Subgroups — C₂×C₇×#3224 #13238009

Order 1792.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 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×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3224	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#496	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×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#459	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, complemented
14	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#447	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×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
26	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₇×#542	—	2	4	no	—
28	C₇×#542	C₂²	1	8	yes	complemented
29	C₇×#535	—	2	4	no	—
30	C₇×#535	C₂²	1	8	yes	complemented
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×#127	C₂²	1	1	yes	characteristic
33	C₂×C₇×#127	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, complemented
39	C₂×C₇×#123	—	2	1	no	—
40	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
41	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₇×#121	—	2	1	no	—
43	C₂×C₇×#121	—	2	1	no	—
44	C₂×C₇×#121	C₂²	1	1	yes	characteristic
45	C₂×C₇×#120	—	2	1	no	—
46	C₂×C₇×#120	—	2	1	no	—
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₇×#117	C₂²	1	1	yes	characteristic
50	C₇×#496	C₂²	1	8	yes	complemented
51	C₇×#495	C₂²	1	8	yes	complemented
52	C₇×#489	C₂²	1	8	yes	complemented
53	C₇×#486	C₂²	1	8	yes	complemented
54	C₇×#464	C₂²	1	8	yes	complemented
55	C₇×#463	C₂²	1	8	yes	complemented
56	C₇×#460	C₂²	1	8	yes	complemented
57	C₇×#459	C₂²	1	8	yes	complemented
58	C₇×#452	C₂²	1	8	yes	complemented
59	C₇×#450	C₂²	1	8	yes	complemented
60	C₇×#449	C₂²	1	8	yes	complemented
61	C₇×#447	C₂²	1	8	yes	complemented
62	C₇×#433	C₂²	1	8	yes	complemented
63	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
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, complemented
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
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, complemented
76	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
77	C₂×#3224	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₇	—	2	1	no	—
79	C₂×C₇×#41	—	2	2	no	—
80	C₂×C₇×#41	—	4	2	no	—
81	C₂×C₇×#41	—	4	2	no	—
82	C₂×C₇×#41	C₂³	1	4	yes	—
83	C₂²×C₇×Q₈	—	2	1	no	—
84	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×D₄	—	2	1	no	—
87	C₂²×C₇×D₄	—	2	1	no	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	—	2	2	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	—	4	2	no	—
95	C₂²×C₇×D₄	—	4	2	no	—
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	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	C₂³	1	4	yes	—
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₂³×C₄×C₇	—	2	1	no	—
103	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
104	C₂×C₇×Q₁₆	—	4	2	no	—
105	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
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	complemented
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
114	C₂×C₇×D₈	—	4	2	no	—
115	C₂×C₇×D₈	—	4	2	no	—
116	C₂×C₇×D₈	—	4	2	no	—
117	C₂×C₇×D₈	C₂³	1	4	yes	—
118	C₂×C₇×D₈	C₂³	1	4	yes	—
119	C₂×C₇×D₈	C₂³	1	4	yes	complemented
120	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
122	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
123	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊Q₈	—	2	2	no	—
125	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
126	C₇×#127	—	2	2	no	—
127	C₇×#127	—	2	2	no	—
128	C₇×#127	C₂³	1	4	yes	—
129	C₇×#127	C₂³	1	4	yes	—
130	C₇×#126	—	2	8	no	—
131	C₇×#124	—	2	8	no	—
132	C₇×#124	—	2	2	no	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	—	2	2	no	—
135	C₇×#124	C₂³	1	4	yes	—
136	C₇×#124	C₂³	1	4	yes	—
137	C₇×#124	C₂³	1	4	yes	complemented
138	C₇×#123	—	2	8	no	—
139	C₇×C₂²⋊Q₈	—	2	2	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	—	2	8	no	—
144	C₇×#121	—	2	8	no	—
145	C₇×#121	C₂³	1	4	yes	—
146	C₇×#120	—	2	8	no	—
147	C₇×#120	—	2	8	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	C₂³	1	4	yes	complemented
152	C₇×#117	D₄	1	4	yes	—
153	C₇×#117	C₂³	1	4	yes	—
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	complemented
176	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
177	C₇×#103	C₂³	1	4	yes	complemented
178	C₇×#103	C₂³	1	4	yes	complemented
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×#102	C₂³	1	4	yes	complemented
184	C₇×#102	C₂³	1	4	yes	complemented
185	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₇×#97	C₂³	1	4	yes	complemented
188	C₄×C₇×C₈	C₂³	1	4	yes	complemented
189	C₂×#542	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
191	#3224	C₂×C₇	1	16	yes	direct product factor
192	C₂×#496	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×#486	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#459	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, complemented
202	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
203	C₂×#447	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	—	2	1	no	—
208	C₂⁴×C₇	—	2	1	no	—
209	C₂⁴×C₇	—	2	4	no	—
210	C₂⁴×C₇	—	4	4	no	—
211	C₂⁴×C₇	—	8	2	no	—
212	C₂⁴×C₇	—	8	2	no	—
213	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
214	C₇×#41	—	4	4	no	—
215	C₇×#41	—	4	4	no	—
216	C₇×#41	—	4	8	no	—
217	C₂×C₇×Q₈	—	2	1	no	—
218	C₂×C₇×Q₈	—	2	1	no	—
219	C₂×C₇×Q₈	—	2	4	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	—	8	2	no	—
225	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
226	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	1	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	1	no	—
232	C₂×C₇×D₄	—	2	1	no	—
233	C₂×C₇×D₄	—	2	1	no	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	—	2	4	no	—
236	C₂×C₇×D₄	—	2	4	no	—
237	C₂×C₇×D₄	—	2	4	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	—	2	2	no	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	2	no	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	4	4	no	—
247	C₂×C₇×D₄	—	4	4	no	—
248	C₂×C₇×D₄	—	4	4	no	—
249	C₂×C₇×D₄	—	4	8	no	—
250	C₂×C₇×D₄	—	4	4	no	—
251	C₂×C₇×D₄	—	8	2	no	—
252	C₂×C₇×D₄	—	8	2	no	—
253	C₂×C₇×D₄	—	8	2	no	—
254	C₂×C₇×D₄	—	8	2	no	—
255	C₂×C₇×D₄	—	8	2	no	—
256	C₂×C₇×D₄	C₂⁴	1	2	yes	—
257	C₂×C₇×D₄	C₂⁴	1	2	yes	—
258	C₂×C₇×D₄	C₂⁴	1	2	yes	—
259	C₂×C₇×D₄	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	1	no	—
263	C₂²×C₄×C₇	—	2	1	no	—
264	C₂²×C₄×C₇	—	2	1	no	—
265	C₂²×C₄×C₇	—	2	1	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	4	4	no	—
269	C₂²×C₄×C₇	—	8	2	no	—
270	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₇×Q₁₆	—	4	4	no	—
279	C₇×SD₁₆	—	4	4	no	—
280	C₇×SD₁₆	—	4	4	no	—
281	C₇×SD₁₆	—	4	4	no	—
282	C₇×SD₁₆	—	4	4	no	—
283	C₇×D₈	—	4	4	no	—
284	C₇×D₈	—	4	4	no	—
285	C₇×D₈	—	4	4	no	—
286	C₂×C₇×C₈	—	2	2	no	—
287	C₂×C₇×C₈	—	2	2	no	—
288	C₂×C₇×C₈	—	2	2	no	—
289	C₂×C₇×C₈	—	2	2	no	—
290	C₂×C₇×C₈	C₂⁴	1	2	yes	—
291	C₂×C₇×C₈	C₂⁴	1	2	yes	—
292	C₂×C₇×C₈	C₂⁴	1	2	yes	—
293	C₂×C₇×C₈	C₂⁴	1	2	yes	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	—	2	1	no	—
299	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
300	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	4	no	—
312	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
313	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
314	C₄²×C₇	—	2	4	no	—
315	C₄²×C₇	C₂×D₄	1	2	yes	—
316	C₄²×C₇	C₂×D₄	1	2	yes	—
317	C₄²×C₇	C₂⁴	1	2	yes	—
318	C₄²×C₇	C₂⁴	1	2	yes	—
319	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
320	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
321	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
322	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
323	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
324	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
325	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
326	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
327	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
328	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
329	#542	—	2	4	no	—
330	#542	C₂²×C₇	1	8	yes	complemented
331	#535	—	2	4	no	—
332	#535	C₂²×C₇	1	8	yes	complemented
333	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
334	C₂×#127	C₂²×C₇	1	1	yes	characteristic
335	C₂×#127	C₂²×C₇	1	1	yes	characteristic
336	C₂×#126	—	2	1	no	—
337	C₂×#124	—	2	1	no	—
338	C₂×#124	C₂²×C₇	1	1	yes	characteristic
339	C₂×#124	C₂²×C₇	1	1	yes	characteristic
340	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
341	C₂×#123	—	2	1	no	—
342	C₂×C₂²⋊Q₈	—	2	1	no	—
343	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
344	C₂×#121	—	2	1	no	—
345	C₂×#121	—	2	1	no	—
346	C₂×#121	C₂²×C₇	1	1	yes	characteristic
347	C₂×#120	—	2	1	no	—
348	C₂×#120	—	2	1	no	—
349	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
351	C₂×#117	C₂²×C₇	1	1	yes	characteristic
352	#496	C₂²×C₇	1	8	yes	complemented
353	#495	C₂²×C₇	1	8	yes	complemented
354	#489	C₂²×C₇	1	8	yes	complemented
355	#486	C₂²×C₇	1	8	yes	complemented
356	#464	C₂²×C₇	1	8	yes	complemented
357	#463	C₂²×C₇	1	8	yes	complemented
358	#460	C₂²×C₇	1	8	yes	complemented
359	#459	C₂²×C₇	1	8	yes	complemented
360	#452	C₂²×C₇	1	8	yes	complemented
361	#450	C₂²×C₇	1	8	yes	complemented
362	#449	C₂²×C₇	1	8	yes	complemented
363	#447	C₂²×C₇	1	8	yes	complemented
364	#433	C₂²×C₇	1	8	yes	complemented
365	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×#102	C₂²×C₇	1	1	yes	characteristic
370	C₂×#102	C₂²×C₇	1	1	yes	characteristic
371	C₂×#102	C₂²×C₇	1	1	yes	characteristic
372	C₂×#102	C₂²×C₇	1	1	yes	characteristic
373	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
377	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	2	2	no	—
382	C₂³×C₇	—	2	2	no	—
383	C₂³×C₇	—	2	2	no	—
384	C₂³×C₇	—	2	2	no	—
385	C₂³×C₇	—	2	2	no	—
386	C₂³×C₇	—	4	8	no	—
387	C₂³×C₇	—	4	2	no	—
388	C₂³×C₇	—	4	2	no	—
389	C₂³×C₇	—	4	2	no	—
390	C₂³×C₇	—	4	2	no	—
391	C₂³×C₇	—	4	2	no	—
392	C₂³×C₇	—	4	2	no	—
393	C₂³×C₇	—	4	2	no	—
394	C₂³×C₇	—	4	2	no	—
395	C₂³×C₇	—	4	2	no	—
396	C₂³×C₇	—	4	2	no	—
397	C₂³×C₇	—	4	2	no	—
398	C₂³×C₇	—	4	2	no	—
399	C₂³×C₇	—	8	4	no	—
400	C₂³×C₇	—	8	4	no	—
401	C₂³×C₇	—	8	16	no	—
402	C₂³×C₇	C₂²×D₄	1	2	yes	—
403	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
404	C₇×Q₈	—	2	2	no	—
405	C₇×Q₈	—	2	2	no	—
406	C₇×Q₈	—	2	2	no	—
407	C₇×Q₈	—	2	2	no	—
408	C₇×Q₈	—	4	2	no	—
409	C₇×Q₈	—	4	2	no	—
410	C₇×Q₈	—	8	4	no	—
411	C₇×D₄	—	2	2	no	—
412	C₇×D₄	—	2	2	no	—
413	C₇×D₄	—	2	2	no	—
414	C₇×D₄	—	2	2	no	—
415	C₇×D₄	—	2	2	no	—
416	C₇×D₄	—	2	2	no	—
417	C₇×D₄	—	2	2	no	—
418	C₇×D₄	—	2	2	no	—
419	C₇×D₄	—	4	8	no	—
420	C₇×D₄	—	4	8	no	—
421	C₇×D₄	—	4	2	no	—
422	C₇×D₄	—	4	2	no	—
423	C₇×D₄	—	4	2	no	—
424	C₇×D₄	—	4	2	no	—
425	C₇×D₄	—	8	4	no	—
426	C₇×D₄	—	8	4	no	—
427	C₇×D₄	—	8	4	no	—
428	C₇×D₄	—	8	4	no	—
429	C₇×D₄	—	8	4	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	4	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	4	8	no	—
443	C₂×C₄×C₇	—	4	2	no	—
444	C₂×C₄×C₇	—	4	2	no	—
445	C₂×C₄×C₇	—	4	2	no	—
446	C₂×C₄×C₇	—	4	2	no	—
447	C₂×C₄×C₇	—	8	4	no	—
448	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
455	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
456	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
457	C₇×C₈	—	2	2	no	—
458	C₇×C₈	—	2	2	no	—
459	C₇×C₈	—	2	2	no	—
460	C₇×C₈	—	2	2	no	—
461	C₂⁵	—	2	1	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	4	2	no	—
464	C₂×#41	—	4	2	no	—
465	C₂×#41	C₂³×C₇	1	4	yes	—
466	C₂²×Q₈	—	2	1	no	—
467	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	4	2	no	—
478	C₂²×D₄	—	4	2	no	—
479	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₇	1	4	yes	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
487	C₂×Q₁₆	—	4	2	no	—
488	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
489	C₂×SD₁₆	—	4	2	no	—
490	C₂×SD₁₆	—	4	2	no	—
491	C₂×SD₁₆	—	4	2	no	—
492	C₂×SD₁₆	—	4	2	no	—
493	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
494	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
496	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
497	C₂×D₈	—	4	2	no	—
498	C₂×D₈	—	4	2	no	—
499	C₂×D₈	—	4	2	no	—
500	C₂×D₈	C₂³×C₇	1	4	yes	—
501	C₂×D₈	C₂³×C₇	1	4	yes	—
502	C₂×D₈	C₂³×C₇	1	4	yes	complemented
503	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
509	#127	—	2	2	no	—
510	#127	—	2	2	no	—
511	#127	C₂³×C₇	1	4	yes	—
512	#127	C₂³×C₇	1	4	yes	—
513	#126	—	2	8	no	—
514	#124	—	2	8	no	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	C₂³×C₇	1	4	yes	—
519	#124	C₂³×C₇	1	4	yes	—
520	#124	C₂³×C₇	1	4	yes	complemented
521	#123	—	2	8	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
525	#121	—	2	2	no	—
526	#121	—	2	8	no	—
527	#121	—	2	8	no	—
528	#121	C₂³×C₇	1	4	yes	—
529	#120	—	2	8	no	—
530	#120	—	2	8	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	C₂³×C₇	1	4	yes	complemented
535	#117	C₇×D₄	1	4	yes	—
536	#117	C₂³×C₇	1	4	yes	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
558	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
559	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
560	#103	C₂³×C₇	1	4	yes	complemented
561	#103	C₂³×C₇	1	4	yes	complemented
562	#102	C₂³×C₇	1	4	yes	—
563	#102	C₂³×C₇	1	4	yes	—
564	#102	C₂³×C₇	1	4	yes	—
565	#102	C₂³×C₇	1	4	yes	—
566	#102	C₂³×C₇	1	4	yes	complemented
567	#102	C₂³×C₇	1	4	yes	complemented
568	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
570	#97	C₂³×C₇	1	4	yes	complemented
571	C₄×C₈	C₂³×C₇	1	4	yes	complemented
572	C₂²×C₇	—	2	2	no	—
573	C₂²×C₇	—	2	2	no	—
574	C₂²×C₇	—	2	2	no	—
575	C₂²×C₇	—	4	4	no	—
576	C₂²×C₇	—	4	2	no	—
577	C₂²×C₇	—	4	2	no	—
578	C₂²×C₇	—	4	2	no	—
579	C₂²×C₇	—	4	2	no	—
580	C₂²×C₇	—	4	2	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	4	2	no	—
583	C₂²×C₇	—	4	2	no	—
584	C₂²×C₇	—	4	2	no	—
585	C₂²×C₇	—	4	2	no	—
586	C₂²×C₇	—	4	2	no	—
587	C₂²×C₇	—	4	2	no	—
588	C₂²×C₇	—	8	16	no	—
589	C₂²×C₇	—	8	4	no	—
590	C₂²×C₇	—	8	4	no	—
591	C₂²×C₇	—	8	4	no	—
592	C₂²×C₇	—	8	4	no	—
593	C₂²×C₇	#535	1	2	yes	—
594	C₂²×C₇	#576	1	2	yes	—
595	C₂²×C₇	#577	1	2	yes	—
596	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₇	—	2	2	no	—
598	C₄×C₇	—	2	2	no	—
599	C₄×C₇	—	2	2	no	—
600	C₄×C₇	—	2	2	no	—
601	C₄×C₇	—	2	2	no	—
602	C₄×C₇	—	4	2	no	—
603	C₄×C₇	—	4	2	no	—
604	C₄×C₇	—	4	2	no	—
605	C₄×C₇	—	4	2	no	—
606	C₄×C₇	#535	1	2	yes	—
607	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂⁴	—	2	1	no	—
610	C₂⁴	—	2	1	no	—
611	C₂⁴	—	2	1	no	—
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	4	4	no	—
615	C₂⁴	—	8	2	no	—
616	C₂⁴	—	8	2	no	—
617	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	#41	—	4	8	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	4	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	8	2	no	—
629	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	8	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	8	2	no	—
656	C₂×D₄	—	8	2	no	—
657	C₂×D₄	—	8	2	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	—	8	2	no	—
660	C₂×D₄	C₂⁴×C₇	1	2	yes	—
661	C₂×D₄	C₂⁴×C₇	1	2	yes	—
662	C₂×D₄	C₂⁴×C₇	1	2	yes	—
663	C₂×D₄	C₂⁴×C₇	1	2	yes	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	8	2	no	—
674	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
678	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
679	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
682	Q₁₆	—	4	4	no	—
683	SD₁₆	—	4	4	no	—
684	SD₁₆	—	4	4	no	—
685	SD₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	4	4	no	—
688	D₈	—	4	4	no	—
689	D₈	—	4	4	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	2	2	no	—
694	C₂×C₈	C₂⁴×C₇	1	2	yes	—
695	C₂×C₈	C₂⁴×C₇	1	2	yes	—
696	C₂×C₈	C₂⁴×C₇	1	2	yes	—
697	C₂×C₈	C₂⁴×C₇	1	2	yes	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
704	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
705	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
717	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
718	C₄²	—	2	4	no	—
719	C₄²	C₂×C₇×D₄	1	2	yes	—
720	C₄²	C₂×C₇×D₄	1	2	yes	—
721	C₄²	C₂⁴×C₇	1	2	yes	—
722	C₄²	C₂⁴×C₇	1	2	yes	—
723	C₂×C₇	—	4	2	no	—
724	C₂×C₇	—	8	2	no	—
725	C₂×C₇	—	8	2	no	—
726	C₂×C₇	—	8	2	no	—
727	C₂×C₇	—	8	2	no	—
728	C₂×C₇	#3224	1	4	yes	direct product factor
729	C₂×C₇	C₂×#535	1	1	yes	characteristic
730	C₂×C₇	C₂×#576	1	1	yes	characteristic
731	C₂×C₇	C₂×#577	1	1	yes	characteristic
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	4	8	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	16	no	—
755	C₂³	C₂²×C₇×D₄	1	2	yes	—
756	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	8	4	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	4	no	—
779	D₄	—	8	4	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
802	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
803	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
804	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
805	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
806	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
807	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
808	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
810	C₈	—	2	2	no	—
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₇	C₂×#3224	1	1	yes	characteristic, direct product factor, Sylow
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	8	16	no	—
832	C₂²	—	8	4	no	—
833	C₂²	—	8	4	no	—
834	C₂²	—	8	4	no	—
835	C₂²	—	8	4	no	—
836	C₂²	C₇×#535	1	2	yes	—
837	C₂²	C₇×#576	1	2	yes	—
838	C₂²	C₇×#577	1	2	yes	—
839	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	C₇×#535	1	2	yes	—
850	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
851	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	2	no	—
856	C₂	—	8	2	no	—
857	C₂	C₇×#3224	1	4	yes	direct product factor
858	C₂	C₂×C₇×#535	1	1	yes	characteristic
859	C₂	C₂×C₇×#576	1	1	yes	characteristic
860	C₂	C₂×C₇×#577	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×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×#535	C₂	semidirect
3. C₇×#3224	C₂	direct (N × H)
4. C₂×C₇×#496	C₂	semidirect
5. C₂×C₇×#495	C₂	semidirect
6. C₂×C₇×#489	C₂	semidirect
7. C₂×C₇×#486	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#460	C₂	semidirect
10. C₂×C₇×#463	C₂	semidirect
11. C₂×C₇×#459	C₂	semidirect
12. C₂×C₇×#452	C₂	semidirect
13. C₂×C₇×#449	C₂	semidirect
14. C₂×C₇×#450	C₂	semidirect
15. C₂×C₇×#447	C₂	semidirect
16. C₂×C₇×#433	C₂	semidirect
19. C₂²×C₇×Q₁₆	C₂²	semidirect
22. C₂²×C₇×SD₁₆	C₂²	semidirect
23. C₂²×C₇×SD₁₆	C₂²	semidirect
26. C₂²×C₇×D₈	C₂²	semidirect
28. C₇×#542	C₂²	semidirect
30. C₇×#535	C₂²	semidirect
31. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₇×#124	C₂²	semidirect
47. C₂×C₄×C₇×Q₈	C₂²	semidirect
48. C₂×C₄×C₇×D₄	C₂²	semidirect
50. C₇×#496	C₂²	semidirect
51. C₇×#495	C₂²	semidirect
52. C₇×#489	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#464	C₂²	semidirect
55. C₇×#463	C₂²	semidirect
56. C₇×#460	C₂²	semidirect
57. C₇×#459	C₂²	semidirect
58. C₇×#452	C₂²	semidirect
59. C₇×#450	C₂²	semidirect
60. C₇×#449	C₂²	semidirect
61. C₇×#447	C₂²	semidirect
62. C₇×#433	C₂²	semidirect
63. C₂×C₇×C₄⋊C₈	C₂²	semidirect
64. C₂×C₇×C₄⋊C₈	C₂²	semidirect
65. C₂×C₇×#103	C₂²	semidirect
66. C₂×C₇×#103	C₂²	semidirect
71. C₂×C₇×#102	C₂²	semidirect
72. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×#97	C₂²	semidirect
76. C₂×C₄×C₇×C₈	C₂²	semidirect
77. C₂×#3224	C₇	direct (N × H)
105. C₂×C₇×Q₁₆	C₂³	semidirect
112. C₂×C₇×SD₁₆	C₂³	semidirect
113. C₂×C₇×SD₁₆	C₂³	semidirect
119. C₂×C₇×D₈	C₂³	semidirect
125. C₇×C₄⋊Q₈	C₂³	semidirect
137. C₇×#124	C₂³	semidirect
149. C₄×C₇×Q₈	C₂³	semidirect
151. C₄×C₇×D₄	C₂³	semidirect
175. C₇×C₄⋊C₈	C₂³	semidirect
176. C₇×C₄⋊C₈	C₂³	semidirect
177. C₇×#103	C₂³	semidirect
178. C₇×#103	C₂³	semidirect
183. C₇×#102	C₂³	semidirect
184. C₇×#102	C₂³	semidirect
187. C₇×#97	C₂³	semidirect
188. C₄×C₇×C₈	C₂³	semidirect
189. C₂×#542	C₂×C₇	semidirect
190. C₂×#535	C₂×C₇	semidirect
191. #3224	C₂×C₇	direct (N × H)
192. C₂×#496	C₂×C₇	semidirect
193. C₂×#495	C₂×C₇	semidirect
194. C₂×#489	C₂×C₇	semidirect
195. C₂×#486	C₂×C₇	semidirect
196. C₂×#464	C₂×C₇	semidirect
197. C₂×#460	C₂×C₇	semidirect
198. C₂×#463	C₂×C₇	semidirect
199. C₂×#459	C₂×C₇	semidirect
200. C₂×#452	C₂×C₇	semidirect
201. C₂×#449	C₂×C₇	semidirect
202. C₂×#450	C₂×C₇	semidirect
203. C₂×#447	C₂×C₇	semidirect
204. C₂×#433	C₂×C₇	semidirect
321. C₂²×Q₁₆	C₂²×C₇	semidirect
324. C₂²×SD₁₆	C₂²×C₇	semidirect
325. C₂²×SD₁₆	C₂²×C₇	semidirect
328. C₂²×D₈	C₂²×C₇	semidirect
330. #542	C₂²×C₇	semidirect
332. #535	C₂²×C₇	semidirect
333. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
340. C₂×#124	C₂²×C₇	semidirect
349. C₂×C₄×Q₈	C₂²×C₇	semidirect
350. C₂×C₄×D₄	C₂²×C₇	semidirect
352. #496	C₂²×C₇	semidirect
353. #495	C₂²×C₇	semidirect
354. #489	C₂²×C₇	semidirect
355. #486	C₂²×C₇	semidirect
356. #464	C₂²×C₇	semidirect
357. #463	C₂²×C₇	semidirect
358. #460	C₂²×C₇	semidirect
359. #459	C₂²×C₇	semidirect
360. #452	C₂²×C₇	semidirect
361. #450	C₂²×C₇	semidirect
362. #449	C₂²×C₇	semidirect
363. #447	C₂²×C₇	semidirect
364. #433	C₂²×C₇	semidirect
365. C₂×C₄⋊C₈	C₂²×C₇	semidirect
366. C₂×C₄⋊C₈	C₂²×C₇	semidirect
367. C₂×#103	C₂²×C₇	semidirect
368. C₂×#103	C₂²×C₇	semidirect
373. C₂×#102	C₂²×C₇	semidirect
374. C₂×#102	C₂²×C₇	semidirect
377. C₂×#97	C₂²×C₇	semidirect
378. C₂×C₄×C₈	C₂²×C₇	semidirect
488. C₂×Q₁₆	C₂³×C₇	semidirect
495. C₂×SD₁₆	C₂³×C₇	semidirect
496. C₂×SD₁₆	C₂³×C₇	semidirect
502. C₂×D₈	C₂³×C₇	semidirect
508. C₄⋊Q₈	C₂³×C₇	semidirect
520. #124	C₂³×C₇	semidirect
532. C₄×Q₈	C₂³×C₇	semidirect
534. C₄×D₄	C₂³×C₇	semidirect
558. C₄⋊C₈	C₂³×C₇	semidirect
559. C₄⋊C₈	C₂³×C₇	semidirect
560. #103	C₂³×C₇	semidirect
561. #103	C₂³×C₇	semidirect
566. #102	C₂³×C₇	semidirect
567. #102	C₂³×C₇	semidirect
570. #97	C₂³×C₇	semidirect
571. C₄×C₈	C₂³×C₇	semidirect
728. C₂×C₇	#3224	direct (N × H)
814. C₇	C₂×#3224	direct (N × H)
857. C₂	C₇×#3224	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×#535	2
C₇×#3224	2
C₂×C₇×#496	2
C₂×C₇×#495	2
C₂×C₇×#489	2
C₂×C₇×#486	2
C₂×C₇×#464	2
C₂×C₇×#460	2
C₂×C₇×#463	2
C₂×C₇×#459	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂×C₇×#450	2
C₂×C₇×#447	2
C₂×C₇×#433	2
C₂×#3224	7

Subgroups — C2×C7×#3224 #13238009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3224 #13238009