Subgroups — C₂×C₇×#3309 #13238353

Order 1792.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3309	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#553	—	2	4	no	—
25	C₇×#553	C₂²	1	8	yes	complemented
26	C₇×#550	—	2	4	no	—
27	C₇×#550	C₂²	1	8	yes	complemented
28	C₂×C₇×#127	—	2	1	no	—
29	C₂×C₇×#127	C₂²	1	1	yes	characteristic
30	C₂×C₇×#126	—	2	1	no	—
31	C₂×C₇×#125	C₂²	1	1	yes	characteristic
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×#121	—	2	1	no	—
34	C₂×C₇×#121	—	2	1	no	—
35	C₂×C₇×#121	—	2	1	no	—
36	C₂×C₇×#121	C₂²	1	1	yes	characteristic
37	C₂×C₇×#121	C₂²	1	1	yes	characteristic
38	C₂×C₇×#121	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	—	2	1	no	—
42	C₂×C₄×C₇×D₄	—	2	1	no	—
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#490	C₂²	1	8	yes	complemented
48	C₇×#482	C₂²	1	8	yes	complemented
49	C₇×#480	C₂²	1	8	yes	complemented
50	C₇×#479	C₂²	1	8	yes	complemented
51	C₇×#469	C₂²	1	8	yes	complemented
52	C₇×#466	C₂²	1	8	yes	complemented
53	C₇×#459	C₂²	1	8	yes	complemented
54	C₇×#449	C₂²	1	8	yes	complemented
55	C₇×#449	C₂²	1	8	yes	complemented
56	C₇×#440	C₂²	1	8	yes	complemented
57	C₇×#435	C₂²	1	8	yes	complemented
58	C₂×C₇×#107	C₂²	1	1	yes	characteristic
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic
60	C₂×C₇×#106	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₇×#417	C₂²	1	8	yes	complemented
63	C₇×#416	C₂²	1	8	yes	complemented
64	C₂×C₇×#103	C₂²	1	1	yes	characteristic
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic
67	C₂×C₇×#102	C₂²	1	1	yes	characteristic
68	C₂×C₇×#102	C₂²	1	1	yes	characteristic
69	C₂×C₇×#102	C₂²	1	1	yes	characteristic
70	C₂×C₇×#102	C₂²	1	1	yes	characteristic
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic
73	C₂×C₇×#102	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic
77	C₂×#3309	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₇×#41	—	2	2	no	—
79	C₂×C₇×#41	—	2	2	no	—
80	C₂×C₇×#41	—	2	4	no	—
81	C₂×C₇×#41	—	2	4	no	—
82	C₂×C₇×#41	—	4	2	no	—
83	C₂×C₇×#41	—	4	2	no	—
84	C₂×C₇×#41	C₂³	1	4	yes	—
85	C₂×C₇×#41	C₂³	1	4	yes	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	—	2	1	no	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	—	2	1	no	—
90	C₂²×C₇×D₄	—	2	1	no	—
91	C₂²×C₇×D₄	—	2	1	no	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	—	2	1	no	—
94	C₂²×C₇×D₄	—	2	1	no	—
95	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
96	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	—	2	1	no	—
100	C₂³×C₄×C₇	—	2	1	no	—
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₂³×C₄×C₇	—	2	1	no	—
103	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
105	C₂×C₇×SD₁₆	—	2	4	no	—
106	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₇×D₈	—	4	2	no	—
108	C₂×C₇×D₈	—	4	2	no	—
109	C₂×C₇×D₈	C₂³	1	4	yes	—
110	C₂×C₇×D₈	C₂³	1	4	yes	—
111	C₂×C₇×M₁₆	—	4	2	no	—
112	C₂×C₇×M₁₆	C₂³	1	4	yes	—
113	C₂²×C₇×C₈	—	4	2	no	—
114	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₂²×C₇×C₈	C₂³	1	4	yes	—
119	C₇×#127	—	2	8	no	—
120	C₇×#127	—	2	2	no	—
121	C₇×#127	C₂³	1	4	yes	—
122	C₇×#126	—	2	8	no	—
123	C₇×#125	—	2	2	no	—
124	C₇×#125	C₂³	1	4	yes	—
125	C₇×#123	—	2	8	no	—
126	C₇×#121	—	2	8	no	—
127	C₇×#121	—	2	2	no	—
128	C₇×#121	—	2	2	no	—
129	C₇×#121	—	2	2	no	—
130	C₇×#121	—	2	2	no	—
131	C₇×#121	—	2	8	no	—
132	C₇×#121	—	2	8	no	—
133	C₇×#121	C₂³	1	4	yes	—
134	C₇×#121	C₂³	1	4	yes	—
135	C₇×#121	C₂³	1	4	yes	—
136	C₇×#121	C₂³	1	4	yes	—
137	C₄×C₇×Q₈	—	2	2	no	—
138	C₄×C₇×Q₈	C₂³	1	4	yes	—
139	C₄×C₇×D₄	—	2	8	no	—
140	C₄×C₇×D₄	—	2	8	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	D₄	1	4	yes	—
143	C₄×C₇×D₄	C₂³	1	4	yes	—
144	C₄×C₇×D₄	C₂³	1	4	yes	—
145	C₇×#117	—	2	2	no	—
146	C₇×#117	C₂³	1	4	yes	—
147	C₂×C₇×C₄⋊C₄	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	—	2	2	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₇	—	2	1	no	—
167	C₂×C₄²×C₇	—	2	1	no	—
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	4	yes	—
170	C₇×#107	C₂³	1	4	yes	—
171	C₇×#106	C₂³	1	4	yes	—
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×#103	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#103	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×#102	C₂³	1	4	yes	—
180	C₇×#102	C₂³	1	4	yes	—
181	C₇×#102	C₂³	1	4	yes	—
182	C₇×#102	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₇×#97	C₂³	1	4	yes	—
186	C₂×#553	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#550	C₂×C₇	1	1	yes	characteristic, complemented
188	#3309	C₂×C₇	1	16	yes	direct product factor
189	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#482	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂⁴×C₇	—	2	1	no	—
203	C₂⁴×C₇	—	2	1	no	—
204	C₂⁴×C₇	—	2	1	no	—
205	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
207	C₇×#41	—	2	8	no	—
208	C₇×#41	—	2	8	no	—
209	C₇×#41	—	4	4	no	—
210	C₇×#41	—	4	4	no	—
211	C₇×#41	—	4	8	no	—
212	C₇×#41	—	4	8	no	—
213	C₂×C₇×Q₈	—	2	1	no	—
214	C₂×C₇×Q₈	—	2	2	no	—
215	C₂×C₇×Q₈	#41	1	4	yes	—
216	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
217	C₂×C₇×D₄	—	2	4	no	—
218	C₂×C₇×D₄	—	2	4	no	—
219	C₂×C₇×D₄	—	2	4	no	—
220	C₂×C₇×D₄	—	2	4	no	—
221	C₂×C₇×D₄	—	2	4	no	—
222	C₂×C₇×D₄	—	2	4	no	—
223	C₂×C₇×D₄	—	2	1	no	—
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	1	no	—
226	C₂×C₇×D₄	—	2	1	no	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	2	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	4	2	no	—
235	C₂×C₇×D₄	—	4	4	no	—
236	C₂×C₇×D₄	—	4	4	no	—
237	C₂×C₇×D₄	—	4	4	no	—
238	C₂×C₇×D₄	—	4	4	no	—
239	C₂×C₇×D₄	—	8	2	no	—
240	C₂×C₇×D₄	—	8	2	no	—
241	C₂×C₇×D₄	—	8	2	no	—
242	C₂×C₇×D₄	—	8	2	no	—
243	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
244	C₂×C₇×D₄	C₂⁴	1	2	yes	—
245	C₂×C₇×D₄	C₂⁴	1	2	yes	—
246	C₂×C₇×D₄	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	—	2	1	no	—
248	C₂²×C₄×C₇	—	2	2	no	—
249	C₂²×C₄×C₇	—	2	2	no	—
250	C₂²×C₄×C₇	—	2	2	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	1	no	—
253	C₂²×C₄×C₇	—	2	1	no	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	4	no	—
257	C₂²×C₄×C₇	—	2	4	no	—
258	C₂²×C₄×C₇	—	2	4	no	—
259	C₂²×C₄×C₇	—	2	4	no	—
260	C₂²×C₄×C₇	—	4	4	no	—
261	C₂²×C₄×C₇	—	4	4	no	—
262	C₂²×C₄×C₇	—	8	2	no	—
263	C₂²×C₄×C₇	—	8	2	no	—
264	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₇×SD₁₆	—	2	8	no	—
274	C₇×D₈	—	4	4	no	—
275	C₇×D₈	—	4	4	no	—
276	C₇×M₁₆	—	4	4	no	—
277	C₂×C₇×C₈	—	2	2	no	—
278	C₂×C₇×C₈	—	2	2	no	—
279	C₂×C₇×C₈	—	2	2	no	—
280	C₂×C₇×C₈	—	2	2	no	—
281	C₂×C₇×C₈	—	4	4	no	—
282	C₂×C₇×C₈	C₂⁴	1	2	yes	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₂×C₇×C₈	C₂⁴	1	2	yes	—
285	C₂×C₇×C₈	C₂⁴	1	2	yes	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	—	2	4	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	1	no	—
294	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₇×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	—	2	4	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
306	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
307	C₄²×C₇	—	2	4	no	—
308	C₄²×C₇	—	2	4	no	—
309	C₄²×C₇	C₂×D₄	1	2	yes	—
310	C₄²×C₇	C₂⁴	1	2	yes	—
311	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
312	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
313	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
314	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
315	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
318	#553	—	2	4	no	—
319	#553	C₂²×C₇	1	8	yes	complemented
320	#550	—	2	4	no	—
321	#550	C₂²×C₇	1	8	yes	complemented
322	C₂×#127	—	2	1	no	—
323	C₂×#127	C₂²×C₇	1	1	yes	characteristic
324	C₂×#126	—	2	1	no	—
325	C₂×#125	C₂²×C₇	1	1	yes	characteristic
326	C₂×#123	—	2	1	no	—
327	C₂×#121	—	2	1	no	—
328	C₂×#121	—	2	1	no	—
329	C₂×#121	—	2	1	no	—
330	C₂×#121	C₂²×C₇	1	1	yes	characteristic
331	C₂×#121	C₂²×C₇	1	1	yes	characteristic
332	C₂×#121	C₂²×C₇	1	1	yes	characteristic
333	C₂×#121	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
335	C₂×C₄×D₄	—	2	1	no	—
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
339	C₂×#117	C₂²×C₇	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
341	#490	C₂²×C₇	1	8	yes	complemented
342	#482	C₂²×C₇	1	8	yes	complemented
343	#480	C₂²×C₇	1	8	yes	complemented
344	#479	C₂²×C₇	1	8	yes	complemented
345	#469	C₂²×C₇	1	8	yes	complemented
346	#466	C₂²×C₇	1	8	yes	complemented
347	#459	C₂²×C₇	1	8	yes	complemented
348	#449	C₂²×C₇	1	8	yes	complemented
349	#449	C₂²×C₇	1	8	yes	complemented
350	#440	C₂²×C₇	1	8	yes	complemented
351	#435	C₂²×C₇	1	8	yes	complemented
352	C₂×#107	C₂²×C₇	1	1	yes	characteristic
353	C₂×#107	C₂²×C₇	1	1	yes	characteristic
354	C₂×#106	C₂²×C₇	1	1	yes	characteristic
355	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
356	#417	C₂²×C₇	1	8	yes	complemented
357	#416	C₂²×C₇	1	8	yes	complemented
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic
359	C₂×#103	C₂²×C₇	1	1	yes	characteristic
360	C₂×#103	C₂²×C₇	1	1	yes	characteristic
361	C₂×#102	C₂²×C₇	1	1	yes	characteristic
362	C₂×#102	C₂²×C₇	1	1	yes	characteristic
363	C₂×#102	C₂²×C₇	1	1	yes	characteristic
364	C₂×#102	C₂²×C₇	1	1	yes	characteristic
365	C₂×#102	C₂²×C₇	1	1	yes	characteristic
366	C₂×#102	C₂²×C₇	1	1	yes	characteristic
367	C₂×#102	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×#97	C₂²×C₇	1	1	yes	characteristic
371	C₂³×C₇	—	2	2	no	—
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	—	2	2	no	—
374	C₂³×C₇	—	2	2	no	—
375	C₂³×C₇	—	2	2	no	—
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	4	2	no	—
381	C₂³×C₇	—	4	2	no	—
382	C₂³×C₇	—	4	2	no	—
383	C₂³×C₇	—	4	2	no	—
384	C₂³×C₇	—	4	2	no	—
385	C₂³×C₇	—	4	2	no	—
386	C₂³×C₇	—	4	2	no	—
387	C₂³×C₇	—	4	2	no	—
388	C₂³×C₇	—	4	2	no	—
389	C₂³×C₇	C₂²×D₄	1	2	yes	—
390	C₂³×C₇	C₂²×D₄	1	2	yes	—
391	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
392	C₇×Q₈	—	2	4	no	—
393	C₇×Q₈	—	2	2	no	—
394	C₇×Q₈	C₂×#41	1	4	yes	—
395	C₇×D₄	—	2	2	no	—
396	C₇×D₄	—	2	2	no	—
397	C₇×D₄	—	2	2	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	2	2	no	—
400	C₇×D₄	—	2	2	no	—
401	C₇×D₄	—	4	4	no	—
402	C₇×D₄	—	4	8	no	—
403	C₇×D₄	—	4	8	no	—
404	C₇×D₄	—	4	8	no	—
405	C₇×D₄	—	4	8	no	—
406	C₇×D₄	—	4	2	no	—
407	C₇×D₄	—	4	2	no	—
408	C₇×D₄	—	4	2	no	—
409	C₇×D₄	—	8	4	no	—
410	C₇×D₄	—	8	4	no	—
411	C₇×D₄	—	8	4	no	—
412	C₇×D₄	—	8	4	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	4	no	—
420	C₂×C₄×C₇	—	2	4	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	4	8	no	—
430	C₂×C₄×C₇	—	4	8	no	—
431	C₂×C₄×C₇	—	4	2	no	—
432	C₂×C₄×C₇	—	4	2	no	—
433	C₂×C₄×C₇	—	4	2	no	—
434	C₂×C₄×C₇	—	4	2	no	—
435	C₂×C₄×C₇	—	8	4	no	—
436	C₂×C₄×C₇	—	8	4	no	—
437	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂×#41	1	2	yes	—
443	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
444	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
445	C₇×C₈	—	2	2	no	—
446	C₇×C₈	—	2	2	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	2	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	2	2	no	—
451	C₂×#41	—	2	4	no	—
452	C₂×#41	—	2	4	no	—
453	C₂×#41	—	4	2	no	—
454	C₂×#41	—	4	2	no	—
455	C₂×#41	C₂³×C₇	1	4	yes	—
456	C₂×#41	C₂³×C₇	1	4	yes	—
457	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
476	C₂×SD₁₆	—	2	4	no	—
477	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
478	C₂×D₈	—	4	2	no	—
479	C₂×D₈	—	4	2	no	—
480	C₂×D₈	C₂³×C₇	1	4	yes	—
481	C₂×D₈	C₂³×C₇	1	4	yes	—
482	C₂×M₁₆	—	4	2	no	—
483	C₂×M₁₆	C₂³×C₇	1	4	yes	—
484	C₂²×C₈	—	4	2	no	—
485	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₇	1	4	yes	—
490	#127	—	2	8	no	—
491	#127	—	2	2	no	—
492	#127	C₂³×C₇	1	4	yes	—
493	#126	—	2	8	no	—
494	#125	—	2	2	no	—
495	#125	C₂³×C₇	1	4	yes	—
496	#123	—	2	8	no	—
497	#121	—	2	8	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	8	no	—
503	#121	—	2	8	no	—
504	#121	C₂³×C₇	1	4	yes	—
505	#121	C₂³×C₇	1	4	yes	—
506	#121	C₂³×C₇	1	4	yes	—
507	#121	C₂³×C₇	1	4	yes	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	C₂³×C₇	1	4	yes	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	8	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	C₇×D₄	1	4	yes	—
514	C₄×D₄	C₂³×C₇	1	4	yes	—
515	C₄×D₄	C₂³×C₇	1	4	yes	—
516	#117	—	2	2	no	—
517	#117	C₂³×C₇	1	4	yes	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	—	2	1	no	—
539	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
540	#107	C₂³×C₇	1	4	yes	—
541	#107	C₂³×C₇	1	4	yes	—
542	#106	C₂³×C₇	1	4	yes	—
543	C₄⋊C₈	C₂³×C₇	1	4	yes	—
544	#103	C₂³×C₇	1	4	yes	—
545	#103	C₂³×C₇	1	4	yes	—
546	#103	C₂³×C₇	1	4	yes	—
547	#102	C₂³×C₇	1	4	yes	—
548	#102	C₂³×C₇	1	4	yes	—
549	#102	C₂³×C₇	1	4	yes	—
550	#102	C₂³×C₇	1	4	yes	—
551	#102	C₂³×C₇	1	4	yes	—
552	#102	C₂³×C₇	1	4	yes	—
553	#102	C₂³×C₇	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
556	#97	C₂³×C₇	1	4	yes	—
557	C₂²×C₇	—	2	2	no	—
558	C₂²×C₇	—	2	2	no	—
559	C₂²×C₇	—	2	2	no	—
560	C₂²×C₇	—	2	2	no	—
561	C₂²×C₇	—	2	2	no	—
562	C₂²×C₇	—	2	2	no	—
563	C₂²×C₇	—	4	4	no	—
564	C₂²×C₇	—	4	4	no	—
565	C₂²×C₇	—	4	2	no	—
566	C₂²×C₇	—	4	2	no	—
567	C₂²×C₇	—	4	2	no	—
568	C₂²×C₇	—	4	2	no	—
569	C₂²×C₇	—	4	2	no	—
570	C₂²×C₇	—	4	2	no	—
571	C₂²×C₇	—	4	2	no	—
572	C₂²×C₇	—	4	2	no	—
573	C₂²×C₇	—	4	2	no	—
574	C₂²×C₇	—	8	4	no	—
575	C₂²×C₇	—	8	4	no	—
576	C₂²×C₇	—	8	4	no	—
577	C₂²×C₇	#546	1	2	yes	—
578	C₂²×C₇	#575	1	2	yes	—
579	C₂²×C₇	#576	1	2	yes	—
580	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₇	—	2	2	no	—
582	C₄×C₇	—	2	2	no	—
583	C₄×C₇	—	2	4	no	—
584	C₄×C₇	—	2	2	no	—
585	C₄×C₇	—	2	2	no	—
586	C₄×C₇	—	4	2	no	—
587	C₄×C₇	—	4	2	no	—
588	C₄×C₇	—	4	2	no	—
589	C₄×C₇	—	4	2	no	—
590	C₄×C₇	#546	1	2	yes	—
591	C₄×C₇	C₂²×#41	1	1	yes	characteristic
592	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	1	no	—
596	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
597	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
598	#41	—	2	8	no	—
599	#41	—	2	8	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	8	no	—
603	#41	—	4	8	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	C₇×#41	1	4	yes	—
607	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	8	2	no	—
631	C₂×D₄	—	8	2	no	—
632	C₂×D₄	—	8	2	no	—
633	C₂×D₄	—	8	2	no	—
634	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
635	C₂×D₄	C₂⁴×C₇	1	2	yes	—
636	C₂×D₄	C₂⁴×C₇	1	2	yes	—
637	C₂×D₄	C₂⁴×C₇	1	2	yes	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	8	2	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
656	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
660	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	SD₁₆	—	2	8	no	—
665	D₈	—	4	4	no	—
666	D₈	—	4	4	no	—
667	M₁₆	—	4	4	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	4	4	no	—
673	C₂×C₈	C₂⁴×C₇	1	2	yes	—
674	C₂×C₈	C₂⁴×C₇	1	2	yes	—
675	C₂×C₈	C₂⁴×C₇	1	2	yes	—
676	C₂×C₈	C₂⁴×C₇	1	2	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
697	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	C₂×C₇×D₄	1	2	yes	—
701	C₄²	C₂⁴×C₇	1	2	yes	—
702	C₂×C₇	—	4	2	no	—
703	C₂×C₇	—	4	2	no	—
704	C₂×C₇	—	8	2	no	—
705	C₂×C₇	—	8	2	no	—
706	C₂×C₇	—	8	2	no	—
707	C₂×C₇	#3309	1	4	yes	direct product factor
708	C₂×C₇	C₂×#546	1	1	yes	characteristic
709	C₂×C₇	C₂×#575	1	1	yes	characteristic
710	C₂×C₇	C₂×#576	1	1	yes	characteristic
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	4	2	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	2	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	C₂²×C₇×D₄	1	2	yes	—
730	C₂³	C₂²×C₇×D₄	1	2	yes	—
731	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
732	Q₈	—	2	2	no	—
733	Q₈	—	2	4	no	—
734	Q₈	C₂×C₇×#41	1	4	yes	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	4	4	no	—
742	D₄	—	4	8	no	—
743	D₄	—	4	8	no	—
744	D₄	—	4	8	no	—
745	D₄	—	4	8	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	2	no	—
748	D₄	—	4	2	no	—
749	D₄	—	8	4	no	—
750	D₄	—	8	4	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	4	8	no	—
770	C₂×C₄	—	4	8	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	8	4	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
778	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
779	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
780	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
781	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂×C₇×#41	1	2	yes	—
783	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
784	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
785	C₈	—	2	2	no	—
786	C₈	—	2	2	no	—
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₇	C₂×#3309	1	1	yes	characteristic, direct product factor, Sylow
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	8	4	no	—
808	C₂²	—	8	4	no	—
809	C₂²	—	8	4	no	—
810	C₂²	C₇×#546	1	2	yes	—
811	C₂²	C₇×#575	1	2	yes	—
812	C₂²	C₇×#576	1	2	yes	—
813	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	C₇×#546	1	2	yes	—
824	C₄	C₂²×C₇×#41	1	1	yes	characteristic
825	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	—	4	2	no	—
827	C₂	—	4	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	—	8	2	no	—
831	C₂	C₇×#3309	1	4	yes	direct product factor
832	C₂	C₂×C₇×#546	1	1	yes	characteristic
833	C₂	C₂×C₇×#575	1	1	yes	characteristic
834	C₂	C₂×C₇×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#553	C₂	semidirect
2. C₂×C₇×#550	C₂	semidirect
3. C₇×#3309	C₂	direct (N × H)
4. C₂×C₇×#490	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#480	C₂	semidirect
7. C₂×C₇×#479	C₂	semidirect
8. C₂×C₇×#469	C₂	semidirect
9. C₂×C₇×#466	C₂	semidirect
10. C₂×C₇×#459	C₂	semidirect
11. C₂×C₇×#449	C₂	semidirect
12. C₂×C₇×#449	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₇×#435	C₂	semidirect
15. C₂×C₇×#417	C₂	semidirect
16. C₂×C₇×#416	C₂	semidirect
25. C₇×#553	C₂²	semidirect
27. C₇×#550	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#482	C₂²	semidirect
49. C₇×#480	C₂²	semidirect
50. C₇×#479	C₂²	semidirect
51. C₇×#469	C₂²	semidirect
52. C₇×#466	C₂²	semidirect
53. C₇×#459	C₂²	semidirect
54. C₇×#449	C₂²	semidirect
55. C₇×#449	C₂²	semidirect
56. C₇×#440	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
62. C₇×#417	C₂²	semidirect
63. C₇×#416	C₂²	semidirect
77. C₂×#3309	C₇	direct (N × H)
186. C₂×#553	C₂×C₇	semidirect
187. C₂×#550	C₂×C₇	semidirect
188. #3309	C₂×C₇	direct (N × H)
189. C₂×#490	C₂×C₇	semidirect
190. C₂×#482	C₂×C₇	semidirect
191. C₂×#480	C₂×C₇	semidirect
192. C₂×#479	C₂×C₇	semidirect
193. C₂×#469	C₂×C₇	semidirect
194. C₂×#466	C₂×C₇	semidirect
195. C₂×#459	C₂×C₇	semidirect
196. C₂×#449	C₂×C₇	semidirect
197. C₂×#449	C₂×C₇	semidirect
198. C₂×#440	C₂×C₇	semidirect
199. C₂×#435	C₂×C₇	semidirect
200. C₂×#417	C₂×C₇	semidirect
201. C₂×#416	C₂×C₇	semidirect
319. #553	C₂²×C₇	semidirect
321. #550	C₂²×C₇	semidirect
341. #490	C₂²×C₇	semidirect
342. #482	C₂²×C₇	semidirect
343. #480	C₂²×C₇	semidirect
344. #479	C₂²×C₇	semidirect
345. #469	C₂²×C₇	semidirect
346. #466	C₂²×C₇	semidirect
347. #459	C₂²×C₇	semidirect
348. #449	C₂²×C₇	semidirect
349. #449	C₂²×C₇	semidirect
350. #440	C₂²×C₇	semidirect
351. #435	C₂²×C₇	semidirect
356. #417	C₂²×C₇	semidirect
357. #416	C₂²×C₇	semidirect
707. C₂×C₇	#3309	direct (N × H)
789. C₇	C₂×#3309	direct (N × H)
831. C₂	C₇×#3309	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#553	2
C₂×C₇×#550	2
C₇×#3309	2
C₂×C₇×#490	2
C₂×C₇×#482	2
C₂×C₇×#480	2
C₂×C₇×#479	2
C₂×C₇×#469	2
C₂×C₇×#466	2
C₂×C₇×#459	2
C₂×C₇×#449	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×C₇×#417	2
C₂×C₇×#416	2
C₂×#3309	7

Subgroups — C2×C7×#3309 #13238353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3309 #13238353