Subgroups — #34259575

Order 20224.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772467	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772435	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762314	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762285	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762265	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762265	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762230	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762230	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762224	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762180	C₂	1	1	yes	maximal, characteristic, complemented
12	#23761869	C₂	1	1	yes	maximal, characteristic, complemented
13	#23761791	C₂	1	1	yes	maximal, characteristic, complemented
14	#23761700	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3100	C₂	1	1	yes	maximal, characteristic
16	#19098641	—	2	1	no	—
17	#19098641	C₂²	1	1	yes	characteristic
18	#19098641	C₂²	1	1	yes	characteristic
19	#19098641	C₂²	1	1	yes	characteristic, complemented
20	#19098641	C₂²	1	1	yes	characteristic, complemented
21	#19098635	—	2	1	no	—
22	#19098635	—	2	1	no	—
23	D₄×C₇₉⋊C₈	—	2	1	no	—
24	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	#19098620	C₂²	1	1	yes	characteristic
29	#19098616	C₂²	1	1	yes	characteristic
30	#19098616	C₂²	1	1	yes	characteristic
31	#19098616	C₂²	1	1	yes	characteristic
32	#19098530	—	2	1	no	—
33	#19098530	—	2	1	no	—
34	#19098527	—	2	1	no	—
35	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
36	#19098316	C₂²	1	1	yes	characteristic, complemented
37	#19098316	C₂²	1	1	yes	characteristic, complemented
38	#19098314	C₂²	1	1	yes	characteristic, complemented
39	#19098314	C₂²	1	1	yes	characteristic, complemented
40	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
41	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
42	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
43	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
44	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
45	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
48	#19098285	C₂²	1	1	yes	characteristic, complemented
49	#19098285	C₂²	1	1	yes	characteristic, complemented
50	#19098284	C₂²	1	1	yes	characteristic, complemented
51	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	#532×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
54	#480×C₇₉	C₄	1	1	yes	characteristic
55	#480×C₇₉	C₄	1	1	yes	characteristic
56	#474×C₇₉	C₄	1	1	yes	characteristic
57	#474×C₇₉	C₄	1	1	yes	characteristic
58	#459×C₇₉	C₄	1	1	yes	characteristic
59	#459×C₇₉	C₄	1	1	yes	characteristic
60	#447×C₇₉	C₄	1	1	yes	characteristic
61	#447×C₇₉	C₄	1	1	yes	characteristic
62	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
63	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
64	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
66	#431×C₇₉	C₂²	1	1	yes	characteristic
67	C₂×#11929608	—	2	1	no	—
68	C₂×#11929608	—	2	1	no	—
69	C₂×#11929608	—	2	1	no	—
70	C₂×#11929608	—	2	1	no	—
71	C₂²×C₇₉⋊C₈	—	2	1	no	—
72	C₂²×C₇₉⋊C₈	—	2	1	no	—
73	C₂²×C₇₉⋊C₈	—	2	1	no	—
74	C₂²×C₇₉⋊C₈	—	2	1	no	—
75	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
78	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
82	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
83	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
84	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
89	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
93	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
94	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
95	#14579072	—	2	1	no	—
96	C₄×C₇₉⋊C₈	—	2	1	no	—
97	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₇₉	—	2	1	no	—
102	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₇₉	—	2	1	no	—
104	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
109	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
110	#124×C₇₉	—	2	1	no	—
111	#121×C₇₉	—	2	1	no	—
112	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
113	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₄×D₄×C₇₉	—	2	1	no	—
115	C₄×D₄×C₇₉	—	2	1	no	—
116	C₄×D₄×C₇₉	—	2	1	no	—
117	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
118	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
125	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
126	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
127	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
128	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
129	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
132	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
133	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
134	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
135	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
144	#11929608	—	8	1	no	—
145	#11929608	—	8	1	no	—
146	#11929608	—	8	1	no	—
147	#11929608	—	8	1	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	1	no	—
151	C₂×C₇₉⋊C₈	—	2	1	no	—
152	C₂×C₇₉⋊C₈	—	2	1	no	—
153	C₂×C₇₉⋊C₈	—	2	1	no	—
154	C₂×C₇₉⋊C₈	—	8	1	no	—
155	C₂×C₇₉⋊C₈	—	8	1	no	—
156	C₂×C₇₉⋊C₈	—	8	1	no	—
157	C₂×C₇₉⋊C₈	—	8	1	no	—
158	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₇₉	—	2	1	no	—
163	#41×C₇₉	—	8	1	no	—
164	#41×C₇₉	—	8	1	no	—
165	C₂×Q₈×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	2	2	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	2	1	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	2	1	no	—
171	C₂×D₄×C₇₉	—	2	1	no	—
172	C₂×D₄×C₇₉	—	4	1	no	—
173	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	2	1	no	—
183	C₂²×C₄×C₇₉	—	2	1	no	—
184	C₂²×C₄×C₇₉	—	8	1	no	—
185	C₂²×C₄×C₇₉	—	8	1	no	—
186	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
189	D₈×C₇₉	—	2	2	no	—
190	D₈×C₇₉	—	2	2	no	—
191	D₈×C₇₉	—	4	1	no	—
192	D₈×C₇₉	—	4	1	no	—
193	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	1	no	—
199	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₇₉	—	2	1	no	—
204	C₂²⋊C₄×C₇₉	—	2	1	no	—
205	C₂²⋊C₄×C₇₉	—	2	1	no	—
206	C₂²⋊C₄×C₇₉	—	2	1	no	—
207	C₂²⋊C₄×C₇₉	—	2	1	no	—
208	C₂²⋊C₄×C₇₉	—	2	1	no	—
209	C₂²⋊C₄×C₇₉	—	2	1	no	—
210	C₂²⋊C₄×C₇₉	—	2	1	no	—
211	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₇₉	#41	1	1	yes	characteristic
214	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	2	1	no	—
217	C₂³×C₇₉	—	2	1	no	—
218	C₂³×C₇₉	—	2	1	no	—
219	C₂³×C₇₉	—	4	2	no	—
220	C₂³×C₇₉	—	4	2	no	—
221	C₂³×C₇₉	—	8	1	no	—
222	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
223	Q₈×C₇₉	—	8	1	no	—
224	D₄×C₇₉	—	2	1	no	—
225	D₄×C₇₉	—	2	1	no	—
226	D₄×C₇₉	—	2	1	no	—
227	D₄×C₇₉	—	2	1	no	—
228	D₄×C₇₉	—	2	1	no	—
229	D₄×C₇₉	—	2	1	no	—
230	D₄×C₇₉	—	2	1	no	—
231	D₄×C₇₉	—	4	2	no	—
232	D₄×C₇₉	—	4	2	no	—
233	D₄×C₇₉	—	8	1	no	—
234	D₄×C₇₉	—	8	1	no	—
235	D₄×C₇₉	—	8	1	no	—
236	D₄×C₇₉	#131	1	2	yes	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	2	1	no	—
244	C₂×C₄×C₇₉	—	2	1	no	—
245	C₂×C₄×C₇₉	—	4	1	no	—
246	C₂×C₄×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	8	1	no	—
255	C₂×C₄×C₇₉	—	8	1	no	—
256	C₂×C₄×C₇₉	—	8	1	no	—
257	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
263	C₈×C₇₉	—	2	1	no	—
264	C₈×C₇₉	—	2	1	no	—
265	C₈×C₇₉	—	2	1	no	—
266	C₈×C₇₉	—	2	1	no	—
267	C₇₉⋊C₈	—	2	1	no	—
268	C₇₉⋊C₈	—	2	1	no	—
269	C₇₉⋊C₈	—	2	1	no	—
270	C₇₉⋊C₈	—	2	1	no	—
271	C₇₉⋊C₈	—	4	1	no	—
272	C₇₉⋊C₈	—	4	1	no	—
273	C₇₉⋊C₈	—	4	1	no	—
274	C₇₉⋊C₈	—	4	1	no	—
275	C₇₉⋊C₈	—	4	1	no	—
276	C₇₉⋊C₈	—	4	1	no	—
277	C₂²×C₇₉	—	2	1	no	—
278	C₂²×C₇₉	—	2	2	no	—
279	C₂²×C₇₉	—	2	1	no	—
280	C₂²×C₇₉	—	2	1	no	—
281	C₂²×C₇₉	—	4	1	no	—
282	C₂²×C₇₉	—	4	1	no	—
283	C₂²×C₇₉	—	4	1	no	—
284	C₂²×C₇₉	—	4	1	no	—
285	C₂²×C₇₉	—	4	1	no	—
286	C₂²×C₇₉	—	4	1	no	—
287	C₂²×C₇₉	—	4	1	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	—	4	1	no	—
290	C₂²×C₇₉	—	4	1	no	—
291	C₂²×C₇₉	—	4	1	no	—
292	C₂²×C₇₉	—	8	4	no	—
293	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₇₉	—	2	1	no	—
295	C₄×C₇₉	—	2	1	no	—
296	C₄×C₇₉	—	2	1	no	—
297	C₄×C₇₉	—	2	1	no	—
298	C₄×C₇₉	—	4	1	no	—
299	C₄×C₇₉	—	4	1	no	—
300	C₄×C₇₉	—	4	1	no	—
301	C₄×C₇₉	—	4	1	no	—
302	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
303	C₄×C₇₉	#568	1	1	yes	characteristic
304	C₄×C₇₉	#576	1	1	yes	characteristic
305	C₄×C₇₉	#576	1	1	yes	characteristic
306	#18026	—	79	1	no	maximal, Sylow
307	C₂×C₇₉	—	4	1	no	—
308	C₂×C₇₉	—	4	2	no	—
309	C₂×C₇₉	—	8	1	no	—
310	C₂×C₇₉	—	8	1	no	—
311	C₂×C₇₉	—	8	1	no	—
312	C₂×C₇₉	#2933	1	1	yes	characteristic
313	C₂×C₇₉	#2948	1	1	yes	characteristic
314	C₂×C₇₉	#2955	1	1	yes	characteristic
315	#3100	D₇₉	1	1	yes	characteristic
316	#2979	—	79	1	no	—
317	#2974	—	79	1	no	—
318	#1594	—	79	1	no	—
319	#1589	—	79	1	no	—
320	#1586	—	79	1	no	—
321	#1586	—	79	1	no	—
322	#1581	—	79	1	no	—
323	#1581	—	79	1	no	—
324	#1580	—	79	1	no	—
325	C₈×D₈	—	79	1	no	—
326	#1572	—	79	1	no	—
327	#1496	—	79	1	no	—
328	#1478	—	79	1	no	—
329	#1454	—	79	1	no	—
330	C₇₉	#18026	1	1	yes	characteristic, complemented, Sylow
331	#532	C₂×D₇₉	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
333	#480	Dic₇₉	1	1	yes	characteristic
334	#480	Dic₇₉	1	1	yes	characteristic
335	#474	Dic₇₉	1	1	yes	characteristic
336	#474	Dic₇₉	1	1	yes	characteristic
337	#459	Dic₇₉	1	1	yes	characteristic
338	#459	Dic₇₉	1	1	yes	characteristic
339	#447	Dic₇₉	1	1	yes	characteristic
340	#447	Dic₇₉	1	1	yes	characteristic
341	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
342	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
343	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
344	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
345	#436	—	79	1	no	—
346	#436	—	79	1	no	—
347	#436	—	79	1	no	—
348	#436	—	79	1	no	—
349	#436	—	158	1	no	—
350	#435	—	158	1	no	—
351	#435	—	158	1	no	—
352	C₈×D₄	—	79	1	no	—
353	C₈×D₄	—	79	1	no	—
354	C₈×D₄	—	79	1	no	—
355	C₈×D₄	—	79	1	no	—
356	C₈×D₄	—	158	1	no	—
357	#432	—	79	1	no	—
358	#431	—	79	1	no	—
359	#431	—	79	1	no	—
360	#431	—	79	1	no	—
361	#431	C₂×D₇₉	1	1	yes	characteristic
362	#408	—	158	1	no	—
363	#408	—	158	1	no	—
364	#407	—	158	1	no	—
365	C₂×C₂²⋊C₈	—	158	1	no	—
366	#335	—	79	1	no	—
367	#335	—	79	1	no	—
368	#334	—	79	1	no	—
369	#334	—	79	1	no	—
370	D₄⋊C₈	—	79	1	no	—
371	D₄⋊C₈	—	79	1	no	—
372	D₄⋊C₈	—	79	1	no	—
373	D₄⋊C₈	—	79	1	no	—
374	D₄⋊C₈	—	79	1	no	—
375	D₄⋊C₈	—	79	1	no	—
376	D₄⋊C₈	—	79	1	no	—
377	D₄⋊C₈	—	79	1	no	—
378	#322	—	79	1	no	—
379	#322	—	79	1	no	—
380	#322	—	79	1	no	—
381	C₈²	—	79	1	no	—
382	C₂×#41	—	2	1	no	—
383	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
386	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
387	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
388	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
389	C₂×M₁₆	—	158	1	no	—
390	C₂×M₁₆	—	158	1	no	—
391	C₂×M₁₆	—	158	1	no	—
392	C₂×M₁₆	—	158	1	no	—
393	C₂²×C₈	—	158	1	no	—
394	C₂²×C₈	—	158	1	no	—
395	C₂²×C₈	—	158	1	no	—
396	C₂²×C₈	—	158	1	no	—
397	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
398	#127	C₂×Dic₇₉	1	1	yes	characteristic
399	#124	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	C₂×Dic₇₉	1	1	yes	characteristic
402	#121	C₂×Dic₇₉	1	1	yes	characteristic
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
407	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
408	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
409	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
410	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
411	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
415	#107	C₂×Dic₇₉	1	1	yes	characteristic
416	#107	C₂×Dic₇₉	1	1	yes	characteristic
417	#107	C₂×Dic₇₉	1	1	yes	characteristic
418	#107	C₂×Dic₇₉	1	1	yes	characteristic
419	C₄⋊C₈	—	79	1	no	—
420	C₄⋊C₈	—	79	1	no	—
421	C₄⋊C₈	—	79	1	no	—
422	C₄⋊C₈	—	79	1	no	—
423	C₄⋊C₈	—	79	1	no	—
424	C₄⋊C₈	—	79	1	no	—
425	C₄⋊C₈	—	158	1	no	—
426	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
427	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
428	#102	C₂×Dic₇₉	1	1	yes	characteristic
429	#102	C₂×Dic₇₉	1	1	yes	characteristic
430	#102	C₂×Dic₇₉	1	1	yes	characteristic
431	#102	C₂×Dic₇₉	1	1	yes	characteristic
432	#102	C₂×Dic₇₉	1	1	yes	characteristic
433	#102	C₂×Dic₇₉	1	1	yes	characteristic
434	#102	C₂×Dic₇₉	1	1	yes	characteristic
435	#102	C₂×Dic₇₉	1	1	yes	characteristic
436	C₂²⋊C₈	—	79	1	no	—
437	C₂²⋊C₈	—	79	1	no	—
438	C₂²⋊C₈	—	158	1	no	—
439	C₂²⋊C₈	—	158	1	no	—
440	C₂²⋊C₈	—	158	1	no	—
441	C₂²⋊C₈	—	158	1	no	—
442	C₂²⋊C₈	—	158	1	no	—
443	C₂²⋊C₈	—	158	1	no	—
444	C₂²⋊C₈	—	158	1	no	—
445	C₂²⋊C₈	—	158	1	no	—
446	C₂²⋊C₈	—	158	1	no	—
447	C₂²⋊C₈	—	158	1	no	—
448	C₂²⋊C₈	—	158	1	no	—
449	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
450	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
451	#97	—	158	1	no	—
452	C₄×C₈	—	79	1	no	—
453	C₄×C₈	—	79	1	no	—
454	C₄×C₈	—	79	1	no	—
455	C₄×C₈	—	79	1	no	—
456	C₄×C₈	—	158	1	no	—
457	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
458	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
459	C₂⁴	—	2	1	no	—
460	#41	—	8	1	no	—
461	#41	—	8	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
471	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
472	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
473	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	—	8	1	no	—
483	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
485	C₂²×C₄	#11929623	1	1	yes	characteristic
486	D₈	—	2	2	no	—
487	D₈	—	2	2	no	—
488	D₈	—	4	1	no	—
489	D₈	—	4	1	no	—
490	M₁₆	—	632	1	no	—
491	M₁₆	—	632	1	no	—
492	M₁₆	—	632	1	no	—
493	M₁₆	—	632	1	no	—
494	C₂×C₈	—	79	1	no	—
495	C₂×C₈	—	79	1	no	—
496	C₂×C₈	—	79	1	no	—
497	C₂×C₈	—	79	1	no	—
498	C₂×C₈	—	632	1	no	—
499	C₂×C₈	—	632	1	no	—
500	C₂×C₈	—	632	1	no	—
501	C₂×C₈	—	632	1	no	—
502	C₂×C₈	—	158	1	no	—
503	C₂×C₈	—	158	1	no	—
504	C₂×C₈	—	158	1	no	—
505	C₂×C₈	—	158	1	no	—
506	C₂×C₈	—	158	1	no	—
507	C₂×C₈	—	158	1	no	—
508	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
509	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
510	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
511	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
527	C₄²	D₄×D₇₉	1	1	yes	characteristic
528	C₄²	#11929623	1	1	yes	characteristic
529	C₄²	C₂³×D₇₉	1	1	yes	characteristic
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	8	1	no	—
537	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
538	Q₈	—	8	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	1	no	—
551	D₄	#14579168	1	2	yes	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
573	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
574	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
575	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
576	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
577	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	316	1	no	—
583	C₈	—	316	1	no	—
584	C₈	—	316	1	no	—
585	C₈	—	316	1	no	—
586	C₈	—	316	1	no	—
587	C₈	—	316	1	no	—
588	C₈	—	158	1	no	—
589	C₈	—	158	1	no	—
590	C₈	—	158	1	no	—
591	C₈	—	158	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	C₂×#14579168	1	1	yes	characteristic
618	C₄	#19099330	1	1	yes	characteristic
619	C₄	#19099364	1	1	yes	characteristic
620	C₄	#19099364	1	1	yes	characteristic
621	C₂	—	4	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	—	8	1	no	—
625	C₂	—	8	1	no	—
626	C₂	#23772127	1	1	yes	characteristic
627	C₂	#23772252	1	1	yes	characteristic
628	C₂	#23772303	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting, prime radical	C₇₉×#3100	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3100	D₇₉
hypocenter	C₇₉	#18026
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. #23772467	C₂	semidirect
2. #23772435	C₂	semidirect
3. #23762314	C₂	semidirect
4. #23762285	C₂	semidirect
5. #23762265	C₂	semidirect
6. #23762265	C₂	semidirect
7. #23762230	C₂	semidirect
8. #23762230	C₂	semidirect
9. #23762224	C₂	semidirect
10. D₈×C₇₉⋊C₈	C₂	semidirect
11. #23762180	C₂	semidirect
12. #23761869	C₂	semidirect
13. #23761791	C₂	semidirect
14. #23761700	C₂	semidirect
19. #19098641	C₂²	semidirect
20. #19098641	C₂²	semidirect
26. D₄×C₇₉⋊C₈	C₂²	semidirect
27. D₄×C₇₉⋊C₈	C₂²	semidirect
36. #19098316	C₂²	semidirect
37. #19098316	C₂²	semidirect
38. #19098314	C₂²	semidirect
39. #19098314	C₂²	semidirect
44. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
45. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
46. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
47. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
48. #19098285	C₂²	semidirect
49. #19098285	C₂²	semidirect
50. #19098284	C₂²	semidirect
51. C₈×C₇₉⋊C₈	C₂²	semidirect
330. C₇₉	#18026	semidirect

Maximal subgroups

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

subgroup	index
#23772467	2
#23772435	2
#23762314	2
#23762285	2
#23762265	2
#23762230	2
#23762224	2
D₈×C₇₉⋊C₈	2
#23762180	2
#23761869	2
#23761791	2
#23761700	2
C₇₉×#3100	2
#18026	79