Subgroups — C₇×#60340 #13237556

Order 1792.

1666 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3461	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₇×#2994	C₂	1	2	yes	maximal, complemented
4	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2992	C₂	1	2	yes	maximal, complemented
7	C₇×#2990	C₂	1	2	yes	maximal, complemented
8	C₇×#2987	C₂	1	2	yes	maximal, complemented
9	C₇×#2985	C₂	1	2	yes	maximal, complemented
10	C₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2970	C₂	1	2	yes	maximal, complemented
12	C₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₇×#2968	C₂	1	2	yes	maximal, complemented
14	C₇×#2967	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2962	C₂	1	2	yes	maximal, complemented
18	C₇×#2961	C₂	1	2	yes	maximal, complemented
19	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#544	C₄	1	1	yes	characteristic
21	C₇×#542	C₄	1	2	yes	—
22	C₇×#542	C₄	1	2	yes	—
23	C₇×#541	C₄	1	2	yes	—
24	C₇×#541	C₄	1	2	yes	—
25	C₇×#539	C₄	1	1	yes	characteristic
26	C₇×#539	C₄	1	1	yes	characteristic
27	C₇×#539	C₄	1	2	yes	—
28	C₇×#537	C₄	1	1	yes	characteristic
29	C₇×#536	C₄	1	2	yes	—
30	C₇×#533	C₂²	1	2	yes	—
31	C₇×#533	C₂²	1	2	yes	—
32	C₇×#529	C₂²	1	1	yes	characteristic
33	C₇×#529	C₂²	1	1	yes	characteristic
34	C₇×#529	C₂²	1	2	yes	—
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₄×C₇×#41	C₂²	1	2	yes	—
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₇×#446	C₂²	1	2	yes	—
40	C₇×#446	C₂²	1	2	yes	—
41	C₇×#446	C₂²	1	2	yes	—
42	C₇×#446	C₂²	1	2	yes	—
43	C₇×#446	C₂²	1	1	yes	characteristic
44	C₇×#446	C₂²	1	2	yes	—
45	C₇×#446	C₂²	1	2	yes	—
46	C₇×#446	C₂²	1	2	yes	—
47	C₇×#446	C₂²	1	2	yes	—
48	C₇×#446	C₂²	1	2	yes	—
49	C₇×#446	C₂²	1	2	yes	—
50	C₇×#446	C₂²	1	2	yes	—
51	C₇×#446	C₂²	1	2	yes	—
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×C₈×Q₈	C₂²	1	1	yes	characteristic
59	C₇×C₈×Q₈	C₂²	1	2	yes	—
60	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
61	C₇×#436	C₂²	1	1	yes	characteristic
62	C₇×#436	C₂²	1	1	yes	characteristic
63	C₇×#436	C₂²	1	2	yes	—
64	C₇×#435	C₂²	1	2	yes	—
65	C₇×#435	C₂²	1	2	yes	—
66	C₇×#435	C₂²	1	2	yes	—
67	C₇×#435	C₂²	1	2	yes	—
68	C₇×#435	C₂²	1	2	yes	—
69	C₇×#435	C₂²	1	2	yes	—
70	C₇×#435	C₂²	1	2	yes	—
71	C₇×#435	C₂²	1	2	yes	—
72	C₇×#435	C₂²	1	2	yes	—
73	C₇×#435	C₂²	1	2	yes	—
74	C₇×#435	C₂²	1	2	yes	—
75	C₇×#435	C₂²	1	2	yes	—
76	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
77	C₇×C₈×D₄	C₂²	1	2	yes	—
78	C₇×C₈×D₄	C₂²	1	2	yes	—
79	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
80	C₇×C₈×D₄	C₂²	1	2	yes	—
81	C₇×C₈×D₄	C₂²	1	2	yes	—
82	C₇×C₈×D₄	C₂²	1	2	yes	—
83	C₇×#433	C₂²	1	2	yes	—
84	C₇×#433	C₂²	1	2	yes	—
85	C₇×#433	C₂²	1	2	yes	—
86	C₇×#433	C₂²	1	2	yes	—
87	C₇×#433	C₂²	1	2	yes	—
88	C₇×#433	C₂²	1	2	yes	—
89	C₇×#433	C₂²	1	2	yes	—
90	C₇×#433	C₂²	1	2	yes	—
91	C₇×#432	C₂²	1	1	yes	characteristic
92	C₇×#432	C₂²	1	1	yes	characteristic
93	C₇×#432	C₂²	1	2	yes	—
94	C₇×#432	C₂²	1	2	yes	—
95	C₇×#432	C₂²	1	2	yes	—
96	C₇×#432	C₂²	1	2	yes	—
97	C₇×#431	C₂²	1	2	yes	—
98	C₇×#431	C₂²	1	2	yes	—
99	C₇×#424	C₂²	1	2	yes	—
100	C₇×#424	C₂²	1	2	yes	—
101	C₇×#424	C₂²	1	2	yes	—
102	C₇×#424	C₂²	1	2	yes	—
103	C₇×#423	C₂²	1	2	yes	—
104	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
108	C₇×#405	C₂²	1	2	yes	—
109	C₇×#405	C₂²	1	2	yes	—
110	C₇×#405	C₂²	1	2	yes	—
111	C₇×#405	C₂²	1	2	yes	—
112	C₄×C₇×M₁₆	C₂²	1	2	yes	—
113	C₂×C₇×#97	C₂²	1	1	yes	characteristic
114	C₂×C₇×#97	C₂²	1	1	yes	characteristic
115	C₂×C₇×#97	C₂²	1	2	yes	—
116	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
117	#60340	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂×C₇×#41	C₂×C₄	1	2	yes	—
119	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
120	C₂×C₇×M₁₆	C₂³	1	2	yes	—
121	C₂×C₇×M₁₆	C₂³	1	2	yes	—
122	C₂×C₇×M₁₆	C₂³	1	2	yes	—
123	C₂×C₇×M₁₆	C₂³	1	2	yes	—
124	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×C₈	C₂³	1	2	yes	—
126	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
129	C₂²×C₇×C₈	C₂³	1	2	yes	—
130	C₂²×C₇×C₈	C₂³	1	2	yes	—
131	C₂²×C₇×C₈	C₂³	1	2	yes	—
132	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
134	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
135	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
136	C₇×#126	C₂×C₄	1	2	yes	—
137	C₇×#126	C₂×C₄	1	2	yes	—
138	C₇×#126	C₂×C₄	1	2	yes	—
139	C₇×#126	C₂×C₄	1	2	yes	—
140	C₇×#126	C₂×C₄	1	2	yes	—
141	C₇×#126	C₂×C₄	1	2	yes	—
142	C₇×#126	C₂×C₄	1	2	yes	—
143	C₇×#126	C₂×C₄	1	2	yes	—
144	C₇×#125	C₂×C₄	1	1	yes	characteristic
145	C₇×#125	C₂×C₄	1	1	yes	characteristic
146	C₇×#125	C₂×C₄	1	2	yes	—
147	C₇×#125	C₂×C₄	1	2	yes	—
148	C₇×#125	C₂×C₄	1	2	yes	—
149	C₇×#125	C₂×C₄	1	2	yes	—
150	C₇×#125	C₂×C₄	1	2	yes	—
151	C₇×#125	C₂×C₄	1	2	yes	—
152	C₇×#125	C₂×C₄	1	2	yes	—
153	C₇×#124	C₂×C₄	1	2	yes	—
154	C₇×#124	C₂×C₄	1	2	yes	—
155	C₇×#124	C₂×C₄	1	1	yes	characteristic
156	C₇×#124	C₂×C₄	1	1	yes	characteristic
157	C₇×#124	C₂×C₄	1	2	yes	—
158	C₇×#123	C₂×C₄	1	2	yes	—
159	C₇×#123	C₂×C₄	1	2	yes	—
160	C₇×#123	C₂×C₄	1	2	yes	—
161	C₇×#123	C₂×C₄	1	2	yes	—
162	C₇×#123	C₂×C₄	1	2	yes	—
163	C₇×#123	C₂×C₄	1	2	yes	—
164	C₇×#123	C₂×C₄	1	2	yes	—
165	C₇×#123	C₂×C₄	1	2	yes	—
166	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
167	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
169	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
170	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
173	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
174	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
175	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
176	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₇×#121	C₂×C₄	1	1	yes	characteristic
180	C₇×#121	C₂×C₄	1	1	yes	characteristic
181	C₇×#121	C₂×C₄	1	2	yes	—
182	C₇×#121	C₂×C₄	1	2	yes	—
183	C₇×#121	C₂×C₄	1	2	yes	—
184	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
185	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
186	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
187	C₄×C₇×Q₈	C₂³	1	2	yes	—
188	C₄×C₇×Q₈	C₂³	1	2	yes	—
189	C₄×C₇×Q₈	C₂³	1	2	yes	—
190	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
192	C₄×C₇×Q₈	C₂³	1	2	yes	—
193	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
194	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
195	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
196	C₄×C₇×D₄	C₂³	1	2	yes	—
197	C₄×C₇×D₄	C₂³	1	2	yes	—
198	C₄×C₇×D₄	C₂³	1	2	yes	—
199	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
200	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₇×#117	C₂×C₄	1	2	yes	—
203	C₇×#117	C₂×C₄	1	2	yes	—
204	C₇×#117	C₂×C₄	1	2	yes	—
205	C₇×#117	C₂³	1	2	yes	—
206	C₇×#117	C₂³	1	2	yes	—
207	C₇×#117	C₂³	1	2	yes	—
208	C₇×#117	C₂³	1	2	yes	—
209	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
210	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
211	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×C₄⋊C₈	C₂³	1	2	yes	—
220	C₇×C₄⋊C₈	C₂³	1	2	yes	—
221	C₇×C₄⋊C₈	C₂³	1	2	yes	—
222	C₇×C₄⋊C₈	C₂³	1	2	yes	—
223	C₇×C₄⋊C₈	C₂³	1	2	yes	—
224	C₇×C₄⋊C₈	C₂³	1	2	yes	—
225	C₇×C₄⋊C₈	C₂³	1	2	yes	—
226	C₇×C₄⋊C₈	C₂³	1	2	yes	—
227	C₇×C₄⋊C₈	C₂³	1	2	yes	—
228	C₇×C₄⋊C₈	C₂³	1	2	yes	—
229	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
230	C₇×C₄⋊C₈	C₂³	1	2	yes	—
231	C₇×C₄⋊C₈	C₂³	1	2	yes	—
232	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₈	C₂³	1	2	yes	—
234	C₇×C₄⋊C₈	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₇×#97	C₂³	1	2	yes	—
250	C₇×#97	C₂³	1	2	yes	—
251	C₇×#97	C₂³	1	2	yes	—
252	C₇×#97	C₂³	1	2	yes	—
253	C₇×#97	C₂³	1	2	yes	—
254	C₇×#97	C₂³	1	2	yes	—
255	C₇×#97	C₂³	1	2	yes	—
256	C₇×#97	C₂³	1	2	yes	—
257	C₇×#97	C₂³	1	2	yes	—
258	C₇×#97	C₂³	1	2	yes	—
259	C₇×#97	C₂³	1	2	yes	—
260	C₇×#97	C₂³	1	2	yes	—
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
264	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
265	C₄×C₇×C₈	C₂³	1	2	yes	—
266	C₄×C₇×C₈	C₂³	1	2	yes	—
267	C₄×C₇×C₈	C₂³	1	2	yes	—
268	C₄×C₇×C₈	C₂³	1	2	yes	—
269	C₄×C₇×C₈	C₂³	1	2	yes	—
270	C₄×C₇×C₈	C₂³	1	2	yes	—
271	#3461	C₂×C₇	1	1	yes	characteristic
272	#2995	C₂×C₇	1	2	yes	complemented
273	#2994	C₂×C₇	1	2	yes	complemented
274	#2992	C₂×C₇	1	1	yes	characteristic, complemented
275	#2992	C₂×C₇	1	1	yes	characteristic, complemented
276	#2992	C₂×C₇	1	2	yes	complemented
277	#2990	C₂×C₇	1	2	yes	complemented
278	#2987	C₂×C₇	1	2	yes	complemented
279	#2985	C₂×C₇	1	2	yes	complemented
280	#2983	C₂×C₇	1	1	yes	characteristic, complemented
281	#2970	C₂×C₇	1	2	yes	complemented
282	#2968	C₂×C₇	1	2	yes	complemented
283	#2968	C₂×C₇	1	2	yes	complemented
284	#2967	C₂×C₇	1	2	yes	complemented
285	#2966	C₂×C₇	1	1	yes	characteristic, complemented
286	#2966	C₂×C₇	1	1	yes	characteristic, complemented
287	#2962	C₂×C₇	1	2	yes	complemented
288	#2961	C₂×C₇	1	2	yes	complemented
289	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
290	C₇×#41	—	4	4	no	—
291	C₂×C₇×Q₈	—	4	2	no	—
292	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
293	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
294	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
295	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
296	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
298	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
299	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
300	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
301	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
302	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
303	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
304	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₇×M₁₆	—	2	4	no	—
318	C₇×M₁₆	—	4	2	no	—
319	C₇×M₁₆	—	4	2	no	—
320	C₇×M₁₆	—	4	2	no	—
321	C₂×C₇×C₈	—	2	2	no	—
322	C₂×C₇×C₈	—	2	4	no	—
323	C₂×C₇×C₈	—	4	2	no	—
324	C₂×C₇×C₈	—	4	1	no	—
325	C₂×C₇×C₈	—	4	1	no	—
326	C₂×C₇×C₈	—	4	1	no	—
327	C₂×C₇×C₈	—	4	2	no	—
328	C₂×C₇×C₈	—	4	2	no	—
329	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₇×C₈	C₂⁴	1	2	yes	—
331	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
334	C₂×C₇×C₈	C₂⁴	1	2	yes	—
335	C₂×C₇×C₈	C₂⁴	1	2	yes	—
336	C₂×C₇×C₈	C₂⁴	1	2	yes	—
337	C₂×C₇×C₈	C₂⁴	1	2	yes	—
338	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
339	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
340	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
341	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
342	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
343	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
344	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
345	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
346	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
347	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
348	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
349	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
350	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
351	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
352	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
353	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
354	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
355	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
356	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
357	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
358	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
359	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
360	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
361	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
362	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
363	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
364	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
365	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
366	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
367	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
368	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
369	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
370	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
371	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
372	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
373	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
374	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
375	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
376	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
377	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
378	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
379	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
380	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
382	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
385	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
386	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
387	C₄²×C₇	C₂²×C₄	1	2	yes	—
388	C₄²×C₇	C₂²×C₄	1	2	yes	—
389	C₄²×C₇	C₂²×C₄	1	2	yes	—
390	C₄²×C₇	C₂²×C₄	1	2	yes	—
391	C₄²×C₇	C₂²×C₄	1	2	yes	—
392	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
393	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
394	C₄²×C₇	C₂²×C₄	1	2	yes	—
395	C₄²×C₇	C₂⁴	1	1	yes	characteristic
396	C₄²×C₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₇	C₂⁴	1	2	yes	—
398	C₄²×C₇	C₂⁴	1	2	yes	—
399	C₄²×C₇	C₂⁴	1	2	yes	—
400	C₄²×C₇	C₂⁴	1	2	yes	—
401	#544	C₄×C₇	1	1	yes	characteristic
402	#542	C₄×C₇	1	2	yes	—
403	#542	C₄×C₇	1	2	yes	—
404	#541	C₄×C₇	1	2	yes	—
405	#541	C₄×C₇	1	2	yes	—
406	#539	C₄×C₇	1	1	yes	characteristic
407	#539	C₄×C₇	1	1	yes	characteristic
408	#539	C₄×C₇	1	2	yes	—
409	#537	C₄×C₇	1	1	yes	characteristic
410	#536	C₄×C₇	1	2	yes	—
411	#533	C₂²×C₇	1	2	yes	—
412	#533	C₂²×C₇	1	2	yes	—
413	#529	C₂²×C₇	1	1	yes	characteristic
414	#529	C₂²×C₇	1	1	yes	characteristic
415	#529	C₂²×C₇	1	2	yes	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	—
418	C₄×#41	C₂²×C₇	1	2	yes	—
419	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
420	#446	C₂²×C₇	1	2	yes	—
421	#446	C₂²×C₇	1	2	yes	—
422	#446	C₂²×C₇	1	2	yes	—
423	#446	C₂²×C₇	1	2	yes	—
424	#446	C₂²×C₇	1	1	yes	characteristic
425	#446	C₂²×C₇	1	2	yes	—
426	#446	C₂²×C₇	1	2	yes	—
427	#446	C₂²×C₇	1	2	yes	—
428	#446	C₂²×C₇	1	2	yes	—
429	#446	C₂²×C₇	1	2	yes	—
430	#446	C₂²×C₇	1	2	yes	—
431	#446	C₂²×C₇	1	2	yes	—
432	#446	C₂²×C₇	1	2	yes	—
433	#446	C₂²×C₇	1	2	yes	—
434	#446	C₂²×C₇	1	1	yes	characteristic
435	#446	C₂²×C₇	1	2	yes	—
436	#446	C₂²×C₇	1	2	yes	—
437	#446	C₂²×C₇	1	2	yes	—
438	#446	C₂²×C₇	1	2	yes	—
439	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
440	C₈×Q₈	C₂²×C₇	1	2	yes	—
441	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
442	#436	C₂²×C₇	1	1	yes	characteristic
443	#436	C₂²×C₇	1	1	yes	characteristic
444	#436	C₂²×C₇	1	2	yes	—
445	#435	C₂²×C₇	1	2	yes	—
446	#435	C₂²×C₇	1	2	yes	—
447	#435	C₂²×C₇	1	2	yes	—
448	#435	C₂²×C₇	1	2	yes	—
449	#435	C₂²×C₇	1	2	yes	—
450	#435	C₂²×C₇	1	2	yes	—
451	#435	C₂²×C₇	1	2	yes	—
452	#435	C₂²×C₇	1	2	yes	—
453	#435	C₂²×C₇	1	2	yes	—
454	#435	C₂²×C₇	1	2	yes	—
455	#435	C₂²×C₇	1	2	yes	—
456	#435	C₂²×C₇	1	2	yes	—
457	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
458	C₈×D₄	C₂²×C₇	1	2	yes	—
459	C₈×D₄	C₂²×C₇	1	2	yes	—
460	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
461	C₈×D₄	C₂²×C₇	1	2	yes	—
462	C₈×D₄	C₂²×C₇	1	2	yes	—
463	C₈×D₄	C₂²×C₇	1	2	yes	—
464	#433	C₂²×C₇	1	2	yes	—
465	#433	C₂²×C₇	1	2	yes	—
466	#433	C₂²×C₇	1	2	yes	—
467	#433	C₂²×C₇	1	2	yes	—
468	#433	C₂²×C₇	1	2	yes	—
469	#433	C₂²×C₇	1	2	yes	—
470	#433	C₂²×C₇	1	2	yes	—
471	#433	C₂²×C₇	1	2	yes	—
472	#432	C₂²×C₇	1	1	yes	characteristic
473	#432	C₂²×C₇	1	1	yes	characteristic
474	#432	C₂²×C₇	1	2	yes	—
475	#432	C₂²×C₇	1	2	yes	—
476	#432	C₂²×C₇	1	2	yes	—
477	#432	C₂²×C₇	1	2	yes	—
478	#431	C₂²×C₇	1	2	yes	—
479	#431	C₂²×C₇	1	2	yes	—
480	#424	C₂²×C₇	1	2	yes	—
481	#424	C₂²×C₇	1	2	yes	—
482	#424	C₂²×C₇	1	2	yes	—
483	#424	C₂²×C₇	1	2	yes	—
484	#423	C₂²×C₇	1	2	yes	—
485	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
486	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
487	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
488	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
489	#405	C₂²×C₇	1	2	yes	—
490	#405	C₂²×C₇	1	2	yes	—
491	#405	C₂²×C₇	1	2	yes	—
492	#405	C₂²×C₇	1	2	yes	—
493	C₄×M₁₆	C₂²×C₇	1	2	yes	—
494	C₂×#97	C₂²×C₇	1	1	yes	characteristic
495	C₂×#97	C₂²×C₇	1	1	yes	characteristic
496	C₂×#97	C₂²×C₇	1	2	yes	—
497	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
498	C₂³×C₇	C₂³×C₄	1	2	yes	—
499	C₂³×C₇	C₂³×C₄	1	2	yes	—
500	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
501	C₇×Q₈	—	4	2	no	—
502	C₇×Q₈	—	4	2	no	—
503	C₇×Q₈	—	4	1	no	—
504	C₇×Q₈	—	4	1	no	—
505	C₇×Q₈	—	4	2	no	—
506	C₇×Q₈	—	4	2	no	—
507	C₇×D₄	—	2	4	no	—
508	C₇×D₄	—	2	4	no	—
509	C₇×D₄	—	4	1	no	—
510	C₇×D₄	—	4	1	no	—
511	C₇×D₄	—	4	2	no	—
512	C₇×D₄	—	4	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	4	1	no	—
523	C₂×C₄×C₇	—	4	2	no	—
524	C₂×C₄×C₇	—	4	2	no	—
525	C₂×C₄×C₇	—	4	1	no	—
526	C₂×C₄×C₇	—	4	1	no	—
527	C₂×C₄×C₇	—	4	2	no	—
528	C₂×C₄×C₇	—	4	2	no	—
529	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
530	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
532	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
533	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
534	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
535	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
536	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
538	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
539	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
540	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
541	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
543	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
545	C₇×C₈	—	2	1	no	—
546	C₇×C₈	—	2	2	no	—
547	C₇×C₈	—	2	2	no	—
548	C₇×C₈	—	2	1	no	—
549	C₇×C₈	—	2	2	no	—
550	C₇×C₈	—	2	2	no	—
551	C₇×C₈	—	2	2	no	—
552	C₇×C₈	—	2	1	no	—
553	C₇×C₈	—	2	2	no	—
554	C₇×C₈	2₋¹⁺⁴	1	2	yes	—
555	C₂×#41	C₂×C₄×C₇	1	2	yes	—
556	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
557	C₂×M₁₆	C₂³×C₇	1	2	yes	—
558	C₂×M₁₆	C₂³×C₇	1	2	yes	—
559	C₂×M₁₆	C₂³×C₇	1	2	yes	—
560	C₂×M₁₆	C₂³×C₇	1	2	yes	—
561	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₇	1	2	yes	—
563	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
566	C₂²×C₈	C₂³×C₇	1	2	yes	—
567	C₂²×C₈	C₂³×C₇	1	2	yes	—
568	C₂²×C₈	C₂³×C₇	1	2	yes	—
569	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
570	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
571	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
572	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
573	#126	C₂×C₄×C₇	1	2	yes	—
574	#126	C₂×C₄×C₇	1	2	yes	—
575	#126	C₂×C₄×C₇	1	2	yes	—
576	#126	C₂×C₄×C₇	1	2	yes	—
577	#126	C₂×C₄×C₇	1	2	yes	—
578	#126	C₂×C₄×C₇	1	2	yes	—
579	#126	C₂×C₄×C₇	1	2	yes	—
580	#126	C₂×C₄×C₇	1	2	yes	—
581	#125	C₂×C₄×C₇	1	1	yes	characteristic
582	#125	C₂×C₄×C₇	1	1	yes	characteristic
583	#125	C₂×C₄×C₇	1	2	yes	—
584	#125	C₂×C₄×C₇	1	2	yes	—
585	#125	C₂×C₄×C₇	1	2	yes	—
586	#125	C₂×C₄×C₇	1	2	yes	—
587	#125	C₂×C₄×C₇	1	2	yes	—
588	#125	C₂×C₄×C₇	1	2	yes	—
589	#125	C₂×C₄×C₇	1	2	yes	—
590	#124	C₂×C₄×C₇	1	2	yes	—
591	#124	C₂×C₄×C₇	1	2	yes	—
592	#124	C₂×C₄×C₇	1	1	yes	characteristic
593	#124	C₂×C₄×C₇	1	1	yes	characteristic
594	#124	C₂×C₄×C₇	1	2	yes	—
595	#123	C₂×C₄×C₇	1	2	yes	—
596	#123	C₂×C₄×C₇	1	2	yes	—
597	#123	C₂×C₄×C₇	1	2	yes	—
598	#123	C₂×C₄×C₇	1	2	yes	—
599	#123	C₂×C₄×C₇	1	2	yes	—
600	#123	C₂×C₄×C₇	1	2	yes	—
601	#123	C₂×C₄×C₇	1	2	yes	—
602	#123	C₂×C₄×C₇	1	2	yes	—
603	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
604	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
605	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
607	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
608	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
609	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
610	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
611	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
612	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
613	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
614	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
615	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
616	#121	C₂×C₄×C₇	1	1	yes	characteristic
617	#121	C₂×C₄×C₇	1	1	yes	characteristic
618	#121	C₂×C₄×C₇	1	2	yes	—
619	#121	C₂×C₄×C₇	1	2	yes	—
620	#121	C₂×C₄×C₇	1	2	yes	—
621	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
622	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
623	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
624	C₄×Q₈	C₂³×C₇	1	2	yes	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
629	C₄×Q₈	C₂³×C₇	1	2	yes	—
630	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
631	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
632	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
633	C₄×D₄	C₂³×C₇	1	2	yes	—
634	C₄×D₄	C₂³×C₇	1	2	yes	—
635	C₄×D₄	C₂³×C₇	1	2	yes	—
636	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₇	1	2	yes	—
639	#117	C₂×C₄×C₇	1	2	yes	—
640	#117	C₂×C₄×C₇	1	2	yes	—
641	#117	C₂×C₄×C₇	1	2	yes	—
642	#117	C₂³×C₇	1	2	yes	—
643	#117	C₂³×C₇	1	2	yes	—
644	#117	C₂³×C₇	1	2	yes	—
645	#117	C₂³×C₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	2	yes	—
653	C₂×C₄²	C₂³×C₇	1	2	yes	—
654	C₄⋊C₈	C₂³×C₇	1	2	yes	—
655	C₄⋊C₈	C₂³×C₇	1	2	yes	—
656	C₄⋊C₈	C₂³×C₇	1	2	yes	—
657	C₄⋊C₈	C₂³×C₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₇	1	2	yes	—
659	C₄⋊C₈	C₂³×C₇	1	2	yes	—
660	C₄⋊C₈	C₂³×C₇	1	2	yes	—
661	C₄⋊C₈	C₂³×C₇	1	2	yes	—
662	C₄⋊C₈	C₂³×C₇	1	2	yes	—
663	C₄⋊C₈	C₂³×C₇	1	2	yes	—
664	C₄⋊C₈	C₂³×C₇	1	2	yes	—
665	C₄⋊C₈	C₂³×C₇	1	2	yes	—
666	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
667	C₄⋊C₈	C₂³×C₇	1	2	yes	—
668	C₄⋊C₈	C₂³×C₇	1	2	yes	—
669	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
670	C₄⋊C₈	C₂³×C₇	1	2	yes	—
671	C₄⋊C₈	C₂³×C₇	1	2	yes	—
672	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
673	C₄⋊C₈	C₂³×C₇	1	2	yes	—
674	C₄⋊C₈	C₂³×C₇	1	2	yes	—
675	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
676	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
684	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
685	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
686	#97	C₂³×C₇	1	2	yes	—
687	#97	C₂³×C₇	1	2	yes	—
688	#97	C₂³×C₇	1	2	yes	—
689	#97	C₂³×C₇	1	2	yes	—
690	#97	C₂³×C₇	1	2	yes	—
691	#97	C₂³×C₇	1	2	yes	—
692	#97	C₂³×C₇	1	2	yes	—
693	#97	C₂³×C₇	1	2	yes	—
694	#97	C₂³×C₇	1	2	yes	—
695	#97	C₂³×C₇	1	2	yes	—
696	#97	C₂³×C₇	1	2	yes	—
697	#97	C₂³×C₇	1	2	yes	—
698	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
699	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
700	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
701	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
702	C₄×C₈	C₂³×C₇	1	2	yes	—
703	C₄×C₈	C₂³×C₇	1	2	yes	—
704	C₄×C₈	C₂³×C₇	1	2	yes	—
705	C₄×C₈	C₂³×C₇	1	2	yes	—
706	C₄×C₈	C₂³×C₇	1	2	yes	—
707	C₄×C₈	C₂³×C₇	1	2	yes	—
708	C₂²×C₇	—	2	1	no	—
709	C₂²×C₇	—	2	1	no	—
710	C₂²×C₇	—	2	2	no	—
711	C₂²×C₇	—	2	2	no	—
712	C₂²×C₇	—	2	2	no	—
713	C₂²×C₇	—	2	2	no	—
714	C₂²×C₇	—	2	2	no	—
715	C₂²×C₇	—	2	2	no	—
716	C₂²×C₇	#568	1	2	yes	—
717	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
718	C₄×C₇	—	2	1	no	—
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	2	2	no	—
721	C₄×C₇	—	2	2	no	—
722	C₄×C₇	—	2	1	no	—
723	C₄×C₇	—	2	1	no	—
724	C₄×C₇	—	2	2	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	2	2	no	—
727	C₄×C₇	—	2	2	no	—
728	C₄×C₇	—	2	1	no	—
729	C₄×C₇	—	2	1	no	—
730	C₄×C₇	—	2	2	no	—
731	C₄×C₇	—	2	2	no	—
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
734	C₄×C₇	#585	1	1	yes	characteristic
735	#41	—	4	4	no	—
736	C₂×Q₈	—	4	2	no	—
737	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
738	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
739	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
740	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
741	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
742	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
743	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
744	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
745	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
746	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
747	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
748	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
749	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
751	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
752	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
753	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
754	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
756	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
757	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
758	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
762	M₁₆	—	2	4	no	—
763	M₁₆	—	4	2	no	—
764	M₁₆	—	4	2	no	—
765	M₁₆	—	4	2	no	—
766	C₂×C₈	—	2	2	no	—
767	C₂×C₈	—	2	4	no	—
768	C₂×C₈	—	4	2	no	—
769	C₂×C₈	—	4	1	no	—
770	C₂×C₈	—	4	1	no	—
771	C₂×C₈	—	4	1	no	—
772	C₂×C₈	—	4	2	no	—
773	C₂×C₈	—	4	2	no	—
774	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₇	1	2	yes	—
776	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₇	1	2	yes	—
778	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₇	1	2	yes	—
780	C₂×C₈	C₂⁴×C₇	1	2	yes	—
781	C₂×C₈	C₂⁴×C₇	1	2	yes	—
782	C₂×C₈	C₂⁴×C₇	1	2	yes	—
783	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
785	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
786	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
787	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
788	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
789	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
791	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
792	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
793	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
798	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
799	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
808	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
809	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
811	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
812	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
813	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
832	C₄²	C₂²×C₄×C₇	1	2	yes	—
833	C₄²	C₂²×C₄×C₇	1	2	yes	—
834	C₄²	C₂²×C₄×C₇	1	2	yes	—
835	C₄²	C₂²×C₄×C₇	1	2	yes	—
836	C₄²	C₂²×C₄×C₇	1	2	yes	—
837	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
838	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
839	C₄²	C₂²×C₄×C₇	1	2	yes	—
840	C₄²	C₂⁴×C₇	1	1	yes	characteristic
841	C₄²	C₂⁴×C₇	1	1	yes	characteristic
842	C₄²	C₂⁴×C₇	1	2	yes	—
843	C₄²	C₂⁴×C₇	1	2	yes	—
844	C₄²	C₂⁴×C₇	1	2	yes	—
845	C₄²	C₂⁴×C₇	1	2	yes	—
846	C₂×C₇	—	2	2	no	—
847	C₂×C₇	—	4	2	no	—
848	C₂×C₇	—	4	2	no	—
849	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
850	C₂×C₇	C₂×#568	1	1	yes	characteristic
851	C₂×C₇	#3573	1	1	yes	characteristic
852	C₂³	C₂³×C₄×C₇	1	2	yes	—
853	C₂³	C₂³×C₄×C₇	1	2	yes	—
854	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
855	Q₈	—	4	2	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	4	1	no	—
858	Q₈	—	4	1	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	4	2	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	4	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	1	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
884	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
889	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
891	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
892	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
893	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
894	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
895	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
896	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
897	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
898	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
899	C₈	—	2	1	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	1	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	1	no	—
907	C₈	—	2	2	no	—
908	C₈	C₇×2₋¹⁺⁴	1	2	yes	—
909	C₇	#60340	1	1	yes	characteristic, direct product factor, Sylow
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	C₇×#568	1	2	yes	—
919	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
936	C₄	C₇×#585	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	4	2	no	—
940	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
941	C₂	C₂×C₇×#568	1	1	yes	characteristic
942	C₂	C₇×#3573	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×#537	C₄
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×#2992	C₂	semidirect
5. C₇×#2992	C₂	semidirect
6. C₇×#2992	C₂	semidirect
7. C₇×#2990	C₂	semidirect
8. C₇×#2987	C₂	semidirect
9. C₇×#2985	C₂	semidirect
10. C₇×#2983	C₂	semidirect
11. C₇×#2970	C₂	semidirect
12. C₇×#2968	C₂	semidirect
13. C₇×#2968	C₂	semidirect
14. C₇×#2967	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2966	C₂	semidirect
17. C₇×#2962	C₂	semidirect
18. C₇×#2961	C₂	semidirect
19. C₂×C₇×#446	C₂	semidirect
117. #60340	C₇	direct (N × H)
272. #2995	C₂×C₇	semidirect
273. #2994	C₂×C₇	semidirect
274. #2992	C₂×C₇	semidirect
275. #2992	C₂×C₇	semidirect
276. #2992	C₂×C₇	semidirect
277. #2990	C₂×C₇	semidirect
278. #2987	C₂×C₇	semidirect
279. #2985	C₂×C₇	semidirect
280. #2983	C₂×C₇	semidirect
281. #2970	C₂×C₇	semidirect
282. #2968	C₂×C₇	semidirect
283. #2968	C₂×C₇	semidirect
284. #2967	C₂×C₇	semidirect
285. #2966	C₂×C₇	semidirect
286. #2966	C₂×C₇	semidirect
287. #2962	C₂×C₇	semidirect
288. #2961	C₂×C₇	semidirect
289. C₂×#446	C₂×C₇	semidirect
909. C₇	#60340	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×#3461	2
C₇×#2995	2
C₇×#2994	2
C₇×#2992	2
C₇×#2990	2
C₇×#2987	2
C₇×#2985	2
C₇×#2983	2
C₇×#2970	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×#2962	2
C₇×#2961	2
C₂×C₇×#446	2
#60340	7

Subgroups — C7×#60340 #13237556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60340 #13237556