Subgroups — #34180962

Order 20224.

688 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23763517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal
4	#23761241	C₂	1	2	yes	maximal, complemented
5	C₄²×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
9	#19098318	—	2	1	no	—
10	#19098318	—	2	1	no	—
11	#19098318	—	2	1	no	—
12	D₄⋊(C₇₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
23	C₄³×C₇₉	C₂²	1	1	yes	characteristic
24	C₂²×C₇₉⋊C₈	—	2	2	no	—
25	C₂²×C₇₉⋊C₈	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
27	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₄×C₇₉⋊C₈	—	2	2	no	—
30	C₄×C₇₉⋊C₈	—	2	2	no	—
31	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₇₉	—	2	1	no	—
33	C₂³×C₄×C₇₉	—	2	1	no	—
34	C₂³×C₄×C₇₉	—	2	1	no	—
35	C₄×D₄×C₇₉	—	2	2	no	—
36	C₄×D₄×C₇₉	—	2	2	no	—
37	C₄×D₄×C₇₉	—	2	2	no	—
38	C₄×D₄×C₇₉	—	2	1	no	—
39	C₄×D₄×C₇₉	—	2	1	no	—
40	C₄×D₄×C₇₉	C₈	1	4	yes	complemented
41	C₄×D₄×C₇₉	D₄	1	2	yes	—
42	C₄×D₄×C₇₉	Q₈	1	2	yes	—
43	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
49	C₂×C₄²×C₇₉	—	2	1	no	—
50	C₂×C₄²×C₇₉	—	2	1	no	—
51	C₂×C₄²×C₇₉	—	2	1	no	—
52	C₂×C₄²×C₇₉	—	4	4	no	—
53	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
60	#95×C₇₉	—	2	1	no	—
61	#95×C₇₉	—	2	1	no	—
62	#95×C₇₉	—	2	1	no	—
63	C₂×C₇₉⋊C₈	—	2	4	no	—
64	C₂×C₇₉⋊C₈	—	4	2	no	—
65	C₂×C₇₉⋊C₈	—	4	2	no	—
66	C₂×C₇₉⋊C₈	—	4	2	no	—
67	C₂×C₇₉⋊C₈	—	4	2	no	—
68	C₂×C₇₉⋊C₈	—	4	2	no	—
69	C₂⁴×C₇₉	—	2	1	no	—
70	C₂×D₄×C₇₉	—	2	1	no	—
71	C₂×D₄×C₇₉	—	2	1	no	—
72	C₂×D₄×C₇₉	—	2	1	no	—
73	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
74	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₇₉	M₁₆	1	2	yes	—
76	C₂²×C₄×C₇₉	—	2	4	no	—
77	C₂²×C₄×C₇₉	—	2	1	no	—
78	C₂²×C₄×C₇₉	—	2	1	no	—
79	C₂²×C₄×C₇₉	—	2	1	no	—
80	C₂²×C₄×C₇₉	—	2	4	no	—
81	C₂²×C₄×C₇₉	—	2	2	no	—
82	C₂²×C₄×C₇₉	—	2	2	no	—
83	C₂²×C₄×C₇₉	—	4	2	no	—
84	C₂²×C₄×C₇₉	—	4	2	no	—
85	C₂²×C₄×C₇₉	—	4	2	no	—
86	C₂²×C₄×C₇₉	—	4	2	no	—
87	C₂²×C₄×C₇₉	—	4	2	no	—
88	C₂²×C₄×C₇₉	—	4	2	no	—
89	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₇₉	—	2	1	no	—
97	C₄⋊C₄×C₇₉	—	2	1	no	—
98	C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₄⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
100	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
101	C₄⋊C₄×C₇₉	M₁₆	1	2	yes	—
102	C₂²⋊C₄×C₇₉	—	2	4	no	—
103	C₂²⋊C₄×C₇₉	—	2	4	no	—
104	C₂²⋊C₄×C₇₉	—	2	2	no	—
105	C₂²⋊C₄×C₇₉	—	2	2	no	—
106	C₄²×C₇₉	—	2	2	no	—
107	C₄²×C₇₉	—	2	1	no	—
108	C₄²×C₇₉	—	2	1	no	—
109	C₄²×C₇₉	—	2	2	no	—
110	C₄²×C₇₉	—	2	2	no	—
111	C₄²×C₇₉	—	4	1	no	—
112	C₄²×C₇₉	—	4	2	no	—
113	C₄²×C₇₉	—	4	2	no	—
114	C₄²×C₇₉	—	4	2	no	—
115	C₄²×C₇₉	C₂×C₈	1	2	yes	—
116	C₄²×C₇₉	M₁₆	1	2	yes	—
117	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₇₉	#41	1	1	yes	characteristic
120	C₄²×C₇₉	#41	1	1	yes	characteristic
121	C₂³×C₇₉	—	2	2	no	—
122	C₂³×C₇₉	—	2	2	no	—
123	C₂³×C₇₉	—	2	2	no	—
124	C₂³×C₇₉	—	4	1	no	—
125	C₂³×C₇₉	—	4	1	no	—
126	C₂³×C₇₉	—	4	1	no	—
127	C₂³×C₇₉	—	4	1	no	—
128	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	D₄×C₇₉	—	2	2	no	—
130	D₄×C₇₉	—	2	2	no	—
131	D₄×C₇₉	—	2	2	no	—
132	D₄×C₇₉	C₄⋊C₈	1	4	yes	complemented
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	1	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	4	8	no	—
148	C₂×C₄×C₇₉	—	4	8	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	4	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	—	4	4	no	—
156	C₂×C₄×C₇₉	—	4	4	no	—
157	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
158	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
159	C₂×C₄×C₇₉	#104	1	2	yes	—
160	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
170	C₂×C₄×C₇₉	#135	1	2	yes	—
171	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
172	C₇₉⋊C₈	—	4	4	no	—
173	C₇₉⋊C₈	—	8	2	no	—
174	C₂²×C₇₉	—	2	4	no	—
175	C₂²×C₇₉	—	4	2	no	—
176	C₂²×C₇₉	—	4	2	no	—
177	C₂²×C₇₉	—	4	2	no	—
178	C₂²×C₇₉	—	4	2	no	—
179	C₂²×C₇₉	—	4	2	no	—
180	C₂²×C₇₉	—	4	2	no	—
181	C₂²×C₇₉	#380	1	1	yes	characteristic
182	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
183	C₂²×C₇₉	#407	1	1	yes	characteristic
184	C₂²×C₇₉	#416	1	1	yes	characteristic
185	C₂²×C₇₉	#418	1	1	yes	characteristic
186	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
187	C₂²×C₇₉	#421	1	1	yes	characteristic
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	2	no	—
191	C₄×C₇₉	—	2	2	no	—
192	C₄×C₇₉	—	2	2	no	—
193	C₄×C₇₉	—	4	2	no	—
194	C₄×C₇₉	—	4	2	no	—
195	C₄×C₇₉	—	4	1	no	—
196	C₄×C₇₉	—	4	2	no	—
197	C₄×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
198	C₄×C₇₉	#423	1	1	yes	characteristic
199	C₄×C₇₉	#431	1	1	yes	characteristic
200	C₄×C₇₉	#432	1	1	yes	characteristic
201	C₄×C₇₉	#463	1	2	yes	—
202	C₄×C₇₉	#478	1	2	yes	—
203	#8565	—	79	1	no	maximal, Sylow
204	C₂×C₇₉	—	4	4	no	—
205	C₂×C₇₉	#1476	1	1	yes	characteristic
206	C₂×C₇₉	#1478	1	1	yes	characteristic
207	C₂×C₇₉	#1488	1	1	yes	characteristic
208	C₂×C₇₉	#1490	1	1	yes	characteristic
209	C₂×C₇₉	#1797	1	1	yes	characteristic
210	C₂×C₇₉	#1804	1	1	yes	characteristic
211	C₂×C₇₉	#1806	1	1	yes	characteristic
212	C₄²×D₄	D₇₉	1	1	yes	characteristic
213	#1831	—	79	1	no	—
214	C₄×C₄⋊C₈	—	79	1	no	—
215	C₂×D₄⋊C₈	—	79	2	no	—
216	#1279	—	79	2	no	—
217	C₇₉	#8565	1	1	yes	characteristic, complemented, Sylow
218	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
219	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
221	C₂²×C₄²	—	2	1	no	—
222	C₂×C₄⋊C₈	—	79	2	no	—
223	C₂×C₄⋊C₈	—	158	1	no	—
224	C₂×C₄×C₈	—	79	2	no	—
225	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
226	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
228	C₄×C₂²⋊C₄	—	2	1	no	—
229	C₄×C₂²⋊C₄	—	2	1	no	—
230	C₄×C₂²⋊C₄	—	2	1	no	—
231	C₄³	C₂×D₇₉	1	1	yes	characteristic
232	#336	—	158	1	no	—
233	#336	—	158	1	no	—
234	#336	—	158	1	no	—
235	D₄⋊C₈	—	158	4	no	—
236	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂²×C₈	—	158	2	no	—
241	C₂²×C₈	—	158	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₇₉⋊C₈	1	4	yes	complemented
248	C₄×D₄	Dic₁₅₈	1	2	yes	—
249	C₄×D₄	D₃₁₆	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	4	4	no	—
260	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
261	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
267	C₄⋊C₈	—	158	4	no	—
268	C₄⋊C₈	—	158	2	no	—
269	C₄⋊C₈	—	158	2	no	—
270	C₄×C₈	—	158	2	no	—
271	C₄×C₈	—	158	2	no	—
272	#95	—	2	1	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	C₂⁴	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	C₄⋊Dic₇₉	1	2	yes	—
280	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	—
281	C₂×D₄	#11929608	1	2	yes	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂×C₈	—	316	2	no	—
303	C₂×C₈	—	316	2	no	—
304	C₂×C₈	—	316	2	no	—
305	C₂×C₈	—	316	2	no	—
306	C₂×C₈	—	316	2	no	—
307	C₂×C₈	—	158	4	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	C₄⋊Dic₇₉	1	2	yes	—
312	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	—
313	C₄⋊C₄	#11929608	1	2	yes	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	2	no	—
327	C₄²	C₂×C₇₉⋊C₈	1	2	yes	—
328	C₄²	#11929608	1	2	yes	—
329	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
330	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
331	C₄²	#11929624	1	1	yes	characteristic
332	C₄²	#11929624	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	C₄⋊(C₇₉⋊C₈)	1	4	yes	complemented
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
370	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
371	C₂×C₄	#14579088	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
373	C₂×C₄	#14579120	1	1	yes	characteristic
374	C₂×C₄	#14579135	1	1	yes	characteristic
375	C₂×C₄	#14579135	1	1	yes	characteristic
376	C₂×C₄	#14579140	1	1	yes	characteristic
377	C₂×C₄	#14579140	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
379	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
380	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
381	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
382	C₂×C₄	#14579181	1	2	yes	—
383	C₂×C₄	#14579187	1	2	yes	—
384	C₈	—	316	4	no	—
385	C₈	—	632	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	#19098423	1	1	yes	characteristic
394	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
395	C₂²	#19098527	1	1	yes	characteristic
396	C₂²	#19098559	1	1	yes	characteristic
397	C₂²	#19098568	1	1	yes	characteristic
398	C₂²	C₂×#14579088	1	1	yes	characteristic
399	C₂²	#19098580	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	C₂×C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
410	C₄	#19098587	1	1	yes	characteristic
411	C₄	#19098616	1	1	yes	characteristic
412	C₄	#19098620	1	1	yes	characteristic
413	C₄	#19098778	1	2	yes	—
414	C₄	#19098863	1	2	yes	—
415	C₂	—	4	4	no	—
416	C₂	#23761782	1	1	yes	characteristic
417	C₂	#23761791	1	1	yes	characteristic
418	C₂	#23761834	1	1	yes	characteristic
419	C₂	#23761843	1	1	yes	characteristic
420	C₂	#23763380	1	1	yes	characteristic
421	C₂	#23763410	1	1	yes	characteristic
422	C₂	#23763420	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄²×D₄×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄²×D₄	D₇₉
hypocenter	C₇₉	#8565
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. #23763517	C₂	semidirect
2. C₄×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
4. #23761241	C₂	semidirect
40. C₄×D₄×C₇₉	C₈	semidirect
132. D₄×C₇₉	C₄⋊C₈	semidirect
217. C₇₉	#8565	semidirect
247. C₄×D₄	C₇₉⋊C₈	semidirect
344. D₄	C₄⋊(C₇₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#23763517	2
C₄×C₄⋊(C₇₉⋊C₈)	2
C₂×D₄⋊(C₇₉⋊C₈)	2
#23761241	2
C₄²×D₄×C₇₉	2
#8565	79