Subgroups — C₂×#23772495 #35153225

Order 20224.

1750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772495	C₂	1	16	yes	maximal, direct product factor
2	C₂×#19098694	C₂	1	2	yes	maximal, complemented
3	C₂×#19098694	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×#19098624	C₂	1	4	yes	maximal
6	C₂×#19098620	C₂	1	1	yes	maximal, characteristic
7	C₂×#19098616	C₂	1	1	yes	maximal, characteristic
8	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
9	#19098694	C₂²	1	16	yes	complemented
10	#19098694	C₂²	1	32	yes	complemented
11	Q₈×C₇₉⋊C₈	C₂²	1	16	yes	complemented
12	#19098624	C₂²	1	32	yes	—
13	#19098620	C₂²	1	8	yes	—
14	#19098616	C₂²	1	8	yes	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	C₂×#14579072	C₂²	1	2	yes	—
22	C₂×#14579072	C₂²	1	4	yes	—
23	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇₉⋊C₈	C₂²	1	4	yes	—
26	#533×C₇₉	C₄	1	8	yes	—
27	#533×C₇₉	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
30	C₂×#125×C₇₉	C₄	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₇₉	C₄	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₇₉	C₄	1	2	yes	—
33	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
35	C₂×#117×C₇₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
37	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
38	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
39	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
40	C₄⋊(C₇₉⋊C₈)	C₂³	1	16	yes	—
41	C₄⋊(C₇₉⋊C₈)	C₂³	1	16	yes	—
42	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
43	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
44	C₂²⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
45	C₂²⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
46	#14579072	C₂³	1	16	yes	—
47	#14579072	C₂³	1	8	yes	—
48	C₄×C₇₉⋊C₈	C₂³	1	16	yes	—
49	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
50	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
51	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
52	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₉	C₂×C₄	1	8	yes	—
57	C₄⋊Q₈×C₇₉	C₂×C₄	1	8	yes	—
58	#125×C₇₉	C₂×C₄	1	16	yes	—
59	C₂²⋊Q₈×C₇₉	C₂×C₄	1	16	yes	—
60	C₂²⋊Q₈×C₇₉	C₂×C₄	1	16	yes	—
61	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
63	C₄×Q₈×C₇₉	C₂³	1	8	yes	—
64	C₄×Q₈×C₇₉	C₂³	1	8	yes	—
65	#117×C₇₉	C₂×C₄	1	8	yes	—
66	#117×C₇₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
77	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
81	C₂×C₇₉⋊C₈	—	2	4	no	—
82	C₂×C₇₉⋊C₈	—	2	4	no	—
83	C₂×C₇₉⋊C₈	—	2	8	no	—
84	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
85	C₂×C₇₉⋊C₈	C₂⁴	1	8	yes	—
86	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
87	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
88	C₂×Q₈×C₇₉	—	2	8	no	—
89	C₂×Q₈×C₇₉	—	4	4	no	—
90	C₂×Q₈×C₇₉	C₂²×C₄	1	8	yes	—
91	C₂×Q₈×C₇₉	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₇₉	—	2	4	no	—
93	C₂²×C₄×C₇₉	—	2	4	no	—
94	C₂²×C₄×C₇₉	—	4	2	no	—
95	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
101	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
108	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
109	C₄⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
110	C₄⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
111	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
112	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
113	C₂²⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
114	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
115	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
116	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
117	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
118	C₄²×C₇₉	C₂²×C₄	1	8	yes	—
119	C₄²×C₇₉	C₂⁴	1	2	yes	—
120	C₄²×C₇₉	C₂⁴	1	2	yes	—
121	C₄²×C₇₉	C₂⁴	1	8	yes	—
122	C₂³×C₇₉	—	2	2	no	—
123	C₂³×C₇₉	—	2	2	no	—
124	C₂³×C₇₉	—	2	2	no	—
125	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
126	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₇₉	—	2	16	no	—
128	Q₈×C₇₉	—	4	8	no	—
129	C₂×C₄×C₇₉	—	2	2	no	—
130	C₂×C₄×C₇₉	—	2	2	no	—
131	C₂×C₄×C₇₉	—	2	8	no	—
132	C₂×C₄×C₇₉	—	2	2	no	—
133	C₂×C₄×C₇₉	—	2	2	no	—
134	C₂×C₄×C₇₉	—	2	8	no	—
135	C₂×C₄×C₇₉	—	2	4	no	—
136	C₂×C₄×C₇₉	—	2	8	no	—
137	C₂×C₄×C₇₉	—	2	4	no	—
138	C₂×C₄×C₇₉	—	4	4	no	—
139	C₂×C₄×C₇₉	#131	1	4	yes	—
140	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
141	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
144	C₂×C₄×C₇₉	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₇₉	C₂³×C₄	1	8	yes	—
146	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₇₉	2₋¹⁺⁴	1	4	yes	—
149	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
150	C₇₉⋊C₈	—	2	4	no	—
151	C₇₉⋊C₈	—	2	8	no	—
152	C₇₉⋊C₈	—	2	4	no	—
153	C₂²×C₇₉	—	2	2	no	—
154	C₂²×C₇₉	—	2	2	no	—
155	C₂²×C₇₉	—	2	2	no	—
156	C₂²×C₇₉	—	4	4	no	—
157	C₂²×C₇₉	#519	1	2	yes	—
158	C₂²×C₇₉	C₂×#131	1	2	yes	—
159	C₂²×C₇₉	#568	1	2	yes	—
160	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
161	C₄×C₇₉	—	2	2	no	—
162	C₄×C₇₉	—	2	2	no	—
163	C₄×C₇₉	—	2	8	no	—
164	C₄×C₇₉	—	2	2	no	—
165	C₄×C₇₉	—	2	2	no	—
166	C₄×C₇₉	—	2	8	no	—
167	C₄×C₇₉	#519	1	2	yes	—
168	C₄×C₇₉	C₂×#131	1	4	yes	—
169	C₄×C₇₉	C₂×2₋¹⁺⁴	1	2	yes	—
170	C₂×#2985	—	79	1	no	maximal, Sylow
171	C₂×C₇₉	—	4	2	no	—
172	C₂×C₇₉	#2985	1	4	yes	complemented
173	C₂×C₇₉	C₂×#519	1	1	yes	characteristic
174	C₂×C₇₉	C₂²×#131	1	1	yes	characteristic
175	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
176	C₂×#533	D₇₉	1	1	yes	characteristic
177	#2985	—	79	16	no	—
178	C₂×#446	—	79	2	no	—
179	C₂×#446	—	79	4	no	—
180	C₂×C₈×Q₈	—	79	2	no	—
181	C₂×#433	—	79	4	no	—
182	C₂×#432	—	79	1	no	—
183	C₂×#431	—	79	1	no	—
184	C₇₉	C₂×#2985	1	1	yes	characteristic, complemented, Sylow
185	#533	Dic₇₉	1	8	yes	—
186	#533	C₂×D₇₉	1	8	yes	—
187	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic
189	C₂×#125	Dic₇₉	1	2	yes	—
190	C₂×C₂²⋊Q₈	Dic₇₉	1	2	yes	—
191	C₂×C₂²⋊Q₈	Dic₇₉	1	2	yes	—
192	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
193	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
194	C₂×#117	C₂×D₇₉	1	2	yes	—
195	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
196	#446	—	79	16	no	—
197	#446	—	79	32	no	—
198	C₈×Q₈	—	79	16	no	—
199	#433	—	79	32	no	—
200	#432	—	79	8	no	—
201	#431	—	79	8	no	—
202	C₂×C₄⋊C₈	—	79	2	no	—
203	C₂×C₄⋊C₈	—	79	2	no	—
204	C₂×C₄⋊C₈	—	79	4	no	—
205	C₂×C₄⋊C₈	—	79	4	no	—
206	C₂×C₂²⋊C₈	—	79	2	no	—
207	C₂×C₂²⋊C₈	—	79	2	no	—
208	C₂×#97	—	79	2	no	—
209	C₂×#97	—	79	4	no	—
210	C₂×C₄×C₈	—	79	1	no	—
211	C₂×C₄×C₈	—	79	1	no	—
212	C₂×C₄×C₈	—	79	4	no	—
213	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
214	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
215	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
218	C₂²×C₈	—	79	2	no	—
219	C₂²×C₈	—	79	2	no	—
220	C₂²×C₈	—	79	4	no	—
221	C₄⋊Q₈	C₂×Dic₇₉	1	8	yes	—
222	C₄⋊Q₈	C₂×Dic₇₉	1	8	yes	—
223	#125	C₂×Dic₇₉	1	16	yes	—
224	C₂²⋊Q₈	C₂×Dic₇₉	1	16	yes	—
225	C₂²⋊Q₈	C₂×Dic₇₉	1	16	yes	—
226	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
227	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
228	C₄×Q₈	C₂²×D₇₉	1	8	yes	—
229	C₄×Q₈	C₂²×D₇₉	1	8	yes	—
230	#117	C₂×Dic₇₉	1	8	yes	—
231	#117	C₂²×D₇₉	1	8	yes	—
232	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
235	C₂×C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
236	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	4	yes	—
239	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
242	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
243	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
244	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
246	C₄⋊C₈	—	79	8	no	—
247	C₄⋊C₈	—	79	8	no	—
248	C₄⋊C₈	—	79	16	no	—
249	C₄⋊C₈	—	79	16	no	—
250	C₂²⋊C₈	—	79	8	no	—
251	C₂²⋊C₈	—	79	8	no	—
252	#97	—	79	8	no	—
253	#97	—	79	16	no	—
254	C₄×C₈	—	79	4	no	—
255	C₄×C₈	—	79	4	no	—
256	C₄×C₈	—	79	16	no	—
257	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
258	C₂×Q₈	—	2	8	no	—
259	C₂×Q₈	—	4	4	no	—
260	C₂×Q₈	C₂²×Dic₇₉	1	8	yes	—
261	C₂×Q₈	C₂²×Dic₇₉	1	8	yes	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
269	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
270	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
275	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
276	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
277	C₂×C₈	—	79	4	no	—
278	C₂×C₈	—	79	4	no	—
279	C₂×C₈	—	79	8	no	—
280	C₂×C₈	—	158	4	no	—
281	C₂×C₈	—	158	4	no	—
282	C₂×C₈	—	158	8	no	—
283	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
284	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
285	C₄⋊C₄	C₂²×Dic₇₉	1	16	yes	—
286	C₄⋊C₄	C₂²×Dic₇₉	1	16	yes	—
287	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
288	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
289	C₂²⋊C₄	C₂²×Dic₇₉	1	16	yes	—
290	C₄²	C₂²×Dic₇₉	1	2	yes	—
291	C₄²	C₂²×Dic₇₉	1	2	yes	—
292	C₄²	C₂²×Dic₇₉	1	4	yes	—
293	C₄²	C₂²×Dic₇₉	1	4	yes	—
294	C₄²	C₂²×Dic₇₉	1	8	yes	—
295	C₄²	C₂³×D₇₉	1	2	yes	—
296	C₄²	C₂³×D₇₉	1	8	yes	—
297	C₄²	C₂³×D₇₉	1	2	yes	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	C₂³×Dic₇₉	1	2	yes	—
302	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
303	Q₈	—	2	16	no	—
304	Q₈	—	4	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	#14579168	1	4	yes	—
316	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
317	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
318	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
319	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
320	C₂×C₄	C₂³×Dic₇₉	1	8	yes	—
321	C₂×C₄	C₂³×Dic₇₉	1	8	yes	—
322	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
323	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
324	C₂×C₄	#14579209	1	4	yes	—
325	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
326	C₈	—	158	4	no	—
327	C₈	—	158	4	no	—
328	C₈	—	158	8	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	4	4	no	—
333	C₂²	#19099041	1	2	yes	—
334	C₂²	C₂×#14579168	1	2	yes	—
335	C₂²	#19099330	1	2	yes	—
336	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
337	C₄	—	2	2	no	—
338	C₄	—	2	8	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	8	no	—
342	C₄	—	2	2	no	—
343	C₄	#19099041	1	2	yes	—
344	C₄	C₂×#14579168	1	4	yes	—
345	C₄	C₂×#14579209	1	2	yes	—
346	C₂	—	4	2	no	—
347	C₂	#23772495	1	4	yes	direct product factor
348	C₂	C₂×#19099041	1	1	yes	characteristic
349	C₂	C₂²×#14579168	1	1	yes	characteristic
350	C₂	C₂×#19099330	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂×#533×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	C₂×#2985
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #23772495	C₂	direct (N × H)
2. C₂×#19098694	C₂	semidirect
3. C₂×#19098694	C₂	semidirect
4. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
9. #19098694	C₂²	semidirect
10. #19098694	C₂²	semidirect
11. Q₈×C₇₉⋊C₈	C₂²	semidirect
172. C₂×C₇₉	#2985	semidirect
184. C₇₉	C₂×#2985	semidirect
347. C₂	#23772495	direct (N × H)

Maximal subgroups

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

subgroup	index
#23772495	2
C₂×#19098694	2
C₂×Q₈×C₇₉⋊C₈	2
C₂×#19098624	2
C₂×#19098620	2
C₂×#19098616	2
C₂×#533×C₇₉	2
C₂×#2985	79

Subgroups — C2×#23772495 #35153225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23772495 #35153225