Subgroups — #34307177

Order 20224.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098694	C₂	1	1	yes	maximal, characteristic
2	#23765878	C₂	1	1	yes	maximal, characteristic
3	#23764121	C₂	1	2	yes	maximal
4	#23764118	C₂	1	1	yes	maximal, characteristic
5	#23764118	C₂	1	2	yes	maximal
6	#23764116	C₂	1	1	yes	maximal, characteristic
7	#23763519	C₂	1	2	yes	maximal
8	#23763516	C₂	1	1	yes	maximal, characteristic
9	#23763258	C₂	1	2	yes	maximal
10	C₄×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₂×C₈×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
12	#19098694	—	2	4	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
15	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
19	C₂×#14579072	C₂²	1	2	yes	—
20	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	#19098470	C₄	1	1	yes	characteristic
22	#19098470	C₄	1	1	yes	characteristic
23	#19098462	C₄	1	1	yes	characteristic
24	#19098462	C₄	1	1	yes	characteristic
25	#19098449	C₄	1	2	yes	—
26	#19098449	C₄	1	2	yes	—
27	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
29	#19098409	C₂²	1	2	yes	—
30	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
31	#19098317	C₂²	1	1	yes	characteristic
32	#19098317	C₂²	1	1	yes	characteristic
33	#19098317	C₂²	1	2	yes	—
34	#19098317	C₂²	1	2	yes	—
35	#19098317	C₂²	1	2	yes	—
36	#19098317	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₇₉	—	2	4	no	—
39	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
43	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
57	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
59	Dic₇₉⋊C₈	—	2	2	no	—
60	Dic₇₉⋊C₈	—	2	4	no	—
61	Dic₇₉⋊C₈	—	2	2	no	—
62	Dic₇₉⋊C₈	—	2	4	no	—
63	#14579072	—	2	4	no	—
64	C₄×C₇₉⋊C₈	—	2	2	no	—
65	C₇₉⋊#95	C₂×C₄	1	2	yes	—
66	C₇₉⋊#95	C₂×C₄	1	2	yes	—
67	C₇₉⋊#95	C₂×C₄	1	2	yes	—
68	C₇₉⋊#95	C₂×C₄	1	2	yes	—
69	C₇₉⋊#95	C₂×C₄	1	2	yes	—
70	C₇₉⋊#95	C₂×C₄	1	2	yes	—
71	C₇₉⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₇₉	D₄	1	4	yes	—
77	C₄×Q₈×C₇₉	Q₈	1	4	yes	—
78	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₇₉	—	2	2	no	—
83	C₄⋊C₈×C₇₉	—	2	4	no	—
84	C₄×C₈×C₇₉	—	2	2	no	—
85	C₄×C₈×C₇₉	—	2	4	no	—
86	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₇₉⋊C₈	—	2	1	no	—
93	C₂×C₇₉⋊C₈	—	2	1	no	—
94	C₂×C₇₉⋊C₈	—	2	2	no	—
95	C₂×C₇₉⋊C₈	—	2	1	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	2	2	no	—
100	C₂×C₇₉⋊C₈	#41	1	2	yes	—
101	C₄⋊Dic₇₉	—	2	4	no	—
102	C₄⋊Dic₇₉	—	2	2	no	—
103	C₄⋊Dic₇₉	—	2	2	no	—
104	C₄⋊Dic₇₉	—	4	2	no	—
105	C₄×Dic₇₉	—	2	2	no	—
106	C₄×Dic₇₉	—	2	2	no	—
107	C₄×Dic₇₉	—	2	2	no	—
108	C₄×Dic₇₉	—	2	1	no	—
109	C₄×Dic₇₉	—	2	2	no	—
110	C₄×Dic₇₉	—	2	1	no	—
111	C₄×Dic₇₉	—	2	2	no	—
112	C₄×Dic₇₉	—	2	1	no	—
113	C₄×Dic₇₉	—	2	1	no	—
114	C₄×Dic₇₉	—	4	1	no	—
115	C₂×Q₈×C₇₉	—	2	2	no	—
116	C₂×Q₈×C₇₉	—	2	2	no	—
117	C₂×Q₈×C₇₉	C₄⋊C₄	1	4	yes	—
118	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₇₉	—	2	1	no	—
124	C₂×C₈×C₇₉	—	2	1	no	—
125	C₂×C₈×C₇₉	—	2	2	no	—
126	C₂×C₈×C₇₉	—	2	2	no	—
127	C₂×C₈×C₇₉	—	2	1	no	—
128	C₂×C₈×C₇₉	—	2	1	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₂×C₈×C₇₉	—	2	1	no	—
131	C₂×C₈×C₇₉	#41	1	2	yes	—
132	C₄⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
133	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
134	C₄²×C₇₉	C₂×D₄	1	2	yes	—
135	C₄²×C₇₉	C₂×D₄	1	4	yes	—
136	C₄²×C₇₉	C₂×Q₈	1	4	yes	—
137	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
138	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
139	Q₈×C₇₉	—	2	8	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	2	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
149	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₇₉	#131	1	2	yes	—
151	C₂×C₄×C₇₉	#131	1	2	yes	—
152	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×Dic₇₉	—	2	1	no	—
159	C₂×Dic₇₉	—	2	1	no	—
160	C₂×Dic₇₉	—	2	2	no	—
161	C₂×Dic₇₉	—	2	2	no	—
162	C₂×Dic₇₉	—	2	1	no	—
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	1	no	—
166	C₂×Dic₇₉	—	2	1	no	—
167	C₂×Dic₇₉	—	2	1	no	—
168	C₂×Dic₇₉	—	2	1	no	—
169	C₂×Dic₇₉	—	2	2	no	—
170	C₂×Dic₇₉	—	2	2	no	—
171	C₂×Dic₇₉	—	2	2	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	#131	1	2	yes	—
176	C₈×C₇₉	—	2	2	no	—
177	C₈×C₇₉	—	4	1	no	—
178	C₈×C₇₉	—	4	2	no	—
179	C₇₉⋊C₈	—	2	2	no	—
180	C₇₉⋊C₈	—	4	1	no	—
181	C₇₉⋊C₈	—	4	2	no	—
182	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
184	C₂²×C₇₉	#519	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
186	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
187	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
188	C₂²×C₇₉	#568	1	1	yes	characteristic
189	C₄×C₇₉	—	2	4	no	—
190	C₄×C₇₉	—	2	2	no	—
191	C₄×C₇₉	—	2	4	no	—
192	C₄×C₇₉	#424	1	4	yes	—
193	C₄×C₇₉	#548	1	1	yes	characteristic
194	C₄×C₇₉	#548	1	1	yes	characteristic
195	C₄×C₇₉	#557	1	1	yes	characteristic
196	C₄×C₇₉	#557	1	1	yes	characteristic
197	Dic₇₉	—	2	2	no	—
198	Dic₇₉	—	4	2	no	—
199	Dic₇₉	—	4	1	no	—
200	Dic₇₉	—	4	2	no	—
201	Dic₇₉	—	4	1	no	—
202	Dic₇₉	—	4	1	no	—
203	#22735	—	79	1	no	maximal, Sylow
204	C₂×C₇₉	#2351	1	1	yes	characteristic
205	C₂×C₇₉	C₂×#424	1	1	yes	characteristic
206	C₂×C₇₉	#2906	1	1	yes	characteristic
207	C₂×C₇₉	#2966	1	1	yes	characteristic
208	C₂×C₇₉	#2969	1	1	yes	characteristic
209	C₂×C₇₉	#2985	1	1	yes	characteristic
210	C₂×C₇₉	#2986	1	1	yes	characteristic
211	C₂×#446	—	79	1	no	—
212	C₂×C₈×Q₈	D₇₉	1	1	yes	characteristic
213	#2295	—	79	1	no	—
214	#1940	—	79	2	no	—
215	#1939	—	79	1	no	—
216	#1939	—	79	2	no	—
217	#1939	—	79	1	no	—
218	#1832	—	79	2	no	—
219	#1831	—	79	1	no	—
220	#1768	—	79	2	no	—
221	C₄×C₄⋊C₈	—	79	1	no	—
222	C₇₉	#22735	1	1	yes	characteristic, complemented, Sylow
223	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
224	#446	—	158	4	no	—
225	C₈×Q₈	—	2	4	no	—
226	C₂×C₄⋊C₈	—	79	1	no	—
227	C₂×C₄⋊C₈	—	79	2	no	—
228	C₂×C₄⋊C₈	—	79	2	no	—
229	C₂×C₄⋊C₈	—	79	1	no	—
230	C₂×C₄⋊C₈	—	79	1	no	—
231	C₂×C₄⋊C₈	—	79	2	no	—
232	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
234	C₂×#97	—	79	2	no	—
235	C₂×C₄×C₈	—	79	1	no	—
236	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
238	#391	—	79	1	no	—
239	#391	—	79	1	no	—
240	#389	—	79	1	no	—
241	#389	—	79	1	no	—
242	#387	—	79	2	no	—
243	#387	—	79	2	no	—
244	C₄×C₄⋊C₄	—	79	1	no	—
245	C₄×C₄⋊C₄	—	79	2	no	—
246	#376	—	79	2	no	—
247	C₄³	—	79	1	no	—
248	#336	—	79	2	no	—
249	#336	—	79	2	no	—
250	#336	—	79	1	no	—
251	#336	—	79	2	no	—
252	#336	—	79	2	no	—
253	#336	—	79	1	no	—
254	C₂²×Q₈	C₄×D₇₉	1	1	yes	characteristic
255	C₂²×C₈	—	79	1	no	—
256	C₂²×C₈	—	79	1	no	—
257	C₂²×C₈	—	79	2	no	—
258	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
259	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
261	C₄×Q₈	Dic₁₅₈	1	4	yes	—
262	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
263	C₂×C₄⋊C₄	—	79	2	no	—
264	C₂×C₄⋊C₄	—	79	2	no	—
265	C₂×C₄⋊C₄	—	79	1	no	—
266	C₂×C₄⋊C₄	—	79	1	no	—
267	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
269	C₂×C₄²	—	79	1	no	—
270	C₂×C₄²	—	79	1	no	—
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	2	no	—
276	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	158	4	no	—
281	C₄⋊C₈	—	158	2	no	—
282	C₄⋊C₈	—	158	2	no	—
283	C₄⋊C₈	—	158	4	no	—
284	C₄⋊C₈	—	158	2	no	—
285	C₄⋊C₈	—	158	4	no	—
286	#97	—	158	4	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	4	no	—
289	C₄×C₈	—	158	2	no	—
290	#95	—	79	2	no	—
291	#95	—	79	2	no	—
292	#95	—	79	2	no	—
293	#95	—	79	2	no	—
294	#95	—	79	2	no	—
295	#95	—	79	2	no	—
296	#95	—	79	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	Dic₇₉⋊C₄	1	4	yes	—
300	C₂²×C₄	—	79	1	no	—
301	C₂²×C₄	—	79	1	no	—
302	C₂²×C₄	—	79	1	no	—
303	C₂²×C₄	—	79	2	no	—
304	C₂²×C₄	—	79	2	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	79	2	no	—
320	C₂×C₈	—	158	1	no	—
321	C₂×C₈	—	158	2	no	—
322	C₂×C₈	—	158	1	no	—
323	C₂×C₈	—	158	2	no	—
324	C₂×C₈	—	158	1	no	—
325	C₂×C₈	—	158	2	no	—
326	C₂×C₈	—	158	1	no	—
327	C₂×C₈	—	158	1	no	—
328	C₂×C₈	#11929625	1	2	yes	—
329	C₄⋊C₄	—	316	2	no	—
330	C₄⋊C₄	—	158	4	no	—
331	C₄⋊C₄	—	158	2	no	—
332	C₄⋊C₄	—	158	2	no	—
333	C₄⋊C₄	Dic₇₉⋊C₄	1	8	yes	—
334	C₄⋊C₄	Dic₇₉⋊C₄	1	4	yes	—
335	C₄²	—	316	1	no	—
336	C₄²	—	158	2	no	—
337	C₄²	—	158	2	no	—
338	C₄²	—	158	1	no	—
339	C₄²	—	158	2	no	—
340	C₄²	—	158	1	no	—
341	C₄²	—	158	1	no	—
342	C₄²	—	158	1	no	—
343	C₄²	—	158	2	no	—
344	C₄²	—	158	2	no	—
345	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
346	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
347	C₄²	C₂×Dic₁₅₈	1	4	yes	—
348	C₄²	C₂×Dic₁₅₈	1	2	yes	—
349	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
350	Q₈	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	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	—	79	2	no	—
358	C₂×C₄	—	158	2	no	—
359	C₂×C₄	—	158	2	no	—
360	C₂×C₄	—	158	1	no	—
361	C₂×C₄	—	158	1	no	—
362	C₂×C₄	—	158	1	no	—
363	C₂×C₄	—	158	1	no	—
364	C₂×C₄	—	158	2	no	—
365	C₂×C₄	—	158	1	no	—
366	C₂×C₄	—	158	1	no	—
367	C₂×C₄	—	158	1	no	—
368	C₂×C₄	—	158	2	no	—
369	C₂×C₄	—	158	2	no	—
370	C₂×C₄	—	158	1	no	—
371	C₂×C₄	—	158	1	no	—
372	C₂×C₄	—	158	2	no	—
373	C₂×C₄	—	158	1	no	—
374	C₂×C₄	—	158	1	no	—
375	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
376	C₂×C₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
377	C₂×C₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
378	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
379	C₂×C₄	#14579167	1	2	yes	—
380	C₂×C₄	#14579167	1	2	yes	—
381	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
382	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
383	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
385	C₂×C₄	#14579208	1	1	yes	characteristic
386	C₂×C₄	#14579209	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	316	1	no	—
391	C₈	—	316	2	no	—
392	C₈	—	158	2	no	—
393	C₂²	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
394	C₂²	C₄×#11929625	1	1	yes	characteristic
395	C₂²	#19099039	1	1	yes	characteristic
396	C₂²	#131×D₇₉	1	1	yes	characteristic
397	C₂²	C₂×#14579167	1	1	yes	characteristic
398	C₂²	C₂×#14579167	1	1	yes	characteristic
399	C₂²	#19099328	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	316	1	no	—
404	C₄	—	316	1	no	—
405	C₄	—	316	2	no	—
406	C₄	—	316	1	no	—
407	C₄	—	316	2	no	—
408	C₄	—	158	2	no	—
409	C₄	#19098589	1	4	yes	—
410	C₄	#19099220	1	1	yes	characteristic
411	C₄	#19099224	1	1	yes	characteristic
412	C₄	#19099289	1	1	yes	characteristic
413	C₄	#19099292	1	1	yes	characteristic
414	C₂	#23766318	1	1	yes	characteristic
415	C₂	C₂×#19098589	1	1	yes	characteristic
416	C₂	#23771966	1	1	yes	characteristic
417	C₂	#23772377	1	1	yes	characteristic
418	C₂	#23772403	1	1	yes	characteristic
419	C₂	#23772491	1	1	yes	characteristic
420	C₂	#23772500	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₂×C₈×Q₈×C₇₉	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×C₈×Q₈	D₇₉
hypocenter	C₇₉	#22735
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
222. C₇₉	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098694	2
#23765878	2
#23764121	2
#23764118	2
#23764116	2
#23763519	2
#23763516	2
#23763258	2
C₄×Dic₇₉⋊C₈	2
C₂×C₈×Q₈×C₇₉	2
#22735	79