Subgroups — #34297832

Order 20224.

1100 conjugacy classes of subgroups.

The subgroup lattice has 524 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	C₄×#14579120	C₂	1	1	yes	maximal, characteristic
3	#23764378	C₂	1	4	yes	maximal, complemented
4	#23764345	C₂	1	4	yes	maximal, complemented
5	#23763499	C₂	1	4	yes	maximal
6	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂×#14579120	—	2	1	no	—
8	#19098620	—	2	1	no	—
9	#19098620	—	2	1	no	—
10	#19098616	—	2	1	no	—
11	#19098616	—	2	1	no	—
12	#19098587	C₂²	1	2	yes	—
13	#19098527	C₂²	1	2	yes	—
14	C₄×#11929608	C₂²	1	2	yes	—
15	C₄×C₄⋊Dic₇₉	—	2	1	no	—
16	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
17	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
18	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
19	#19098409	—	2	1	no	—
20	C₄²×Dic₇₉	C₂²	1	2	yes	—
21	#19098322	C₂²	1	16	yes	—
22	#533×C₇₉	—	2	1	no	—
23	#533×C₇₉	—	2	1	no	—
24	#533×C₇₉	—	2	1	no	—
25	#533×C₇₉	—	2	1	no	—
26	#533×C₇₉	C₄	1	2	yes	complemented
27	#533×C₇₉	C₄	1	2	yes	complemented
28	#533×C₇₉	C₂²	1	2	yes	—
29	#533×C₇₉	C₂²	1	2	yes	—
30	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic, complemented
31	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic, complemented
32	C₂×#125×C₇₉	C₄	1	2	yes	complemented
33	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
35	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
36	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
37	C₂×#117×C₇₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#11929608	C₂³	1	4	yes	—
40	#14579120	—	2	8	no	—
41	C₂×C₄⋊Dic₇₉	—	2	2	no	—
42	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
43	C₂×C₄×Dic₇₉	—	2	2	no	—
44	C₂×C₄×Dic₇₉	—	2	2	no	—
45	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
46	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
50	#14579072	—	2	2	no	—
51	C₄×C₇₉⋊C₈	—	2	2	no	—
52	C₇₉⋊#95	—	2	2	no	—
53	C₇₉⋊#95	—	2	2	no	—
54	C₂²×Q₈×C₇₉	—	2	1	no	—
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
64	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
65	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
66	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
67	#125×C₇₉	—	2	2	no	—
68	#125×C₇₉	—	2	2	no	—
69	#125×C₇₉	C₂×C₄	1	4	yes	—
70	#125×C₇₉	C₂×C₄	1	4	yes	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	2	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	C₂²⋊Q₈×C₇₉	—	2	2	no	—
79	C₄×Q₈×C₇₉	—	2	2	no	—
80	C₄×Q₈×C₇₉	—	2	2	no	—
81	C₄×Q₈×C₇₉	—	2	2	no	—
82	C₄×Q₈×C₇₉	—	2	2	no	—
83	C₄×Q₈×C₇₉	—	2	2	no	—
84	C₄×Q₈×C₇₉	—	2	2	no	—
85	C₄×Q₈×C₇₉	—	2	2	no	—
86	C₄×Q₈×C₇₉	—	2	2	no	—
87	#117×C₇₉	—	2	2	no	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	C₂×C₄	1	4	yes	—
90	#117×C₇₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
98	C₂×C₄²×C₇₉	—	2	2	no	—
99	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×Dic₇₉	—	2	4	no	—
112	#11929608	—	2	8	no	—
113	C₂×C₇₉⋊C₈	—	2	4	no	—
114	C₄⋊Dic₇₉	—	2	8	no	—
115	C₂²⋊Dic₇₉	—	2	8	no	—
116	C₄×Dic₇₉	—	2	8	no	—
117	C₄×Dic₇₉	—	2	8	no	—
118	C₄×Dic₇₉	—	4	4	no	—
119	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₇₉	—	2	2	no	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂×Q₈×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×Q₈×C₇₉	—	4	4	no	—
125	C₂×Q₈×C₇₉	—	4	4	no	—
126	C₂²×C₄×C₇₉	—	2	4	no	—
127	C₂²×C₄×C₇₉	—	2	4	no	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	4	2	no	—
131	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₇₉	—	2	4	no	—
150	C₄⋊C₄×C₇₉	—	2	4	no	—
151	C₄⋊C₄×C₇₉	—	2	4	no	—
152	C₄⋊C₄×C₇₉	—	2	4	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
160	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	2	4	no	—
163	C₄²×C₇₉	—	2	4	no	—
164	C₄²×C₇₉	—	2	4	no	—
165	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₇₉	—	2	2	no	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	4	1	no	—
184	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₇₉	—	4	4	no	—
188	Q₈×C₇₉	—	4	4	no	—
189	Q₈×C₇₉	—	4	4	no	—
190	Q₈×C₇₉	—	4	4	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	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	2	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	4	no	—
205	C₂×C₄×C₇₉	—	2	4	no	—
206	C₂×C₄×C₇₉	—	4	1	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	1	no	—
209	C₂×C₄×C₇₉	—	4	4	no	—
210	C₂×C₄×C₇₉	—	4	4	no	—
211	C₂×C₄×C₇₉	#104	1	4	yes	—
212	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₉	2₋¹⁺⁴	1	4	yes	—
225	C₂×Dic₇₉	—	2	8	no	—
226	C₂×Dic₇₉	—	4	4	no	—
227	C₂×Dic₇₉	—	4	4	no	—
228	C₇₉⋊C₈	—	4	4	no	—
229	C₂²×C₇₉	—	2	1	no	—
230	C₂²×C₇₉	—	2	1	no	—
231	C₂²×C₇₉	—	2	1	no	—
232	C₂²×C₇₉	—	2	1	no	—
233	C₂²×C₇₉	—	2	1	no	—
234	C₂²×C₇₉	—	2	1	no	—
235	C₂²×C₇₉	—	2	1	no	—
236	C₂²×C₇₉	—	4	4	no	—
237	C₂²×C₇₉	C₂×#104	1	2	yes	—
238	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₇₉	#536	1	2	yes	—
240	C₄×C₇₉	—	2	1	no	—
241	C₄×C₇₉	—	2	1	no	—
242	C₄×C₇₉	—	2	1	no	—
243	C₄×C₇₉	—	2	1	no	—
244	C₄×C₇₉	—	2	1	no	—
245	C₄×C₇₉	—	2	1	no	—
246	C₄×C₇₉	—	2	1	no	—
247	C₄×C₇₉	—	4	4	no	—
248	C₄×C₇₉	—	4	4	no	—
249	C₄×C₇₉	C₂×#104	1	2	yes	—
250	C₄×C₇₉	C₂×#104	1	2	yes	—
251	C₄×C₇₉	#421	1	2	yes	—
252	C₄×C₇₉	#519	1	2	yes	—
253	C₄×C₇₉	#536	1	2	yes	—
254	Dic₇₉	—	4	8	no	—
255	#21844	—	79	1	no	maximal, Sylow
256	C₂×C₇₉	—	2	2	no	—
257	C₂×C₇₉	—	2	2	no	—
258	C₂×C₇₉	—	4	1	no	—
259	C₂×C₇₉	#2310	1	1	yes	characteristic
260	C₂×C₇₉	C₂²×#104	1	1	yes	characteristic
261	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
262	C₂×#533	D₇₉	1	1	yes	characteristic
263	#2920	—	79	1	no	—
264	C₄×#117	—	79	1	no	—
265	#1994	—	79	4	no	—
266	#1986	—	79	4	no	—
267	#1826	—	79	4	no	—
268	C₇₉	#21844	1	1	yes	characteristic, complemented, Sylow
269	#533	—	2	1	no	—
270	#533	—	2	1	no	—
271	#533	—	2	1	no	—
272	#533	—	2	1	no	—
273	#533	Dic₇₉	1	2	yes	complemented
274	#533	Dic₇₉	1	2	yes	complemented
275	#533	C₂×D₇₉	1	2	yes	—
276	#533	C₂×D₇₉	1	2	yes	—
277	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic, complemented
278	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic, complemented
279	C₂×#125	Dic₇₉	1	2	yes	complemented
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₂²⋊Q₈	—	2	1	no	—
282	C₂×C₄×Q₈	—	2	1	no	—
283	C₂×C₄×Q₈	—	2	1	no	—
284	C₂×#117	—	158	1	no	—
285	C₂×#117	C₂×D₇₉	1	2	yes	—
286	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
287	#432	—	158	1	no	—
288	#432	—	158	1	no	—
289	#431	—	158	1	no	—
290	#431	—	158	1	no	—
291	#423	—	79	2	no	—
292	#407	—	79	2	no	—
293	C₄×M₁₆	—	79	2	no	—
294	C₄×C₄⋊C₄	—	79	2	no	—
295	C₄×C₄⋊C₄	—	158	1	no	—
296	C₄×C₂²⋊C₄	—	79	2	no	—
297	C₄×C₂²⋊C₄	—	158	1	no	—
298	#376	—	158	1	no	—
299	C₄³	—	79	2	no	—
300	#339	—	79	16	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
304	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
306	C₂×M₁₆	—	79	4	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
312	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
313	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
314	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
315	#125	—	2	2	no	—
316	#125	—	2	2	no	—
317	#125	C₂×Dic₇₉	1	4	yes	—
318	#125	C₂×Dic₇₉	1	4	yes	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	—	2	2	no	—
337	#117	—	158	8	no	—
338	#117	C₂×Dic₇₉	1	4	yes	—
339	#117	C₂²×D₇₉	1	4	yes	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	158	2	no	—
345	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	158	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	79	4	no	—
351	C₂×C₄²	—	158	2	no	—
352	C₂×C₄²	—	158	2	no	—
353	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
354	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
355	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
356	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
357	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
358	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
359	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
360	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
365	C₄⋊C₈	—	158	2	no	—
366	C₄⋊C₈	—	158	2	no	—
367	C₂²⋊C₈	—	158	2	no	—
368	C₂²⋊C₈	—	158	2	no	—
369	#97	—	158	2	no	—
370	C₄×C₈	—	158	2	no	—
371	#95	—	158	2	no	—
372	#95	—	158	2	no	—
373	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	4	4	no	—
379	C₂×Q₈	—	4	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	158	4	no	—
386	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
404	M₁₆	—	158	8	no	—
405	C₂×C₈	—	158	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	158	8	no	—
417	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
418	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	158	8	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	316	4	no	—
425	C₄²	—	158	8	no	—
426	C₄²	—	158	8	no	—
427	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
428	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
429	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
430	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
431	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
432	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
433	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
434	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
435	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
436	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
437	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
438	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
440	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
447	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
448	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	316	4	no	—
474	C₂×C₄	—	316	4	no	—
475	C₂×C₄	—	158	8	no	—
476	C₂×C₄	#14579088	1	4	yes	—
477	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
478	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
479	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
482	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
484	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
485	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
486	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
487	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
489	C₂×C₄	#14579209	1	4	yes	—
490	C₈	—	316	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	4	no	—
499	C₂²	C₂×#14579088	1	2	yes	—
500	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
501	C₂²	#19099137	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	316	8	no	—
512	C₄	C₂×#14579088	1	2	yes	—
513	C₄	C₂×#14579088	1	2	yes	—
514	C₄	#19098580	1	2	yes	—
515	C₄	#19099041	1	2	yes	—
516	C₄	#19099137	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	#23765986	1	1	yes	characteristic
521	C₂	C₂²×#14579088	1	1	yes	characteristic
522	C₂	C₂×#19098580	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#533×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	#21844
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #23764378	C₂	semidirect
4. #23764345	C₂	semidirect
26. #533×C₇₉	C₄	semidirect
27. #533×C₇₉	C₄	semidirect
30. C₂×C₄⋊Q₈×C₇₉	C₄	semidirect
31. C₂×C₄⋊Q₈×C₇₉	C₄	semidirect
32. C₂×#125×C₇₉	C₄	semidirect
268. C₇₉	#21844	semidirect
273. #533	Dic₇₉	semidirect
274. #533	Dic₇₉	semidirect
277. C₂×C₄⋊Q₈	Dic₇₉	semidirect
278. C₂×C₄⋊Q₈	Dic₇₉	semidirect
279. C₂×#125	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
C₄×#14579120	2
#23764378	2
#23764345	2
#23763499	2
C₂×#533×C₇₉	2
#21844	79