Subgroups — #34178149

Order 20224.

986 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#23765783	C₂	1	1	yes	maximal, characteristic
3	#23761267	C₂	1	4	yes	maximal, complemented
4	C₇₉×#2280	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₇₉⋊C₈	C₄	1	2	yes	complemented
6	C₂×#14579120	—	2	1	no	—
7	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	complemented
12	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	#19098426	C₄	1	2	yes	complemented
14	#19098423	—	2	1	no	—
15	#19098423	C₂²	1	2	yes	—
16	#19098419	—	2	1	no	—
17	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
18	C₄×C₂²⋊Dic₇₉	C₄	1	2	yes	complemented
19	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₉	—	2	1	no	—
21	#381×C₇₉	C₄	1	2	yes	complemented
22	#380×C₇₉	—	2	1	no	—
23	#380×C₇₉	C₂²	1	2	yes	—
24	#379×C₇₉	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
26	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	complemented
27	C₂²×C₇₉⋊C₈	—	2	2	no	—
28	C₂²×C₇₉⋊C₈	—	2	2	no	—
29	C₂²×C₇₉⋊C₈	—	4	4	no	—
30	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
31	#14579120	—	4	4	no	—
32	C₂×C₄⋊Dic₇₉	—	2	2	no	—
33	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
34	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
35	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
36	C₂×C₄×Dic₇₉	—	2	2	no	—
37	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
41	C₇₉⋊#95	—	2	2	no	—
42	C₇₉⋊#95	C₂×C₄	1	4	yes	—
43	C₂⁵×C₇₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	—	4	4	no	—
45	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	#117×C₇₉	—	4	4	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄²×C₇₉	—	2	2	no	—
65	#95×C₇₉	—	2	2	no	—
66	#95×C₇₉	C₂×C₄	1	4	yes	—
67	C₂²×Dic₇₉	—	2	4	no	—
68	C₂×C₇₉⋊C₈	—	2	4	no	—
69	C₂×C₇₉⋊C₈	—	4	4	no	—
70	C₂×C₇₉⋊C₈	—	4	4	no	—
71	C₂×C₇₉⋊C₈	—	4	4	no	—
72	C₄⋊Dic₇₉	—	4	4	no	—
73	C₂²⋊Dic₇₉	—	4	4	no	—
74	C₂²⋊Dic₇₉	—	4	4	no	—
75	C₂²⋊Dic₇₉	—	4	4	no	—
76	C₄×Dic₇₉	—	4	4	no	—
77	C₂⁴×C₇₉	—	2	4	no	—
78	C₂⁴×C₇₉	—	4	2	no	—
79	C₂⁴×C₇₉	—	4	2	no	—
80	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	—	2	4	no	—
88	C₂²×C₄×C₇₉	—	2	4	no	—
89	C₂²×C₄×C₇₉	—	2	4	no	—
90	C₂²×C₄×C₇₉	—	2	4	no	—
91	C₂²×C₄×C₇₉	—	4	2	no	—
92	C₂²×C₄×C₇₉	—	4	2	no	—
93	C₂²×C₄×C₇₉	—	4	2	no	—
94	C₂²×C₄×C₇₉	—	4	2	no	—
95	C₂²×C₄×C₇₉	—	4	2	no	—
96	C₂²×C₄×C₇₉	—	4	2	no	—
97	C₂²×C₄×C₇₉	—	4	2	no	—
98	C₂²×C₄×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	—	4	2	no	—
100	C₂²×C₄×C₇₉	—	4	2	no	—
101	C₂²×C₄×C₇₉	—	4	2	no	—
102	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
130	C₄⋊C₄×C₇₉	—	4	4	no	—
131	C₂²⋊C₄×C₇₉	—	4	4	no	—
132	C₂²⋊C₄×C₇₉	—	4	4	no	—
133	C₂²⋊C₄×C₇₉	—	4	4	no	—
134	C₄²×C₇₉	—	4	4	no	—
135	C₂³×C₇₉	—	2	2	no	—
136	C₂³×C₇₉	—	2	2	no	—
137	C₂³×C₇₉	—	2	2	no	—
138	C₂³×C₇₉	—	2	2	no	—
139	C₂³×C₇₉	—	2	2	no	—
140	C₂³×C₇₉	—	2	2	no	—
141	C₂³×C₇₉	—	2	2	no	—
142	C₂³×C₇₉	—	2	2	no	—
143	C₂³×C₇₉	—	2	2	no	—
144	C₂³×C₇₉	—	2	2	no	—
145	C₂³×C₇₉	—	2	2	no	—
146	C₂³×C₇₉	—	2	2	no	—
147	C₂³×C₇₉	—	4	1	no	—
148	C₂³×C₇₉	—	4	1	no	—
149	C₂³×C₇₉	—	4	1	no	—
150	C₂³×C₇₉	—	4	1	no	—
151	C₂³×C₇₉	—	4	1	no	—
152	C₂³×C₇₉	—	4	1	no	—
153	C₂³×C₇₉	—	4	1	no	—
154	C₂³×C₇₉	—	4	1	no	—
155	C₂³×C₇₉	—	4	16	no	—
156	C₂³×C₇₉	#95	1	1	yes	characteristic
157	C₂³×C₇₉	#95	1	1	yes	characteristic
158	C₂³×C₇₉	#95	1	1	yes	characteristic
159	C₂³×C₇₉	#95	1	1	yes	characteristic
160	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂³×C₇₉	#135	1	4	yes	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	4	1	no	—
180	C₂×C₄×C₇₉	—	4	1	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	—	4	1	no	—
184	C₂×C₄×C₇₉	—	4	1	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	—	4	1	no	—
189	C₂×C₄×C₇₉	—	4	1	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	4	no	—
192	C₂×C₄×C₇₉	—	4	4	no	—
193	C₂×C₄×C₇₉	—	4	4	no	—
194	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
195	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
196	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
197	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
198	C₂×C₄×C₇₉	#99	1	4	yes	—
199	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₇₉	—	4	4	no	—
204	C₂×Dic₇₉	—	4	4	no	—
205	C₂×Dic₇₉	—	4	4	no	—
206	C₇₉⋊C₈	—	4	4	no	—
207	C₂²×C₇₉	—	2	8	no	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	—	2	1	no	—
210	C₂²×C₇₉	—	2	1	no	—
211	C₂²×C₇₉	—	2	1	no	—
212	C₂²×C₇₉	—	2	1	no	—
213	C₂²×C₇₉	—	2	1	no	—
214	C₂²×C₇₉	—	2	1	no	—
215	C₂²×C₇₉	—	2	1	no	—
216	C₂²×C₇₉	—	2	1	no	—
217	C₂²×C₇₉	—	2	1	no	—
218	C₂²×C₇₉	—	2	1	no	—
219	C₂²×C₇₉	—	2	1	no	—
220	C₂²×C₇₉	—	2	1	no	—
221	C₂²×C₇₉	—	2	1	no	—
222	C₂²×C₇₉	—	2	1	no	—
223	C₂²×C₇₉	—	2	1	no	—
224	C₂²×C₇₉	—	4	4	no	—
225	C₂²×C₇₉	—	4	4	no	—
226	C₂²×C₇₉	—	4	4	no	—
227	C₂²×C₇₉	—	4	4	no	—
228	C₂²×C₇₉	—	4	4	no	—
229	C₂²×C₇₉	—	4	4	no	—
230	C₂²×C₇₉	H(3,ℤ/4)	1	2	yes	—
231	C₂²×C₇₉	#342	1	2	yes	—
232	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
233	C₂²×C₇₉	#416	1	2	yes	—
234	C₂²×C₇₉	#416	1	2	yes	—
235	C₂²×C₇₉	#427	1	2	yes	—
236	C₄×C₇₉	—	2	1	no	—
237	C₄×C₇₉	—	2	1	no	—
238	C₄×C₇₉	—	2	1	no	—
239	C₄×C₇₉	—	2	1	no	—
240	C₄×C₇₉	—	2	1	no	—
241	C₄×C₇₉	—	2	1	no	—
242	C₄×C₇₉	—	8	4	no	—
243	C₄×C₇₉	#342	1	2	yes	—
244	C₄×C₇₉	C₂×#99	1	2	yes	—
245	Dic₇₉	—	8	4	no	—
246	#7982	—	79	1	no	maximal, Sylow
247	C₂×C₇₉	—	2	2	no	—
248	C₂×C₇₉	—	2	2	no	—
249	C₂×C₇₉	—	2	2	no	—
250	C₂×C₇₉	—	2	2	no	—
251	C₂×C₇₉	—	2	2	no	—
252	C₂×C₇₉	—	4	1	no	—
253	C₂×C₇₉	—	4	1	no	—
254	C₂×C₇₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
255	C₂×C₇₉	#1735	1	1	yes	characteristic
256	C₂×C₇₉	C₂×#342	1	1	yes	characteristic
257	C₂²×C₂²⋊C₈	—	79	1	no	—
258	#2280	—	79	1	no	—
259	#2280	D₇₉	1	1	yes	characteristic
260	#1289	—	79	4	no	—
261	C₇₉	#7982	1	1	yes	characteristic, complemented, Sylow
262	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
263	C₂³×C₈	—	79	2	no	—
264	C₂×#117	—	2	1	no	—
265	C₂×#117	—	158	1	no	—
266	C₂×C₂²⋊C₈	—	79	2	no	—
267	C₂×C₂²⋊C₈	—	79	2	no	—
268	C₂×C₂²⋊C₈	—	158	1	no	—
269	C₂×C₂²⋊C₈	—	158	1	no	—
270	C₂×C₂²⋊C₈	—	158	1	no	—
271	C₂×C₂²⋊C₈	—	158	1	no	—
272	#381	—	79	2	no	—
273	#381	Dic₇₉	1	2	yes	complemented
274	#380	—	2	1	no	—
275	#380	—	79	2	no	—
276	#380	—	158	1	no	—
277	#380	C₂×D₇₉	1	2	yes	—
278	#379	—	2	1	no	—
279	#379	—	158	1	no	—
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	C₄×C₂²⋊C₄	—	79	2	no	—
282	C₄×C₂²⋊C₄	—	158	1	no	—
283	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	complemented
284	C₂⁵	C₂²⋊D₇₉	1	1	yes	characteristic
285	C₂³×C₄	—	4	4	no	—
286	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
287	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
288	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
289	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
290	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
291	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
292	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
293	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
294	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
295	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
296	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
297	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
298	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
299	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
300	C₂²×C₈	—	316	4	no	—
301	C₂²×C₈	—	79	4	no	—
302	C₂²×C₈	—	158	2	no	—
303	C₂²×C₈	—	158	2	no	—
304	#117	—	4	4	no	—
305	#117	—	316	4	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	158	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	158	2	no	—
312	C₂×C₂²⋊C₄	—	158	2	no	—
313	C₂×C₂²⋊C₄	—	158	2	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	158	2	no	—
316	C₂²⋊C₈	—	158	2	no	—
317	C₂²⋊C₈	—	158	2	no	—
318	C₂²⋊C₈	—	158	2	no	—
319	C₂²⋊C₈	—	158	2	no	—
320	#95	—	2	2	no	—
321	#95	—	79	4	no	—
322	#95	—	158	2	no	—
323	#95	C₂×Dic₇₉	1	4	yes	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
328	C₂⁴	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
329	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
330	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
331	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
332	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
333	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	158	4	no	—
350	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
351	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
352	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
353	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
354	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
361	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
362	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
365	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
369	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
370	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
371	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
374	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
377	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
378	C₂×C₈	—	316	4	no	—
379	C₂×C₈	—	316	4	no	—
380	C₂×C₈	—	316	4	no	—
381	C₂×C₈	—	158	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	316	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	316	4	no	—
388	C₂²⋊C₄	—	316	4	no	—
389	C₂²⋊C₄	—	316	4	no	—
390	C₄²	—	4	4	no	—
391	C₄²	—	316	4	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	16	no	—
413	C₂³	C₇₉⋊#95	1	1	yes	characteristic
414	C₂³	C₇₉⋊#95	1	1	yes	characteristic
415	C₂³	C₇₉⋊#95	1	1	yes	characteristic
416	C₂³	C₇₉⋊#95	1	1	yes	characteristic
417	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
418	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
419	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
420	C₂³	#14579181	1	4	yes	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	316	4	no	—
452	C₂×C₄	—	316	4	no	—
453	C₂×C₄	—	316	4	no	—
454	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
455	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
456	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
457	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
458	C₂×C₄	#14579075	1	4	yes	—
459	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
460	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
463	C₈	—	316	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	#19098319	1	2	yes	—
488	C₂²	#19098329	1	2	yes	—
489	C₂²	C₂×C₇₉⋊#95	1	1	yes	characteristic
490	C₂²	#19098557	1	2	yes	—
491	C₂²	#19098559	1	2	yes	—
492	C₂²	#19098599	1	2	yes	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	8	4	no	—
500	C₄	—	632	4	no	—
501	C₄	#19098329	1	2	yes	—
502	C₄	C₂×#14579075	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	2	2	no	—
508	C₂	—	4	1	no	—
509	C₂	—	4	1	no	—
510	C₂	C₂×#19098319	1	1	yes	characteristic
511	C₂	#23763116	1	1	yes	characteristic
512	C₂	C₂×#19098329	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₇₉⋊#95
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₇₉×#2280	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂⁵×C₇₉	D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	#2280	D₇₉
hypocenter	C₇₉	#7982
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ #2280

Complements

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

N	H ≅ G/N	type
3. #23761267	C₂	semidirect
5. C₂³×C₇₉⋊C₈	C₄	semidirect
11. C₂×C₂²⋊(C₇₉⋊C₈)	C₄	semidirect
13. #19098426	C₄	semidirect
18. C₄×C₂²⋊Dic₇₉	C₄	semidirect
21. #381×C₇₉	C₄	semidirect
26. C₄×C₂²⋊C₄×C₇₉	C₄	semidirect
261. C₇₉	#7982	semidirect
273. #381	Dic₇₉	semidirect
283. C₄×C₂²⋊C₄	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊(C₇₉⋊C₈)	2
#23765783	2
#23761267	2
C₇₉×#2280	2
#7982	79