Subgroups — #34296040

Order 20224.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766149	C₂	1	1	yes	maximal, characteristic, complemented
2	#23765761	C₂	1	1	yes	maximal, characteristic
3	#23764353	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764170	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763987	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763980	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763663	C₂	1	1	yes	maximal, characteristic
8	#23763649	C₂	1	1	yes	maximal, characteristic
9	#23763410	C₂	1	1	yes	maximal, characteristic
10	#23763300	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763259	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763227	C₂	1	1	yes	maximal, characteristic
14	#102×Dic₇₉	C₂	1	1	yes	maximal, characteristic
15	C₂×#476×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂×D₄×Dic₇₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×Dic₇₉	C₂²	1	1	yes	characteristic
18	C₂×#14579095	C₂²	1	1	yes	characteristic
19	C₂×#14579093	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#14579082	C₂²	1	1	yes	characteristic
22	C₂×#14579082	C₂²	1	1	yes	characteristic
23	C₂×#14579071	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
25	#19098470	—	2	1	no	—
26	#19098470	—	2	1	no	—
27	#19098462	C₂²	1	1	yes	characteristic
28	#19098462	C₂²	1	1	yes	characteristic
29	#19098449	—	2	1	no	—
30	#19098449	—	2	1	no	—
31	#19098429	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×Dic₇₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
37	C₂²⋊C₄×Dic₇₉	—	2	1	no	—
38	C₂²⋊C₄×Dic₇₉	—	2	1	no	—
39	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
40	#19098409	C₂²	1	1	yes	characteristic
41	C₂×C₇₉⋊#95	—	2	1	no	—
42	#19098326	C₂²	1	1	yes	characteristic
43	#19098326	C₂²	1	1	yes	characteristic
44	#19098325	C₂²	1	1	yes	characteristic
45	#19098325	C₂²	1	1	yes	characteristic
46	#19098325	C₂²	1	1	yes	characteristic
47	#19098325	C₂²	1	1	yes	characteristic
48	#19098325	C₂²	1	1	yes	characteristic
49	#19098325	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
54	#476×C₇₉	C₄	1	8	yes	complemented
55	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
58	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
60	C₂³×Dic₇₉	—	2	1	no	—
61	C₂³×Dic₇₉	—	2	1	no	—
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	D₄×Dic₇₉	—	2	2	no	—
65	D₄×Dic₇₉	—	2	2	no	—
66	D₄×Dic₇₉	—	2	2	no	—
67	D₄×Dic₇₉	Q₈	1	4	yes	complemented
68	C₂×C₄⋊Dic₇₉	—	2	1	no	—
69	C₂×C₄⋊Dic₇₉	—	2	1	no	—
70	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
75	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
76	C₂×C₄×Dic₇₉	—	2	1	no	—
77	C₂×C₄×Dic₇₉	—	2	1	no	—
78	C₂×C₄×Dic₇₉	—	2	1	no	—
79	C₂×C₄×Dic₇₉	—	2	1	no	—
80	C₂×C₄×Dic₇₉	—	2	1	no	—
81	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
83	#14579095	—	2	2	no	—
84	#14579093	—	2	2	no	—
85	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
86	#14579082	—	2	2	no	—
87	#14579082	—	2	2	no	—
88	#14579071	—	2	2	no	—
89	C₈×Dic₇₉	—	2	2	no	—
90	C₇₉⋊#95	—	2	1	no	—
91	C₇₉⋊#95	—	2	1	no	—
92	C₇₉⋊#95	—	2	1	no	—
93	C₇₉⋊#95	—	2	1	no	—
94	C₇₉⋊#95	—	2	1	no	—
95	C₇₉⋊#95	—	2	1	no	—
96	C₇₉⋊#95	—	2	1	no	—
97	C₇₉⋊#95	—	2	1	no	—
98	C₇₉⋊#95	—	2	1	no	—
99	C₇₉⋊#95	D₄	1	1	yes	characteristic
100	C₇₉⋊#95	D₄	1	1	yes	characteristic
101	C₇₉⋊#95	D₄	1	1	yes	characteristic
102	C₇₉⋊#95	D₄	1	1	yes	characteristic
103	C₂²×Q₈×C₇₉	—	2	1	no	—
104	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₇₉	—	2	2	no	—
109	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	complemented
110	C₄×D₄×C₇₉	—	2	2	no	—
111	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
112	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	#106×C₇₉	C₂×C₄	1	4	yes	complemented
119	#106×C₇₉	C₂×C₄	1	4	yes	complemented
120	C₄⋊C₈×C₇₉	C₂×C₄	1	4	yes	complemented
121	#102×C₇₉	C₂×C₄	1	4	yes	—
122	#102×C₇₉	C₂×C₄	1	4	yes	—
123	C₂²×Dic₇₉	—	2	4	no	—
124	C₂²×Dic₇₉	—	2	4	no	—
125	C₂²×Dic₇₉	—	2	1	no	—
126	C₂²×Dic₇₉	—	2	1	no	—
127	C₂²×Dic₇₉	—	2	1	no	—
128	C₂²×Dic₇₉	—	2	1	no	—
129	C₂²×Dic₇₉	—	8	1	no	—
130	C₂²×Dic₇₉	—	8	1	no	—
131	C₂²×Dic₇₉	—	8	1	no	—
132	C₂²×Dic₇₉	—	8	1	no	—
133	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₄⋊Dic₇₉	—	2	1	no	—
144	C₄⋊Dic₇₉	—	2	1	no	—
145	C₄⋊Dic₇₉	—	2	1	no	—
146	C₄⋊Dic₇₉	—	2	1	no	—
147	C₄⋊Dic₇₉	—	2	1	no	—
148	C₄⋊Dic₇₉	—	2	1	no	—
149	C₄⋊Dic₇₉	—	8	1	no	—
150	C₄⋊Dic₇₉	—	8	1	no	—
151	C₄⋊Dic₇₉	C₂×Q₈	1	2	yes	—
152	C₄⋊Dic₇₉	#41	1	2	yes	—
153	C₂²⋊Dic₇₉	—	2	4	no	—
154	C₂²⋊Dic₇₉	—	2	4	no	—
155	C₄×Dic₇₉	—	2	1	no	—
156	C₄×Dic₇₉	—	2	1	no	—
157	C₄×Dic₇₉	—	8	1	no	—
158	C₄×Dic₇₉	—	8	1	no	—
159	C₄×Dic₇₉	—	8	1	no	—
160	C₄×Dic₇₉	—	8	1	no	—
161	C₄×Dic₇₉	—	8	1	no	—
162	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
163	C₄×Dic₇₉	#41	1	2	yes	—
164	C₂⁴×C₇₉	—	2	1	no	—
165	C₂×Q₈×C₇₉	—	2	4	no	—
166	C₂×Q₈×C₇₉	—	8	1	no	—
167	C₂×Q₈×C₇₉	—	8	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	C₂²×C₄	1	2	yes	—
172	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
173	C₂×D₄×C₇₉	#41	1	2	yes	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	4	no	—
178	C₂²×C₄×C₇₉	—	8	1	no	—
179	C₂²×C₄×C₇₉	—	8	1	no	—
180	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
183	C₂×C₈×C₇₉	—	2	1	no	—
184	C₂×C₈×C₇₉	—	2	1	no	—
185	C₂×C₈×C₇₉	—	2	1	no	—
186	C₂×C₈×C₇₉	—	2	1	no	—
187	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
189	C₄⋊C₄×C₇₉	—	2	4	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
194	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
196	C₂²⋊C₄×C₇₉	—	2	4	no	—
197	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
198	C₄²×C₇₉	#41	1	2	yes	—
199	C₂³×C₇₉	—	2	2	no	—
200	C₂³×C₇₉	—	2	2	no	—
201	C₂³×C₇₉	—	2	2	no	—
202	C₂³×C₇₉	—	4	1	no	—
203	C₂³×C₇₉	—	4	1	no	—
204	C₂³×C₇₉	—	4	1	no	—
205	C₂³×C₇₉	—	4	1	no	—
206	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₇₉	—	8	4	no	—
208	D₄×C₇₉	—	2	2	no	—
209	D₄×C₇₉	—	2	2	no	—
210	D₄×C₇₉	—	2	2	no	—
211	D₄×C₇₉	C₄×Q₈	1	4	yes	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	1	no	—
215	C₂×C₄×C₇₉	—	2	1	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	2	no	—
218	C₂×C₄×C₇₉	—	2	2	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	no	—
224	C₂×C₄×C₇₉	—	4	1	no	—
225	C₂×C₄×C₇₉	—	8	4	no	—
226	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
234	C₂×Dic₇₉	—	2	1	no	—
235	C₂×Dic₇₉	—	2	1	no	—
236	C₂×Dic₇₉	—	2	1	no	—
237	C₂×Dic₇₉	—	2	1	no	—
238	C₂×Dic₇₉	—	2	2	no	—
239	C₂×Dic₇₉	—	2	1	no	—
240	C₂×Dic₇₉	—	2	1	no	—
241	C₂×Dic₇₉	—	2	2	no	—
242	C₂×Dic₇₉	—	2	1	no	—
243	C₂×Dic₇₉	—	2	1	no	—
244	C₂×Dic₇₉	—	2	1	no	—
245	C₂×Dic₇₉	—	2	1	no	—
246	C₂×Dic₇₉	—	4	1	no	—
247	C₂×Dic₇₉	—	4	1	no	—
248	C₂×Dic₇₉	—	4	1	no	—
249	C₂×Dic₇₉	—	4	1	no	—
250	C₂×Dic₇₉	—	4	1	no	—
251	C₂×Dic₇₉	—	4	1	no	—
252	C₂×Dic₇₉	—	4	1	no	—
253	C₂×Dic₇₉	—	4	1	no	—
254	C₂×Dic₇₉	—	4	1	no	—
255	C₂×Dic₇₉	—	4	1	no	—
256	C₂×Dic₇₉	—	8	4	no	—
257	C₂×Dic₇₉	—	8	4	no	—
258	C₂×Dic₇₉	C₂²⋊Q₈	1	2	yes	—
259	C₂×Dic₇₉	C₂²⋊Q₈	1	2	yes	—
260	C₈×C₇₉	—	2	2	no	—
261	C₈×C₇₉	—	2	2	no	—
262	C₇₉⋊C₈	—	4	1	no	—
263	C₇₉⋊C₈	—	4	1	no	—
264	C₂²×C₇₉	—	2	4	no	—
265	C₂²×C₇₉	—	4	2	no	—
266	C₂²×C₇₉	—	4	2	no	—
267	C₂²×C₇₉	—	4	2	no	—
268	C₂²×C₇₉	—	4	2	no	—
269	C₂²×C₇₉	—	4	2	no	—
270	C₂²×C₇₉	—	4	2	no	—
271	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
273	C₂²×C₇₉	#525	1	1	yes	characteristic
274	C₂²×C₇₉	#576	1	1	yes	characteristic
275	C₂²×C₇₉	#577	1	1	yes	characteristic
276	C₂²×C₇₉	#577	1	1	yes	characteristic
277	C₂²×C₇₉	#577	1	1	yes	characteristic
278	C₄×C₇₉	—	2	2	no	—
279	C₄×C₇₉	—	2	2	no	—
280	C₄×C₇₉	—	4	2	no	—
281	C₄×C₇₉	—	4	2	no	—
282	C₄×C₇₉	—	4	2	no	—
283	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
284	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
285	C₄×C₇₉	#529	1	1	yes	characteristic
286	C₄×C₇₉	#533	1	1	yes	characteristic
287	Dic₇₉	—	2	2	no	—
288	Dic₇₉	—	2	2	no	—
289	Dic₇₉	—	4	2	no	—
290	Dic₇₉	—	4	1	no	—
291	Dic₇₉	—	4	2	no	—
292	Dic₇₉	—	4	1	no	—
293	Dic₇₉	—	8	1	no	—
294	Dic₇₉	—	8	1	no	—
295	#21623	—	79	1	no	maximal, Sylow
296	C₂×C₇₉	—	4	4	no	—
297	C₂×C₇₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
298	C₂×C₇₉	#2946	1	1	yes	characteristic
299	C₂×C₇₉	#2949	1	1	yes	characteristic
300	C₂×C₇₉	#3081	1	1	yes	characteristic
301	C₂×C₇₉	#3084	1	1	yes	characteristic
302	C₂×C₇₉	#3118	1	1	yes	characteristic
303	C₂×C₇₉	#3125	1	1	yes	characteristic
304	C₂×#476	D₇₉	1	1	yes	characteristic
305	#2331	—	79	1	no	—
306	#2275	—	79	1	no	—
307	#1988	—	79	1	no	—
308	#1949	—	79	1	no	—
309	#1920	—	79	1	no	—
310	#1919	—	79	1	no	—
311	#1864	—	79	1	no	—
312	#1862	—	79	1	no	—
313	#1804	—	79	1	no	—
314	#1776	—	79	1	no	—
315	C₄×#106	—	79	1	no	—
316	#1768	—	79	1	no	—
317	#1762	—	79	1	no	—
318	C₄×#102	—	79	1	no	—
319	C₇₉	#21623	1	1	yes	characteristic, complemented, Sylow
320	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
321	C₂×C₄×D₄	—	79	1	no	—
322	C₂×C₄×D₄	—	79	1	no	—
323	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
324	#476	Dic₇₉	1	8	yes	complemented
325	C₂×#107	—	79	1	no	—
326	C₂×#106	—	79	1	no	—
327	C₂×#106	C₂×D₇₉	1	1	yes	characteristic
328	C₂×#106	C₂×D₇₉	1	1	yes	characteristic
329	C₂×C₄⋊C₈	—	79	1	no	—
330	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
331	C₂×#102	—	79	1	no	—
332	C₂×#102	—	79	1	no	—
333	C₂×#102	C₂×D₇₉	1	1	yes	characteristic
334	C₂×#102	C₂×D₇₉	1	1	yes	characteristic
335	C₂×#97	—	79	1	no	—
336	C₂×C₄×C₈	—	79	1	no	—
337	#391	—	158	1	no	—
338	#391	—	158	1	no	—
339	#389	—	79	1	no	—
340	#389	—	79	1	no	—
341	#387	—	158	1	no	—
342	#387	—	158	1	no	—
343	#382	—	79	1	no	—
344	C₄×C₄⋊C₄	—	79	1	no	—
345	C₄×C₄⋊C₄	—	79	1	no	—
346	C₄×C₄⋊C₄	—	79	1	no	—
347	C₄×C₄⋊C₄	—	79	1	no	—
348	C₄×C₄⋊C₄	—	79	1	no	—
349	C₄×C₂²⋊C₄	—	158	1	no	—
350	C₄×C₂²⋊C₄	—	158	1	no	—
351	C₄×C₂²⋊C₄	—	158	1	no	—
352	#376	—	79	1	no	—
353	C₂×#95	—	158	1	no	—
354	#340	—	79	1	no	—
355	#340	—	79	1	no	—
356	#340	—	79	1	no	—
357	#340	—	79	1	no	—
358	#340	—	79	1	no	—
359	#340	—	79	1	no	—
360	#340	—	79	1	no	—
361	#340	—	79	1	no	—
362	#336	—	79	1	no	—
363	#336	—	79	1	no	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	—	158	1	no	—
368	C₂³×C₄	—	158	1	no	—
369	C₂²×C₈	—	79	1	no	—
370	C₂²×C₈	—	79	1	no	—
371	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	C₂×Dic₇₉	1	4	yes	complemented
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	79	4	no	—
377	C₄×D₄	—	158	2	no	—
378	C₄×D₄	—	158	2	no	—
379	C₄×D₄	—	158	2	no	—
380	C₄×D₄	C₂×Dic₇₉	1	4	yes	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	79	1	no	—
383	C₂×C₄⋊C₄	—	79	1	no	—
384	C₂×C₄⋊C₄	—	79	1	no	—
385	C₂×C₄⋊C₄	—	79	1	no	—
386	C₂×C₄⋊C₄	—	158	1	no	—
387	C₂×C₄⋊C₄	—	158	1	no	—
388	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	158	1	no	—
393	C₂×C₂²⋊C₄	—	158	1	no	—
394	C₂×C₄²	—	79	1	no	—
395	C₂×C₄²	—	79	1	no	—
396	C₂×C₄²	—	158	1	no	—
397	C₂×C₄²	—	158	1	no	—
398	C₂×C₄²	—	158	1	no	—
399	C₂×C₄²	—	158	1	no	—
400	C₂×C₄²	—	158	1	no	—
401	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
402	#107	—	158	2	no	—
403	#106	—	158	2	no	—
404	#106	C₂×Dic₇₉	1	4	yes	complemented
405	#106	C₂×Dic₇₉	1	4	yes	complemented
406	C₄⋊C₈	—	158	2	no	—
407	C₄⋊C₈	C₂×Dic₇₉	1	4	yes	complemented
408	#102	—	158	2	no	—
409	#102	—	158	2	no	—
410	#102	C₂×Dic₇₉	1	4	yes	—
411	#102	C₂×Dic₇₉	1	4	yes	—
412	#97	—	158	2	no	—
413	C₄×C₈	—	158	2	no	—
414	#95	—	79	1	no	—
415	#95	—	79	1	no	—
416	#95	—	79	1	no	—
417	#95	—	79	1	no	—
418	#95	—	158	1	no	—
419	#95	—	158	1	no	—
420	#95	—	158	1	no	—
421	#95	—	158	1	no	—
422	#95	—	158	1	no	—
423	#95	—	158	1	no	—
424	#95	—	158	1	no	—
425	#95	—	158	1	no	—
426	#95	—	158	1	no	—
427	C₂⁴	—	2	1	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	8	1	no	—
430	C₂×Q₈	—	8	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
435	C₂×D₄	Q₈×D₇₉	1	2	yes	—
436	C₂×D₄	#11929625	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	8	1	no	—
442	C₂²×C₄	—	8	1	no	—
443	C₂²×C₄	—	79	1	no	—
444	C₂²×C₄	—	79	1	no	—
445	C₂²×C₄	—	79	1	no	—
446	C₂²×C₄	—	79	1	no	—
447	C₂²×C₄	—	632	1	no	—
448	C₂²×C₄	—	632	1	no	—
449	C₂²×C₄	—	632	1	no	—
450	C₂²×C₄	—	632	1	no	—
451	C₂²×C₄	—	158	1	no	—
452	C₂²×C₄	—	158	1	no	—
453	C₂²×C₄	—	158	1	no	—
454	C₂²×C₄	—	158	1	no	—
455	C₂²×C₄	—	158	4	no	—
456	C₂²×C₄	—	158	4	no	—
457	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
459	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	158	1	no	—
465	C₂×C₈	—	158	1	no	—
466	C₂×C₈	—	158	1	no	—
467	C₂×C₈	—	158	1	no	—
468	C₂×C₈	—	158	1	no	—
469	C₂×C₈	—	158	1	no	—
470	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
471	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	79	2	no	—
477	C₄⋊C₄	—	79	2	no	—
478	C₄⋊C₄	—	632	1	no	—
479	C₄⋊C₄	—	632	1	no	—
480	C₄⋊C₄	—	158	1	no	—
481	C₄⋊C₄	—	158	1	no	—
482	C₄⋊C₄	—	158	1	no	—
483	C₄⋊C₄	—	158	1	no	—
484	C₄⋊C₄	—	158	1	no	—
485	C₄⋊C₄	—	158	1	no	—
486	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
487	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
488	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	158	4	no	—
491	C₂²⋊C₄	—	158	4	no	—
492	C₄²	—	79	2	no	—
493	C₄²	—	79	2	no	—
494	C₄²	—	632	1	no	—
495	C₄²	—	632	1	no	—
496	C₄²	—	632	1	no	—
497	C₄²	—	632	1	no	—
498	C₄²	—	632	1	no	—
499	C₄²	—	158	1	no	—
500	C₄²	—	158	1	no	—
501	C₄²	C₂²×Dic₇₉	1	2	yes	—
502	C₄²	#11929623	1	2	yes	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
511	Q₈	—	8	4	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	Q₈×Dic₇₉	1	4	yes	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	—	316	1	no	—
531	C₂×C₄	—	316	1	no	—
532	C₂×C₄	—	316	1	no	—
533	C₂×C₄	—	316	1	no	—
534	C₂×C₄	—	316	1	no	—
535	C₂×C₄	—	316	1	no	—
536	C₂×C₄	—	316	1	no	—
537	C₂×C₄	—	316	1	no	—
538	C₂×C₄	—	316	1	no	—
539	C₂×C₄	—	316	1	no	—
540	C₂×C₄	—	79	2	no	—
541	C₂×C₄	—	79	2	no	—
542	C₂×C₄	—	632	4	no	—
543	C₂×C₄	—	632	4	no	—
544	C₂×C₄	—	158	2	no	—
545	C₂×C₄	—	158	1	no	—
546	C₂×C₄	—	158	1	no	—
547	C₂×C₄	—	158	2	no	—
548	C₂×C₄	—	158	1	no	—
549	C₂×C₄	—	158	1	no	—
550	C₂×C₄	—	158	1	no	—
551	C₂×C₄	—	158	1	no	—
552	C₂×C₄	—	158	1	no	—
553	C₂×C₄	—	158	1	no	—
554	C₂×C₄	—	158	1	no	—
555	C₂×C₄	—	158	1	no	—
556	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
557	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
558	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
559	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
560	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
561	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
562	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
563	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
564	C₈	—	2	2	no	—
565	C₈	—	2	2	no	—
566	C₈	—	316	1	no	—
567	C₈	—	316	1	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
576	C₂²	C₂²⋊Q₈×D₇₉	1	1	yes	characteristic
577	C₂²	#19099076	1	1	yes	characteristic
578	C₂²	#19099367	1	1	yes	characteristic
579	C₂²	#19099369	1	1	yes	characteristic
580	C₂²	#19099369	1	1	yes	characteristic
581	C₂²	#19099373	1	1	yes	characteristic
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	316	2	no	—
588	C₄	—	316	2	no	—
589	C₄	—	316	1	no	—
590	C₄	—	316	1	no	—
591	C₄	—	632	1	no	—
592	C₄	—	632	1	no	—
593	C₄	—	158	2	no	—
594	C₄	—	158	2	no	—
595	C₄	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
596	C₄	#41×Dic₇₉	1	1	yes	characteristic
597	C₄	#19099099	1	1	yes	characteristic
598	C₄	#19099115	1	1	yes	characteristic
599	C₂	—	4	4	no	—
600	C₂	C₂²⋊Q₈×Dic₇₉	1	1	yes	characteristic
601	C₂	#23772233	1	1	yes	characteristic
602	C₂	#23772260	1	1	yes	characteristic
603	C₂	#23773226	1	1	yes	characteristic
604	C₂	#23773257	1	1	yes	characteristic
605	C₂	#23773589	1	1	yes	characteristic
606	C₂	#23773682	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#476×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂²×D₄×C₇₉	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#476	D₇₉
hypocenter	C₇₉	#21623
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#476

Complements

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

N	H ≅ G/N	type
1. #23766149	C₂	semidirect
3. #23764353	C₂	semidirect
4. #23764170	C₂	semidirect
5. #23763987	C₂	semidirect
6. #23763980	C₂	semidirect
10. #23763300	C₂	semidirect
11. #106×Dic₇₉	C₂	semidirect
12. #23763259	C₂	semidirect
54. #476×C₇₉	C₄	semidirect
67. D₄×Dic₇₉	Q₈	semidirect
109. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
118. #106×C₇₉	C₂×C₄	semidirect
119. #106×C₇₉	C₂×C₄	semidirect
120. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
319. C₇₉	#21623	semidirect
324. #476	Dic₇₉	semidirect
374. C₄⋊Q₈	C₂×Dic₇₉	semidirect
404. #106	C₂×Dic₇₉	semidirect
405. #106	C₂×Dic₇₉	semidirect
407. 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
#23766149	2
#23765761	2
#23764353	2
#23764170	2
#23763987	2
#23763980	2
#23763663	2
#23763649	2
#23763410	2
#23763300	2
#106×Dic₇₉	2
#23763259	2
#23763227	2
#102×Dic₇₉	2
C₂×#476×C₇₉	2
#21623	79