Subgroups — C₂×C₇×#3220 #13238007

Order 1792.

2342 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3220	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#459	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#447	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₇×D₈	C₂²	1	2	yes	—
17	C₂²×C₇×D₈	C₂²	1	2	yes	—
18	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
19	C₇×#540	—	2	4	no	—
20	C₇×#540	C₂²	1	8	yes	complemented
21	C₇×#535	—	2	4	no	—
22	C₇×#535	C₂²	1	8	yes	complemented
23	C₂×C₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₇×#127	C₂²	1	1	yes	characteristic
25	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#123	—	2	2	no	—
30	C₂×C₇×#121	—	2	2	no	—
31	C₂×C₇×#121	—	2	2	no	—
32	C₂×C₇×#121	C₂²	1	2	yes	—
33	C₂×C₇×#120	—	2	2	no	—
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₇×#496	C₂²	1	8	yes	complemented
37	C₇×#493	C₂²	1	8	yes	complemented
38	C₇×#490	C₂²	1	8	yes	complemented
39	C₇×#488	C₂²	1	8	yes	complemented
40	C₇×#463	C₂²	1	16	yes	complemented
41	C₇×#459	C₂²	1	16	yes	complemented
42	C₇×#449	C₂²	1	16	yes	complemented
43	C₇×#447	C₂²	1	16	yes	complemented
44	C₇×#433	C₂²	1	8	yes	complemented
45	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₇×#103	C₂²	1	2	yes	complemented
47	C₂×C₇×#102	C₂²	1	2	yes	—
48	C₂×C₇×#102	C₂²	1	2	yes	—
49	C₂×C₇×#102	C₂²	1	2	yes	complemented
50	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×#3220	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁵×C₇	—	2	1	no	—
55	C₂×C₇×#41	—	2	2	no	—
56	C₂×C₇×#41	—	4	4	no	—
57	C₂×C₇×#41	C₂³	1	4	yes	—
58	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×D₄	—	2	1	no	—
60	C₂²×C₇×D₄	—	2	2	no	—
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	—	2	2	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	4	4	no	—
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
69	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₇×D₄	C₂³	1	2	yes	—
71	C₂²×C₇×D₄	C₂³	1	4	yes	—
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	2	no	—
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₇×SD₁₆	—	4	4	no	—
76	C₂×C₇×SD₁₆	C₂³	1	8	yes	complemented
77	C₂×C₇×D₈	—	4	4	no	—
78	C₂×C₇×D₈	—	4	4	no	—
79	C₂×C₇×D₈	—	4	4	no	—
80	C₂×C₇×D₈	C₂³	1	8	yes	—
81	C₂×C₇×D₈	C₂³	1	8	yes	—
82	C₂×C₇×D₈	C₂³	1	8	yes	complemented
83	C₂²×C₇×C₈	C₂³	1	2	yes	—
84	C₂²×C₇×C₈	C₂³	1	2	yes	—
85	C₇×#127	—	2	2	no	—
86	C₇×#127	—	2	2	no	—
87	C₇×#127	—	2	2	no	—
88	C₇×#127	C₂³	1	4	yes	—
89	C₇×#127	C₂³	1	4	yes	—
90	C₇×#127	C₂³	1	4	yes	complemented
91	C₇×#125	—	2	2	no	—
92	C₇×#125	C₂³	1	4	yes	complemented
93	C₇×#124	—	2	2	no	—
94	C₇×#124	—	2	2	no	—
95	C₇×#124	C₂³	1	4	yes	—
96	C₇×#124	C₂³	1	4	yes	—
97	C₇×#123	—	2	16	no	—
98	C₇×#121	—	2	4	no	—
99	C₇×#121	—	2	16	no	—
100	C₇×#121	—	2	16	no	—
101	C₇×#121	C₂³	1	8	yes	—
102	C₇×#120	—	2	16	no	—
103	C₄×C₇×D₄	—	2	4	no	—
104	C₄×C₇×D₄	C₂³	1	8	yes	complemented
105	C₇×#117	D₄	1	4	yes	—
106	C₇×#117	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	—	2	2	no	—
108	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
118	C₇×#103	C₂³	1	8	yes	complemented
119	C₇×#102	C₂³	1	8	yes	—
120	C₇×#102	C₂³	1	8	yes	—
121	C₇×#102	C₂³	1	8	yes	complemented
122	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
123	C₇×#97	C₂³	1	4	yes	complemented
124	C₄×C₇×C₈	C₂³	1	4	yes	complemented
125	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
127	#3220	C₂×C₇	1	16	yes	direct product factor
128	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#493	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#490	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#463	C₂×C₇	1	2	yes	complemented
133	C₂×#459	C₂×C₇	1	2	yes	complemented
134	C₂×#449	C₂×C₇	1	2	yes	complemented
135	C₂×#447	C₂×C₇	1	2	yes	complemented
136	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂⁴×C₇	—	2	2	no	—
138	C₂⁴×C₇	—	2	1	no	—
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	—	2	1	no	—
141	C₂⁴×C₇	—	2	4	no	—
142	C₂⁴×C₇	—	4	4	no	—
143	C₂⁴×C₇	—	8	4	no	—
144	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
145	C₇×#41	—	4	8	no	—
146	C₇×#41	—	4	8	no	—
147	C₂×C₇×Q₈	—	2	1	no	—
148	C₂×C₇×Q₈	—	2	4	no	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×D₄	—	2	4	no	—
151	C₂×C₇×D₄	—	2	8	no	—
152	C₂×C₇×D₄	—	2	2	no	—
153	C₂×C₇×D₄	—	2	4	no	—
154	C₂×C₇×D₄	—	2	1	no	—
155	C₂×C₇×D₄	—	2	1	no	—
156	C₂×C₇×D₄	—	2	1	no	—
157	C₂×C₇×D₄	—	2	8	no	—
158	C₂×C₇×D₄	—	2	8	no	—
159	C₂×C₇×D₄	—	2	8	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	4	no	—
163	C₂×C₇×D₄	—	2	4	no	—
164	C₂×C₇×D₄	—	2	4	no	—
165	C₂×C₇×D₄	—	4	8	no	—
166	C₂×C₇×D₄	—	4	4	no	—
167	C₂×C₇×D₄	—	4	8	no	—
168	C₂×C₇×D₄	—	4	4	no	—
169	C₂×C₇×D₄	—	8	4	no	—
170	C₂×C₇×D₄	—	8	4	no	—
171	C₂×C₇×D₄	—	8	4	no	—
172	C₂×C₇×D₄	—	8	4	no	—
173	C₂×C₇×D₄	C₂⁴	1	2	yes	—
174	C₂×C₇×D₄	C₂⁴	1	2	yes	—
175	C₂×C₇×D₄	C₂⁴	1	2	yes	—
176	C₂×C₇×D₄	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₇	—	2	4	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	2	no	—
180	C₂²×C₄×C₇	—	2	4	no	—
181	C₂²×C₄×C₇	—	2	8	no	—
182	C₂²×C₄×C₇	—	4	4	no	—
183	C₂²×C₄×C₇	—	8	4	no	—
184	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₇×SD₁₆	—	4	8	no	—
191	C₇×D₈	—	4	8	no	—
192	C₇×D₈	—	4	8	no	—
193	C₇×D₈	—	4	8	no	—
194	C₂×C₇×C₈	—	2	4	no	—
195	C₂×C₇×C₈	—	2	4	no	—
196	C₂×C₇×C₈	C₂⁴	1	4	yes	—
197	C₂×C₇×C₈	C₂⁴	1	4	yes	—
198	C₇×C₄⋊C₄	—	2	8	no	—
199	C₇×C₄⋊C₄	—	2	2	no	—
200	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₇×C₂²⋊C₄	—	2	8	no	—
206	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
207	C₄²×C₇	C₂×D₄	1	2	yes	—
208	C₄²×C₇	C₂×D₄	1	2	yes	—
209	C₄²×C₇	C₂⁴	1	2	yes	—
210	C₄²×C₇	C₂⁴	1	2	yes	—
211	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
212	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
213	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
214	C₂²×D₈	C₂²×C₇	1	2	yes	—
215	C₂²×D₈	C₂²×C₇	1	2	yes	—
216	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
217	#540	—	2	4	no	—
218	#540	C₂²×C₇	1	8	yes	complemented
219	#535	—	2	4	no	—
220	#535	C₂²×C₇	1	8	yes	complemented
221	C₂×#127	C₂²×C₇	1	1	yes	characteristic
222	C₂×#127	C₂²×C₇	1	1	yes	characteristic
223	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
224	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
225	C₂×#124	C₂²×C₇	1	1	yes	characteristic
226	C₂×#124	C₂²×C₇	1	1	yes	characteristic
227	C₂×#123	—	2	2	no	—
228	C₂×#121	—	2	2	no	—
229	C₂×#121	—	2	2	no	—
230	C₂×#121	C₂²×C₇	1	2	yes	—
231	C₂×#120	—	2	2	no	—
232	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
233	C₂×#117	C₂²×C₇	1	1	yes	characteristic
234	#496	C₂²×C₇	1	8	yes	complemented
235	#493	C₂²×C₇	1	8	yes	complemented
236	#490	C₂²×C₇	1	8	yes	complemented
237	#488	C₂²×C₇	1	8	yes	complemented
238	#463	C₂²×C₇	1	16	yes	complemented
239	#459	C₂²×C₇	1	16	yes	complemented
240	#449	C₂²×C₇	1	16	yes	complemented
241	#447	C₂²×C₇	1	16	yes	complemented
242	#433	C₂²×C₇	1	8	yes	complemented
243	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
244	C₂×#103	C₂²×C₇	1	2	yes	complemented
245	C₂×#102	C₂²×C₇	1	2	yes	—
246	C₂×#102	C₂²×C₇	1	2	yes	—
247	C₂×#102	C₂²×C₇	1	2	yes	complemented
248	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
249	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
250	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	2	4	no	—
254	C₂³×C₇	—	2	2	no	—
255	C₂³×C₇	—	2	2	no	—
256	C₂³×C₇	—	2	2	no	—
257	C₂³×C₇	—	4	8	no	—
258	C₂³×C₇	—	4	2	no	—
259	C₂³×C₇	—	4	2	no	—
260	C₂³×C₇	—	4	2	no	—
261	C₂³×C₇	—	4	4	no	—
262	C₂³×C₇	—	4	4	no	—
263	C₂³×C₇	—	4	4	no	—
264	C₂³×C₇	—	4	4	no	—
265	C₂³×C₇	—	4	4	no	—
266	C₂³×C₇	—	4	4	no	—
267	C₂³×C₇	—	8	8	no	—
268	C₂³×C₇	—	8	16	no	—
269	C₂³×C₇	C₂²×D₄	1	2	yes	—
270	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
271	C₇×Q₈	—	2	4	no	—
272	C₇×Q₈	—	4	2	no	—
273	C₇×D₄	—	2	4	no	—
274	C₇×D₄	—	2	4	no	—
275	C₇×D₄	—	2	4	no	—
276	C₇×D₄	—	2	4	no	—
277	C₇×D₄	—	2	4	no	—
278	C₇×D₄	—	4	8	no	—
279	C₇×D₄	—	4	8	no	—
280	C₇×D₄	—	4	4	no	—
281	C₇×D₄	—	4	2	no	—
282	C₇×D₄	—	4	2	no	—
283	C₇×D₄	—	4	2	no	—
284	C₇×D₄	—	8	8	no	—
285	C₇×D₄	—	8	8	no	—
286	C₇×D₄	—	8	8	no	—
287	C₇×D₄	—	8	8	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	4	no	—
290	C₂×C₄×C₇	—	2	4	no	—
291	C₂×C₄×C₇	—	2	4	no	—
292	C₂×C₄×C₇	—	2	4	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	4	no	—
295	C₂×C₄×C₇	—	4	8	no	—
296	C₂×C₄×C₇	—	4	2	no	—
297	C₂×C₄×C₇	—	4	4	no	—
298	C₂×C₄×C₇	—	8	8	no	—
299	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
304	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
305	C₇×C₈	—	2	4	no	—
306	C₇×C₈	—	2	4	no	—
307	C₂⁵	—	2	1	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	4	4	no	—
310	C₂×#41	C₂³×C₇	1	4	yes	—
311	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	4	4	no	—
320	C₂²×D₄	C₂³×C₇	1	2	yes	—
321	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₇	1	4	yes	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
328	C₂×SD₁₆	—	4	4	no	—
329	C₂×SD₁₆	C₂³×C₇	1	8	yes	complemented
330	C₂×D₈	—	4	4	no	—
331	C₂×D₈	—	4	4	no	—
332	C₂×D₈	—	4	4	no	—
333	C₂×D₈	C₂³×C₇	1	8	yes	—
334	C₂×D₈	C₂³×C₇	1	8	yes	—
335	C₂×D₈	C₂³×C₇	1	8	yes	complemented
336	C₂²×C₈	C₂³×C₇	1	2	yes	—
337	C₂²×C₈	C₂³×C₇	1	2	yes	—
338	#127	—	2	2	no	—
339	#127	—	2	2	no	—
340	#127	—	2	2	no	—
341	#127	C₂³×C₇	1	4	yes	—
342	#127	C₂³×C₇	1	4	yes	—
343	#127	C₂³×C₇	1	4	yes	complemented
344	#125	—	2	2	no	—
345	#125	C₂³×C₇	1	4	yes	complemented
346	#124	—	2	2	no	—
347	#124	—	2	2	no	—
348	#124	C₂³×C₇	1	4	yes	—
349	#124	C₂³×C₇	1	4	yes	—
350	#123	—	2	16	no	—
351	#121	—	2	4	no	—
352	#121	—	2	16	no	—
353	#121	—	2	16	no	—
354	#121	C₂³×C₇	1	8	yes	—
355	#120	—	2	16	no	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	C₂³×C₇	1	8	yes	complemented
358	#117	C₇×D₄	1	4	yes	—
359	#117	C₂³×C₇	1	4	yes	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
368	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
370	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
371	#103	C₂³×C₇	1	8	yes	complemented
372	#102	C₂³×C₇	1	8	yes	—
373	#102	C₂³×C₇	1	8	yes	—
374	#102	C₂³×C₇	1	8	yes	complemented
375	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
376	#97	C₂³×C₇	1	4	yes	complemented
377	C₄×C₈	C₂³×C₇	1	4	yes	complemented
378	C₂²×C₇	—	2	2	no	—
379	C₂²×C₇	—	2	4	no	—
380	C₂²×C₇	—	4	4	no	—
381	C₂²×C₇	—	4	2	no	—
382	C₂²×C₇	—	4	2	no	—
383	C₂²×C₇	—	4	2	no	—
384	C₂²×C₇	—	4	4	no	—
385	C₂²×C₇	—	4	4	no	—
386	C₂²×C₇	—	4	4	no	—
387	C₂²×C₇	—	4	4	no	—
388	C₂²×C₇	—	4	4	no	—
389	C₂²×C₇	—	4	4	no	—
390	C₂²×C₇	—	8	16	no	—
391	C₂²×C₇	—	8	4	no	—
392	C₂²×C₇	—	8	8	no	—
393	C₂²×C₇	—	8	4	no	—
394	C₂²×C₇	—	8	4	no	—
395	C₂²×C₇	#535	1	2	yes	—
396	C₂²×C₇	#576	1	4	yes	—
397	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₇	—	2	2	no	—
399	C₄×C₇	—	2	4	no	—
400	C₄×C₇	—	2	4	no	—
401	C₄×C₇	—	4	2	no	—
402	C₄×C₇	—	4	4	no	—
403	C₄×C₇	#535	1	2	yes	—
404	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	4	4	no	—
411	C₂⁴	—	8	4	no	—
412	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
413	#41	—	4	8	no	—
414	#41	—	4	8	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	8	4	no	—
438	C₂×D₄	—	8	4	no	—
439	C₂×D₄	—	8	4	no	—
440	C₂×D₄	—	8	4	no	—
441	C₂×D₄	C₂⁴×C₇	1	2	yes	—
442	C₂×D₄	C₂⁴×C₇	1	2	yes	—
443	C₂×D₄	C₂⁴×C₇	1	2	yes	—
444	C₂×D₄	C₂⁴×C₇	1	4	yes	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	8	4	no	—
452	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
453	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
454	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
458	SD₁₆	—	4	8	no	—
459	D₈	—	4	8	no	—
460	D₈	—	4	8	no	—
461	D₈	—	4	8	no	—
462	C₂×C₈	—	2	4	no	—
463	C₂×C₈	—	2	4	no	—
464	C₂×C₈	C₂⁴×C₇	1	4	yes	—
465	C₂×C₈	C₂⁴×C₇	1	4	yes	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
475	C₄²	C₂×C₇×D₄	1	2	yes	—
476	C₄²	C₂×C₇×D₄	1	2	yes	—
477	C₄²	C₂⁴×C₇	1	2	yes	—
478	C₄²	C₂⁴×C₇	1	2	yes	—
479	C₂×C₇	—	4	2	no	—
480	C₂×C₇	—	8	2	no	—
481	C₂×C₇	—	8	4	no	—
482	C₂×C₇	—	8	2	no	—
483	C₂×C₇	—	8	2	no	—
484	C₂×C₇	#3220	1	4	yes	direct product factor
485	C₂×C₇	C₂×#535	1	1	yes	characteristic
486	C₂×C₇	C₂×#576	1	2	yes	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	8	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	8	8	no	—
504	C₂³	—	8	16	no	—
505	C₂³	C₂²×C₇×D₄	1	2	yes	—
506	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
507	Q₈	—	2	4	no	—
508	Q₈	—	4	2	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	4	8	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	8	8	no	—
521	D₄	—	8	8	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	8	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	8	8	no	—
535	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
536	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
537	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
538	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
539	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
540	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	2	4	no	—
543	C₇	C₂×#3220	1	1	yes	characteristic, direct product factor, Sylow
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	16	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	8	no	—
561	C₂²	C₇×#535	1	2	yes	—
562	C₂²	C₇×#576	1	4	yes	—
563	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	2	no	—
569	C₄	C₇×#535	1	2	yes	—
570	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	2	no	—
574	C₂	—	8	4	no	—
575	C₂	—	8	2	no	—
576	C₂	C₇×#3220	1	4	yes	direct product factor
577	C₂	C₂×C₇×#535	1	1	yes	characteristic
578	C₂	C₂×C₇×#576	1	2	yes	—

	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×#540	C₂	semidirect
2. C₂×C₇×#535	C₂	semidirect
3. C₇×#3220	C₂	direct (N × H)
4. C₂×C₇×#496	C₂	semidirect
5. C₂×C₇×#493	C₂	semidirect
6. C₂×C₇×#490	C₂	semidirect
7. C₂×C₇×#488	C₂	semidirect
8. C₂×C₇×#463	C₂	semidirect
9. C₂×C₇×#459	C₂	semidirect
10. C₂×C₇×#449	C₂	semidirect
11. C₂×C₇×#447	C₂	semidirect
12. C₂×C₇×#433	C₂	semidirect
15. C₂²×C₇×SD₁₆	C₂²	semidirect
18. C₂²×C₇×D₈	C₂²	semidirect
20. C₇×#540	C₂²	semidirect
22. C₇×#535	C₂²	semidirect
25. C₂×C₇×#127	C₂²	semidirect
26. C₂×C₇×#125	C₂²	semidirect
34. C₂×C₄×C₇×D₄	C₂²	semidirect
36. C₇×#496	C₂²	semidirect
37. C₇×#493	C₂²	semidirect
38. C₇×#490	C₂²	semidirect
39. C₇×#488	C₂²	semidirect
40. C₇×#463	C₂²	semidirect
41. C₇×#459	C₂²	semidirect
42. C₇×#449	C₂²	semidirect
43. C₇×#447	C₂²	semidirect
44. C₇×#433	C₂²	semidirect
45. C₂×C₇×C₄⋊C₈	C₂²	semidirect
46. C₂×C₇×#103	C₂²	semidirect
49. C₂×C₇×#102	C₂²	semidirect
51. C₂×C₇×#97	C₂²	semidirect
52. C₂×C₄×C₇×C₈	C₂²	semidirect
53. C₂×#3220	C₇	direct (N × H)
76. C₂×C₇×SD₁₆	C₂³	semidirect
82. C₂×C₇×D₈	C₂³	semidirect
90. C₇×#127	C₂³	semidirect
92. C₇×#125	C₂³	semidirect
104. C₄×C₇×D₄	C₂³	semidirect
117. C₇×C₄⋊C₈	C₂³	semidirect
118. C₇×#103	C₂³	semidirect
121. C₇×#102	C₂³	semidirect
123. C₇×#97	C₂³	semidirect
124. C₄×C₇×C₈	C₂³	semidirect
125. C₂×#540	C₂×C₇	semidirect
126. C₂×#535	C₂×C₇	semidirect
127. #3220	C₂×C₇	direct (N × H)
128. C₂×#496	C₂×C₇	semidirect
129. C₂×#493	C₂×C₇	semidirect
130. C₂×#490	C₂×C₇	semidirect
131. C₂×#488	C₂×C₇	semidirect
132. C₂×#463	C₂×C₇	semidirect
133. C₂×#459	C₂×C₇	semidirect
134. C₂×#449	C₂×C₇	semidirect
135. C₂×#447	C₂×C₇	semidirect
136. C₂×#433	C₂×C₇	semidirect
213. C₂²×SD₁₆	C₂²×C₇	semidirect
216. C₂²×D₈	C₂²×C₇	semidirect
218. #540	C₂²×C₇	semidirect
220. #535	C₂²×C₇	semidirect
223. C₂×#127	C₂²×C₇	semidirect
224. C₂×#125	C₂²×C₇	semidirect
232. C₂×C₄×D₄	C₂²×C₇	semidirect
234. #496	C₂²×C₇	semidirect
235. #493	C₂²×C₇	semidirect
236. #490	C₂²×C₇	semidirect
237. #488	C₂²×C₇	semidirect
238. #463	C₂²×C₇	semidirect
239. #459	C₂²×C₇	semidirect
240. #449	C₂²×C₇	semidirect
241. #447	C₂²×C₇	semidirect
242. #433	C₂²×C₇	semidirect
243. C₂×C₄⋊C₈	C₂²×C₇	semidirect
244. C₂×#103	C₂²×C₇	semidirect
247. C₂×#102	C₂²×C₇	semidirect
249. C₂×#97	C₂²×C₇	semidirect
250. C₂×C₄×C₈	C₂²×C₇	semidirect
329. C₂×SD₁₆	C₂³×C₇	semidirect
335. C₂×D₈	C₂³×C₇	semidirect
343. #127	C₂³×C₇	semidirect
345. #125	C₂³×C₇	semidirect
357. C₄×D₄	C₂³×C₇	semidirect
370. C₄⋊C₈	C₂³×C₇	semidirect
371. #103	C₂³×C₇	semidirect
374. #102	C₂³×C₇	semidirect
376. #97	C₂³×C₇	semidirect
377. C₄×C₈	C₂³×C₇	semidirect
484. C₂×C₇	#3220	direct (N × H)
543. C₇	C₂×#3220	direct (N × H)
576. C₂	C₇×#3220	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×#540	2
C₂×C₇×#535	2
C₇×#3220	2
C₂×C₇×#496	2
C₂×C₇×#493	2
C₂×C₇×#490	2
C₂×C₇×#488	2
C₂×C₇×#463	2
C₂×C₇×#459	2
C₂×C₇×#449	2
C₂×C₇×#447	2
C₂×C₇×#433	2
C₂×#3220	7

Subgroups — C2×C7×#3220 #13238007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3220 #13238007