Subgroups — #34307059

Order 20224.

896 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098687	C₂	1	2	yes	maximal
2	C₄²×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
3	#23764116	C₂	1	2	yes	maximal
4	#23764115	C₂	1	4	yes	maximal
5	#23763551	C₂	1	2	yes	maximal
6	C₄⋊C₈×Dic₇₉	C₂	1	2	yes	maximal
7	C₄×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1842	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Dic₁₅₈	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₁₅₈	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
12	#19098687	—	2	8	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₇₉⋊C₈	C₂²	1	4	yes	—
16	C₂×Dic₇₉⋊C₈	C₂²	1	4	yes	—
17	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
18	C₂×C₈×Dic₇₉	C₂²	1	4	yes	—
19	C₄×Dic₇₉⋊C₄	C₄	1	2	yes	—
20	C₄×Dic₇₉⋊C₄	C₄	1	2	yes	—
21	C₄×Dic₇₉⋊C₄	C₂²	1	2	yes	—
22	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
24	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
25	C₄²×Dic₇₉	C₂²	1	2	yes	—
26	#19098318	C₂²	1	2	yes	—
27	#19098317	C₂²	1	4	yes	—
28	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
31	C₄³×C₇₉	C₂²	1	1	yes	characteristic
32	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
34	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
35	C₄×Dic₁₅₈	—	2	4	no	—
36	C₄×Dic₁₅₈	C₈	1	8	yes	complemented
37	C₄×Dic₁₅₈	D₄	1	4	yes	—
38	C₄×Dic₁₅₈	Q₈	1	4	yes	—
39	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
42	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
47	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
48	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
50	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
51	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₇₉⋊C₈)	Q₈	1	4	yes	complemented
53	Dic₇₉⋊C₈	—	2	8	no	—
54	Dic₇₉⋊C₈	—	4	4	no	—
55	C₄×C₇₉⋊C₈	—	2	4	no	—
56	C₈×Dic₇₉	—	2	8	no	—
57	C₇₉⋊#95	C₂×C₄	1	2	yes	—
58	C₇₉⋊#95	C₂×C₄	1	2	yes	—
59	C₇₉⋊#95	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
61	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₇₉	—	2	4	no	—
69	C₄⋊C₈×C₇₉	—	2	4	no	—
70	C₄⋊C₈×C₇₉	—	4	2	no	—
71	C₂×Dic₁₅₈	C₄⋊C₄	1	4	yes	—
72	C₂×Dic₁₅₈	C₂×C₈	1	4	yes	—
73	C₂×Dic₁₅₈	M₁₆	1	4	yes	—
74	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
75	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
76	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
77	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
78	C₂×C₇₉⋊C₈	—	2	2	no	—
79	C₂×C₇₉⋊C₈	—	2	2	no	—
80	C₂×C₇₉⋊C₈	—	2	2	no	—
81	C₂×C₇₉⋊C₈	—	2	2	no	—
82	C₂×C₇₉⋊C₈	—	2	2	no	—
83	C₂×C₇₉⋊C₈	C₂×Q₈	1	4	yes	—
84	C₄⋊Dic₇₉	—	2	2	no	—
85	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
86	C₄⋊Dic₇₉	C₂×C₈	1	4	yes	—
87	Dic₇₉⋊C₄	—	2	4	no	—
88	Dic₇₉⋊C₄	C₄⋊C₄	1	8	yes	—
89	Dic₇₉⋊C₄	C₂×C₈	1	8	yes	—
90	C₄×Dic₇₉	—	2	4	no	—
91	C₄×Dic₇₉	—	2	4	no	—
92	C₄×Dic₇₉	—	2	2	no	—
93	C₄×Dic₇₉	—	2	2	no	—
94	C₄×Dic₇₉	—	4	2	no	—
95	C₄×Dic₇₉	C₂×C₈	1	8	yes	—
96	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
97	C₄×Dic₇₉	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₇₉	—	2	4	no	—
106	C₂×C₈×C₇₉	—	2	4	no	—
107	C₂×C₈×C₇₉	—	2	4	no	—
108	C₄²×C₇₉	—	2	2	no	—
109	C₄²×C₇₉	—	2	2	no	—
110	C₄²×C₇₉	—	2	1	no	—
111	C₄²×C₇₉	—	2	1	no	—
112	C₄²×C₇₉	—	4	1	no	—
113	C₄²×C₇₉	C₂×C₈	1	4	yes	—
114	C₄²×C₇₉	C₂×D₄	1	2	yes	—
115	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
116	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
117	C₄²×C₇₉	#41	1	2	yes	—
118	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₇₉	—	2	1	no	—
120	C₂×C₄×C₇₉	—	2	1	no	—
121	C₂×C₄×C₇₉	—	2	1	no	—
122	C₂×C₄×C₇₉	—	2	1	no	—
123	C₂×C₄×C₇₉	—	2	1	no	—
124	C₂×C₄×C₇₉	—	2	1	no	—
125	C₂×C₄×C₇₉	—	2	1	no	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
131	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
136	C₂×C₄×C₇₉	#131	1	2	yes	—
137	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
141	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×Dic₇₉	—	2	2	no	—
144	C₂×Dic₇₉	—	2	2	no	—
145	C₂×Dic₇₉	—	2	2	no	—
146	C₂×Dic₇₉	—	2	2	no	—
147	C₂×Dic₇₉	—	2	2	no	—
148	C₂×Dic₇₉	—	2	2	no	—
149	C₂×Dic₇₉	—	2	2	no	—
150	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×Dic₇₉	C₂²×C₈	1	4	yes	—
153	C₂×Dic₇₉	C₂²×C₈	1	4	yes	—
154	C₂×Dic₇₉	C₂×M₁₆	1	4	yes	—
155	Dic₁₅₈	C₄⋊C₈	1	16	yes	complemented
156	C₈×C₇₉	—	4	4	no	—
157	C₇₉⋊C₈	—	2	4	no	—
158	C₇₉⋊C₈	—	4	2	no	—
159	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
161	C₂²×C₇₉	#520	1	1	yes	characteristic
162	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
163	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
164	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
165	C₂²×C₇₉	#568	1	1	yes	characteristic
166	C₄×C₇₉	—	2	2	no	—
167	C₄×C₇₉	—	2	2	no	—
168	C₄×C₇₉	—	2	2	no	—
169	C₄×C₇₉	—	4	1	no	—
170	C₄×C₇₉	C₂×C₄⋊C₈	1	4	yes	—
171	C₄×C₇₉	C₈×Q₈	1	4	yes	complemented
172	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
173	C₄×C₇₉	#550	1	1	yes	characteristic
174	C₄×C₇₉	#557	1	1	yes	characteristic
175	C₄×C₇₉	Q₈²	1	1	yes	characteristic
176	Dic₇₉	—	2	4	no	—
177	Dic₇₉	—	2	4	no	—
178	Dic₇₉	—	4	2	no	—
179	Dic₇₉	C₂×C₄⋊C₈	1	8	yes	—
180	Q₈×C₄⋊C₈	—	79	1	no	maximal, Sylow
181	C₂×C₇₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₇₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
183	C₂×C₇₉	#2906	1	1	yes	characteristic
184	C₂×C₇₉	C₂×C₈×Q₈	1	1	yes	characteristic
185	C₂×C₇₉	Q₈×M₁₆	1	1	yes	characteristic
186	C₂×C₇₉	#2988	1	1	yes	characteristic
187	C₂×C₇₉	#2991	1	1	yes	characteristic
188	C₂×C₈×Q₈	—	79	2	no	—
189	C₄²×Q₈	—	79	1	no	—
190	#1939	—	79	4	no	—
191	#1939	—	79	2	no	—
192	#1842	—	79	2	no	—
193	#1842	D₇₉	1	1	yes	characteristic
194	C₄×C₄⋊C₈	—	79	2	no	—
195	C₄×C₄⋊C₈	—	79	1	no	—
196	C₇₉	Q₈×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
197	C₂×C₄×Q₈	—	79	1	no	—
198	C₂×C₄×Q₈	—	79	1	no	—
199	C₂×C₄×Q₈	—	79	1	no	—
200	C₈×Q₈	—	158	8	no	—
201	C₂×C₄⋊C₈	—	79	4	no	—
202	C₂×C₄⋊C₈	—	79	1	no	—
203	C₂×C₄⋊C₈	—	79	4	no	—
204	C₂×C₄⋊C₈	—	79	1	no	—
205	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
206	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
207	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
208	C₂×C₄×C₈	—	79	4	no	—
209	C₂×C₄×C₈	—	79	2	no	—
210	C₄×C₄⋊C₄	—	79	1	no	—
211	C₄×C₄⋊C₄	—	79	2	no	—
212	C₄×C₄⋊C₄	—	79	1	no	—
213	C₄×C₄⋊C₄	—	79	1	no	—
214	C₄×C₄⋊C₄	—	79	2	no	—
215	C₄×C₄⋊C₄	—	79	2	no	—
216	C₄³	—	79	2	no	—
217	C₄³	C₂×D₇₉	1	1	yes	characteristic
218	#336	—	79	4	no	—
219	#336	—	79	2	no	—
220	C₂²×Q₈	—	79	1	no	—
221	C₂²×C₈	—	79	2	no	—
222	C₂²×C₈	—	79	2	no	—
223	C₂²×C₈	C₂²×D₇₉	1	4	yes	—
224	C₄×Q₈	—	79	8	no	—
225	C₄×Q₈	—	79	4	no	—
226	C₄×Q₈	—	79	4	no	—
227	C₄×Q₈	—	158	4	no	—
228	C₂×C₄⋊C₄	—	79	2	no	—
229	C₂×C₄⋊C₄	—	79	2	no	—
230	C₂×C₄⋊C₄	—	79	1	no	—
231	C₂×C₄⋊C₄	—	79	1	no	—
232	C₂×C₄⋊C₄	—	79	2	no	—
233	C₂×C₄⋊C₄	—	79	1	no	—
234	C₂×C₄²	—	79	2	no	—
235	C₂×C₄²	—	79	2	no	—
236	C₂×C₄²	—	79	2	no	—
237	C₂×C₄²	—	79	2	no	—
238	C₂×C₄²	—	79	2	no	—
239	C₂×C₄²	—	79	2	no	—
240	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	4	2	no	—
250	C₄⋊C₈	—	316	4	no	—
251	C₄⋊C₈	—	79	4	no	—
252	C₄⋊C₈	—	158	8	no	—
253	C₄⋊C₈	—	158	2	no	—
254	C₄×C₈	—	158	8	no	—
255	C₄×C₈	—	158	4	no	—
256	#95	—	79	2	no	—
257	#95	—	79	2	no	—
258	#95	—	79	2	no	—
259	C₂×Q₈	—	79	4	no	—
260	C₂×Q₈	—	79	4	no	—
261	C₂×Q₈	—	79	4	no	—
262	C₂²×C₄	—	79	2	no	—
263	C₂²×C₄	—	79	2	no	—
264	C₂²×C₄	—	79	2	no	—
265	C₂²×C₄	—	79	2	no	—
266	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
272	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	79	4	no	—
277	C₂×C₈	—	158	2	no	—
278	C₂×C₈	—	158	2	no	—
279	C₂×C₈	—	158	2	no	—
280	C₂×C₈	—	158	2	no	—
281	C₂×C₈	—	158	2	no	—
282	C₄⋊C₄	—	79	8	no	—
283	C₄⋊C₄	—	79	4	no	—
284	C₄⋊C₄	—	79	8	no	—
285	C₄⋊C₄	—	79	4	no	—
286	C₄⋊C₄	—	158	4	no	—
287	C₄⋊C₄	—	158	2	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	316	2	no	—
294	C₄²	—	79	4	no	—
295	C₄²	—	79	8	no	—
296	C₄²	—	79	4	no	—
297	C₄²	—	158	4	no	—
298	C₄²	—	158	2	no	—
299	C₄²	—	158	2	no	—
300	C₄²	—	158	4	no	—
301	C₄²	C₈×D₇₉	1	4	yes	—
302	C₄²	D₄×D₇₉	1	2	yes	—
303	C₄²	Q₈×D₇₉	1	2	yes	—
304	C₄²	Q₈×D₇₉	1	2	yes	—
305	C₄²	#11929623	1	2	yes	—
306	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
307	Q₈	—	79	16	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	79	4	no	—
318	C₂×C₄	—	79	4	no	—
319	C₂×C₄	—	79	4	no	—
320	C₂×C₄	—	79	4	no	—
321	C₂×C₄	—	79	4	no	—
322	C₂×C₄	—	158	2	no	—
323	C₂×C₄	—	158	2	no	—
324	C₂×C₄	—	158	2	no	—
325	C₂×C₄	—	158	2	no	—
326	C₂×C₄	—	158	2	no	—
327	C₂×C₄	—	158	2	no	—
328	C₂×C₄	—	158	2	no	—
329	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
330	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
331	C₂×C₄	#14579126	1	2	yes	—
332	C₂×C₄	#14579126	1	2	yes	—
333	C₂×C₄	C₂×C₈×D₇₉	1	2	yes	—
334	C₂×C₄	C₂×C₈×D₇₉	1	2	yes	—
335	C₂×C₄	C₂×C₈×D₇₉	1	2	yes	—
336	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
337	C₂×C₄	#14579169	1	2	yes	—
338	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
339	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
341	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
342	C₂×C₄	#14579206	1	1	yes	characteristic
343	C₂×C₄	#14579209	1	1	yes	characteristic
344	C₈	—	4	4	no	—
345	C₈	—	316	2	no	—
346	C₈	—	158	4	no	—
347	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
348	C₂²	C₂×#14579126	1	1	yes	characteristic
349	C₂²	#19099044	1	1	yes	characteristic
350	C₂²	C₂²×C₈×D₇₉	1	1	yes	characteristic
351	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
352	C₂²	C₂×#14579169	1	1	yes	characteristic
353	C₂²	#19099329	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	316	2	no	—
359	C₄	—	79	8	no	—
360	C₄	—	158	4	no	—
361	C₄	—	158	4	no	—
362	C₄	C₄⋊C₈×D₇₉	1	4	yes	—
363	C₄	#19098687	1	4	yes	complemented
364	C₄	#19099228	1	1	yes	characteristic
365	C₄	#19099233	1	1	yes	characteristic
366	C₄	#19099288	1	1	yes	characteristic
367	C₄	#19099293	1	1	yes	characteristic
368	C₂	#23766312	1	1	yes	characteristic
369	C₂	C₂×C₄⋊C₈×D₇₉	1	1	yes	characteristic
370	C₂	#23771969	1	1	yes	characteristic
371	C₂	C₂×#19098687	1	1	yes	characteristic
372	C₂	#23772351	1	1	yes	characteristic
373	C₂	#23772509	1	1	yes	characteristic
374	C₂	#23772530	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₈
Fitting	C₇₉×#1842	C₂
socle, prime radical	C₂³×C₇₉	C₂³×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1842	D₇₉
hypocenter	C₇₉	Q₈×C₄⋊C₈
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
36. C₄×Dic₁₅₈	C₈	semidirect
52. C₄⋊(C₇₉⋊C₈)	Q₈	semidirect
155. Dic₁₅₈	C₄⋊C₈	semidirect
171. C₄×C₇₉	C₈×Q₈	semidirect
196. C₇₉	Q₈×C₄⋊C₈	semidirect
363. C₄	#19098687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098687	2
C₄²×Dic₁₅₈	2
#23764116	2
#23764115	2
#23763551	2
C₄⋊C₈×Dic₇₉	2
C₄×C₄⋊(C₇₉⋊C₈)	2
C₇₉×#1842	2
Q₈×C₄⋊C₈	79