Subgroups — C₂×C₇×#3260 #13238127

Order 1792.

1882 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic
3	C₇×#3260	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#460	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₇×#541	—	2	4	no	—
16	C₇×#541	C₂²	1	8	yes	complemented
17	C₇×#540	—	2	4	no	—
18	C₇×#540	C₂²	1	8	yes	—
19	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#127	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	2	no	—
22	C₂×C₇×#125	—	2	2	no	—
23	C₂×C₇×#125	C₂²	1	1	yes	characteristic
24	C₂×C₇×#125	C₂²	1	1	yes	characteristic
25	C₂×C₇×#123	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×#121	—	2	2	no	—
28	C₂×C₇×#121	C₂²	1	2	yes	—
29	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₇×#117	C₂²	1	1	yes	characteristic
32	C₇×#479	C₂²	1	16	yes	complemented
33	C₇×#478	C₂²	1	16	yes	complemented
34	C₇×#468	C₂²	1	16	yes	complemented
35	C₇×#465	C₂²	1	16	yes	complemented
36	C₇×#461	C₂²	1	16	yes	complemented
37	C₇×#460	C₂²	1	16	yes	complemented
38	C₂×C₇×#107	C₂²	1	2	yes	—
39	C₂×C₇×#106	C₂²	1	2	yes	—
40	C₇×#424	C₂²	1	8	yes	complemented
41	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₇×#103	C₂²	1	2	yes	—
44	C₂×C₇×#103	C₂²	1	2	yes	—
45	C₂×C₇×#102	C₂²	1	2	yes	—
46	C₂×C₇×#102	C₂²	1	2	yes	—
47	C₂×#3260	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	C₂³	1	2	yes	—
49	C₂²×C₇×D₄	—	2	2	no	—
50	C₂²×C₇×D₄	—	2	2	no	—
51	C₂²×C₇×D₄	C₂³	1	2	yes	—
52	C₂³×C₄×C₇	—	2	2	no	—
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂×C₇×SD₁₆	—	4	4	no	—
55	C₂×C₇×SD₁₆	—	4	4	no	—
56	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
58	C₂×C₇×M₁₆	—	4	2	no	—
59	C₂×C₇×M₁₆	C₂³	1	4	yes	—
60	C₂²×C₇×C₈	—	4	2	no	—
61	C₂²×C₇×C₈	C₂³	1	2	yes	—
62	C₂²×C₇×C₈	C₂³	1	2	yes	—
63	C₂²×C₇×C₈	C₂³	1	4	yes	—
64	C₇×C₄⋊Q₈	—	2	2	no	—
65	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
66	C₇×#127	—	2	2	no	—
67	C₇×#127	C₂³	1	4	yes	—
68	C₇×#126	—	2	16	no	—
69	C₇×#125	—	2	16	no	—
70	C₇×#125	—	2	2	no	—
71	C₇×#125	—	2	2	no	—
72	C₇×#125	C₂³	1	4	yes	—
73	C₇×#125	C₂³	1	4	yes	—
74	C₇×#123	—	2	16	no	—
75	C₇×C₂²⋊Q₈	—	2	4	no	—
76	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
77	C₇×#121	—	2	4	no	—
78	C₇×#121	—	2	16	no	—
79	C₇×#121	C₂³	1	8	yes	—
80	C₄×C₇×Q₈	—	2	4	no	—
81	C₄×C₇×Q₈	C₂³	1	8	yes	—
82	C₄×C₇×D₄	—	2	4	no	—
83	C₄×C₇×D₄	C₂³	1	8	yes	—
84	C₇×#117	D₄	1	4	yes	—
85	C₇×#117	C₂³	1	4	yes	—
86	C₂×C₇×C₄⋊C₄	—	2	2	no	—
87	C₂×C₇×C₄⋊C₄	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	—	2	2	no	—
89	C₂×C₇×C₄⋊C₄	—	2	2	no	—
90	C₂×C₇×C₄⋊C₄	—	2	2	no	—
91	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
98	C₂×C₄²×C₇	—	2	2	no	—
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₇×#107	C₂³	1	8	yes	—
102	C₇×#106	C₂³	1	8	yes	—
103	C₇×C₄⋊C₈	C₂³	1	8	yes	—
104	C₇×C₄⋊C₈	C₂³	1	8	yes	—
105	C₇×#103	C₂³	1	8	yes	—
106	C₇×#103	C₂³	1	8	yes	—
107	C₇×#102	C₂³	1	8	yes	—
108	C₇×#102	C₂³	1	8	yes	—
109	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
110	C₂×#540	C₂×C₇	1	1	yes	characteristic
111	#3260	C₂×C₇	1	16	yes	direct product factor
112	C₂×#479	C₂×C₇	1	2	yes	complemented
113	C₂×#478	C₂×C₇	1	2	yes	complemented
114	C₂×#468	C₂×C₇	1	2	yes	complemented
115	C₂×#465	C₂×C₇	1	2	yes	complemented
116	C₂×#460	C₂×C₇	1	2	yes	complemented
117	C₂×#461	C₂×C₇	1	2	yes	complemented
118	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂⁴×C₇	—	2	2	no	—
120	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	2	4	no	—
123	C₂×C₇×Q₈	—	2	4	no	—
124	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
125	C₂×C₇×D₄	—	2	8	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	—	2	8	no	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	4	no	—
130	C₂×C₇×D₄	—	8	4	no	—
131	C₂×C₇×D₄	—	8	4	no	—
132	C₂×C₇×D₄	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	8	no	—
139	C₂²×C₄×C₇	—	8	4	no	—
140	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₇×SD₁₆	—	4	8	no	—
147	C₇×SD₁₆	—	4	8	no	—
148	C₇×M₁₆	—	4	4	no	—
149	C₂×C₇×C₈	—	2	4	no	—
150	C₂×C₇×C₈	—	2	4	no	—
151	C₂×C₇×C₈	—	4	4	no	—
152	C₂×C₇×C₈	C₂⁴	1	4	yes	—
153	C₂×C₇×C₈	C₂⁴	1	4	yes	—
154	C₇×C₄⋊C₄	—	2	8	no	—
155	C₇×C₄⋊C₄	—	2	8	no	—
156	C₇×C₄⋊C₄	—	2	8	no	—
157	C₇×C₄⋊C₄	—	2	8	no	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
162	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
163	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
164	C₇×C₂²⋊C₄	—	2	8	no	—
165	C₇×C₂²⋊C₄	—	2	8	no	—
166	C₇×C₂²⋊C₄	—	2	8	no	—
167	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
168	C₄²×C₇	—	2	8	no	—
169	C₄²×C₇	C₂×D₄	1	2	yes	—
170	C₄²×C₇	C₂×D₄	1	2	yes	—
171	C₄²×C₇	C₂⁴	1	2	yes	—
172	C₄²×C₇	C₂⁴	1	2	yes	—
173	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
174	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
175	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
176	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
177	#541	—	2	4	no	—
178	#541	C₂²×C₇	1	8	yes	complemented
179	#540	—	2	4	no	—
180	#540	C₂²×C₇	1	8	yes	—
181	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
182	C₂×#127	C₂²×C₇	1	1	yes	characteristic
183	C₂×#126	—	2	2	no	—
184	C₂×#125	—	2	2	no	—
185	C₂×#125	C₂²×C₇	1	1	yes	characteristic
186	C₂×#125	C₂²×C₇	1	1	yes	characteristic
187	C₂×#123	—	2	2	no	—
188	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
189	C₂×#121	—	2	2	no	—
190	C₂×#121	C₂²×C₇	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
193	C₂×#117	C₂²×C₇	1	1	yes	characteristic
194	#479	C₂²×C₇	1	16	yes	complemented
195	#478	C₂²×C₇	1	16	yes	complemented
196	#468	C₂²×C₇	1	16	yes	complemented
197	#465	C₂²×C₇	1	16	yes	complemented
198	#461	C₂²×C₇	1	16	yes	complemented
199	#460	C₂²×C₇	1	16	yes	complemented
200	C₂×#107	C₂²×C₇	1	2	yes	—
201	C₂×#106	C₂²×C₇	1	2	yes	—
202	#424	C₂²×C₇	1	8	yes	complemented
203	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
205	C₂×#103	C₂²×C₇	1	2	yes	—
206	C₂×#103	C₂²×C₇	1	2	yes	—
207	C₂×#102	C₂²×C₇	1	2	yes	—
208	C₂×#102	C₂²×C₇	1	2	yes	—
209	C₂³×C₇	—	2	2	no	—
210	C₂³×C₇	—	2	4	no	—
211	C₂³×C₇	—	2	4	no	—
212	C₂³×C₇	—	4	4	no	—
213	C₂³×C₇	—	4	4	no	—
214	C₂³×C₇	—	4	4	no	—
215	C₂³×C₇	C₂²×D₄	1	2	yes	—
216	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
217	C₇×Q₈	—	2	4	no	—
218	C₇×Q₈	—	2	4	no	—
219	C₇×Q₈	—	4	4	no	—
220	C₇×D₄	—	2	4	no	—
221	C₇×D₄	—	2	4	no	—
222	C₇×D₄	—	4	4	no	—
223	C₇×D₄	—	8	8	no	—
224	C₇×D₄	—	8	8	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	4	no	—
227	C₂×C₄×C₇	—	2	4	no	—
228	C₂×C₄×C₇	—	2	4	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	4	no	—
233	C₂×C₄×C₇	—	2	4	no	—
234	C₂×C₄×C₇	—	4	4	no	—
235	C₂×C₄×C₇	—	4	4	no	—
236	C₂×C₄×C₇	—	4	4	no	—
237	C₂×C₄×C₇	—	8	8	no	—
238	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
243	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
244	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
245	C₇×C₈	—	2	4	no	—
246	C₇×C₈	—	2	4	no	—
247	C₂²×Q₈	C₂³×C₇	1	2	yes	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	C₂³×C₇	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
253	C₂×SD₁₆	—	4	4	no	—
254	C₂×SD₁₆	—	4	4	no	—
255	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
256	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
257	C₂×M₁₆	—	4	2	no	—
258	C₂×M₁₆	C₂³×C₇	1	4	yes	—
259	C₂²×C₈	—	4	2	no	—
260	C₂²×C₈	C₂³×C₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₇	1	4	yes	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
265	#127	—	2	2	no	—
266	#127	C₂³×C₇	1	4	yes	—
267	#126	—	2	16	no	—
268	#125	—	2	16	no	—
269	#125	—	2	2	no	—
270	#125	—	2	2	no	—
271	#125	C₂³×C₇	1	4	yes	—
272	#125	C₂³×C₇	1	4	yes	—
273	#123	—	2	16	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
276	#121	—	2	4	no	—
277	#121	—	2	16	no	—
278	#121	C₂³×C₇	1	8	yes	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	C₂³×C₇	1	8	yes	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	C₂³×C₇	1	8	yes	—
283	#117	C₇×D₄	1	4	yes	—
284	#117	C₂³×C₇	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
300	#107	C₂³×C₇	1	8	yes	—
301	#106	C₂³×C₇	1	8	yes	—
302	C₄⋊C₈	C₂³×C₇	1	8	yes	—
303	C₄⋊C₈	C₂³×C₇	1	8	yes	—
304	#103	C₂³×C₇	1	8	yes	—
305	#103	C₂³×C₇	1	8	yes	—
306	#102	C₂³×C₇	1	8	yes	—
307	#102	C₂³×C₇	1	8	yes	—
308	C₂²×C₇	—	2	2	no	—
309	C₂²×C₇	—	2	4	no	—
310	C₂²×C₇	—	4	4	no	—
311	C₂²×C₇	—	4	4	no	—
312	C₂²×C₇	—	4	4	no	—
313	C₂²×C₇	—	4	4	no	—
314	C₂²×C₇	—	8	8	no	—
315	C₂²×C₇	#537	1	2	yes	—
316	C₂²×C₇	#577	1	4	yes	—
317	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
318	C₄×C₇	—	2	2	no	—
319	C₄×C₇	—	2	4	no	—
320	C₄×C₇	—	2	4	no	—
321	C₄×C₇	—	4	4	no	—
322	C₄×C₇	—	4	4	no	—
323	C₄×C₇	—	4	4	no	—
324	C₄×C₇	#537	1	2	yes	—
325	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	C₂⁴	—	2	2	no	—
328	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	8	4	no	—
339	C₂×D₄	—	8	4	no	—
340	C₂×D₄	C₂⁴×C₇	1	4	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	8	4	no	—
348	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
350	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
354	SD₁₆	—	4	8	no	—
355	SD₁₆	—	4	8	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	C₂⁴×C₇	1	4	yes	—
361	C₂×C₈	C₂⁴×C₇	1	4	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
370	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
376	C₄²	—	2	8	no	—
377	C₄²	C₂×C₇×D₄	1	2	yes	—
378	C₄²	C₂×C₇×D₄	1	2	yes	—
379	C₄²	C₂⁴×C₇	1	2	yes	—
380	C₄²	C₂⁴×C₇	1	2	yes	—
381	C₂×C₇	—	4	2	no	—
382	C₂×C₇	—	8	4	no	—
383	C₂×C₇	#3260	1	4	yes	direct product factor
384	C₂×C₇	C₂×#537	1	1	yes	characteristic
385	C₂×C₇	C₂×#577	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	C₂²×C₇×D₄	1	2	yes	—
393	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
394	Q₈	—	2	4	no	—
395	Q₈	—	2	4	no	—
396	Q₈	—	4	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	8	no	—
401	D₄	—	8	8	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	8	8	no	—
415	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
416	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
417	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
418	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
419	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	4	no	—
424	C₇	C₂×#3260	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	8	no	—
432	C₂²	C₇×#537	1	2	yes	—
433	C₂²	C₇×#577	1	4	yes	—
434	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₇×#537	1	2	yes	—
442	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
443	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₇×#3260	1	4	yes	direct product factor
447	C₂	C₂×C₇×#537	1	1	yes	characteristic
448	C₂	C₂×C₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#540	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×#541	C₂	semidirect
3. C₇×#3260	C₂	direct (N × H)
4. C₂×C₇×#479	C₂	semidirect
5. C₂×C₇×#478	C₂	semidirect
6. C₂×C₇×#468	C₂	semidirect
7. C₂×C₇×#465	C₂	semidirect
8. C₂×C₇×#460	C₂	semidirect
9. C₂×C₇×#461	C₂	semidirect
10. C₂×C₇×#424	C₂	semidirect
16. C₇×#541	C₂²	semidirect
32. C₇×#479	C₂²	semidirect
33. C₇×#478	C₂²	semidirect
34. C₇×#468	C₂²	semidirect
35. C₇×#465	C₂²	semidirect
36. C₇×#461	C₂²	semidirect
37. C₇×#460	C₂²	semidirect
40. C₇×#424	C₂²	semidirect
47. C₂×#3260	C₇	direct (N × H)
109. C₂×#541	C₂×C₇	semidirect
111. #3260	C₂×C₇	direct (N × H)
112. C₂×#479	C₂×C₇	semidirect
113. C₂×#478	C₂×C₇	semidirect
114. C₂×#468	C₂×C₇	semidirect
115. C₂×#465	C₂×C₇	semidirect
116. C₂×#460	C₂×C₇	semidirect
117. C₂×#461	C₂×C₇	semidirect
118. C₂×#424	C₂×C₇	semidirect
178. #541	C₂²×C₇	semidirect
194. #479	C₂²×C₇	semidirect
195. #478	C₂²×C₇	semidirect
196. #468	C₂²×C₇	semidirect
197. #465	C₂²×C₇	semidirect
198. #461	C₂²×C₇	semidirect
199. #460	C₂²×C₇	semidirect
202. #424	C₂²×C₇	semidirect
383. C₂×C₇	#3260	direct (N × H)
424. C₇	C₂×#3260	direct (N × H)
446. C₂	C₇×#3260	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×#541	2
C₂×C₇×#540	2
C₇×#3260	2
C₂×C₇×#479	2
C₂×C₇×#478	2
C₂×C₇×#468	2
C₂×C₇×#465	2
C₂×C₇×#460	2
C₂×C₇×#461	2
C₂×C₇×#424	2
C₂×#3260	7

Subgroups — C2×C7×#3260 #13238127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3260 #13238127