Subgroups — #34304883

Order 20224.

1010 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#23766357	C₂	1	1	yes	maximal, characteristic
3	#23764366	C₂	1	2	yes	maximal
4	#23764362	C₂	1	1	yes	maximal, characteristic
5	#23764358	C₂	1	2	yes	maximal
6	#23764353	C₂	1	1	yes	maximal, characteristic
7	#23763415	C₂	1	2	yes	maximal
8	#23763405	C₂	1	1	yes	maximal, characteristic
9	C₄×#14579085	C₂	1	1	yes	maximal, characteristic
10	C₄×#14579085	C₂	1	2	yes	maximal
11	C₂×#557×C₇₉	C₂	1	1	yes	maximal, characteristic
12	Q₈×C₇₉⋊C₈	—	2	4	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
15	C₂×#14579085	C₂²	1	2	yes	—
16	C₂×#14579085	C₂²	1	1	yes	characteristic
17	C₂×#14579085	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
20	#19098470	—	2	1	no	—
21	#19098449	—	2	2	no	—
22	#19098433	C₂²	1	1	yes	characteristic
23	#19098429	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₇₉	—	2	1	no	—
25	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
27	#19098325	C₂²	1	2	yes	—
28	#19098325	C₂²	1	1	yes	characteristic
29	#19098325	C₂²	1	2	yes	—
30	#19098325	C₂²	1	1	yes	characteristic
31	#19098325	C₂²	1	2	yes	—
32	#19098325	C₂²	1	2	yes	—
33	#19098325	C₂²	1	2	yes	—
34	#557×C₇₉	—	2	4	no	—
35	#557×C₇₉	C₄	1	8	yes	complemented
36	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
37	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#125×C₇₉	—	2	2	no	—
39	C₂×#125×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
41	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
44	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₇₉	—	2	1	no	—
48	C₂×C₄⋊Dic₇₉	—	2	1	no	—
49	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₇₉	—	2	1	no	—
53	C₂×C₄×Dic₇₉	—	2	2	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
56	#14579085	—	2	4	no	—
57	#14579085	—	2	2	no	—
58	#14579085	Q₈	1	4	yes	complemented
59	C₄×C₇₉⋊C₈	—	2	4	no	—
60	C₄×C₇₉⋊C₈	—	2	2	no	—
61	C₇₉⋊#95	—	2	1	no	—
62	C₇₉⋊#95	—	2	2	no	—
63	C₇₉⋊#95	—	2	2	no	—
64	C₇₉⋊#95	—	2	2	no	—
65	C₂²×Q₈×C₇₉	—	2	1	no	—
66	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
67	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	—	2	8	no	—
69	C₄⋊Q₈×C₇₉	—	2	2	no	—
70	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
71	#125×C₇₉	—	2	16	no	—
72	#125×C₇₉	—	2	4	no	—
73	#125×C₇₉	C₂×C₄	1	8	yes	—
74	C₄×Q₈×C₇₉	—	2	8	no	—
75	C₄×Q₈×C₇₉	—	2	4	no	—
76	C₄×Q₈×C₇₉	—	2	2	no	—
77	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
78	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
79	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
80	C₄×Q₈×C₇₉	D₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₇₉	—	2	2	no	—
91	C₂×C₄²×C₇₉	—	2	1	no	—
92	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
94	C₂²×Dic₇₉	—	2	1	no	—
95	C₂²×Dic₇₉	—	2	1	no	—
96	C₂²×Dic₇₉	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	2	no	—
101	C₂×C₇₉⋊C₈	—	2	1	no	—
102	C₂×C₇₉⋊C₈	—	2	1	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
106	C₄⋊Dic₇₉	—	2	1	no	—
107	C₄⋊Dic₇₉	—	2	2	no	—
108	C₄⋊Dic₇₉	—	2	1	no	—
109	C₄⋊Dic₇₉	—	2	1	no	—
110	C₄⋊Dic₇₉	—	2	2	no	—
111	C₄⋊Dic₇₉	—	4	2	no	—
112	C₄⋊Dic₇₉	—	8	1	no	—
113	C₄⋊Dic₇₉	C₂×Q₈	1	2	yes	—
114	C₄×Dic₇₉	—	4	2	no	—
115	C₄×Dic₇₉	—	8	2	no	—
116	C₂×Q₈×C₇₉	—	2	4	no	—
117	C₂×Q₈×C₇₉	—	2	2	no	—
118	C₂×Q₈×C₇₉	—	2	2	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	—	2	1	no	—
121	C₂×Q₈×C₇₉	—	2	1	no	—
122	C₂×Q₈×C₇₉	—	4	2	no	—
123	C₂×Q₈×C₇₉	—	4	2	no	—
124	C₂×Q₈×C₇₉	C₂²⋊C₄	1	4	yes	—
125	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
127	C₂×Q₈×C₇₉	#41	1	2	yes	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	2	1	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₇₉	—	2	8	no	—
137	C₄⋊C₄×C₇₉	—	2	4	no	—
138	C₄⋊C₄×C₇₉	—	2	8	no	—
139	C₄⋊C₄×C₇₉	—	2	4	no	—
140	C₄⋊C₄×C₇₉	—	2	8	no	—
141	C₄⋊C₄×C₇₉	—	2	1	no	—
142	C₄⋊C₄×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
144	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	8	yes	—
145	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
147	C₄²×C₇₉	—	2	8	no	—
148	C₄²×C₇₉	—	2	4	no	—
149	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
150	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₇₉	C₂×D₄	1	4	yes	—
152	C₄²×C₇₉	C₂×D₄	1	2	yes	—
153	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₇₉	—	2	2	no	—
155	Q₈×C₇₉	—	2	2	no	—
156	Q₈×C₇₉	—	2	2	no	—
157	Q₈×C₇₉	—	2	8	no	—
158	Q₈×C₇₉	—	4	8	no	—
159	Q₈×C₇₉	C₄×Q₈	1	4	yes	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	1	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	4	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	4	2	no	—
173	C₂×C₄×C₇₉	—	4	1	no	—
174	C₂×C₄×C₇₉	—	4	1	no	—
175	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₇₉	#135	1	2	yes	—
180	C₂×C₄×C₇₉	#135	1	2	yes	—
181	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₇₉	—	2	2	no	—
188	C₂×Dic₇₉	—	4	1	no	—
189	C₂×Dic₇₉	—	4	1	no	—
190	C₂×Dic₇₉	—	4	1	no	—
191	C₂×Dic₇₉	—	4	2	no	—
192	C₂×Dic₇₉	—	4	1	no	—
193	C₂×Dic₇₉	—	4	2	no	—
194	C₂×Dic₇₉	—	4	2	no	—
195	C₂×Dic₇₉	—	4	1	no	—
196	C₇₉⋊C₈	—	2	2	no	—
197	C₇₉⋊C₈	—	4	2	no	—
198	C₇₉⋊C₈	—	4	1	no	—
199	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₇₉	#548	1	1	yes	characteristic
201	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
203	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
204	C₂²×C₇₉	#577	1	1	yes	characteristic
205	C₂²×C₇₉	#578	1	1	yes	characteristic
206	C₄×C₇₉	—	2	4	no	—
207	C₄×C₇₉	—	2	4	no	—
208	C₄×C₇₉	—	2	4	no	—
209	C₄×C₇₉	—	2	2	no	—
210	C₄×C₇₉	—	4	4	no	—
211	C₄×C₇₉	—	4	2	no	—
212	C₄×C₇₉	#416	1	4	yes	—
213	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₄×C₇₉	#519	1	1	yes	characteristic
215	C₄×C₇₉	#548	1	1	yes	characteristic
216	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
217	Dic₇₉	—	4	2	no	—
218	Dic₇₉	—	8	1	no	—
219	Dic₇₉	—	8	2	no	—
220	#22521	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₇₉	C₂×#416	1	1	yes	characteristic
223	C₂×C₇₉	#2898	1	1	yes	characteristic
224	C₂×C₇₉	#3364	1	1	yes	characteristic
225	C₂×C₇₉	#3365	1	1	yes	characteristic
226	C₂×C₇₉	#3381	1	1	yes	characteristic
227	C₂×C₇₉	#3383	1	1	yes	characteristic
228	C₂×#557	D₇₉	1	1	yes	characteristic
229	C₂×C₈×Q₈	—	79	1	no	—
230	#2355	—	79	1	no	—
231	#1991	—	79	2	no	—
232	#1990	—	79	1	no	—
233	#1989	—	79	2	no	—
234	#1988	—	79	1	no	—
235	#1805	—	79	2	no	—
236	#1803	—	79	1	no	—
237	C₄×#103	—	79	1	no	—
238	C₄×#103	—	79	2	no	—
239	C₇₉	#22521	1	1	yes	characteristic, complemented, Sylow
240	#557	—	2	4	no	—
241	#557	Dic₇₉	1	8	yes	complemented
242	C₂×C₄⋊Q₈	—	2	1	no	—
243	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
244	C₂×#125	—	2	2	no	—
245	C₂×#125	C₂×D₇₉	1	2	yes	—
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
249	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
250	C₈×Q₈	—	158	4	no	—
251	C₂×C₄⋊C₈	—	79	1	no	—
252	C₂×C₄⋊C₈	—	79	2	no	—
253	C₂×#103	—	79	1	no	—
254	C₂×#103	—	79	2	no	—
255	C₂×#103	—	79	1	no	—
256	C₂×C₄×C₈	—	79	1	no	—
257	C₂×C₄×C₈	—	79	2	no	—
258	#391	—	158	1	no	—
259	#387	—	158	2	no	—
260	#384	—	79	1	no	—
261	#382	—	79	2	no	—
262	C₄×C₄⋊C₄	—	79	1	no	—
263	C₄×C₄⋊C₄	—	79	2	no	—
264	C₄×C₄⋊C₄	—	158	1	no	—
265	#340	—	79	2	no	—
266	#340	—	79	2	no	—
267	#340	—	79	2	no	—
268	#340	—	79	2	no	—
269	#340	—	79	1	no	—
270	#340	—	79	2	no	—
271	#340	—	79	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
274	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
275	C₂²×C₈	—	79	1	no	—
276	C₂²×C₈	—	79	2	no	—
277	C₂²×C₈	—	79	1	no	—
278	C₄⋊Q₈	—	2	8	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	C₂×Dic₇₉	1	4	yes	—
281	#125	—	2	16	no	—
282	#125	—	2	4	no	—
283	#125	C₂×Dic₇₉	1	8	yes	—
284	C₄×Q₈	—	2	8	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
288	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
289	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
290	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	79	1	no	—
297	C₂×C₄⋊C₄	—	79	1	no	—
298	C₂×C₄⋊C₄	—	79	2	no	—
299	C₂×C₄⋊C₄	—	158	1	no	—
300	C₂×C₄⋊C₄	—	158	1	no	—
301	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	158	1	no	—
308	C₂×C₄²	—	158	2	no	—
309	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
310	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
311	C₄⋊C₈	—	158	4	no	—
312	C₄⋊C₈	—	158	2	no	—
313	#103	—	79	4	no	—
314	#103	—	158	4	no	—
315	#103	—	158	2	no	—
316	C₄×C₈	—	158	4	no	—
317	C₄×C₈	—	158	2	no	—
318	#95	—	158	1	no	—
319	#95	—	158	2	no	—
320	#95	—	158	2	no	—
321	#95	—	158	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	C₂²⋊Dic₇₉	1	4	yes	—
331	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
332	C₂×Q₈	Q₈×D₇₉	1	2	yes	—
333	C₂×Q₈	#11929625	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	158	1	no	—
338	C₂²×C₄	—	158	2	no	—
339	C₂²×C₄	—	158	1	no	—
340	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
341	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
342	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
345	C₂×C₈	—	79	2	no	—
346	C₂×C₈	—	158	2	no	—
347	C₂×C₈	—	158	1	no	—
348	C₂×C₈	—	158	2	no	—
349	C₂×C₈	—	158	1	no	—
350	C₂×C₈	—	158	2	no	—
351	C₂×C₈	—	158	1	no	—
352	C₂×C₈	—	158	1	no	—
353	C₂×C₈	—	158	1	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	316	2	no	—
362	C₄⋊C₄	—	79	2	no	—
363	C₄⋊C₄	—	632	1	no	—
364	C₄⋊C₄	—	158	1	no	—
365	C₄⋊C₄	—	158	2	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	2	no	—
368	C₄⋊C₄	—	158	1	no	—
369	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
370	C₄⋊C₄	C₂²⋊Dic₇₉	1	8	yes	—
371	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
372	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	316	2	no	—
376	C₄²	—	632	2	no	—
377	C₄²	C₂²×Dic₇₉	1	4	yes	—
378	C₄²	C₂²×Dic₇₉	1	2	yes	—
379	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
380	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
381	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	8	no	—
386	Q₈	—	4	8	no	—
387	Q₈	Q₈×Dic₇₉	1	4	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	316	1	no	—
404	C₂×C₄	—	316	1	no	—
405	C₂×C₄	—	316	1	no	—
406	C₂×C₄	—	316	2	no	—
407	C₂×C₄	—	316	1	no	—
408	C₂×C₄	—	316	2	no	—
409	C₂×C₄	—	316	2	no	—
410	C₂×C₄	—	316	1	no	—
411	C₂×C₄	—	158	2	no	—
412	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	4	yes	—
413	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
414	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	4	yes	—
415	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
416	C₂×C₄	#14579181	1	2	yes	—
417	C₂×C₄	#14579181	1	2	yes	—
418	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
422	C₂×C₄	#14579209	1	1	yes	characteristic
423	C₂×C₄	#14579209	1	1	yes	characteristic
424	C₈	—	316	2	no	—
425	C₈	—	316	1	no	—
426	C₈	—	158	2	no	—
427	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
428	C₂²	#19099224	1	1	yes	characteristic
429	C₂²	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
430	C₂²	C₂×#14579181	1	1	yes	characteristic
431	C₂²	C₂×#14579181	1	1	yes	characteristic
432	C₂²	#19099371	1	1	yes	characteristic
433	C₂²	#19099378	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	316	2	no	—
441	C₄	—	632	1	no	—
442	C₄	—	632	2	no	—
443	C₄	#19098559	1	4	yes	—
444	C₄	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
445	C₄	#19099041	1	1	yes	characteristic
446	C₄	#19099224	1	1	yes	characteristic
447	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
448	C₂	Q₈×C₂²⋊Dic₇₉	1	1	yes	characteristic
449	C₂	C₂×#19098559	1	1	yes	characteristic
450	C₂	#23771933	1	1	yes	characteristic
451	C₂	#23776085	1	1	yes	characteristic
452	C₂	#23776096	1	1	yes	characteristic
453	C₂	#23776271	1	1	yes	characteristic
454	C₂	#23776287	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#557×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#557	D₇₉
hypocenter	C₇₉	#22521
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
35. #557×C₇₉	C₄	semidirect
58. #14579085	Q₈	semidirect
239. C₇₉	#22521	semidirect
241. #557	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₇₉⋊C₈	2
#23766357	2
#23764366	2
#23764362	2
#23764358	2
#23764353	2
#23763415	2
#23763405	2
C₄×#14579085	2
C₂×#557×C₇₉	2
#22521	79