Subgroups — C₇×#60342 #13237558

Order 1792.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2992	C₂	1	2	yes	maximal, complemented
6	C₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2989	C₂	1	2	yes	maximal, complemented
8	C₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2987	C₂	1	2	yes	maximal, complemented
10	C₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2970	C₂	1	2	yes	maximal, complemented
14	C₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2968	C₂	1	2	yes	maximal, complemented
17	C₇×#2967	C₂	1	2	yes	maximal, complemented
18	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2961	C₂	1	2	yes	maximal, complemented
23	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#557	C₄	1	1	yes	characteristic
25	C₇×#556	C₄	1	2	yes	—
26	C₇×#556	C₄	1	1	yes	characteristic
27	C₇×#552	C₄	1	1	yes	characteristic
28	C₇×#552	C₄	1	2	yes	—
29	C₇×#552	C₄	1	1	yes	characteristic
30	C₇×#552	C₄	1	2	yes	—
31	C₇×D₄×Q₈	C₄	1	1	yes	characteristic
32	C₇×#548	C₄	1	1	yes	characteristic
33	C₇×#548	C₄	1	1	yes	characteristic
34	C₇×#547	C₄	1	1	yes	characteristic
35	C₇×#547	C₄	1	2	yes	—
36	C₇×#533	C₂²	1	2	yes	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#529	C₂²	1	1	yes	characteristic
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#529	C₂²	1	2	yes	—
41	C₇×#529	C₂²	1	1	yes	characteristic
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	C₇×#446	C₂²	1	2	yes	—
48	C₇×#446	C₂²	1	1	yes	characteristic
49	C₇×#446	C₂²	1	1	yes	characteristic
50	C₇×#446	C₂²	1	1	yes	characteristic
51	C₇×#446	C₂²	1	1	yes	characteristic
52	C₇×#446	C₂²	1	2	yes	—
53	C₇×#446	C₂²	1	1	yes	characteristic
54	C₇×#446	C₂²	1	2	yes	—
55	C₇×#446	C₂²	1	2	yes	—
56	C₇×#446	C₂²	1	2	yes	—
57	C₇×#446	C₂²	1	2	yes	—
58	C₇×#446	C₂²	1	2	yes	—
59	C₇×#446	C₂²	1	2	yes	—
60	C₇×#446	C₂²	1	1	yes	characteristic
61	C₇×#446	C₂²	1	2	yes	—
62	C₇×#446	C₂²	1	1	yes	characteristic
63	C₇×#446	C₂²	1	2	yes	—
64	C₇×#446	C₂²	1	1	yes	characteristic
65	C₇×#446	C₂²	1	1	yes	characteristic
66	C₇×#446	C₂²	1	2	yes	—
67	C₇×#446	C₂²	1	2	yes	—
68	C₇×#446	C₂²	1	1	yes	characteristic
69	C₇×#446	C₂²	1	2	yes	—
70	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
71	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
72	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
73	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
74	C₇×#436	C₂²	1	1	yes	characteristic
75	C₇×#436	C₂²	1	1	yes	characteristic
76	C₇×#436	C₂²	1	1	yes	characteristic
77	C₇×#436	C₂²	1	2	yes	—
78	C₇×#436	C₂²	1	1	yes	characteristic
79	C₇×#436	C₂²	1	2	yes	—
80	C₇×#435	C₂²	1	1	yes	characteristic
81	C₇×#435	C₂²	1	1	yes	characteristic
82	C₇×#435	C₂²	1	1	yes	characteristic
83	C₇×#435	C₂²	1	1	yes	characteristic
84	C₇×#435	C₂²	1	2	yes	—
85	C₇×#435	C₂²	1	2	yes	—
86	C₇×#435	C₂²	1	2	yes	—
87	C₇×#435	C₂²	1	2	yes	—
88	C₇×#435	C₂²	1	2	yes	—
89	C₇×#435	C₂²	1	2	yes	—
90	C₇×#435	C₂²	1	2	yes	—
91	C₇×#435	C₂²	1	2	yes	—
92	C₇×#435	C₂²	1	2	yes	—
93	C₇×#435	C₂²	1	2	yes	—
94	C₇×C₈×D₄	C₂²	1	2	yes	—
95	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
96	C₇×C₈×D₄	C₂²	1	2	yes	—
97	C₇×C₈×D₄	C₂²	1	2	yes	—
98	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
99	C₇×#433	C₂²	1	2	yes	—
100	C₇×#433	C₂²	1	2	yes	—
101	C₇×#433	C₂²	1	2	yes	—
102	C₇×#433	C₂²	1	2	yes	—
103	C₇×#433	C₂²	1	2	yes	—
104	C₇×#433	C₂²	1	2	yes	—
105	C₇×#432	C₂²	1	1	yes	characteristic
106	C₇×#432	C₂²	1	2	yes	—
107	C₇×#432	C₂²	1	2	yes	—
108	C₇×#432	C₂²	1	2	yes	—
109	C₇×#432	C₂²	1	1	yes	characteristic
110	C₇×#432	C₂²	1	2	yes	—
111	C₇×#432	C₂²	1	2	yes	—
112	C₇×#431	C₂²	1	1	yes	characteristic
113	C₇×#431	C₂²	1	1	yes	characteristic
114	C₇×#431	C₂²	1	1	yes	characteristic
115	C₇×#431	C₂²	1	2	yes	—
116	C₇×#431	C₂²	1	1	yes	characteristic
117	C₇×#424	C₂²	1	2	yes	—
118	C₇×#424	C₂²	1	2	yes	—
119	C₇×#424	C₂²	1	2	yes	—
120	C₇×#423	C₂²	1	2	yes	—
121	C₇×#423	C₂²	1	2	yes	—
122	C₇×#423	C₂²	1	1	yes	characteristic
123	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
124	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
125	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₇×#405	C₂²	1	2	yes	—
127	C₇×#405	C₂²	1	2	yes	—
128	C₇×#405	C₂²	1	2	yes	—
129	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
130	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
131	C₄×C₇×M₁₆	C₂²	1	2	yes	—
132	C₂×C₇×#97	C₂²	1	2	yes	—
133	C₂×C₇×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
135	#60342	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₇×#41	C₂×C₄	1	2	yes	—
138	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₇×M₁₆	C₂³	1	2	yes	—
144	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×M₁₆	C₂³	1	2	yes	—
147	C₂×C₇×M₁₆	C₂³	1	2	yes	—
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	2	yes	—
150	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×C₈	C₂³	1	2	yes	—
152	C₂²×C₇×C₈	C₂³	1	2	yes	—
153	C₂²×C₇×C₈	C₂³	1	2	yes	—
154	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
155	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
157	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
158	C₇×#126	C₂×C₄	1	2	yes	—
159	C₇×#126	C₂×C₄	1	2	yes	—
160	C₇×#126	C₂×C₄	1	2	yes	—
161	C₇×#126	C₂×C₄	1	2	yes	—
162	C₇×#126	C₂×C₄	1	2	yes	—
163	C₇×#126	C₂×C₄	1	2	yes	—
164	C₇×#125	C₂×C₄	1	1	yes	characteristic
165	C₇×#125	C₂×C₄	1	2	yes	—
166	C₇×#125	C₂×C₄	1	2	yes	—
167	C₇×#125	C₂×C₄	1	1	yes	characteristic
168	C₇×#125	C₂×C₄	1	2	yes	—
169	C₇×#125	C₂×C₄	1	2	yes	—
170	C₇×#125	C₂×C₄	1	2	yes	—
171	C₇×#124	C₂×C₄	1	1	yes	characteristic
172	C₇×#124	C₂×C₄	1	1	yes	characteristic
173	C₇×#124	C₂×C₄	1	2	yes	—
174	C₇×#124	C₂×C₄	1	2	yes	—
175	C₇×#123	C₂×C₄	1	2	yes	—
176	C₇×#123	C₂×C₄	1	2	yes	—
177	C₇×#123	C₂×C₄	1	2	yes	—
178	C₇×#123	C₂×C₄	1	2	yes	—
179	C₇×#123	C₂×C₄	1	2	yes	—
180	C₇×#123	C₂×C₄	1	2	yes	—
181	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
189	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
190	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₇×#121	C₂×C₄	1	1	yes	characteristic
193	C₇×#121	C₂×C₄	1	1	yes	characteristic
194	C₇×#121	C₂×C₄	1	2	yes	—
195	C₇×#121	C₂×C₄	1	2	yes	—
196	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
198	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
200	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
201	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
202	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
203	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
204	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
205	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
206	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
207	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
208	C₄×C₇×Q₈	C₂³	1	2	yes	—
209	C₄×C₇×Q₈	C₂³	1	2	yes	—
210	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×Q₈	C₂³	1	2	yes	—
212	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
213	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
214	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
216	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
217	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
218	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
219	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
220	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
221	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
222	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
224	C₄×C₇×D₄	C₂³	1	2	yes	—
225	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
226	C₄×C₇×D₄	C₂³	1	2	yes	—
227	C₇×#117	C₂×C₄	1	1	yes	characteristic
228	C₇×#117	C₂×C₄	1	2	yes	—
229	C₇×#117	C₂×C₄	1	1	yes	characteristic
230	C₇×#117	C₂×C₄	1	2	yes	—
231	C₇×#117	C₂×C₄	1	1	yes	characteristic
232	C₇×#117	C₂×C₄	1	2	yes	—
233	C₇×#117	C₂×C₄	1	1	yes	characteristic
234	C₇×#117	C₂×C₄	1	2	yes	—
235	C₇×#117	C₂³	1	2	yes	—
236	C₇×#117	C₂³	1	2	yes	—
237	C₇×#117	C₂³	1	2	yes	—
238	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
239	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
240	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
242	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₇	C₂³	1	2	yes	—
244	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₇	C₂³	1	2	yes	—
246	C₂×C₄²×C₇	C₂³	1	2	yes	—
247	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
248	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₈	C₂³	1	2	yes	—
251	C₇×C₄⋊C₈	C₂³	1	2	yes	—
252	C₇×C₄⋊C₈	C₂³	1	2	yes	—
253	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₇×C₄⋊C₈	C₂³	1	2	yes	—
255	C₇×C₄⋊C₈	C₂³	1	2	yes	—
256	C₇×C₄⋊C₈	C₂³	1	2	yes	—
257	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₇×C₄⋊C₈	C₂³	1	2	yes	—
259	C₇×C₄⋊C₈	C₂³	1	2	yes	—
260	C₇×C₄⋊C₈	C₂³	1	2	yes	—
261	C₇×C₄⋊C₈	C₂³	1	2	yes	—
262	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₇×C₄⋊C₈	C₂³	1	2	yes	—
265	C₇×C₄⋊C₈	C₂³	1	2	yes	—
266	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₇×C₄⋊C₈	C₂³	1	2	yes	—
269	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₇×C₄⋊C₈	C₂³	1	2	yes	—
272	C₇×C₄⋊C₈	C₂³	1	2	yes	—
273	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₇×#97	C₂³	1	2	yes	—
287	C₇×#97	C₂³	1	1	yes	characteristic
288	C₇×#97	C₂³	1	2	yes	—
289	C₇×#97	C₂³	1	2	yes	—
290	C₇×#97	C₂³	1	2	yes	—
291	C₇×#97	C₂³	1	2	yes	—
292	C₇×#97	C₂³	1	2	yes	—
293	C₇×#97	C₂³	1	1	yes	characteristic
294	C₇×#97	C₂³	1	1	yes	characteristic
295	C₇×#97	C₂³	1	2	yes	—
296	C₇×#97	C₂³	1	1	yes	characteristic
297	C₇×#97	C₂³	1	2	yes	—
298	C₇×#97	C₂³	1	2	yes	—
299	C₇×#97	C₂³	1	2	yes	—
300	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
301	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
303	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
304	C₄×C₇×C₈	C₂³	1	2	yes	—
305	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₇×C₈	C₂³	1	2	yes	—
308	C₄×C₇×C₈	C₂³	1	2	yes	—
309	C₄×C₇×C₈	C₂³	1	2	yes	—
310	C₄×C₇×C₈	C₂³	1	2	yes	—
311	#3482	C₂×C₇	1	1	yes	characteristic
312	#2995	C₂×C₇	1	2	yes	complemented
313	#2994	C₂×C₇	1	1	yes	characteristic, complemented
314	#2993	C₂×C₇	1	1	yes	characteristic, complemented
315	#2992	C₂×C₇	1	2	yes	complemented
316	#2990	C₂×C₇	1	1	yes	characteristic, complemented
317	#2989	C₂×C₇	1	2	yes	complemented
318	#2989	C₂×C₇	1	1	yes	characteristic, complemented
319	#2987	C₂×C₇	1	2	yes	complemented
320	#2985	C₂×C₇	1	1	yes	characteristic, complemented
321	#2984	C₂×C₇	1	1	yes	characteristic, complemented
322	#2983	C₂×C₇	1	1	yes	characteristic, complemented
323	#2970	C₂×C₇	1	2	yes	complemented
324	#2970	C₂×C₇	1	1	yes	characteristic, complemented
325	#2969	C₂×C₇	1	1	yes	characteristic, complemented
326	#2968	C₂×C₇	1	2	yes	complemented
327	#2967	C₂×C₇	1	2	yes	complemented
328	#2966	C₂×C₇	1	1	yes	characteristic, complemented
329	#2965	C₂×C₇	1	1	yes	characteristic, complemented
330	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
331	#2962	C₂×C₇	1	1	yes	characteristic, complemented
332	#2961	C₂×C₇	1	2	yes	complemented
333	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
334	C₇×#41	—	4	2	no	—
335	C₇×#41	—	4	4	no	—
336	C₇×#41	—	4	2	no	—
337	C₂×C₇×Q₈	—	4	2	no	—
338	C₂×C₇×Q₈	—	4	2	no	—
339	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
343	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
344	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
346	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
349	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
352	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
354	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
355	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
356	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
357	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
358	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
360	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
361	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
362	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
363	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
365	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
369	C₇×M₁₆	—	2	2	no	—
370	C₇×M₁₆	—	2	2	no	—
371	C₇×M₁₆	—	4	1	no	—
372	C₇×M₁₆	—	4	2	no	—
373	C₇×M₁₆	—	4	2	no	—
374	C₇×M₁₆	—	4	2	no	—
375	C₇×M₁₆	—	4	1	no	—
376	C₂×C₇×C₈	—	2	2	no	—
377	C₂×C₇×C₈	—	2	4	no	—
378	C₂×C₇×C₈	—	4	2	no	—
379	C₂×C₇×C₈	—	4	2	no	—
380	C₂×C₇×C₈	—	4	2	no	—
381	C₂×C₇×C₈	—	4	1	no	—
382	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₇×C₈	C₂⁴	1	2	yes	—
387	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₇×C₈	C₂⁴	1	2	yes	—
390	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₇×C₈	C₂⁴	1	2	yes	—
392	C₂×C₇×C₈	C₂⁴	1	2	yes	—
393	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
394	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
401	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
402	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
403	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
404	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
405	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
406	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
410	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
411	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
413	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
414	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
418	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
419	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
420	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
421	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
422	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
423	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
424	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
425	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
426	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
427	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
429	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
430	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
431	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
433	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
434	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
436	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
437	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
442	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
443	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
444	C₄²×C₇	C₂²×C₄	1	2	yes	—
445	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
447	C₄²×C₇	C₂²×C₄	1	2	yes	—
448	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₇	C₂²×C₄	1	2	yes	—
450	C₄²×C₇	C₂²×C₄	1	2	yes	—
451	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₇	C₂²×C₄	1	2	yes	—
453	C₄²×C₇	C₂²×C₄	1	2	yes	—
454	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
455	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
456	C₄²×C₇	C₂⁴	1	1	yes	characteristic
457	C₄²×C₇	C₂⁴	1	1	yes	characteristic
458	C₄²×C₇	C₂⁴	1	2	yes	—
459	C₄²×C₇	C₂⁴	1	1	yes	characteristic
460	C₄²×C₇	C₂⁴	1	2	yes	—
461	C₄²×C₇	C₂⁴	1	2	yes	—
462	C₄²×C₇	C₂⁴	1	1	yes	characteristic
463	#557	C₄×C₇	1	1	yes	characteristic
464	#556	C₄×C₇	1	2	yes	—
465	#556	C₄×C₇	1	1	yes	characteristic
466	#552	C₄×C₇	1	1	yes	characteristic
467	#552	C₄×C₇	1	2	yes	—
468	#552	C₄×C₇	1	1	yes	characteristic
469	#552	C₄×C₇	1	2	yes	—
470	D₄×Q₈	C₄×C₇	1	1	yes	characteristic
471	#548	C₄×C₇	1	1	yes	characteristic
472	#548	C₄×C₇	1	1	yes	characteristic
473	#547	C₄×C₇	1	1	yes	characteristic
474	#547	C₄×C₇	1	2	yes	—
475	#533	C₂²×C₇	1	2	yes	—
476	#533	C₂²×C₇	1	1	yes	characteristic
477	#529	C₂²×C₇	1	1	yes	characteristic
478	#529	C₂²×C₇	1	2	yes	—
479	#529	C₂²×C₇	1	2	yes	—
480	#529	C₂²×C₇	1	1	yes	characteristic
481	C₄×#41	C₂²×C₇	1	1	yes	characteristic
482	C₄×#41	C₂²×C₇	1	2	yes	—
483	C₄×#41	C₂²×C₇	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
485	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
486	#446	C₂²×C₇	1	2	yes	—
487	#446	C₂²×C₇	1	1	yes	characteristic
488	#446	C₂²×C₇	1	1	yes	characteristic
489	#446	C₂²×C₇	1	1	yes	characteristic
490	#446	C₂²×C₇	1	1	yes	characteristic
491	#446	C₂²×C₇	1	2	yes	—
492	#446	C₂²×C₇	1	1	yes	characteristic
493	#446	C₂²×C₇	1	2	yes	—
494	#446	C₂²×C₇	1	2	yes	—
495	#446	C₂²×C₇	1	2	yes	—
496	#446	C₂²×C₇	1	2	yes	—
497	#446	C₂²×C₇	1	2	yes	—
498	#446	C₂²×C₇	1	2	yes	—
499	#446	C₂²×C₇	1	1	yes	characteristic
500	#446	C₂²×C₇	1	2	yes	—
501	#446	C₂²×C₇	1	1	yes	characteristic
502	#446	C₂²×C₇	1	2	yes	—
503	#446	C₂²×C₇	1	1	yes	characteristic
504	#446	C₂²×C₇	1	1	yes	characteristic
505	#446	C₂²×C₇	1	2	yes	—
506	#446	C₂²×C₇	1	2	yes	—
507	#446	C₂²×C₇	1	1	yes	characteristic
508	#446	C₂²×C₇	1	2	yes	—
509	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
510	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
511	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
512	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
513	#436	C₂²×C₇	1	1	yes	characteristic
514	#436	C₂²×C₇	1	1	yes	characteristic
515	#436	C₂²×C₇	1	1	yes	characteristic
516	#436	C₂²×C₇	1	2	yes	—
517	#436	C₂²×C₇	1	1	yes	characteristic
518	#436	C₂²×C₇	1	2	yes	—
519	#435	C₂²×C₇	1	1	yes	characteristic
520	#435	C₂²×C₇	1	1	yes	characteristic
521	#435	C₂²×C₇	1	1	yes	characteristic
522	#435	C₂²×C₇	1	1	yes	characteristic
523	#435	C₂²×C₇	1	2	yes	—
524	#435	C₂²×C₇	1	2	yes	—
525	#435	C₂²×C₇	1	2	yes	—
526	#435	C₂²×C₇	1	2	yes	—
527	#435	C₂²×C₇	1	2	yes	—
528	#435	C₂²×C₇	1	2	yes	—
529	#435	C₂²×C₇	1	2	yes	—
530	#435	C₂²×C₇	1	2	yes	—
531	#435	C₂²×C₇	1	2	yes	—
532	#435	C₂²×C₇	1	2	yes	—
533	C₈×D₄	C₂²×C₇	1	2	yes	—
534	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
535	C₈×D₄	C₂²×C₇	1	2	yes	—
536	C₈×D₄	C₂²×C₇	1	2	yes	—
537	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
538	#433	C₂²×C₇	1	2	yes	—
539	#433	C₂²×C₇	1	2	yes	—
540	#433	C₂²×C₇	1	2	yes	—
541	#433	C₂²×C₇	1	2	yes	—
542	#433	C₂²×C₇	1	2	yes	—
543	#433	C₂²×C₇	1	2	yes	—
544	#432	C₂²×C₇	1	1	yes	characteristic
545	#432	C₂²×C₇	1	2	yes	—
546	#432	C₂²×C₇	1	2	yes	—
547	#432	C₂²×C₇	1	2	yes	—
548	#432	C₂²×C₇	1	1	yes	characteristic
549	#432	C₂²×C₇	1	2	yes	—
550	#432	C₂²×C₇	1	2	yes	—
551	#431	C₂²×C₇	1	1	yes	characteristic
552	#431	C₂²×C₇	1	1	yes	characteristic
553	#431	C₂²×C₇	1	1	yes	characteristic
554	#431	C₂²×C₇	1	2	yes	—
555	#431	C₂²×C₇	1	1	yes	characteristic
556	#424	C₂²×C₇	1	2	yes	—
557	#424	C₂²×C₇	1	2	yes	—
558	#424	C₂²×C₇	1	2	yes	—
559	#423	C₂²×C₇	1	2	yes	—
560	#423	C₂²×C₇	1	2	yes	—
561	#423	C₂²×C₇	1	1	yes	characteristic
562	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
563	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
564	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
565	#405	C₂²×C₇	1	2	yes	—
566	#405	C₂²×C₇	1	2	yes	—
567	#405	C₂²×C₇	1	2	yes	—
568	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
569	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
570	C₄×M₁₆	C₂²×C₇	1	2	yes	—
571	C₂×#97	C₂²×C₇	1	2	yes	—
572	C₂×#97	C₂²×C₇	1	2	yes	—
573	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
574	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
575	C₂³×C₇	C₂³×C₄	1	2	yes	—
576	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
577	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
578	C₇×Q₈	—	2	2	no	—
579	C₇×Q₈	—	2	2	no	—
580	C₇×Q₈	—	2	2	no	—
581	C₇×Q₈	—	4	2	no	—
582	C₇×Q₈	—	4	2	no	—
583	C₇×Q₈	—	4	1	no	—
584	C₇×Q₈	—	4	2	no	—
585	C₇×D₄	—	2	2	no	—
586	C₇×D₄	—	2	4	no	—
587	C₇×D₄	—	2	2	no	—
588	C₇×D₄	—	2	2	no	—
589	C₇×D₄	—	4	1	no	—
590	C₇×D₄	—	4	2	no	—
591	C₇×D₄	—	4	2	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	2	4	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	2	no	—
596	C₂×C₄×C₇	—	2	2	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	2	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	1	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	4	2	no	—
606	C₂×C₄×C₇	—	4	2	no	—
607	C₂×C₄×C₇	—	4	2	no	—
608	C₂×C₄×C₇	—	4	1	no	—
609	C₂×C₄×C₇	—	4	2	no	—
610	C₂×C₄×C₇	—	4	1	no	—
611	C₂×C₄×C₇	—	4	2	no	—
612	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
613	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
614	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
615	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
616	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
618	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
619	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
623	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
626	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
627	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
628	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
629	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
630	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
631	C₇×C₈	—	2	1	no	—
632	C₇×C₈	—	2	2	no	—
633	C₇×C₈	—	2	1	no	—
634	C₇×C₈	—	2	1	no	—
635	C₇×C₈	—	2	2	no	—
636	C₇×C₈	—	2	2	no	—
637	C₇×C₈	—	2	1	no	—
638	C₇×C₈	—	2	2	no	—
639	C₇×C₈	—	2	1	no	—
640	C₇×C₈	—	2	1	no	—
641	C₇×C₈	—	2	1	no	—
642	C₇×C₈	2₋¹⁺⁴	1	2	yes	—
643	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
644	C₂×#41	C₂×C₄×C₇	1	2	yes	—
645	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
646	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
647	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
648	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
649	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
650	C₂×M₁₆	C₂³×C₇	1	2	yes	—
651	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
652	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
653	C₂×M₁₆	C₂³×C₇	1	2	yes	—
654	C₂×M₁₆	C₂³×C₇	1	2	yes	—
655	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
656	C₂²×C₈	C₂³×C₇	1	2	yes	—
657	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
658	C₂²×C₈	C₂³×C₇	1	2	yes	—
659	C₂²×C₈	C₂³×C₇	1	2	yes	—
660	C₂²×C₈	C₂³×C₇	1	2	yes	—
661	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
662	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
663	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
664	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
665	#126	C₂×C₄×C₇	1	2	yes	—
666	#126	C₂×C₄×C₇	1	2	yes	—
667	#126	C₂×C₄×C₇	1	2	yes	—
668	#126	C₂×C₄×C₇	1	2	yes	—
669	#126	C₂×C₄×C₇	1	2	yes	—
670	#126	C₂×C₄×C₇	1	2	yes	—
671	#125	C₂×C₄×C₇	1	1	yes	characteristic
672	#125	C₂×C₄×C₇	1	2	yes	—
673	#125	C₂×C₄×C₇	1	2	yes	—
674	#125	C₂×C₄×C₇	1	1	yes	characteristic
675	#125	C₂×C₄×C₇	1	2	yes	—
676	#125	C₂×C₄×C₇	1	2	yes	—
677	#125	C₂×C₄×C₇	1	2	yes	—
678	#124	C₂×C₄×C₇	1	1	yes	characteristic
679	#124	C₂×C₄×C₇	1	1	yes	characteristic
680	#124	C₂×C₄×C₇	1	2	yes	—
681	#124	C₂×C₄×C₇	1	2	yes	—
682	#123	C₂×C₄×C₇	1	2	yes	—
683	#123	C₂×C₄×C₇	1	2	yes	—
684	#123	C₂×C₄×C₇	1	2	yes	—
685	#123	C₂×C₄×C₇	1	2	yes	—
686	#123	C₂×C₄×C₇	1	2	yes	—
687	#123	C₂×C₄×C₇	1	2	yes	—
688	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
689	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
691	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
692	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
693	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
698	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
699	#121	C₂×C₄×C₇	1	1	yes	characteristic
700	#121	C₂×C₄×C₇	1	1	yes	characteristic
701	#121	C₂×C₄×C₇	1	2	yes	—
702	#121	C₂×C₄×C₇	1	2	yes	—
703	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
704	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
705	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
706	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
707	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
708	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
709	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
710	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
711	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
712	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₇	1	2	yes	—
716	C₄×Q₈	C₂³×C₇	1	2	yes	—
717	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₇	1	2	yes	—
719	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
720	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
721	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
722	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
723	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
724	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
725	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
726	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
727	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
728	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₇	1	2	yes	—
730	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₇	1	2	yes	—
732	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₇	1	2	yes	—
734	#117	C₂×C₄×C₇	1	1	yes	characteristic
735	#117	C₂×C₄×C₇	1	2	yes	—
736	#117	C₂×C₄×C₇	1	1	yes	characteristic
737	#117	C₂×C₄×C₇	1	2	yes	—
738	#117	C₂×C₄×C₇	1	1	yes	characteristic
739	#117	C₂×C₄×C₇	1	2	yes	—
740	#117	C₂×C₄×C₇	1	1	yes	characteristic
741	#117	C₂×C₄×C₇	1	2	yes	—
742	#117	C₂³×C₇	1	2	yes	—
743	#117	C₂³×C₇	1	2	yes	—
744	#117	C₂³×C₇	1	2	yes	—
745	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
747	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
749	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₇	1	2	yes	—
751	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₇	1	2	yes	—
753	C₂×C₄²	C₂³×C₇	1	2	yes	—
754	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
755	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
756	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
757	C₄⋊C₈	C₂³×C₇	1	2	yes	—
758	C₄⋊C₈	C₂³×C₇	1	2	yes	—
759	C₄⋊C₈	C₂³×C₇	1	2	yes	—
760	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
761	C₄⋊C₈	C₂³×C₇	1	2	yes	—
762	C₄⋊C₈	C₂³×C₇	1	2	yes	—
763	C₄⋊C₈	C₂³×C₇	1	2	yes	—
764	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
765	C₄⋊C₈	C₂³×C₇	1	2	yes	—
766	C₄⋊C₈	C₂³×C₇	1	2	yes	—
767	C₄⋊C₈	C₂³×C₇	1	2	yes	—
768	C₄⋊C₈	C₂³×C₇	1	2	yes	—
769	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
770	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₇	1	2	yes	—
772	C₄⋊C₈	C₂³×C₇	1	2	yes	—
773	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
774	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
775	C₄⋊C₈	C₂³×C₇	1	2	yes	—
776	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
777	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
778	C₄⋊C₈	C₂³×C₇	1	2	yes	—
779	C₄⋊C₈	C₂³×C₇	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
781	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
782	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
784	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
786	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
787	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
788	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
793	#97	C₂³×C₇	1	2	yes	—
794	#97	C₂³×C₇	1	1	yes	characteristic
795	#97	C₂³×C₇	1	2	yes	—
796	#97	C₂³×C₇	1	2	yes	—
797	#97	C₂³×C₇	1	2	yes	—
798	#97	C₂³×C₇	1	2	yes	—
799	#97	C₂³×C₇	1	2	yes	—
800	#97	C₂³×C₇	1	1	yes	characteristic
801	#97	C₂³×C₇	1	1	yes	characteristic
802	#97	C₂³×C₇	1	2	yes	—
803	#97	C₂³×C₇	1	1	yes	characteristic
804	#97	C₂³×C₇	1	2	yes	—
805	#97	C₂³×C₇	1	2	yes	—
806	#97	C₂³×C₇	1	2	yes	—
807	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
808	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
809	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
810	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
811	C₄×C₈	C₂³×C₇	1	2	yes	—
812	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
813	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
814	C₄×C₈	C₂³×C₇	1	2	yes	—
815	C₄×C₈	C₂³×C₇	1	2	yes	—
816	C₄×C₈	C₂³×C₇	1	2	yes	—
817	C₄×C₈	C₂³×C₇	1	2	yes	—
818	C₂²×C₇	—	2	1	no	—
819	C₂²×C₇	—	2	1	no	—
820	C₂²×C₇	—	2	2	no	—
821	C₂²×C₇	—	2	1	no	—
822	C₂²×C₇	—	2	1	no	—
823	C₂²×C₇	—	2	1	no	—
824	C₂²×C₇	—	2	1	no	—
825	C₂²×C₇	—	2	1	no	—
826	C₂²×C₇	—	2	1	no	—
827	C₂²×C₇	—	2	2	no	—
828	C₂²×C₇	—	2	2	no	—
829	C₂²×C₇	#568	1	2	yes	—
830	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
831	C₄×C₇	—	2	1	no	—
832	C₄×C₇	—	2	2	no	—
833	C₄×C₇	—	2	1	no	—
834	C₄×C₇	—	2	1	no	—
835	C₄×C₇	—	2	1	no	—
836	C₄×C₇	—	2	2	no	—
837	C₄×C₇	—	2	1	no	—
838	C₄×C₇	—	2	1	no	—
839	C₄×C₇	—	2	2	no	—
840	C₄×C₇	—	2	1	no	—
841	C₄×C₇	—	2	1	no	—
842	C₄×C₇	—	2	1	no	—
843	C₄×C₇	—	2	2	no	—
844	C₄×C₇	—	2	1	no	—
845	C₄×C₇	—	2	2	no	—
846	C₄×C₇	—	2	2	no	—
847	C₄×C₇	—	2	2	no	—
848	C₄×C₇	#568	1	2	yes	—
849	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
850	C₄×C₇	#585	1	1	yes	characteristic
851	#41	—	4	2	no	—
852	#41	—	4	4	no	—
853	#41	—	4	2	no	—
854	C₂×Q₈	—	4	2	no	—
855	C₂×Q₈	—	4	2	no	—
856	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
857	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
858	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
859	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
860	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
861	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
862	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
863	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
864	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
865	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
866	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
867	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
868	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
869	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
870	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
871	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
872	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
873	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
874	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
875	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
876	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
877	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
878	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
879	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
880	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
881	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
886	M₁₆	—	2	2	no	—
887	M₁₆	—	2	2	no	—
888	M₁₆	—	4	1	no	—
889	M₁₆	—	4	2	no	—
890	M₁₆	—	4	2	no	—
891	M₁₆	—	4	2	no	—
892	M₁₆	—	4	1	no	—
893	C₂×C₈	—	2	2	no	—
894	C₂×C₈	—	2	4	no	—
895	C₂×C₈	—	4	2	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	—	4	2	no	—
898	C₂×C₈	—	4	1	no	—
899	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₇	1	2	yes	—
904	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₇	1	2	yes	—
907	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₇	1	2	yes	—
909	C₂×C₈	C₂⁴×C₇	1	2	yes	—
910	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
911	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
912	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
914	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
915	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
916	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
917	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
918	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
919	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
920	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
921	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
922	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
923	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
927	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
928	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
929	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
932	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
933	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
934	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
935	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
936	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
937	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
940	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
941	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
942	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
943	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
944	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
945	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
946	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
947	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
948	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
949	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
950	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
952	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
954	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
957	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
958	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
959	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
960	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
961	C₄²	C₂²×C₄×C₇	1	2	yes	—
962	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
963	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
964	C₄²	C₂²×C₄×C₇	1	2	yes	—
965	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
966	C₄²	C₂²×C₄×C₇	1	2	yes	—
967	C₄²	C₂²×C₄×C₇	1	2	yes	—
968	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
969	C₄²	C₂²×C₄×C₇	1	2	yes	—
970	C₄²	C₂²×C₄×C₇	1	2	yes	—
971	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
972	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
973	C₄²	C₂⁴×C₇	1	1	yes	characteristic
974	C₄²	C₂⁴×C₇	1	1	yes	characteristic
975	C₄²	C₂⁴×C₇	1	2	yes	—
976	C₄²	C₂⁴×C₇	1	1	yes	characteristic
977	C₄²	C₂⁴×C₇	1	2	yes	—
978	C₄²	C₂⁴×C₇	1	2	yes	—
979	C₄²	C₂⁴×C₇	1	1	yes	characteristic
980	C₂×C₇	—	2	2	no	—
981	C₂×C₇	—	4	1	no	—
982	C₂×C₇	—	4	1	no	—
983	C₂×C₇	—	4	2	no	—
984	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
985	C₂×C₇	C₂×#568	1	1	yes	characteristic
986	C₂×C₇	C₂×#568	1	1	yes	characteristic
987	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
988	C₂³	C₂³×C₄×C₇	1	2	yes	—
989	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
990	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	4	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	1	no	—
997	Q₈	—	4	2	no	—
998	D₄	—	2	2	no	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	4	1	no	—
1003	D₄	—	4	2	no	—
1004	D₄	—	4	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	1	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1026	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1027	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1028	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1029	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1030	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1031	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1032	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1034	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1035	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1036	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1037	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1038	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1039	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1040	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1041	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1042	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	2	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	2	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	C₇×2₋¹⁺⁴	1	2	yes	—
1056	C₇	#60342	1	1	yes	characteristic, direct product factor, Sylow
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	C₇×#568	1	2	yes	—
1069	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	C₇×#568	1	2	yes	—
1088	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1089	C₄	C₇×#585	1	1	yes	characteristic
1090	C₂	—	2	2	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₂	C₂×C₇×#568	1	1	yes	characteristic
1096	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×#3482	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2995	C₂	semidirect
3. C₇×#2994	C₂	semidirect
4. C₇×#2993	C₂	semidirect
5. C₇×#2992	C₂	semidirect
6. C₇×#2990	C₂	semidirect
7. C₇×#2989	C₂	semidirect
8. C₇×#2989	C₂	semidirect
9. C₇×#2987	C₂	semidirect
10. C₇×#2985	C₂	semidirect
11. C₇×#2984	C₂	semidirect
12. C₇×#2983	C₂	semidirect
13. C₇×#2970	C₂	semidirect
14. C₇×#2970	C₂	semidirect
15. C₇×#2969	C₂	semidirect
16. C₇×#2968	C₂	semidirect
17. C₇×#2967	C₂	semidirect
18. C₇×#2966	C₂	semidirect
19. C₇×#2965	C₂	semidirect
20. C₇×Q₈×M₁₆	C₂	semidirect
21. C₇×#2962	C₂	semidirect
22. C₇×#2961	C₂	semidirect
23. C₂×C₇×#446	C₂	semidirect
135. #60342	C₇	direct (N × H)
312. #2995	C₂×C₇	semidirect
313. #2994	C₂×C₇	semidirect
314. #2993	C₂×C₇	semidirect
315. #2992	C₂×C₇	semidirect
316. #2990	C₂×C₇	semidirect
317. #2989	C₂×C₇	semidirect
318. #2989	C₂×C₇	semidirect
319. #2987	C₂×C₇	semidirect
320. #2985	C₂×C₇	semidirect
321. #2984	C₂×C₇	semidirect
322. #2983	C₂×C₇	semidirect
323. #2970	C₂×C₇	semidirect
324. #2970	C₂×C₇	semidirect
325. #2969	C₂×C₇	semidirect
326. #2968	C₂×C₇	semidirect
327. #2967	C₂×C₇	semidirect
328. #2966	C₂×C₇	semidirect
329. #2965	C₂×C₇	semidirect
330. Q₈×M₁₆	C₂×C₇	semidirect
331. #2962	C₂×C₇	semidirect
332. #2961	C₂×C₇	semidirect
333. C₂×#446	C₂×C₇	semidirect
1056. C₇	#60342	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×#3482	2
C₇×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2992	2
C₇×#2990	2
C₇×#2989	2
C₇×#2987	2
C₇×#2985	2
C₇×#2984	2
C₇×#2983	2
C₇×#2970	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×#2965	2
C₇×Q₈×M₁₆	2
C₇×#2962	2
C₇×#2961	2
C₂×C₇×#446	2
#60342	7

Subgroups — C7×#60342 #13237558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60342 #13237558