Subgroups — C₇×#60254 #13237470

Order 1792.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#2987	C₂	1	4	yes	maximal, complemented
3	C₇×#2986	C₂	1	2	yes	maximal, complemented
4	C₇×#2985	C₂	1	2	yes	maximal, complemented
5	C₇×#2985	C₂	1	4	yes	maximal, complemented
6	C₇×#2984	C₂	1	2	yes	maximal, complemented
7	C₇×#2983	C₂	1	2	yes	maximal, complemented
8	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2962	C₂	1	2	yes	maximal, complemented
11	C₇×#2961	C₂	1	2	yes	maximal, complemented
12	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2925	C₂	1	1	yes	maximal, characteristic
15	C₇×#2925	C₂	1	2	yes	maximal
16	C₇×#2923	C₂	1	2	yes	maximal
17	C₇×#2922	C₂	1	1	yes	maximal, characteristic
18	C₇×Q₈²	C₄	1	1	yes	characteristic
19	C₇×#557	C₄	1	1	yes	characteristic
20	C₇×#557	C₄	1	2	yes	—
21	C₇×#554	C₄	1	2	yes	—
22	C₇×#554	C₄	1	1	yes	characteristic
23	C₇×#554	C₄	1	4	yes	—
24	C₇×#554	C₄	1	2	yes	—
25	C₇×D₄×Q₈	C₄	1	1	yes	characteristic
26	C₇×D₄×Q₈	C₄	1	2	yes	—
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#533	C₂²	1	2	yes	—
29	C₇×#533	C₂²	1	2	yes	—
30	C₇×#533	C₂²	1	4	yes	—
31	C₄×C₇×#41	C₂²	1	1	yes	characteristic
32	C₄×C₇×#41	C₂²	1	2	yes	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
35	C₇×#446	C₂²	1	1	yes	characteristic
36	C₇×#446	C₂²	1	1	yes	characteristic
37	C₇×#446	C₂²	1	1	yes	characteristic
38	C₇×#446	C₂²	1	2	yes	—
39	C₇×#446	C₂²	1	1	yes	characteristic
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	4	yes	—
44	C₇×#446	C₂²	1	4	yes	—
45	C₇×#446	C₂²	1	4	yes	—
46	C₇×#446	C₂²	1	4	yes	—
47	C₇×#446	C₂²	1	2	yes	—
48	C₇×#446	C₂²	1	4	yes	—
49	C₇×#446	C₂²	1	4	yes	—
50	C₇×#446	C₂²	1	4	yes	—
51	C₇×#446	C₂²	1	4	yes	—
52	C₇×#446	C₂²	1	2	yes	—
53	C₇×#446	C₂²	1	4	yes	—
54	C₇×C₈×Q₈	C₂²	1	2	yes	—
55	C₇×C₈×Q₈	C₂²	1	2	yes	—
56	C₇×C₈×Q₈	C₂²	1	2	yes	—
57	C₇×C₈×Q₈	C₂²	1	4	yes	—
58	C₇×C₈×Q₈	C₂²	1	2	yes	—
59	C₇×#433	C₂²	1	2	yes	—
60	C₇×#433	C₂²	1	2	yes	—
61	C₇×#433	C₂²	1	4	yes	—
62	C₇×#433	C₂²	1	4	yes	—
63	C₇×#433	C₂²	1	4	yes	—
64	C₇×#433	C₂²	1	4	yes	—
65	C₇×#433	C₂²	1	4	yes	—
66	C₇×#432	C₂²	1	4	yes	—
67	C₇×#432	C₂²	1	4	yes	—
68	C₇×#432	C₂²	1	4	yes	—
69	C₇×#432	C₂²	1	2	yes	—
70	C₇×#431	C₂²	1	2	yes	—
71	C₇×#431	C₂²	1	2	yes	—
72	C₇×#431	C₂²	1	2	yes	—
73	C₇×#431	C₂²	1	4	yes	—
74	C₇×#424	C₂²	1	1	yes	characteristic
75	C₇×#424	C₂²	1	1	yes	characteristic
76	C₇×#424	C₂²	1	2	yes	—
77	C₇×#424	C₂²	1	2	yes	—
78	C₇×#423	C₂²	1	1	yes	characteristic
79	C₇×#423	C₂²	1	2	yes	—
80	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
82	C₇×#408	C₂²	1	1	yes	characteristic
83	C₇×#408	C₂²	1	1	yes	characteristic
84	C₇×#408	C₂²	1	2	yes	—
85	C₇×#405	C₂²	1	2	yes	—
86	C₇×#405	C₂²	1	2	yes	—
87	C₇×#405	C₂²	1	2	yes	—
88	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
89	C₄×C₇×M₁₆	C₂²	1	2	yes	—
90	C₂×C₇×#97	C₂²	1	2	yes	—
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
92	#60254	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	C₂³	1	1	yes	characteristic
94	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
96	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×M₁₆	C₂³	1	2	yes	—
99	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×C₈	C₂³	1	2	yes	—
102	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
103	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
104	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
105	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
106	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
107	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
108	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
109	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
110	C₇×#125	C₂×C₄	1	2	yes	—
111	C₇×#125	C₂×C₄	1	2	yes	—
112	C₇×#125	C₂×C₄	1	2	yes	—
113	C₇×#125	C₂×C₄	1	4	yes	—
114	C₇×#125	C₂×C₄	1	4	yes	—
115	C₇×#125	C₂×C₄	1	4	yes	—
116	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
117	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
118	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
119	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
120	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
121	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
122	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
123	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
124	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
125	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
126	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
127	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
128	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
129	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
130	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
131	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
132	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
133	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
134	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
135	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
136	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
137	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
138	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₄×C₇×Q₈	C₂³	1	2	yes	—
140	C₄×C₇×Q₈	C₂³	1	2	yes	—
141	C₄×C₇×Q₈	C₂³	1	4	yes	—
142	C₄×C₇×Q₈	C₂³	1	2	yes	—
143	C₄×C₇×Q₈	C₂³	1	4	yes	—
144	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
145	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
146	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
147	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
148	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
149	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
151	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
152	C₇×#117	C₂³	1	1	yes	characteristic
153	C₇×#117	C₂³	1	2	yes	—
154	C₇×#117	C₂³	1	2	yes	—
155	C₇×#117	C₂³	1	4	yes	—
156	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
160	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇	C₂³	1	2	yes	—
162	C₂×C₄²×C₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₇	C₂³	1	4	yes	—
164	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
165	C₇×C₄⋊C₈	C₂³	1	2	yes	—
166	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
167	C₇×C₄⋊C₈	C₂³	1	2	yes	—
168	C₇×C₄⋊C₈	C₂³	1	2	yes	—
169	C₇×C₄⋊C₈	C₂³	1	2	yes	—
170	C₇×C₄⋊C₈	C₂³	1	2	yes	—
171	C₇×C₄⋊C₈	C₂³	1	2	yes	—
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×C₄⋊C₈	C₂³	1	2	yes	—
174	C₇×C₄⋊C₈	C₂³	1	4	yes	—
175	C₇×C₄⋊C₈	C₂³	1	2	yes	—
176	C₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊C₈	C₂³	1	4	yes	—
180	C₇×C₄⋊C₈	C₂³	1	4	yes	—
181	C₇×C₄⋊C₈	C₂³	1	4	yes	—
182	C₇×C₄⋊C₈	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
185	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₇×#97	C₂³	1	2	yes	—
190	C₇×#97	C₂³	1	2	yes	—
191	C₇×#97	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	4	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₇×#97	C₂³	1	4	yes	—
196	C₇×#97	C₂³	1	4	yes	—
197	C₇×#97	C₂³	1	4	yes	—
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
200	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×C₈	C₂³	1	2	yes	—
203	C₄×C₇×C₈	C₂³	1	4	yes	—
204	C₄×C₇×C₈	C₂³	1	4	yes	—
205	C₄×C₇×C₈	C₂³	1	4	yes	—
206	C₄×C₇×C₈	C₂³	1	4	yes	—
207	Q₈×#41	C₂×C₇	1	1	yes	characteristic
208	#2987	C₂×C₇	1	4	yes	complemented
209	#2986	C₂×C₇	1	2	yes	complemented
210	#2985	C₂×C₇	1	2	yes	complemented
211	#2985	C₂×C₇	1	4	yes	complemented
212	#2984	C₂×C₇	1	2	yes	complemented
213	#2983	C₂×C₇	1	2	yes	complemented
214	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
215	#2962	C₂×C₇	1	1	yes	characteristic, complemented
216	#2962	C₂×C₇	1	2	yes	complemented
217	#2961	C₂×C₇	1	2	yes	complemented
218	#2960	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
220	#2925	C₂×C₇	1	1	yes	characteristic
221	#2925	C₂×C₇	1	2	yes	—
222	#2923	C₂×C₇	1	2	yes	—
223	#2922	C₂×C₇	1	1	yes	characteristic
224	C₇×#41	—	2	2	no	—
225	C₇×#41	—	2	2	no	—
226	C₂×C₇×Q₈	—	4	2	no	—
227	C₂×C₇×Q₈	—	4	4	no	—
228	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
232	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
233	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
234	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
235	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
236	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
237	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
239	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
240	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
241	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
242	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
244	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
248	C₇×M₁₆	—	2	2	no	—
249	C₇×M₁₆	—	2	2	no	—
250	C₇×M₁₆	—	2	4	no	—
251	C₂×C₇×C₈	—	2	2	no	—
252	C₂×C₇×C₈	—	2	4	no	—
253	C₂×C₇×C₈	—	2	2	no	—
254	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
255	C₂×C₇×C₈	C₂⁴	1	2	yes	—
256	C₂×C₇×C₈	C₂⁴	1	2	yes	—
257	C₂×C₇×C₈	C₂⁴	1	4	yes	—
258	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
261	C₂×C₇×C₈	C₂⁴	1	2	yes	—
262	C₂×C₇×C₈	C₂⁴	1	2	yes	—
263	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
264	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
265	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
266	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
267	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
268	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
269	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
270	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
271	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
272	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
273	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
274	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
275	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
277	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
278	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
279	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
280	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
281	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
282	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
283	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
284	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
285	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
288	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
289	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
290	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
291	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
292	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
293	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
294	C₄²×C₇	C₂²×C₄	1	2	yes	—
295	C₄²×C₇	C₂²×C₄	1	4	yes	—
296	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
297	C₄²×C₇	C₂²×C₄	1	2	yes	—
298	C₄²×C₇	C₂²×C₄	1	4	yes	—
299	C₄²×C₇	C₂²×C₄	1	2	yes	—
300	C₄²×C₇	C₂²×C₄	1	2	yes	—
301	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
302	C₄²×C₇	C₂⁴	1	1	yes	characteristic
303	C₄²×C₇	C₂⁴	1	1	yes	characteristic
304	C₄²×C₇	C₂⁴	1	2	yes	—
305	C₄²×C₇	C₂⁴	1	4	yes	—
306	C₄²×C₇	C₂⁴	1	2	yes	—
307	C₄²×C₇	C₂⁴	1	2	yes	—
308	Q₈²	C₄×C₇	1	1	yes	characteristic
309	#557	C₄×C₇	1	1	yes	characteristic
310	#557	C₄×C₇	1	2	yes	—
311	#554	C₄×C₇	1	2	yes	—
312	#554	C₄×C₇	1	1	yes	characteristic
313	#554	C₄×C₇	1	4	yes	—
314	#554	C₄×C₇	1	2	yes	—
315	D₄×Q₈	C₄×C₇	1	1	yes	characteristic
316	D₄×Q₈	C₄×C₇	1	2	yes	—
317	#533	C₂²×C₇	1	1	yes	characteristic
318	#533	C₂²×C₇	1	2	yes	—
319	#533	C₂²×C₇	1	2	yes	—
320	#533	C₂²×C₇	1	4	yes	—
321	C₄×#41	C₂²×C₇	1	1	yes	characteristic
322	C₄×#41	C₂²×C₇	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
325	#446	C₂²×C₇	1	1	yes	characteristic
326	#446	C₂²×C₇	1	1	yes	characteristic
327	#446	C₂²×C₇	1	1	yes	characteristic
328	#446	C₂²×C₇	1	2	yes	—
329	#446	C₂²×C₇	1	1	yes	characteristic
330	#446	C₂²×C₇	1	2	yes	—
331	#446	C₂²×C₇	1	2	yes	—
332	#446	C₂²×C₇	1	2	yes	—
333	#446	C₂²×C₇	1	4	yes	—
334	#446	C₂²×C₇	1	4	yes	—
335	#446	C₂²×C₇	1	4	yes	—
336	#446	C₂²×C₇	1	4	yes	—
337	#446	C₂²×C₇	1	2	yes	—
338	#446	C₂²×C₇	1	4	yes	—
339	#446	C₂²×C₇	1	4	yes	—
340	#446	C₂²×C₇	1	4	yes	—
341	#446	C₂²×C₇	1	4	yes	—
342	#446	C₂²×C₇	1	2	yes	—
343	#446	C₂²×C₇	1	4	yes	—
344	C₈×Q₈	C₂²×C₇	1	2	yes	—
345	C₈×Q₈	C₂²×C₇	1	2	yes	—
346	C₈×Q₈	C₂²×C₇	1	2	yes	—
347	C₈×Q₈	C₂²×C₇	1	4	yes	—
348	C₈×Q₈	C₂²×C₇	1	2	yes	—
349	#433	C₂²×C₇	1	2	yes	—
350	#433	C₂²×C₇	1	2	yes	—
351	#433	C₂²×C₇	1	4	yes	—
352	#433	C₂²×C₇	1	4	yes	—
353	#433	C₂²×C₇	1	4	yes	—
354	#433	C₂²×C₇	1	4	yes	—
355	#433	C₂²×C₇	1	4	yes	—
356	#432	C₂²×C₇	1	4	yes	—
357	#432	C₂²×C₇	1	4	yes	—
358	#432	C₂²×C₇	1	4	yes	—
359	#432	C₂²×C₇	1	2	yes	—
360	#431	C₂²×C₇	1	2	yes	—
361	#431	C₂²×C₇	1	2	yes	—
362	#431	C₂²×C₇	1	2	yes	—
363	#431	C₂²×C₇	1	4	yes	—
364	#424	C₂²×C₇	1	1	yes	characteristic
365	#424	C₂²×C₇	1	1	yes	characteristic
366	#424	C₂²×C₇	1	2	yes	—
367	#424	C₂²×C₇	1	2	yes	—
368	#423	C₂²×C₇	1	1	yes	characteristic
369	#423	C₂²×C₇	1	2	yes	—
370	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
372	#408	C₂²×C₇	1	1	yes	characteristic
373	#408	C₂²×C₇	1	1	yes	characteristic
374	#408	C₂²×C₇	1	2	yes	—
375	#405	C₂²×C₇	1	2	yes	—
376	#405	C₂²×C₇	1	2	yes	—
377	#405	C₂²×C₇	1	2	yes	—
378	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
379	C₄×M₁₆	C₂²×C₇	1	2	yes	—
380	C₂×#97	C₂²×C₇	1	2	yes	—
381	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
382	C₂³×C₇	C₂³×C₄	1	2	yes	—
383	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
384	C₇×Q₈	—	2	2	no	—
385	C₇×Q₈	—	2	2	no	—
386	C₇×Q₈	—	2	2	no	—
387	C₇×Q₈	—	2	4	no	—
388	C₇×Q₈	—	4	2	no	—
389	C₇×Q₈	—	4	4	no	—
390	C₇×Q₈	—	4	2	no	—
391	C₇×Q₈	—	4	4	no	—
392	C₇×D₄	—	2	4	no	—
393	C₇×D₄	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	4	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	—	4	2	no	—
400	C₂×C₄×C₇	—	4	2	no	—
401	C₂×C₄×C₇	—	4	4	no	—
402	C₂×C₄×C₇	—	4	2	no	—
403	C₂×C₄×C₇	—	4	4	no	—
404	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
405	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
414	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
418	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
419	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
420	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
421	C₇×C₈	—	2	1	no	—
422	C₇×C₈	—	2	1	no	—
423	C₇×C₈	—	2	2	no	—
424	C₇×C₈	—	2	2	no	—
425	C₇×C₈	—	2	1	no	—
426	C₇×C₈	—	2	1	no	—
427	C₇×C₈	—	2	2	no	—
428	C₇×C₈	—	2	2	no	—
429	C₇×C₈	—	2	4	no	—
430	C₂×#41	C₂³×C₇	1	1	yes	characteristic
431	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
433	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₇	1	2	yes	—
436	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₇	1	2	yes	—
439	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
440	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
441	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
442	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	—
443	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
444	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
445	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
446	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	—
447	#125	C₂×C₄×C₇	1	2	yes	—
448	#125	C₂×C₄×C₇	1	2	yes	—
449	#125	C₂×C₄×C₇	1	2	yes	—
450	#125	C₂×C₄×C₇	1	4	yes	—
451	#125	C₂×C₄×C₇	1	4	yes	—
452	#125	C₂×C₄×C₇	1	4	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
456	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
457	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
458	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
459	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
460	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
461	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
462	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
463	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
464	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
465	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
466	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
467	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
468	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
469	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
470	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
471	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
472	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
473	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
474	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
475	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
476	C₄×Q₈	C₂³×C₇	1	2	yes	—
477	C₄×Q₈	C₂³×C₇	1	2	yes	—
478	C₄×Q₈	C₂³×C₇	1	4	yes	—
479	C₄×Q₈	C₂³×C₇	1	2	yes	—
480	C₄×Q₈	C₂³×C₇	1	4	yes	—
481	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
482	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
483	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
484	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
485	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
486	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
487	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
488	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
489	#117	C₂³×C₇	1	1	yes	characteristic
490	#117	C₂³×C₇	1	2	yes	—
491	#117	C₂³×C₇	1	2	yes	—
492	#117	C₂³×C₇	1	4	yes	—
493	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
496	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
497	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₇	1	2	yes	—
500	C₂×C₄²	C₂³×C₇	1	4	yes	—
501	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
502	C₄⋊C₈	C₂³×C₇	1	2	yes	—
503	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
504	C₄⋊C₈	C₂³×C₇	1	2	yes	—
505	C₄⋊C₈	C₂³×C₇	1	2	yes	—
506	C₄⋊C₈	C₂³×C₇	1	2	yes	—
507	C₄⋊C₈	C₂³×C₇	1	2	yes	—
508	C₄⋊C₈	C₂³×C₇	1	2	yes	—
509	C₄⋊C₈	C₂³×C₇	1	4	yes	—
510	C₄⋊C₈	C₂³×C₇	1	2	yes	—
511	C₄⋊C₈	C₂³×C₇	1	4	yes	—
512	C₄⋊C₈	C₂³×C₇	1	2	yes	—
513	C₄⋊C₈	C₂³×C₇	1	2	yes	—
514	C₄⋊C₈	C₂³×C₇	1	2	yes	—
515	C₄⋊C₈	C₂³×C₇	1	2	yes	—
516	C₄⋊C₈	C₂³×C₇	1	4	yes	—
517	C₄⋊C₈	C₂³×C₇	1	4	yes	—
518	C₄⋊C₈	C₂³×C₇	1	4	yes	—
519	C₄⋊C₈	C₂³×C₇	1	4	yes	—
520	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
521	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
522	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
523	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
524	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
526	#97	C₂³×C₇	1	2	yes	—
527	#97	C₂³×C₇	1	2	yes	—
528	#97	C₂³×C₇	1	2	yes	—
529	#97	C₂³×C₇	1	2	yes	—
530	#97	C₂³×C₇	1	4	yes	—
531	#97	C₂³×C₇	1	2	yes	—
532	#97	C₂³×C₇	1	4	yes	—
533	#97	C₂³×C₇	1	4	yes	—
534	#97	C₂³×C₇	1	4	yes	—
535	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
536	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₇	1	2	yes	—
540	C₄×C₈	C₂³×C₇	1	4	yes	—
541	C₄×C₈	C₂³×C₇	1	4	yes	—
542	C₄×C₈	C₂³×C₇	1	4	yes	—
543	C₄×C₈	C₂³×C₇	1	4	yes	—
544	C₂²×C₇	—	2	1	no	—
545	C₂²×C₇	—	2	1	no	—
546	C₂²×C₇	—	2	2	no	—
547	C₂²×C₇	—	2	2	no	—
548	C₂²×C₇	—	2	2	no	—
549	C₂²×C₇	#519	1	2	yes	—
550	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
551	C₄×C₇	—	2	2	no	—
552	C₄×C₇	—	2	1	no	—
553	C₄×C₇	—	2	2	no	—
554	C₄×C₇	—	2	2	no	—
555	C₄×C₇	—	2	2	no	—
556	C₄×C₇	—	2	4	no	—
557	C₄×C₇	—	2	1	no	—
558	C₄×C₇	—	2	2	no	—
559	C₄×C₇	—	2	1	no	—
560	C₄×C₇	—	2	2	no	—
561	C₄×C₇	—	2	2	no	—
562	C₄×C₇	—	2	4	no	—
563	C₄×C₇	#519	1	2	yes	—
564	C₄×C₇	#568	1	2	yes	—
565	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	C₂×Q₈	—	4	2	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
572	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
573	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
574	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
575	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
576	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
577	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
578	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
579	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
580	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
581	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
582	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
584	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
585	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
587	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
588	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
591	M₁₆	—	2	2	no	—
592	M₁₆	—	2	2	no	—
593	M₁₆	—	2	4	no	—
594	C₂×C₈	—	2	2	no	—
595	C₂×C₈	—	2	4	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
598	C₂×C₈	C₂⁴×C₇	1	2	yes	—
599	C₂×C₈	C₂⁴×C₇	1	2	yes	—
600	C₂×C₈	C₂⁴×C₇	1	4	yes	—
601	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
602	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
603	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
604	C₂×C₈	C₂⁴×C₇	1	2	yes	—
605	C₂×C₈	C₂⁴×C₇	1	2	yes	—
606	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
607	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
608	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
609	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
610	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
611	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
612	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
613	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
614	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
615	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
616	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
618	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
619	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
620	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
621	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
622	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
623	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
624	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
625	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
626	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
627	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
628	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
629	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
630	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
631	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
632	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
633	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
634	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
635	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
637	C₄²	C₂²×C₄×C₇	1	2	yes	—
638	C₄²	C₂²×C₄×C₇	1	4	yes	—
639	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
640	C₄²	C₂²×C₄×C₇	1	2	yes	—
641	C₄²	C₂²×C₄×C₇	1	4	yes	—
642	C₄²	C₂²×C₄×C₇	1	2	yes	—
643	C₄²	C₂²×C₄×C₇	1	2	yes	—
644	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
645	C₄²	C₂⁴×C₇	1	1	yes	characteristic
646	C₄²	C₂⁴×C₇	1	1	yes	characteristic
647	C₄²	C₂⁴×C₇	1	2	yes	—
648	C₄²	C₂⁴×C₇	1	4	yes	—
649	C₄²	C₂⁴×C₇	1	2	yes	—
650	C₄²	C₂⁴×C₇	1	2	yes	—
651	C₂×C₇	—	2	2	no	—
652	C₂×C₇	—	4	2	no	—
653	C₂×C₇	C₂×#519	1	1	yes	characteristic
654	C₂×C₇	C₂×#568	1	1	yes	characteristic
655	C₂×C₇	#3573	1	1	yes	characteristic
656	C₂³	C₂³×C₄×C₇	1	2	yes	—
657	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	4	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	4	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
679	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
680	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
681	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
682	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
684	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
685	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
686	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
687	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
688	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
689	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
690	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
691	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
692	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
693	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
694	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₈	—	2	2	no	—
702	C₈	—	2	2	no	—
703	C₈	—	2	4	no	—
704	C₇	#60254	1	1	yes	characteristic, direct product factor, Sylow
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	C₇×#519	1	2	yes	—
711	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	4	no	—
723	C₄	—	2	2	no	—
724	C₄	C₇×#519	1	2	yes	—
725	C₄	C₇×#568	1	2	yes	—
726	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
727	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	C₂×C₇×#519	1	1	yes	characteristic
731	C₂	C₂×C₇×#568	1	1	yes	characteristic
732	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	C₂×C₇×#41	C₂³
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×#2987	C₂	semidirect
3. C₇×#2986	C₂	semidirect
4. C₇×#2985	C₂	semidirect
5. C₇×#2985	C₂	semidirect
6. C₇×#2984	C₂	semidirect
7. C₇×#2983	C₂	semidirect
8. C₇×Q₈×M₁₆	C₂	semidirect
9. C₇×#2962	C₂	semidirect
10. C₇×#2962	C₂	semidirect
11. C₇×#2961	C₂	semidirect
12. C₇×#2960	C₂	semidirect
13. C₂×C₇×#446	C₂	semidirect
92. #60254	C₇	direct (N × H)
208. #2987	C₂×C₇	semidirect
209. #2986	C₂×C₇	semidirect
210. #2985	C₂×C₇	semidirect
211. #2985	C₂×C₇	semidirect
212. #2984	C₂×C₇	semidirect
213. #2983	C₂×C₇	semidirect
214. Q₈×M₁₆	C₂×C₇	semidirect
215. #2962	C₂×C₇	semidirect
216. #2962	C₂×C₇	semidirect
217. #2961	C₂×C₇	semidirect
218. #2960	C₂×C₇	semidirect
219. C₂×#446	C₂×C₇	semidirect
704. C₇	#60254	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×Q₈×#41	2
C₇×#2987	2
C₇×#2986	2
C₇×#2985	2
C₇×#2984	2
C₇×#2983	2
C₇×Q₈×M₁₆	2
C₇×#2962	2
C₇×#2961	2
C₇×#2960	2
C₂×C₇×#446	2
C₇×#2925	2
C₇×#2923	2
C₇×#2922	2
#60254	7

Subgroups — C7×#60254 #13237470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60254 #13237470