Subgroups — #34287130

Order 20224.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098590	C₂	1	1	yes	maximal, characteristic
2	#23765898	C₂	1	1	yes	maximal, characteristic
3	#23763272	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763272	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763267	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763259	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763259	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763186	C₂	1	1	yes	maximal, characteristic
12	#23763186	C₂	1	1	yes	maximal, characteristic
13	#23763179	C₂	1	1	yes	maximal, characteristic
14	#23763174	C₂	1	1	yes	maximal, characteristic
15	C₂×#433×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	#19098590	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×#14579071	C₂²	1	1	yes	characteristic
24	C₂×#14579071	C₂²	1	1	yes	characteristic
25	C₂×#14579071	C₂²	1	1	yes	characteristic
26	C₂×#14579071	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
31	#19098456	C₄	1	2	yes	—
32	#19098456	C₄	1	2	yes	—
33	#19098449	C₄	1	2	yes	—
34	#19098449	C₄	1	2	yes	—
35	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
39	#19098409	C₂²	1	1	yes	characteristic
40	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
41	#19098317	C₂²	1	1	yes	characteristic
42	#19098317	C₂²	1	1	yes	characteristic
43	#19098317	C₂²	1	1	yes	characteristic
44	#19098317	C₂²	1	1	yes	characteristic
45	#19098317	C₂²	1	1	yes	characteristic
46	#19098317	C₂²	1	1	yes	characteristic
47	#19098317	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
50	#433×C₇₉	C₄	1	8	yes	complemented
51	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×#11929608	—	4	1	no	—
58	C₂×#11929608	—	4	1	no	—
59	C₂×#11929608	C₂×C₄	1	4	yes	—
60	C₂²×C₇₉⋊C₈	—	4	1	no	—
61	C₂²×C₇₉⋊C₈	—	4	1	no	—
62	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
77	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
78	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
79	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
80	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
81	#14579071	—	4	1	no	—
82	#14579071	—	4	1	no	—
83	#14579071	—	4	1	no	—
84	#14579071	—	4	1	no	—
85	C₈×Dic₇₉	—	4	1	no	—
86	C₈×Dic₇₉	—	4	1	no	—
87	C₈×Dic₇₉	—	4	1	no	—
88	C₈×Dic₇₉	—	4	1	no	—
89	C₇₉⋊#95	C₂×C₄	1	2	yes	—
90	C₇₉⋊#95	C₂×C₄	1	2	yes	—
91	C₇₉⋊#95	C₂×C₄	1	2	yes	—
92	C₇₉⋊#95	C₂×C₄	1	2	yes	—
93	C₇₉⋊#95	C₂×C₄	1	2	yes	—
94	C₇₉⋊#95	C₂×C₄	1	2	yes	—
95	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	#117×C₇₉	C₂×C₄	1	4	yes	—
101	#117×C₇₉	C₂×C₄	1	4	yes	—
102	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
109	C₄⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
110	C₂²⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
111	C₂²⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
112	#97×C₇₉	C₂×C₄	1	4	yes	—
113	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	—
114	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
117	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
118	#11929608	—	4	4	no	—
119	C₂×C₇₉⋊C₈	—	2	1	no	—
120	C₂×C₇₉⋊C₈	—	2	1	no	—
121	C₂×C₇₉⋊C₈	—	2	1	no	—
122	C₂×C₇₉⋊C₈	—	2	1	no	—
123	C₂×C₇₉⋊C₈	—	2	1	no	—
124	C₂×C₇₉⋊C₈	—	2	1	no	—
125	C₂×C₇₉⋊C₈	—	2	1	no	—
126	C₂×C₇₉⋊C₈	—	2	1	no	—
127	C₂×C₇₉⋊C₈	—	4	4	no	—
128	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
132	C₄⋊Dic₇₉	—	2	4	no	—
133	C₄⋊Dic₇₉	—	4	2	no	—
134	C₂²⋊Dic₇₉	—	2	4	no	—
135	C₂²⋊Dic₇₉	—	4	2	no	—
136	C₄×Dic₇₉	—	2	4	no	—
137	C₄×Dic₇₉	—	2	1	no	—
138	C₄×Dic₇₉	—	2	1	no	—
139	C₄×Dic₇₉	—	2	1	no	—
140	C₄×Dic₇₉	—	2	1	no	—
141	C₄×Dic₇₉	—	2	1	no	—
142	C₄×Dic₇₉	—	2	1	no	—
143	C₄×Dic₇₉	—	2	1	no	—
144	C₄×Dic₇₉	—	2	1	no	—
145	C₄×Dic₇₉	—	4	2	no	—
146	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	—	2	1	no	—
148	C₂²×C₄×C₇₉	—	2	1	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₇₉	—	2	1	no	—
160	C₂×C₈×C₇₉	—	2	1	no	—
161	C₂×C₈×C₇₉	—	2	1	no	—
162	C₂×C₈×C₇₉	—	2	1	no	—
163	C₂×C₈×C₇₉	—	2	1	no	—
164	C₂×C₈×C₇₉	—	2	1	no	—
165	C₂×C₈×C₇₉	—	2	1	no	—
166	C₂×C₈×C₇₉	—	2	1	no	—
167	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₇₉	C₄²	1	4	yes	—
172	C₄⋊C₄×C₇₉	C₄²	1	4	yes	—
173	C₂²⋊C₄×C₇₉	C₄²	1	4	yes	—
174	C₂²⋊C₄×C₇₉	C₄²	1	4	yes	—
175	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
176	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
177	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
178	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
179	C₂³×C₇₉	—	2	1	no	—
180	C₂³×C₇₉	—	2	1	no	—
181	C₂³×C₇₉	—	2	2	no	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	C₂×C₄²	1	2	yes	—
184	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	—	2	1	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	2	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	2	no	—
195	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
196	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
199	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×Dic₇₉	—	2	2	no	—
207	C₂×Dic₇₉	—	2	2	no	—
208	C₂×Dic₇₉	—	2	2	no	—
209	C₂×Dic₇₉	—	2	2	no	—
210	C₂×Dic₇₉	—	2	2	no	—
211	C₂×Dic₇₉	—	2	2	no	—
212	C₂×Dic₇₉	—	2	2	no	—
213	C₂×Dic₇₉	—	2	2	no	—
214	C₂×Dic₇₉	—	2	2	no	—
215	C₂×Dic₇₉	—	2	2	no	—
216	C₂×Dic₇₉	—	2	2	no	—
217	C₂×Dic₇₉	#131	1	4	yes	—
218	C₈×C₇₉	—	2	2	no	—
219	C₈×C₇₉	—	2	2	no	—
220	C₈×C₇₉	—	2	2	no	—
221	C₈×C₇₉	—	2	2	no	—
222	C₇₉⋊C₈	—	2	2	no	—
223	C₇₉⋊C₈	—	2	2	no	—
224	C₇₉⋊C₈	—	2	2	no	—
225	C₇₉⋊C₈	—	2	2	no	—
226	C₂²×C₇₉	—	2	2	no	—
227	C₂²×C₇₉	—	2	2	no	—
228	C₂²×C₇₉	—	2	2	no	—
229	C₂²×C₇₉	—	4	2	no	—
230	C₂²×C₇₉	—	4	2	no	—
231	C₂²×C₇₉	C₂²×C₄²	1	1	yes	characteristic
232	C₂²×C₇₉	#520	1	1	yes	characteristic
233	C₂²×C₇₉	#520	1	1	yes	characteristic
234	C₂²×C₇₉	C₂×#131	1	2	yes	—
235	C₂²×C₇₉	#568	1	2	yes	—
236	C₄×C₇₉	—	2	2	no	—
237	C₄×C₇₉	—	2	2	no	—
238	C₄×C₇₉	—	2	2	no	—
239	C₄×C₇₉	—	2	2	no	—
240	C₄×C₇₉	—	2	2	no	—
241	C₄×C₇₉	#518	1	1	yes	characteristic
242	C₄×C₇₉	#519	1	1	yes	characteristic
243	C₄×C₇₉	#520	1	1	yes	characteristic
244	C₄×C₇₉	#520	1	1	yes	characteristic
245	Dic₇₉	—	2	4	no	—
246	Dic₇₉	—	4	2	no	—
247	Dic₇₉	—	4	2	no	—
248	Dic₇₉	—	4	2	no	—
249	#20553	—	79	1	no	maximal, Sylow
250	C₂×C₇₉	—	4	2	no	—
251	C₂×C₇₉	#2274	1	1	yes	characteristic
252	C₂×C₇₉	C₄×#131	1	1	yes	characteristic
253	C₂×C₇₉	#2875	1	1	yes	characteristic
254	C₂×C₇₉	#2992	1	2	yes	—
255	C₂×C₇₉	#2993	1	2	yes	—
256	C₂×#433	D₇₉	1	1	yes	characteristic
257	C₂×#424	—	79	1	no	—
258	#2298	—	79	1	no	—
259	#1771	—	79	1	no	—
260	#1771	—	79	1	no	—
261	#1770	—	79	1	no	—
262	C₈×C₄⋊C₄	—	79	1	no	—
263	#1768	—	79	1	no	—
264	#1768	—	79	1	no	—
265	#1767	—	79	1	no	—
266	C₄×C₄⋊C₈	—	79	1	no	—
267	#1753	—	79	1	no	—
268	#1753	—	79	1	no	—
269	#1752	—	79	1	no	—
270	C₈×C₂²⋊C₄	—	79	1	no	—
271	C₇₉	#20553	1	1	yes	characteristic, complemented, Sylow
272	C₂²×M₁₆	—	79	1	no	—
273	C₂³×C₈	—	79	1	no	—
274	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
275	#433	Dic₇₉	1	8	yes	complemented
276	#424	—	79	8	no	—
277	C₂×C₄⋊C₈	—	79	1	no	—
278	C₂×C₄⋊C₈	—	79	1	no	—
279	C₂×C₄⋊C₈	—	79	1	no	—
280	C₂×C₄⋊C₈	—	79	1	no	—
281	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
285	C₂×#97	—	79	1	no	—
286	C₂×#97	—	79	1	no	—
287	C₂×#97	—	79	1	no	—
288	C₂×#97	—	79	1	no	—
289	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
290	C₂×C₄×C₈	—	79	1	no	—
291	C₂×C₄×C₈	—	79	1	no	—
292	C₂×C₄×C₈	—	79	1	no	—
293	C₂×C₄×C₈	—	79	1	no	—
294	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
295	#388	—	79	2	no	—
296	#388	—	79	2	no	—
297	#387	—	79	2	no	—
298	#387	—	79	2	no	—
299	C₄×C₄⋊C₄	—	79	1	no	—
300	C₄×C₄⋊C₄	—	79	1	no	—
301	C₄×C₂²⋊C₄	—	79	1	no	—
302	C₄×C₂²⋊C₄	—	79	1	no	—
303	#376	—	79	1	no	—
304	C₄³	—	79	1	no	—
305	#336	—	79	1	no	—
306	#336	—	79	1	no	—
307	#336	—	79	1	no	—
308	#336	—	79	1	no	—
309	#336	—	79	1	no	—
310	#336	—	79	1	no	—
311	#336	—	79	1	no	—
312	#336	—	79	1	no	—
313	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
314	C₂×M₁₆	—	316	1	no	—
315	C₂×M₁₆	—	316	1	no	—
316	C₂×M₁₆	—	79	4	no	—
317	C₂²×C₈	—	316	1	no	—
318	C₂²×C₈	—	316	1	no	—
319	C₂²×C₈	—	79	4	no	—
320	C₂²×C₈	—	79	1	no	—
321	C₂²×C₈	—	79	1	no	—
322	C₂²×C₈	—	79	1	no	—
323	C₂²×C₈	—	79	1	no	—
324	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
328	#117	C₄×D₇₉	1	4	yes	—
329	#117	C₂×Dic₇₉	1	4	yes	—
330	C₂×C₄⋊C₄	—	79	2	no	—
331	C₂×C₄⋊C₄	—	79	2	no	—
332	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	79	2	no	—
335	C₂×C₂²⋊C₄	—	79	2	no	—
336	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
338	C₂×C₄²	—	79	2	no	—
339	C₂×C₄²	—	79	2	no	—
340	C₂×C₄²	—	79	1	no	—
341	C₂×C₄²	—	79	1	no	—
342	C₂×C₄²	—	79	1	no	—
343	C₂×C₄²	—	79	1	no	—
344	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
346	C₄⋊C₈	—	79	4	no	—
347	C₄⋊C₈	—	79	4	no	—
348	C₄⋊C₈	—	79	4	no	—
349	C₄⋊C₈	—	79	4	no	—
350	C₄⋊C₈	C₂×Dic₇₉	1	4	yes	—
351	C₄⋊C₈	C₂×Dic₇₉	1	4	yes	—
352	C₂²⋊C₈	C₂×Dic₇₉	1	4	yes	—
353	C₂²⋊C₈	C₂×Dic₇₉	1	4	yes	—
354	#97	—	316	1	no	—
355	#97	—	316	1	no	—
356	#97	—	316	1	no	—
357	#97	—	316	1	no	—
358	#97	C₂×Dic₇₉	1	4	yes	—
359	C₄×C₈	—	316	1	no	—
360	C₄×C₈	—	316	1	no	—
361	C₄×C₈	—	316	1	no	—
362	C₄×C₈	—	316	1	no	—
363	C₄×C₈	C₂×Dic₇₉	1	4	yes	—
364	#95	—	79	2	no	—
365	#95	—	79	2	no	—
366	#95	—	79	2	no	—
367	#95	—	79	2	no	—
368	#95	—	79	2	no	—
369	#95	—	79	2	no	—
370	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	79	2	no	—
376	C₂²×C₄	—	79	2	no	—
377	C₂²×C₄	—	79	2	no	—
378	C₂²×C₄	—	79	2	no	—
379	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
385	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
386	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
387	M₁₆	—	316	4	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	316	4	no	—
397	C₂×C₈	—	79	2	no	—
398	C₂×C₈	—	79	2	no	—
399	C₂×C₈	—	79	2	no	—
400	C₂×C₈	—	79	2	no	—
401	C₂×C₈	—	158	1	no	—
402	C₂×C₈	—	158	1	no	—
403	C₂×C₈	—	158	1	no	—
404	C₂×C₈	—	158	1	no	—
405	C₂×C₈	—	158	1	no	—
406	C₂×C₈	—	158	1	no	—
407	C₂×C₈	—	158	1	no	—
408	C₂×C₈	—	158	1	no	—
409	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
410	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
411	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
412	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
413	C₄⋊C₄	—	316	2	no	—
414	C₄⋊C₄	—	158	4	no	—
415	C₄⋊C₄	C₄×Dic₇₉	1	4	yes	—
416	C₄⋊C₄	C₄×Dic₇₉	1	4	yes	—
417	C₂²⋊C₄	—	316	2	no	—
418	C₂²⋊C₄	—	158	4	no	—
419	C₂²⋊C₄	C₄×Dic₇₉	1	4	yes	—
420	C₂²⋊C₄	C₄×Dic₇₉	1	4	yes	—
421	C₄²	—	316	2	no	—
422	C₄²	—	158	4	no	—
423	C₄²	—	158	1	no	—
424	C₄²	—	158	1	no	—
425	C₄²	—	158	1	no	—
426	C₄²	—	158	1	no	—
427	C₄²	—	158	1	no	—
428	C₄²	—	158	1	no	—
429	C₄²	—	158	1	no	—
430	C₄²	—	158	1	no	—
431	C₄²	C₂×C₄×D₇₉	1	2	yes	—
432	C₄²	C₂×C₄×D₇₉	1	2	yes	—
433	C₄²	C₂²×Dic₇₉	1	2	yes	—
434	C₄²	C₂²×Dic₇₉	1	2	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂×C₄×Dic₇₉	1	2	yes	—
440	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	79	4	no	—
452	C₂×C₄	—	158	2	no	—
453	C₂×C₄	—	158	2	no	—
454	C₂×C₄	—	158	2	no	—
455	C₂×C₄	—	158	2	no	—
456	C₂×C₄	—	158	2	no	—
457	C₂×C₄	—	158	2	no	—
458	C₂×C₄	—	158	2	no	—
459	C₂×C₄	—	158	2	no	—
460	C₂×C₄	—	158	2	no	—
461	C₂×C₄	—	158	2	no	—
462	C₂×C₄	—	158	2	no	—
463	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
464	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
465	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
466	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
467	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
468	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
469	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
470	C₂×C₄	#14579207	1	1	yes	characteristic
471	C₂×C₄	#14579207	1	1	yes	characteristic
472	C₂×C₄	#14579208	1	1	yes	characteristic
473	C₂×C₄	#14579208	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	158	2	no	—
479	C₈	—	158	2	no	—
480	C₈	—	158	2	no	—
481	C₈	—	158	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂²×C₄×Dic₇₉	1	1	yes	characteristic
488	C₂²	#19099043	1	1	yes	characteristic
489	C₂²	#19099043	1	1	yes	characteristic
490	C₂²	#131×D₇₉	1	2	yes	—
491	C₂²	#19099328	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	316	2	no	—
498	C₄	—	316	2	no	—
499	C₄	—	316	2	no	—
500	C₄	—	158	4	no	—
501	C₄	#19099037	1	1	yes	characteristic
502	C₄	#19099040	1	1	yes	characteristic
503	C₄	#19099046	1	1	yes	characteristic
504	C₄	#19099046	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	#23765756	1	1	yes	characteristic
507	C₂	#131×Dic₇₉	1	1	yes	characteristic
508	C₂	#23771826	1	1	yes	characteristic
509	C₂	#23772534	1	2	yes	—
510	C₂	#23772543	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂²×C₄²
Fitting	C₂×#433×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#433	D₇₉
hypocenter	C₇₉	#20553
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
3. #23763272	C₂	semidirect
4. #23763272	C₂	semidirect
5. #23763267	C₂	semidirect
6. C₈×C₄⋊Dic₇₉	C₂	semidirect
7. #23763259	C₂	semidirect
8. #23763259	C₂	semidirect
9. #23763255	C₂	semidirect
10. C₄⋊C₈×Dic₇₉	C₂	semidirect
18. #19098590	C₄	semidirect
50. #433×C₇₉	C₄	semidirect
271. C₇₉	#20553	semidirect
275. #433	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098590	2
#23765898	2
#23763272	2
#23763267	2
C₈×C₄⋊Dic₇₉	2
#23763259	2
#23763255	2
C₄⋊C₈×Dic₇₉	2
#23763186	2
#23763179	2
#23763174	2
C₂×#433×C₇₉	2
#20553	79