇×D₄	—	4	2	no	—
665	C₇×D₄	—	4	2	no	—
666	C₇×D₄	—	4	2	no	—
667	C₇×D₄	—	8	1	no	—
668	C₇×D₄	—	8	1	no	—
669	C₇×D₄	—	8	1	no	—
670	C₇×D₄	—	8	1	no	—
671	C₇×D₄	—	8	1	no	—
672	C₇×D₄	—	8	1	no	—
673	C₇×D₄	—	8	1	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	2	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	2	no	—
678	C₂×C₄×C₇	—	2	2	no	—
679	C₂×C₄×C₇	—	2	1	no	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	2	no	—
682	C₂×C₄×C₇	—	2	2	no	—
683	C₂×C₄×C₇	—	2	2	no	—
684	C₂×C₄×C₇	—	2	1	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	2	1	no	—
687	C₂×C₄×C₇	—	2	1	no	—
688	C₂×C₄×C₇	—	4	1	no	—
689	C₂×C₄×C₇	—	4	1	no	—
690	C₂×C₄×C₇	—	4	1	no	—
691	C₂×C₄×C₇	—	4	1	no	—
692	C₂×C₄×C₇	—	4	1	no	—
693	C₂×C₄×C₇	—	4	2	no	—
694	C₂×C₄×C₇	—	4	2	no	—
695	C₂×C₄×C₇	—	4	2	no	—
696	C₂×C₄×C₇	—	4	2	no	—
697	C₂×C₄×C₇	—	4	2	no	—
698	C₂×C₄×C₇	—	8	1	no	—
699	C₂×C₄×C₇	—	8	1	no	—
700	C₂×C₄×C₇	—	8	1	no	—
701	C₂×C₄×C₇	—	8	1	no	—
702	C₂×C₄×C₇	—	8	1	no	—
703	C₂×C₄×C₇	—	8	1	no	—
704	C₂×C₄×C₇	—	8	1	no	—
705	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
709	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
710	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
714	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
717	C₇×C₈	—	2	2	no	—
718	C₇×C₈	—	2	2	no	—
719	C₇×C₈	—	2	2	no	—
720	C₇×C₈	—	2	2	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₇	1	1	yes	characteristic
724	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
725	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
728	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
729	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
737	C₂×M₁₆	C₂³×C₇	1	2	yes	—
738	C₂²×C₈	C₂³×C₇	1	2	yes	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
743	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
744	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
746	#127	C₂³×C₇	1	1	yes	characteristic
747	#127	C₂³×C₇	1	1	yes	characteristic
748	#126	—	2	1	no	—
749	#126	—	2	1	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	—	2	1	no	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	1	no	—
769	#125	—	2	1	no	—
770	#125	—	2	1	no	—
771	#125	C₂³×C₇	1	2	yes	—
772	#125	C₂³×C₇	1	2	yes	—
773	#125	C₂³×C₇	1	1	yes	characteristic
774	#125	C₂³×C₇	1	1	yes	characteristic
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	—	2	1	no	—
778	#124	—	2	1	no	—
779	#124	C₂³×C₇	1	1	yes	characteristic
780	#124	C₂³×C₇	1	1	yes	characteristic
781	#123	—	2	1	no	—
782	#123	—	2	1	no	—
783	#123	—	2	1	no	—
784	#123	—	2	1	no	—
785	#123	—	2	1	no	—
786	#123	—	2	1	no	—
787	#123	—	2	1	no	—
788	#123	—	2	1	no	—
789	#123	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	C₂³×C₇	1	1	yes	characteristic
815	#121	C₂³×C₇	1	1	yes	characteristic
816	#121	C₂³×C₇	1	1	yes	characteristic
817	#121	C₂³×C₇	1	1	yes	characteristic
818	#121	C₂³×C₇	1	1	yes	characteristic
819	#121	C₂³×C₇	1	1	yes	characteristic
820	#120	—	2	1	no	—
821	#120	—	2	1	no	—
822	#120	—	2	1	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	C₂³×C₇	1	2	yes	—
828	C₄×Q₈	C₂³×C₇	1	2	yes	—
829	C₄×Q₈	C₂³×C₇	1	2	yes	—
830	C₄×Q₈	C₂³×C₇	1	2	yes	—
831	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
849	#117	—	2	1	no	—
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	C₇×D₄	1	1	yes	characteristic
853	#117	C₇×D₄	1	1	yes	characteristic
854	#117	C₇×D₄	1	1	yes	characteristic
855	#117	C₇×D₄	1	1	yes	characteristic
856	#117	C₂³×C₇	1	1	yes	characteristic
857	#117	C₂³×C₇	1	1	yes	characteristic
858	#117	C₂³×C₇	1	1	yes	characteristic
859	#117	C₂³×C₇	1	1	yes	characteristic
860	#117	C₂³×C₇	1	1	yes	characteristic
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
875	C₂×C₂²⋊C₄	—	2	1	no	—
876	C₂×C₂²⋊C₄	—	2	1	no	—
877	C₂×C₂²⋊C₄	—	2	1	no	—
878	C₂×C₂²⋊C₄	—	2	1	no	—
879	C₂×C₂²⋊C₄	—	2	1	no	—
880	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
881	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
882	C₂×C₄²	—	2	1	no	—
883	C₂×C₄²	—	2	1	no	—
884	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
885	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
886	#107	C₂³×C₇	1	2	yes	—
887	#107	C₂³×C₇	1	2	yes	—
888	#107	C₂³×C₇	1	2	yes	—
889	#107	C₂³×C₇	1	2	yes	—
890	#106	C₂³×C₇	1	2	yes	—
891	#106	C₂³×C₇	1	2	yes	—
892	#106	C₂³×C₇	1	2	yes	—
893	#106	C₂³×C₇	1	2	yes	—
894	C₄⋊C₈	C₂³×C₇	1	2	yes	—
895	C₄⋊C₈	C₂³×C₇	1	2	yes	—
896	C₄⋊C₈	C₂³×C₇	1	2	yes	—
897	C₄⋊C₈	C₂³×C₇	1	2	yes	—
898	#103	C₂³×C₇	1	2	yes	—
899	#103	C₂³×C₇	1	2	yes	—
900	#103	C₂³×C₇	1	2	yes	—
901	#103	C₂³×C₇	1	2	yes	—
902	#103	C₂³×C₇	1	2	yes	—
903	#103	C₂³×C₇	1	2	yes	—
904	#103	C₂³×C₇	1	2	yes	—
905	#103	C₂³×C₇	1	2	yes	—
906	#103	C₂³×C₇	1	2	yes	—
907	#103	C₂³×C₇	1	2	yes	—
908	#102	C₂³×C₇	1	2	yes	—
909	#102	C₂³×C₇	1	2	yes	—
910	#102	C₂³×C₇	1	2	yes	—
911	#102	C₂³×C₇	1	2	yes	—
912	#102	C₂³×C₇	1	2	yes	—
913	#102	C₂³×C₇	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
918	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
920	#97	C₂³×C₇	1	2	yes	—
921	#97	C₂³×C₇	1	2	yes	—
922	C₄×C₈	C₂³×C₇	1	2	yes	—
923	C₄×C₈	C₂³×C₇	1	2	yes	—
924	C₂²×C₇	—	2	1	no	—
925	C₂²×C₇	—	2	1	no	—
926	C₂²×C₇	—	2	1	no	—
927	C₂²×C₇	—	2	1	no	—
928	C₂²×C₇	—	2	1	no	—
929	C₂²×C₇	—	2	1	no	—
930	C₂²×C₇	—	2	1	no	—
931	C₂²×C₇	—	2	1	no	—
932	C₂²×C₇	—	4	1	no	—
933	C₂²×C₇	—	4	1	no	—
934	C₂²×C₇	—	4	1	no	—
935	C₂²×C₇	—	4	1	no	—
936	C₂²×C₇	—	4	1	no	—
937	C₂²×C₇	—	4	1	no	—
938	C₂²×C₇	—	4	1	no	—
939	C₂²×C₇	—	4	1	no	—
940	C₂²×C₇	—	4	1	no	—
941	C₂²×C₇	—	8	2	no	—
942	C₂²×C₇	—	16	2	no	—
943	C₂²×C₇	#577	1	2	yes	—
944	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
945	C₄×C₇	—	2	1	no	—
946	C₄×C₇	—	2	1	no	—
947	C₄×C₇	—	2	1	no	—
948	C₄×C₇	—	2	1	no	—
949	C₄×C₇	—	2	1	no	—
950	C₄×C₇	—	2	1	no	—
951	C₄×C₇	—	2	1	no	—
952	C₄×C₇	—	2	1	no	—
953	C₄×C₇	—	2	1	no	—
954	C₄×C₇	—	2	1	no	—
955	C₄×C₇	—	2	1	no	—
956	C₄×C₇	—	4	2	no	—
957	C₄×C₇	—	4	1	no	—
958	C₄×C₇	—	4	1	no	—
959	C₄×C₇	—	4	2	no	—
960	C₄×C₇	—	4	2	no	—
961	C₄×C₇	—	4	2	no	—
962	C₄×C₇	—	4	1	no	—
963	C₄×C₇	—	4	1	no	—
964	C₄×C₇	—	4	1	no	—
965	C₄×C₇	#585	1	2	yes	—
966	C₂⁴	—	2	1	no	—
967	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
968	#41	—	4	2	no	—
969	#41	—	8	2	no	—
970	#41	—	8	2	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	1	no	—
974	C₂×Q₈	—	2	1	no	—
975	C₂×Q₈	—	4	2	no	—
976	C₂×Q₈	—	4	2	no	—
977	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
978	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
979	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	4	2	no	—
993	C₂×D₄	—	8	2	no	—
994	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
996	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	4	2	no	—
1010	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1011	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1012	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1013	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1014	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1015	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1016	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1020	Q₁₆	—	4	2	no	—
1021	Q₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	SD₁₆	—	4	2	no	—
1024	SD₁₆	—	4	2	no	—
1025	SD₁₆	—	4	2	no	—
1026	SD₁₆	—	4	2	no	—
1027	SD₁₆	—	4	2	no	—
1028	M₁₆	—	4	2	no	—
1029	C₂×C₈	—	4	2	no	—
1030	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1031	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1032	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1033	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1072	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1102	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1103	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	2	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	—	2	2	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1116	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1117	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1118	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1119	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1123	C₂×C₇	—	2	2	no	—
1124	C₂×C₇	—	4	1	no	—
1125	C₂×C₇	—	4	1	no	—
1126	C₂×C₇	—	8	1	no	—
1127	C₂×C₇	—	8	1	no	—
1128	C₂×C₇	—	8	1	no	—
1129	C₂×C₇	#3449	1	1	yes	characteristic
1130	C₂×C₇	C₂×#577	1	1	yes	characteristic
1131	C₂×C₇	#3586	1	1	yes	characteristic
1132	C₂³	—	2	2	no	—
1133	C₂³	—	2	1	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	4	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	2	no	—
1139	C₂³	—	8	1	no	—
1140	C₂³	—	8	1	no	—
1141	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1142	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1143	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1144	Q₈	—	2	2	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	2	2	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	8	1	no	—
1152	Q₈	—	8	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	8	1	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	1	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	1	no	—
1166	D₄	—	8	1	no	—
1167	D₄	—	8	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	8	1	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	—	8	1	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1200	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1201	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1202	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1203	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1204	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1205	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1206	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1207	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1208	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1209	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1210	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1211	C₈	—	2	2	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₈	—	2	2	no	—
1215	C₇	#60982	1	1	yes	characteristic, direct product factor, Sylow
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	8	2	no	—
1234	C₂²	—	16	2	no	—
1235	C₂²	C₇×#577	1	2	yes	—
1236	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	2	no	—
1257	C₄	C₇×#585	1	2	yes	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₇×#3449	1	1	yes	characteristic
1265	C₂	C₂×C₇×#577	1	1	yes	characteristic
1266	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×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#541	C₂	semidirect
3. C₇×#3260	C₂	semidirect
4. C₇×#3258	C₂	semidirect
5. C₇×#3242	C₂	semidirect
6. C₇×#3234	C₂	semidirect
7. C₇×#3232	C₂	semidirect
8. C₇×#3222	C₂	semidirect
9. C₇×#3218	C₂	semidirect
10. C₇×#3206	C₂	semidirect
11. C₇×#3196	C₂	semidirect
12. C₇×#3193	C₂	semidirect
13. C₇×#3190	C₂	semidirect
14. C₇×#3187	C₂	semidirect
15. C₇×#3178	C₂	semidirect
16. C₇×#3174	C₂	semidirect
17. C₇×#3123	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₇×#3117	C₂	semidirect
20. C₇×#3112	C₂	semidirect
21. C₇×#3108	C₂	semidirect
22. C₇×#3103	C₂	semidirect
23. C₇×#2924	C₂	semidirect
41. C₇×#541	C₂²	semidirect
42. C₇×#541	C₂²	semidirect
48. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
55. C₂×C₇×#125	C₂²	semidirect
62. C₂×C₄×C₇×Q₈	C₂²	semidirect
63. C₂×C₄×C₇×Q₈	C₂²	semidirect
65. C₇×#501	C₂²	semidirect
66. C₇×#499	C₂²	semidirect
67. C₇×#497	C₂²	semidirect
68. C₇×#492	C₂²	semidirect
69. C₇×#491	C₂²	semidirect
70. C₇×#490	C₂²	semidirect
71. C₇×#488	C₂²	semidirect
72. C₇×#487	C₂²	semidirect
76. C₇×#484	C₂²	semidirect
78. C₇×#483	C₂²	semidirect
81. C₇×#481	C₂²	semidirect
84. C₇×#480	C₂²	semidirect
85. C₇×#479	C₂²	semidirect
86. C₇×#479	C₂²	semidirect
87. C₇×#479	C₂²	semidirect
88. C₇×#478	C₂²	semidirect
89. C₇×#478	C₂²	semidirect
90. C₇×#478	C₂²	semidirect
91. C₇×#477	C₂²	semidirect
92. C₇×#475	C₂²	semidirect
93. C₇×#470	C₂²	semidirect
96. C₇×#468	C₂²	semidirect
97. C₇×#467	C₂²	semidirect
100. C₇×#465	C₂²	semidirect
101. C₇×#464	C₂²	semidirect
102. C₇×#464	C₂²	semidirect
103. C₇×#462	C₂²	semidirect
104. C₇×#461	C₂²	semidirect
105. C₇×#461	C₂²	semidirect
106. C₇×#461	C₂²	semidirect
107. C₇×#460	C₂²	semidirect
108. C₇×#460	C₂²	semidirect
111. C₇×#451	C₂²	semidirect
112. C₇×#451	C₂²	semidirect
119. C₇×#448	C₂²	semidirect
120. C₇×#448	C₂²	semidirect
121. C₇×#441	C₂²	semidirect
122. C₇×#440	C₂²	semidirect
123. C₇×#440	C₂²	semidirect
124. C₇×#440	C₂²	semidirect
125. C₄×C₇×Q₁₆	C₂²	semidirect
126. C₄×C₇×SD₁₆	C₂²	semidirect
127. C₄×C₇×SD₁₆	C₂²	semidirect
128. C₄×C₇×SD₁₆	C₂²	semidirect
131. C₇×#432	C₂²	semidirect
132. C₇×#432	C₂²	semidirect
133. C₇×#431	C₂²	semidirect
134. C₇×#431	C₂²	semidirect
135. C₇×#424	C₂²	semidirect
138. C₇×#405	C₂²	semidirect
139. #60982	C₇	direct (N × H)
344. C₂×#541	C₂×C₇	semidirect
345. #3260	C₂×C₇	semidirect
346. #3258	C₂×C₇	semidirect
347. #3242	C₂×C₇	semidirect
348. #3234	C₂×C₇	semidirect
349. #3232	C₂×C₇	semidirect
350. #3222	C₂×C₇	semidirect
351. #3218	C₂×C₇	semidirect
352. #3206	C₂×C₇	semidirect
353. #3196	C₂×C₇	semidirect
354. #3193	C₂×C₇	semidirect
355. #3190	C₂×C₇	semidirect
356. #3187	C₂×C₇	semidirect
357. #3178	C₂×C₇	semidirect
358. #3174	C₂×C₇	semidirect
359. #3123	C₂×C₇	semidirect
360. #3120	C₂×C₇	semidirect
361. #3117	C₂×C₇	semidirect
362. #3112	C₂×C₇	semidirect
363. #3108	C₂×C₇	semidirect
364. #3103	C₂×C₇	semidirect
365. #2924	C₂×C₇	semidirect
540. #541	C₂²×C₇	semidirect
541. #541	C₂²×C₇	semidirect
547. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
554. C₂×#125	C₂²×C₇	semidirect
561. C₂×C₄×Q₈	C₂²×C₇	semidirect
562. C₂×C₄×Q₈	C₂²×C₇	semidirect
564. #501	C₂²×C₇	semidirect
565. #499	C₂²×C₇	semidirect
566. #497	C₂²×C₇	semidirect
567. #492	C₂²×C₇	semidirect
568. #491	C₂²×C₇	semidirect
569. #490	C₂²×C₇	semidirect
570. #488	C₂²×C₇	semidirect
571. #487	C₂²×C₇	semidirect
575. #484	C₂²×C₇	semidirect
577. #483	C₂²×C₇	semidirect
580. #481	C₂²×C₇	semidirect
583. #480	C₂²×C₇	semidirect
584. #479	C₂²×C₇	semidirect
585. #479	C₂²×C₇	semidirect
586. #479	C₂²×C₇	semidirect
587. #478	C₂²×C₇	semidirect
588. #478	C₂²×C₇	semidirect
589. #478	C₂²×C₇	semidirect
590. #477	C₂²×C₇	semidirect
591. #475	C₂²×C₇	semidirect
592. #470	C₂²×C₇	semidirect
595. #468	C₂²×C₇	semidirect
596. #467	C₂²×C₇	semidirect
599. #465	C₂²×C₇	semidirect
600. #464	C₂²×C₇	semidirect
601. #464	C₂²×C₇	semidirect
602. #462	C₂²×C₇	semidirect
603. #461	C₂²×C₇	semidirect
604. #461	C₂²×C₇	semidirect
605. #461	C₂²×C₇	semidirect
606. #460	C₂²×C₇	semidirect
607. #460	C₂²×C₇	semidirect
610. #451	C₂²×C₇	semidirect
611. #451	C₂²×C₇	semidirect
618. #448	C₂²×C₇	semidirect
619. #448	C₂²×C₇	semidirect
620. #441	C₂²×C₇	semidirect
621. #440	C₂²×C₇	semidirect
622. #440	C₂²×C₇	semidirect
623. #440	C₂²×C₇	semidirect
624. C₄×Q₁₆	C₂²×C₇	semidirect
625. C₄×SD₁₆	C₂²×C₇	semidirect
626. C₄×SD₁₆	C₂²×C₇	semidirect
627. C₄×SD₁₆	C₂²×C₇	semidirect
630. #432	C₂²×C₇	semidirect
631. #432	C₂²×C₇	semidirect
632. #431	C₂²×C₇	semidirect
633. #431	C₂²×C₇	semidirect
634. #424	C₂²×C₇	semidirect
637. #405	C₂²×C₇	semidirect
1215. C₇	#60982	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3494	2
C₂×C₇×#541	2
C₇×#3260	2
C₇×#3258	2
C₇×#3242	2
C₇×#3234	2
C₇×#3232	2
C₇×#3222	2
C₇×#3218	2
C₇×#3206	2
C₇×#3196	2
C₇×#3193	2
C₇×#3190	2
C₇×#3187	2
C₇×#3178	2
C₇×#3174	2
C₇×#3123	2
C₇×#3120	2
C₇×#3117	2
C₇×#3112	2
C₇×#3108	2
C₇×#3103	2
C₇×#2924	2
#60982	7

Subgroups — C7×#60982 #13238198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60982 #13238198