Subgroups — #34178062

Order 20224.

634 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772033	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098429	C₂	1	1	yes	maximal, characteristic
3	#23761260	C₂	1	4	yes	maximal, complemented
4	C₇₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₇₉	—	2	1	no	—
6	#19098620	—	2	1	no	—
7	#19098620	—	2	1	no	—
8	#19098616	C₄	1	2	yes	complemented
9	#19098616	C₂²	1	2	yes	—
10	#19098587	—	2	1	no	—
11	#19098527	—	2	1	no	—
12	C₄×#11929608	C₄	1	2	yes	complemented
13	#19098429	—	2	1	no	—
14	#19098429	—	2	1	no	—
15	#19098429	C₄	1	2	yes	—
16	#19098429	C₂²	1	2	yes	—
17	C₂×C₇₉⋊#95	—	2	1	no	—
18	C₂×C₇₉⋊#95	C₄	1	2	yes	—
19	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	#432×C₇₉	—	2	1	no	—
21	#432×C₇₉	C₄	1	2	yes	complemented
22	#431×C₇₉	—	2	1	no	—
23	#431×C₇₉	C₄	1	2	yes	complemented
24	#423×C₇₉	C₂²	1	2	yes	—
25	#407×C₇₉	—	2	1	no	—
26	C₄×M₁₆×C₇₉	—	2	1	no	—
27	C₂³×Dic₇₉	—	2	2	no	—
28	C₂×#11929608	—	2	2	no	—
29	C₂×C₄⋊Dic₇₉	—	2	2	no	—
30	C₂×C₄⋊Dic₇₉	—	2	2	no	—
31	C₂×C₄⋊Dic₇₉	—	4	4	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
36	#14579072	—	2	2	no	—
37	C₄×C₇₉⋊C₈	C₂×C₄	1	4	yes	complemented
38	C₇₉⋊#95	—	2	2	no	—
39	C₇₉⋊#95	—	2	2	no	—
40	C₇₉⋊#95	—	2	2	no	—
41	C₇₉⋊#95	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
45	C₂×M₁₆×C₇₉	—	2	2	no	—
46	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₉	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₇₉	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₇₉	—	2	2	no	—
59	C₄⋊C₈×C₇₉	C₂×C₄	1	4	yes	complemented
60	C₂²⋊C₈×C₇₉	—	2	2	no	—
61	C₂²⋊C₈×C₇₉	—	2	2	no	—
62	#97×C₇₉	—	2	2	no	—
63	C₄×C₈×C₇₉	—	2	2	no	—
64	C₂²×Dic₇₉	—	2	4	no	—
65	C₂²×Dic₇₉	—	4	4	no	—
66	C₂²×Dic₇₉	—	4	4	no	—
67	C₂²×Dic₇₉	—	4	4	no	—
68	#11929608	—	4	4	no	—
69	C₂×C₇₉⋊C₈	—	2	4	no	—
70	C₄⋊Dic₇₉	—	4	4	no	—
71	C₄⋊Dic₇₉	—	4	4	no	—
72	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	—	2	2	no	—
74	C₂²×C₄×C₇₉	—	2	2	no	—
75	C₂²×C₄×C₇₉	—	4	2	no	—
76	C₂²×C₄×C₇₉	—	4	2	no	—
77	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
95	M₁₆×C₇₉	—	4	2	no	—
96	M₁₆×C₇₉	—	4	2	no	—
97	C₂×C₈×C₇₉	—	2	4	no	—
98	C₄²×C₇₉	C₄²	1	1	yes	characteristic
99	C₄²×C₇₉	C₄²	1	1	yes	characteristic
100	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
114	C₂³×C₇₉	—	2	2	no	—
115	C₂³×C₇₉	—	2	2	no	—
116	C₂³×C₇₉	—	2	1	no	—
117	C₂³×C₇₉	—	2	1	no	—
118	C₂³×C₇₉	#95	1	1	yes	characteristic
119	C₂³×C₇₉	#95	1	1	yes	characteristic
120	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₇₉	—	2	2	no	—
122	C₂×C₄×C₇₉	—	2	2	no	—
123	C₂×C₄×C₇₉	—	2	2	no	—
124	C₂×C₄×C₇₉	—	2	2	no	—
125	C₂×C₄×C₇₉	—	2	1	no	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	2	no	—
128	C₂×C₄×C₇₉	—	2	2	no	—
129	C₂×C₄×C₇₉	—	2	2	no	—
130	C₂×C₄×C₇₉	—	2	2	no	—
131	C₂×C₄×C₇₉	—	4	1	no	—
132	C₂×C₄×C₇₉	—	4	1	no	—
133	C₂×C₄×C₇₉	—	4	1	no	—
134	C₂×C₄×C₇₉	—	4	1	no	—
135	C₂×C₄×C₇₉	—	4	1	no	—
136	C₂×C₄×C₇₉	—	4	1	no	—
137	C₂×C₄×C₇₉	—	4	1	no	—
138	C₂×C₄×C₇₉	—	4	1	no	—
139	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₇₉	#137	1	2	yes	—
153	C₂×Dic₇₉	—	4	4	no	—
154	C₂×Dic₇₉	—	4	4	no	—
155	C₂×Dic₇₉	—	4	4	no	—
156	C₂×Dic₇₉	—	8	8	no	—
157	C₈×C₇₉	—	4	4	no	—
158	C₇₉⋊C₈	—	4	4	no	—
159	C₂²×C₇₉	—	2	4	no	—
160	C₂²×C₇₉	—	2	4	no	—
161	C₂²×C₇₉	—	2	1	no	—
162	C₂²×C₇₉	—	2	1	no	—
163	C₂²×C₇₉	—	2	1	no	—
164	C₂²×C₇₉	—	2	1	no	—
165	C₂²×C₇₉	—	2	1	no	—
166	C₂²×C₇₉	—	2	1	no	—
167	C₂²×C₇₉	H(3,ℤ/4)	1	2	yes	—
168	C₂²×C₇₉	#344	1	2	yes	—
169	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
170	C₂²×C₇₉	#418	1	1	yes	characteristic
171	C₂²×C₇₉	#419	1	1	yes	characteristic
172	C₄×C₇₉	—	2	1	no	—
173	C₄×C₇₉	—	2	1	no	—
174	C₄×C₇₉	—	2	1	no	—
175	C₄×C₇₉	—	2	1	no	—
176	C₄×C₇₉	—	2	1	no	—
177	C₄×C₇₉	—	2	1	no	—
178	C₄×C₇₉	—	2	1	no	—
179	C₄×C₇₉	—	2	1	no	—
180	C₄×C₇₉	—	2	1	no	—
181	C₄×C₇₉	—	2	1	no	—
182	C₄×C₇₉	#417	1	2	yes	—
183	C₄×C₇₉	#428	1	2	yes	—
184	Dic₇₉	—	8	4	no	—
185	#7959	—	79	1	no	maximal, Sylow
186	C₂×C₇₉	—	2	1	no	—
187	C₂×C₇₉	—	2	2	no	—
188	C₂×C₇₉	—	2	2	no	—
189	C₂×C₇₉	—	2	1	no	—
190	C₂×C₇₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
191	C₂×C₇₉	#1736	1	1	yes	characteristic
192	C₂×C₇₉	C₂×#344	1	1	yes	characteristic
193	#2920	—	79	1	no	—
194	#2920	D₇₉	1	1	yes	characteristic
195	C₂×#382	—	79	1	no	—
196	#1286	—	79	4	no	—
197	C₇₉	#7959	1	1	yes	characteristic, complemented, Sylow
198	C₂²×C₄⋊C₄	—	158	1	no	—
199	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
200	#432	—	2	1	no	—
201	#432	—	158	1	no	—
202	#432	—	158	1	no	—
203	#432	Dic₇₉	1	2	yes	complemented
204	#431	—	2	1	no	—
205	#431	—	79	2	no	—
206	#431	—	79	2	no	—
207	#431	Dic₇₉	1	2	yes	complemented
208	#423	—	158	1	no	—
209	#423	C₂×D₇₉	1	2	yes	—
210	#407	—	2	1	no	—
211	#407	—	158	1	no	—
212	C₄×M₁₆	—	2	1	no	—
213	C₄×M₁₆	—	79	2	no	—
214	#382	—	79	2	no	—
215	#382	—	79	2	no	—
216	#382	—	158	1	no	—
217	#382	—	158	1	no	—
218	C₂×#95	—	79	2	no	—
219	C₂×#95	—	158	1	no	—
220	C₂³×C₄	—	158	2	no	—
221	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
222	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
223	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	158	2	no	—
226	C₂×C₄⋊C₄	—	316	4	no	—
227	C₂×C₄⋊C₄	—	158	2	no	—
228	C₂×C₄⋊C₄	—	158	2	no	—
229	C₂×C₄²	Dic₁₅₈	1	1	yes	characteristic
230	C₂×C₄²	Dic₁₅₈	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
234	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	158	2	no	—
243	C₄⋊C₈	—	158	2	no	—
244	C₄⋊C₈	C₂×Dic₇₉	1	4	yes	complemented
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	158	2	no	—
248	C₂²⋊C₈	—	158	2	no	—
249	#97	—	2	2	no	—
250	#97	—	158	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	79	4	no	—
253	#95	—	79	4	no	—
254	#95	—	158	2	no	—
255	#95	—	158	2	no	—
256	#95	—	158	2	no	—
257	C₂⁴	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	316	4	no	—
263	C₂²×C₄	—	316	4	no	—
264	C₂²×C₄	—	316	4	no	—
265	C₂²×C₄	—	158	4	no	—
266	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
275	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	316	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	158	4	no	—
289	C₄⋊C₄	—	316	4	no	—
290	C₄⋊C₄	—	316	4	no	—
291	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
292	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
293	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
295	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
296	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
297	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
299	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
300	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
301	C₄²	C₄⋊Dic₇₉	1	1	yes	characteristic
302	C₄²	C₄⋊Dic₇₉	1	1	yes	characteristic
303	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
304	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
305	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
306	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	C₇₉⋊#95	1	1	yes	characteristic
312	C₂³	C₇₉⋊#95	1	1	yes	characteristic
313	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	316	4	no	—
333	C₂×C₄	—	316	4	no	—
334	C₂×C₄	—	316	4	no	—
335	C₂×C₄	—	632	8	no	—
336	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
343	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
345	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
348	C₂×C₄	#14579186	1	2	yes	—
349	C₂×C₄	#14579191	1	2	yes	—
350	C₈	—	4	4	no	—
351	C₈	—	316	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	#19098320	1	2	yes	—
361	C₂²	#19098335	1	2	yes	—
362	C₂²	C₂×C₇₉⋊#95	1	1	yes	characteristic
363	C₂²	#19098567	1	1	yes	characteristic
364	C₂²	#19098571	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	632	4	no	—
376	C₄	#19098564	1	2	yes	—
377	C₄	#19098606	1	2	yes	—
378	C₂	—	2	1	no	—
379	C₂	—	2	1	no	—
380	C₂	—	2	2	no	—
381	C₂	—	2	2	no	—
382	C₂	C₂×#19098320	1	1	yes	characteristic
383	C₂	#23763121	1	1	yes	characteristic
384	C₂	C₂×#19098335	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₇₉⋊#95
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2920	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂⁴×C₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2920	D₇₉
hypocenter	C₇₉	#7959
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #23761260	C₂	semidirect
8. #19098616	C₄	semidirect
12. C₄×#11929608	C₄	semidirect
21. #432×C₇₉	C₄	semidirect
23. #431×C₇₉	C₄	semidirect
37. C₄×C₇₉⋊C₈	C₂×C₄	semidirect
59. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
197. C₇₉	#7959	semidirect
203. #432	Dic₇₉	semidirect
207. #431	Dic₇₉	semidirect
244. C₄⋊C₈	C₂×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772033	2
C₂×#19098429	2
#23761260	2
C₇₉×#2920	2
#7959	79