Subgroups — C₂×C₇×#3225 #13238012

Order 1792.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3225	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic
14	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
27	C₇×#542	—	2	4	no	—
28	C₇×#542	C₂²	1	8	yes	complemented
29	C₇×#536	—	2	4	no	—
30	C₇×#536	C₂²	1	8	yes	complemented
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#126	—	2	1	no	—
35	C₂×C₇×#124	—	2	1	no	—
36	C₂×C₇×#124	C₂²	1	1	yes	characteristic
37	C₂×C₇×#124	C₂²	1	1	yes	characteristic
38	C₂×C₇×#124	C₂²	1	1	yes	characteristic
39	C₂×C₇×#123	—	2	1	no	—
40	C₂×C₇×#123	—	2	1	no	—
41	C₂×C₇×#123	—	2	1	no	—
42	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×#121	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₇×#117	C₂²	1	1	yes	characteristic
50	C₇×#497	C₂²	1	8	yes	complemented
51	C₇×#495	C₂²	1	8	yes	complemented
52	C₇×#489	C₂²	1	8	yes	complemented
53	C₇×#487	C₂²	1	8	yes	complemented
54	C₇×#464	C₂²	1	8	yes	complemented
55	C₇×#463	C₂²	1	8	yes	complemented
56	C₇×#462	C₂²	1	8	yes	complemented
57	C₇×#461	C₂²	1	8	yes	complemented
58	C₇×#452	C₂²	1	8	yes	complemented
59	C₇×#451	C₂²	1	8	yes	complemented
60	C₇×#449	C₂²	1	8	yes	—
61	C₇×#448	C₂²	1	8	yes	complemented
62	C₇×#433	C₂²	1	8	yes	complemented
63	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
68	C₂×C₇×#103	C₂²	1	1	yes	characteristic
69	C₂×C₇×#103	C₂²	1	1	yes	characteristic
70	C₂×C₇×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
77	C₂×#3225	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₇×#41	—	2	2	no	—
79	C₂×C₇×#41	—	4	2	no	—
80	C₂×C₇×#41	—	4	2	no	—
81	C₂×C₇×#41	C₂³	1	4	yes	—
82	C₂²×C₇×Q₈	—	2	1	no	—
83	C₂²×C₇×Q₈	—	2	2	no	—
84	C₂²×C₇×Q₈	—	2	1	no	—
85	C₂²×C₇×Q₈	—	4	2	no	—
86	C₂²×C₇×Q₈	—	4	2	no	—
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×Q₈	C₂³	1	4	yes	—
92	C₂²×C₇×D₄	—	2	1	no	—
93	C₂²×C₇×D₄	—	2	1	no	—
94	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₇	—	2	1	no	—
97	C₂³×C₄×C₇	—	2	1	no	—
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₇×Q₁₆	—	4	2	no	—
101	C₂×C₇×Q₁₆	—	4	2	no	—
102	C₂×C₇×Q₁₆	—	4	2	no	—
103	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₇×SD₁₆	—	4	2	no	—
107	C₂×C₇×SD₁₆	—	4	2	no	—
108	C₂×C₇×SD₁₆	—	4	2	no	—
109	C₂×C₇×SD₁₆	—	4	2	no	—
110	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×D₈	—	4	2	no	—
115	C₂×C₇×D₈	C₂³	1	4	yes	—
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
119	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
120	C₇×C₄⋊Q₈	—	2	2	no	—
121	C₇×C₄⋊Q₈	—	2	2	no	—
122	C₇×C₄⋊Q₈	—	2	2	no	—
123	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
126	C₇×#126	—	2	8	no	—
127	C₇×#124	—	2	8	no	—
128	C₇×#124	—	2	2	no	—
129	C₇×#124	—	2	2	no	—
130	C₇×#124	—	2	2	no	—
131	C₇×#124	C₂³	1	4	yes	—
132	C₇×#124	C₂³	1	4	yes	—
133	C₇×#124	C₂³	1	4	yes	—
134	C₇×#123	—	2	8	no	—
135	C₇×#123	—	2	8	no	—
136	C₇×#123	—	2	8	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	8	no	—
139	C₇×C₂²⋊Q₈	—	2	8	no	—
140	C₇×C₂²⋊Q₈	—	2	8	no	—
141	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	C₂³	1	4	yes	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	C₂³	1	4	yes	—
146	C₄×C₇×D₄	—	2	2	no	—
147	C₄×C₇×D₄	C₂³	1	4	yes	—
148	C₇×#117	D₄	1	4	yes	—
149	C₇×#117	C₂³	1	4	yes	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	—	2	1	no	—
153	C₂×C₇×C₄⋊C₄	—	2	1	no	—
154	C₂×C₇×C₄⋊C₄	—	2	1	no	—
155	C₂×C₇×C₄⋊C₄	—	2	1	no	—
156	C₂×C₇×C₄⋊C₄	—	2	1	no	—
157	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
167	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
172	C₂×C₄²×C₇	—	2	1	no	—
173	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₇×C₄⋊C₈	C₂³	1	4	yes	—
176	C₇×C₄⋊C₈	C₂³	1	4	yes	—
177	C₇×#103	C₂³	1	4	yes	—
178	C₇×#103	C₂³	1	4	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	4	yes	—
183	C₇×#102	C₂³	1	4	yes	—
184	C₇×#102	C₂³	1	4	yes	—
185	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₇×#97	C₂³	1	4	yes	—
188	C₄×C₇×C₈	C₂³	1	4	yes	—
189	C₂×#542	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
191	#3225	C₂×C₇	1	16	yes	direct product factor
192	C₂×#497	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#495	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#449	C₂×C₇	1	1	yes	characteristic
202	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#448	C₂×C₇	1	1	yes	characteristic, complemented
204	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
205	C₂⁴×C₇	—	2	1	no	—
206	C₂⁴×C₇	—	2	1	no	—
207	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
208	C₇×#41	—	4	4	no	—
209	C₇×#41	—	4	4	no	—
210	C₇×#41	—	4	8	no	—
211	C₂×C₇×Q₈	—	2	1	no	—
212	C₂×C₇×Q₈	—	2	4	no	—
213	C₂×C₇×Q₈	—	2	1	no	—
214	C₂×C₇×Q₈	—	2	1	no	—
215	C₂×C₇×Q₈	—	2	1	no	—
216	C₂×C₇×Q₈	—	2	4	no	—
217	C₂×C₇×Q₈	—	2	2	no	—
218	C₂×C₇×Q₈	—	2	2	no	—
219	C₂×C₇×Q₈	—	2	2	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	—	2	2	no	—
222	C₂×C₇×Q₈	—	2	2	no	—
223	C₂×C₇×Q₈	—	2	2	no	—
224	C₂×C₇×Q₈	—	2	2	no	—
225	C₂×C₇×Q₈	—	4	4	no	—
226	C₂×C₇×Q₈	—	4	4	no	—
227	C₂×C₇×Q₈	—	4	4	no	—
228	C₂×C₇×Q₈	—	4	8	no	—
229	C₂×C₇×Q₈	—	8	2	no	—
230	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
231	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
232	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
233	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	—	2	4	no	—
236	C₂×C₇×D₄	—	2	1	no	—
237	C₂×C₇×D₄	—	2	1	no	—
238	C₂×C₇×D₄	—	2	2	no	—
239	C₂×C₇×D₄	—	2	2	no	—
240	C₂×C₇×D₄	—	2	2	no	—
241	C₂×C₇×D₄	—	2	2	no	—
242	C₂×C₇×D₄	—	4	4	no	—
243	C₂×C₇×D₄	—	8	2	no	—
244	C₂×C₇×D₄	C₂⁴	1	2	yes	—
245	C₂×C₇×D₄	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	2	2	no	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	1	no	—
250	C₂²×C₄×C₇	—	2	1	no	—
251	C₂²×C₄×C₇	—	2	1	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	4	no	—
256	C₂²×C₄×C₇	—	2	4	no	—
257	C₂²×C₄×C₇	—	4	4	no	—
258	C₂²×C₄×C₇	—	4	4	no	—
259	C₂²×C₄×C₇	—	8	2	no	—
260	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₇×Q₁₆	—	4	4	no	—
269	C₇×Q₁₆	—	4	4	no	—
270	C₇×Q₁₆	—	4	4	no	—
271	C₇×SD₁₆	—	4	4	no	—
272	C₇×SD₁₆	—	4	4	no	—
273	C₇×SD₁₆	—	4	4	no	—
274	C₇×SD₁₆	—	4	4	no	—
275	C₇×D₈	—	4	4	no	—
276	C₂×C₇×C₈	—	2	2	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	C₂⁴	1	2	yes	—
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	2	yes	—
283	C₂×C₇×C₈	C₂⁴	1	2	yes	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	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	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
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×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
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	—	2	4	no	—
306	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
307	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
308	C₄²×C₇	—	2	4	no	—
309	C₄²×C₇	C₂×D₄	1	2	yes	—
310	C₄²×C₇	C₂×D₄	1	2	yes	—
311	C₄²×C₇	C₂⁴	1	2	yes	—
312	C₄²×C₇	C₂⁴	1	2	yes	—
313	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
314	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
315	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
316	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
317	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
318	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
319	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
320	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
321	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
322	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
323	#542	—	2	4	no	—
324	#542	C₂²×C₇	1	8	yes	complemented
325	#536	—	2	4	no	—
326	#536	C₂²×C₇	1	8	yes	complemented
327	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
328	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
329	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
330	C₂×#126	—	2	1	no	—
331	C₂×#124	—	2	1	no	—
332	C₂×#124	C₂²×C₇	1	1	yes	characteristic
333	C₂×#124	C₂²×C₇	1	1	yes	characteristic
334	C₂×#124	C₂²×C₇	1	1	yes	characteristic
335	C₂×#123	—	2	1	no	—
336	C₂×#123	—	2	1	no	—
337	C₂×#123	—	2	1	no	—
338	C₂×C₂²⋊Q₈	—	2	1	no	—
339	C₂×C₂²⋊Q₈	—	2	1	no	—
340	C₂×C₂²⋊Q₈	—	2	1	no	—
341	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
342	C₂×#121	C₂²×C₇	1	1	yes	characteristic
343	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
345	C₂×#117	C₂²×C₇	1	1	yes	characteristic
346	#497	C₂²×C₇	1	8	yes	complemented
347	#495	C₂²×C₇	1	8	yes	complemented
348	#489	C₂²×C₇	1	8	yes	complemented
349	#487	C₂²×C₇	1	8	yes	complemented
350	#464	C₂²×C₇	1	8	yes	complemented
351	#463	C₂²×C₇	1	8	yes	complemented
352	#462	C₂²×C₇	1	8	yes	complemented
353	#461	C₂²×C₇	1	8	yes	complemented
354	#452	C₂²×C₇	1	8	yes	complemented
355	#451	C₂²×C₇	1	8	yes	complemented
356	#449	C₂²×C₇	1	8	yes	—
357	#448	C₂²×C₇	1	8	yes	complemented
358	#433	C₂²×C₇	1	8	yes	complemented
359	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
360	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
361	C₂×#103	C₂²×C₇	1	1	yes	characteristic
362	C₂×#103	C₂²×C₇	1	1	yes	characteristic
363	C₂×#103	C₂²×C₇	1	1	yes	characteristic
364	C₂×#103	C₂²×C₇	1	1	yes	characteristic
365	C₂×#103	C₂²×C₇	1	1	yes	characteristic
366	C₂×#103	C₂²×C₇	1	1	yes	characteristic
367	C₂×#102	C₂²×C₇	1	1	yes	characteristic
368	C₂×#102	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×#97	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
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	—	4	2	no	—
379	C₂³×C₇	—	4	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	C₂²×D₄	1	2	yes	—
385	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₇×Q₈	—	2	2	no	—
387	C₇×Q₈	—	2	2	no	—
388	C₇×Q₈	—	2	2	no	—
389	C₇×Q₈	—	2	2	no	—
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	2	2	no	—
392	C₇×Q₈	—	2	2	no	—
393	C₇×Q₈	—	2	2	no	—
394	C₇×Q₈	—	4	8	no	—
395	C₇×Q₈	—	4	2	no	—
396	C₇×Q₈	—	4	2	no	—
397	C₇×Q₈	—	4	2	no	—
398	C₇×Q₈	—	4	2	no	—
399	C₇×Q₈	—	8	4	no	—
400	C₇×D₄	—	2	2	no	—
401	C₇×D₄	—	2	2	no	—
402	C₇×D₄	—	2	2	no	—
403	C₇×D₄	—	2	2	no	—
404	C₇×D₄	—	4	8	no	—
405	C₇×D₄	—	4	2	no	—
406	C₇×D₄	—	4	2	no	—
407	C₇×D₄	—	8	4	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	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	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	4	8	no	—
423	C₂×C₄×C₇	—	4	8	no	—
424	C₂×C₄×C₇	—	4	2	no	—
425	C₂×C₄×C₇	—	4	2	no	—
426	C₂×C₄×C₇	—	4	2	no	—
427	C₂×C₄×C₇	—	4	2	no	—
428	C₂×C₄×C₇	—	4	2	no	—
429	C₂×C₄×C₇	—	4	2	no	—
430	C₂×C₄×C₇	—	8	4	no	—
431	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
439	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
440	C₇×C₈	—	2	2	no	—
441	C₇×C₈	—	2	2	no	—
442	C₇×C₈	—	2	2	no	—
443	C₇×C₈	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	4	2	no	—
446	C₂×#41	—	4	2	no	—
447	C₂×#41	C₂³×C₇	1	4	yes	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	—	4	2	no	—
452	C₂²×Q₈	—	4	2	no	—
453	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₇	1	4	yes	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
466	C₂×Q₁₆	—	4	2	no	—
467	C₂×Q₁₆	—	4	2	no	—
468	C₂×Q₁₆	—	4	2	no	—
469	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
470	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
471	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
472	C₂×SD₁₆	—	4	2	no	—
473	C₂×SD₁₆	—	4	2	no	—
474	C₂×SD₁₆	—	4	2	no	—
475	C₂×SD₁₆	—	4	2	no	—
476	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
477	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
479	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
480	C₂×D₈	—	4	2	no	—
481	C₂×D₈	C₂³×C₇	1	4	yes	—
482	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
490	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
492	#126	—	2	8	no	—
493	#124	—	2	8	no	—
494	#124	—	2	2	no	—
495	#124	—	2	2	no	—
496	#124	—	2	2	no	—
497	#124	C₂³×C₇	1	4	yes	—
498	#124	C₂³×C₇	1	4	yes	—
499	#124	C₂³×C₇	1	4	yes	—
500	#123	—	2	8	no	—
501	#123	—	2	8	no	—
502	#123	—	2	8	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	8	no	—
505	C₂²⋊Q₈	—	2	8	no	—
506	C₂²⋊Q₈	—	2	8	no	—
507	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
508	#121	—	2	2	no	—
509	#121	C₂³×C₇	1	4	yes	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	C₂³×C₇	1	4	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	C₂³×C₇	1	4	yes	—
514	#117	C₇×D₄	1	4	yes	—
515	#117	C₂³×C₇	1	4	yes	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	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	C₇×D₄	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
536	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
538	C₂×C₄²	—	2	1	no	—
539	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₇	1	4	yes	—
542	C₄⋊C₈	C₂³×C₇	1	4	yes	—
543	#103	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	#103	C₂³×C₇	1	4	yes	—
548	#103	C₂³×C₇	1	4	yes	—
549	#102	C₂³×C₇	1	4	yes	—
550	#102	C₂³×C₇	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
553	#97	C₂³×C₇	1	4	yes	—
554	C₄×C₈	C₂³×C₇	1	4	yes	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	2	no	—
558	C₂²×C₇	—	4	4	no	—
559	C₂²×C₇	—	4	2	no	—
560	C₂²×C₇	—	4	2	no	—
561	C₂²×C₇	—	4	2	no	—
562	C₂²×C₇	—	4	2	no	—
563	C₂²×C₇	—	4	2	no	—
564	C₂²×C₇	—	4	2	no	—
565	C₂²×C₇	—	8	4	no	—
566	C₂²×C₇	—	8	4	no	—
567	C₂²×C₇	#535	1	2	yes	—
568	C₂²×C₇	#577	1	2	yes	—
569	C₂²×C₇	#578	1	2	yes	—
570	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₇	—	2	2	no	—
572	C₄×C₇	—	2	2	no	—
573	C₄×C₇	—	2	2	no	—
574	C₄×C₇	—	2	2	no	—
575	C₄×C₇	—	2	2	no	—
576	C₄×C₇	—	4	2	no	—
577	C₄×C₇	—	4	2	no	—
578	C₄×C₇	—	4	2	no	—
579	C₄×C₇	—	4	2	no	—
580	C₄×C₇	—	4	2	no	—
581	C₄×C₇	—	4	2	no	—
582	C₄×C₇	#535	1	2	yes	—
583	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
588	#41	—	4	4	no	—
589	#41	—	4	4	no	—
590	#41	—	4	8	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	4	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	—	4	4	no	—
608	C₂×Q₈	—	4	8	no	—
609	C₂×Q₈	—	8	2	no	—
610	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
611	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	8	2	no	—
624	C₂×D₄	C₂⁴×C₇	1	2	yes	—
625	C₂×D₄	C₂⁴×C₇	1	2	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
643	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
644	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
645	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
648	Q₁₆	—	4	4	no	—
649	Q₁₆	—	4	4	no	—
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	4	no	—
654	SD₁₆	—	4	4	no	—
655	D₈	—	4	4	no	—
656	C₂×C₈	—	2	2	no	—
657	C₂×C₈	—	2	2	no	—
658	C₂×C₈	—	2	2	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	C₂⁴×C₇	1	2	yes	—
661	C₂×C₈	C₂⁴×C₇	1	2	yes	—
662	C₂×C₈	C₂⁴×C₇	1	2	yes	—
663	C₂×C₈	C₂⁴×C₇	1	2	yes	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
674	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
687	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
688	C₄²	—	2	4	no	—
689	C₄²	C₂×C₇×D₄	1	2	yes	—
690	C₄²	C₂×C₇×D₄	1	2	yes	—
691	C₄²	C₂⁴×C₇	1	2	yes	—
692	C₄²	C₂⁴×C₇	1	2	yes	—
693	C₂×C₇	—	4	2	no	—
694	C₂×C₇	—	8	2	no	—
695	C₂×C₇	—	8	2	no	—
696	C₂×C₇	#3225	1	4	yes	direct product factor
697	C₂×C₇	C₂×#535	1	1	yes	characteristic
698	C₂×C₇	C₂×#577	1	1	yes	characteristic
699	C₂×C₇	C₂×#578	1	1	yes	characteristic
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	C₂²×C₇×D₄	1	2	yes	—
712	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	8	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	8	4	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
759	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
760	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
761	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
762	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
763	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
764	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
766	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₇	C₂×#3225	1	1	yes	characteristic, direct product factor, Sylow
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	8	4	no	—
783	C₂²	—	8	4	no	—
784	C₂²	C₇×#535	1	2	yes	—
785	C₂²	C₇×#577	1	2	yes	—
786	C₂²	C₇×#578	1	2	yes	—
787	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	C₇×#535	1	2	yes	—
800	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
801	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	2	no	—
805	C₂	C₇×#3225	1	4	yes	direct product factor
806	C₂	C₂×C₇×#535	1	1	yes	characteristic
807	C₂	C₂×C₇×#577	1	1	yes	characteristic
808	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#542	C₂	semidirect
2. C₂×C₇×#536	C₂	semidirect
3. C₇×#3225	C₂	direct (N × H)
4. C₂×C₇×#497	C₂	semidirect
5. C₂×C₇×#495	C₂	semidirect
6. C₂×C₇×#489	C₂	semidirect
7. C₂×C₇×#487	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#462	C₂	semidirect
10. C₂×C₇×#463	C₂	semidirect
11. C₂×C₇×#461	C₂	semidirect
12. C₂×C₇×#452	C₂	semidirect
14. C₂×C₇×#451	C₂	semidirect
15. C₂×C₇×#448	C₂	semidirect
16. C₂×C₇×#433	C₂	semidirect
28. C₇×#542	C₂²	semidirect
30. C₇×#536	C₂²	semidirect
50. C₇×#497	C₂²	semidirect
51. C₇×#495	C₂²	semidirect
52. C₇×#489	C₂²	semidirect
53. C₇×#487	C₂²	semidirect
54. C₇×#464	C₂²	semidirect
55. C₇×#463	C₂²	semidirect
56. C₇×#462	C₂²	semidirect
57. C₇×#461	C₂²	semidirect
58. C₇×#452	C₂²	semidirect
59. C₇×#451	C₂²	semidirect
61. C₇×#448	C₂²	semidirect
62. C₇×#433	C₂²	semidirect
77. C₂×#3225	C₇	direct (N × H)
189. C₂×#542	C₂×C₇	semidirect
190. C₂×#536	C₂×C₇	semidirect
191. #3225	C₂×C₇	direct (N × H)
192. C₂×#497	C₂×C₇	semidirect
193. C₂×#495	C₂×C₇	semidirect
194. C₂×#489	C₂×C₇	semidirect
195. C₂×#487	C₂×C₇	semidirect
196. C₂×#464	C₂×C₇	semidirect
197. C₂×#462	C₂×C₇	semidirect
198. C₂×#463	C₂×C₇	semidirect
199. C₂×#461	C₂×C₇	semidirect
200. C₂×#452	C₂×C₇	semidirect
202. C₂×#451	C₂×C₇	semidirect
203. C₂×#448	C₂×C₇	semidirect
204. C₂×#433	C₂×C₇	semidirect
324. #542	C₂²×C₇	semidirect
326. #536	C₂²×C₇	semidirect
346. #497	C₂²×C₇	semidirect
347. #495	C₂²×C₇	semidirect
348. #489	C₂²×C₇	semidirect
349. #487	C₂²×C₇	semidirect
350. #464	C₂²×C₇	semidirect
351. #463	C₂²×C₇	semidirect
352. #462	C₂²×C₇	semidirect
353. #461	C₂²×C₇	semidirect
354. #452	C₂²×C₇	semidirect
355. #451	C₂²×C₇	semidirect
357. #448	C₂²×C₇	semidirect
358. #433	C₂²×C₇	semidirect
696. C₂×C₇	#3225	direct (N × H)
771. C₇	C₂×#3225	direct (N × H)
805. C₂	C₇×#3225	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×#542	2
C₂×C₇×#536	2
C₇×#3225	2
C₂×C₇×#497	2
C₂×C₇×#495	2
C₂×C₇×#489	2
C₂×C₇×#487	2
C₂×C₇×#464	2
C₂×C₇×#462	2
C₂×C₇×#463	2
C₂×C₇×#461	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂×C₇×#451	2
C₂×C₇×#448	2
C₂×C₇×#433	2
C₂×#3225	7

Subgroups — C2×C7×#3225 #13238012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3225 #13238012