Subgroups — #34294736

Order 20224.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098685	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098680	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772118	C₂	1	1	yes	maximal, characteristic, complemented
4	#23771828	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764320	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764176	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764050	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764050	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763729	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763729	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763420	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763277	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763247	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763240	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3035	C₂	1	1	yes	maximal, characteristic
16	C₂×#14579168	C₂²	1	1	yes	characteristic
17	C₂×#14579168	C₂²	1	1	yes	characteristic
18	C₂×#14579168	C₂²	1	1	yes	characteristic
19	C₂×#14579168	C₂²	1	1	yes	characteristic
20	#19098685	—	2	4	no	—
21	#19098680	—	2	4	no	—
22	#19098635	—	2	1	no	—
23	#19098635	—	2	1	no	—
24	#19098635	—	2	1	no	—
25	#19098635	—	2	1	no	—
26	C₂×#14579097	C₂²	1	1	yes	characteristic
27	C₂×#14579097	C₂²	1	1	yes	characteristic
28	#19098587	C₂²	1	1	yes	characteristic
29	C₂×#14579088	C₂²	1	1	yes	characteristic
30	C₂×#14579088	C₂²	1	1	yes	characteristic
31	C₂×#14579088	C₂²	1	1	yes	characteristic
32	C₂×#14579088	C₂²	1	1	yes	characteristic
33	C₂×#14579088	C₂²	1	1	yes	characteristic
34	C₂×#14579088	C₂²	1	1	yes	characteristic
35	#19098530	C₂²	1	1	yes	characteristic
36	#19098530	C₂²	1	1	yes	characteristic
37	#19098519	—	2	1	no	—
38	#19098519	—	2	1	no	—
39	#19098519	C₂²	1	1	yes	characteristic
40	#19098519	C₂²	1	1	yes	characteristic
41	C₄×#11929608	—	2	1	no	—
42	C₄×#11929608	C₂²	1	1	yes	characteristic
43	C₂×#14579072	—	2	1	no	—
44	C₂×#14579072	C₂²	1	1	yes	characteristic
45	C₂×#14579071	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
48	#19098328	C₂²	1	1	yes	characteristic
49	#19098328	C₂²	1	1	yes	characteristic
50	#19098322	C₂²	1	1	yes	characteristic
51	#19098322	C₂²	1	1	yes	characteristic
52	#19098317	C₂²	1	1	yes	characteristic
53	#19098317	C₂²	1	1	yes	characteristic
54	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
56	#532×C₇₉	C₂²	1	1	yes	characteristic
57	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
58	#464×C₇₉	C₄	1	1	yes	characteristic, complemented
59	#464×C₇₉	C₄	1	1	yes	characteristic, complemented
60	#463×C₇₉	C₄	1	1	yes	characteristic, complemented
61	#463×C₇₉	C₄	1	1	yes	characteristic, complemented
62	#462×C₇₉	C₄	1	1	yes	characteristic, complemented
63	#461×C₇₉	C₄	1	1	yes	characteristic, complemented
64	#460×C₇₉	C₄	1	1	yes	characteristic, complemented
65	#459×C₇₉	C₄	1	1	yes	characteristic, complemented
66	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
67	#416×C₇₉	C₂²	1	1	yes	characteristic
68	#416×C₇₉	C₂²	1	1	yes	characteristic
69	#14579168	—	2	2	no	—
70	#14579168	—	2	2	no	—
71	#14579168	—	2	2	no	—
72	#14579168	—	2	2	no	—
73	#14579168	—	2	2	no	—
74	#14579168	—	2	2	no	—
75	#14579168	—	2	2	no	—
76	#14579168	D₄	1	4	yes	complemented
77	C₂×#11929608	—	2	1	no	—
78	C₂×#11929608	—	2	1	no	—
79	C₂×#11929608	—	2	1	no	—
80	C₂×#11929608	—	2	1	no	—
81	C₂×#11929608	C₂³	1	1	yes	characteristic
82	C₂×#11929608	C₂³	1	1	yes	characteristic
83	C₂×#11929608	C₂³	1	1	yes	characteristic
84	C₂×#11929608	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
90	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊Dic₇₉	—	2	1	no	—
92	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
94	#14579097	—	2	2	no	—
95	#14579097	—	2	2	no	—
96	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
97	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
98	#14579088	—	2	2	no	—
99	#14579088	—	2	2	no	—
100	#14579088	—	2	2	no	—
101	#14579088	—	2	2	no	—
102	#14579088	—	2	2	no	—
103	#14579088	—	2	2	no	—
104	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
105	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
106	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
107	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
108	#14579072	—	2	1	no	—
109	#14579072	—	2	1	no	—
110	#14579072	—	2	1	no	—
111	#14579072	D₄	1	1	yes	characteristic
112	#14579072	D₄	1	1	yes	characteristic
113	#14579072	D₄	1	1	yes	characteristic
114	#14579072	D₄	1	1	yes	characteristic
115	#14579071	—	2	2	no	—
116	C₄×C₇₉⋊C₈	—	2	1	no	—
117	C₄×C₇₉⋊C₈	—	2	1	no	—
118	C₄×C₇₉⋊C₈	—	2	1	no	—
119	C₈×Dic₇₉	—	2	2	no	—
120	C₇₉⋊#95	—	2	1	no	—
121	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
122	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
124	#135×C₇₉	—	2	2	no	—
125	#135×C₇₉	—	2	2	no	—
126	#135×C₇₉	—	2	2	no	—
127	#135×C₇₉	—	2	2	no	—
128	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
132	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
133	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
134	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
135	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
136	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
139	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
140	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
141	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
142	#121×C₇₉	—	2	1	no	—
143	#121×C₇₉	—	2	1	no	—
144	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
145	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
146	C₄×D₄×C₇₉	—	2	1	no	—
147	C₄×D₄×C₇₉	—	2	1	no	—
148	C₄×D₄×C₇₉	—	2	1	no	—
149	C₄×D₄×C₇₉	—	2	1	no	—
150	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
152	#117×C₇₉	—	2	1	no	—
153	#117×C₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₇₉	—	2	1	no	—
155	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
157	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
158	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
159	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
160	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
161	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
162	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
163	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
164	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
165	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
166	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
167	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
168	C₂²×Dic₇₉	—	2	1	no	—
169	C₂²×Dic₇₉	—	2	1	no	—
170	#11929608	—	2	4	no	—
171	#11929608	—	2	4	no	—
172	#11929608	—	2	1	no	—
173	#11929608	—	2	1	no	—
174	#11929608	—	2	1	no	—
175	#11929608	—	2	1	no	—
176	#11929608	—	2	1	no	—
177	#11929608	—	2	1	no	—
178	#11929608	—	4	2	no	—
179	#11929608	—	4	2	no	—
180	#11929608	C₂×D₄	1	2	yes	—
181	#11929608	#41	1	2	yes	—
182	C₂×C₇₉⋊C₈	—	2	4	no	—
183	C₂×C₇₉⋊C₈	—	2	4	no	—
184	C₂×C₇₉⋊C₈	—	2	1	no	—
185	C₂×C₇₉⋊C₈	—	2	1	no	—
186	C₂×C₇₉⋊C₈	—	2	1	no	—
187	C₂×C₇₉⋊C₈	—	2	1	no	—
188	C₂×C₇₉⋊C₈	—	2	1	no	—
189	C₂×C₇₉⋊C₈	—	2	1	no	—
190	C₂×C₇₉⋊C₈	—	4	2	no	—
191	C₂×C₇₉⋊C₈	—	4	2	no	—
192	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
195	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₇₉⋊C₈	#41	1	2	yes	—
198	C₄⋊Dic₇₉	—	4	2	no	—
199	C₄×Dic₇₉	—	2	1	no	—
200	C₄×Dic₇₉	—	2	1	no	—
201	C₄×Dic₇₉	—	2	1	no	—
202	C₄×Dic₇₉	—	2	1	no	—
203	#41×C₇₉	—	2	1	no	—
204	#41×C₇₉	—	2	1	no	—
205	#41×C₇₉	—	2	1	no	—
206	#41×C₇₉	—	2	1	no	—
207	#41×C₇₉	—	2	1	no	—
208	#41×C₇₉	—	2	1	no	—
209	#41×C₇₉	—	2	1	no	—
210	#41×C₇₉	—	2	1	no	—
211	#41×C₇₉	—	2	1	no	—
212	#41×C₇₉	—	2	1	no	—
213	#41×C₇₉	C₂×D₄	1	2	yes	—
214	#41×C₇₉	#41	1	2	yes	—
215	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
216	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
217	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₇₉	—	2	1	no	—
219	C₂×D₄×C₇₉	—	2	1	no	—
220	C₂×D₄×C₇₉	—	2	1	no	—
221	C₂×D₄×C₇₉	—	2	1	no	—
222	C₂×D₄×C₇₉	—	2	1	no	—
223	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
224	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
225	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₇₉	—	2	1	no	—
227	C₂²×C₄×C₇₉	—	2	1	no	—
228	C₂²×C₄×C₇₉	—	2	1	no	—
229	C₂²×C₄×C₇₉	—	2	1	no	—
230	C₂²×C₄×C₇₉	—	2	1	no	—
231	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
232	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
233	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₇₉	—	2	2	no	—
235	Q₁₆×C₇₉	—	2	2	no	—
236	SD₁₆×C₇₉	—	2	2	no	—
237	SD₁₆×C₇₉	—	2	2	no	—
238	SD₁₆×C₇₉	—	2	2	no	—
239	SD₁₆×C₇₉	—	2	2	no	—
240	D₈×C₇₉	—	2	2	no	—
241	D₈×C₇₉	—	2	2	no	—
242	C₂×C₈×C₇₉	—	2	1	no	—
243	C₂×C₈×C₇₉	—	2	1	no	—
244	C₂×C₈×C₇₉	—	2	1	no	—
245	C₂×C₈×C₇₉	—	2	1	no	—
246	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
250	C₄⋊C₄×C₇₉	—	2	1	no	—
251	C₄⋊C₄×C₇₉	—	2	1	no	—
252	C₄⋊C₄×C₇₉	—	2	1	no	—
253	C₄⋊C₄×C₇₉	—	2	1	no	—
254	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
255	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
256	C₂²⋊C₄×C₇₉	—	2	1	no	—
257	C₂²⋊C₄×C₇₉	—	2	1	no	—
258	C₂²⋊C₄×C₇₉	—	2	1	no	—
259	C₂²⋊C₄×C₇₉	—	2	1	no	—
260	C₂²⋊C₄×C₇₉	—	2	1	no	—
261	C₂²⋊C₄×C₇₉	—	2	1	no	—
262	C₂²⋊C₄×C₇₉	—	2	1	no	—
263	C₄²×C₇₉	—	2	1	no	—
264	C₄²×C₇₉	—	2	1	no	—
265	C₄²×C₇₉	—	2	1	no	—
266	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
267	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
268	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
270	C₂³×C₇₉	—	2	1	no	—
271	C₂³×C₇₉	—	2	1	no	—
272	C₂³×C₇₉	—	2	1	no	—
273	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
274	Q₈×C₇₉	—	2	1	no	—
275	Q₈×C₇₉	—	2	1	no	—
276	Q₈×C₇₉	—	2	1	no	—
277	Q₈×C₇₉	—	2	1	no	—
278	Q₈×C₇₉	—	2	1	no	—
279	Q₈×C₇₉	C₄×D₄	1	2	yes	—
280	D₄×C₇₉	—	2	2	no	—
281	D₄×C₇₉	—	2	2	no	—
282	D₄×C₇₉	—	2	1	no	—
283	D₄×C₇₉	—	2	1	no	—
284	D₄×C₇₉	—	2	1	no	—
285	D₄×C₇₉	—	2	1	no	—
286	D₄×C₇₉	—	2	1	no	—
287	D₄×C₇₉	—	4	1	no	—
288	D₄×C₇₉	—	4	1	no	—
289	D₄×C₇₉	—	4	1	no	—
290	D₄×C₇₉	—	4	1	no	—
291	D₄×C₇₉	—	8	1	no	—
292	D₄×C₇₉	—	8	1	no	—
293	D₄×C₇₉	C₄×D₄	1	2	yes	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	2	no	—
296	C₂×C₄×C₇₉	—	2	2	no	—
297	C₂×C₄×C₇₉	—	2	1	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	1	no	—
301	C₂×C₄×C₇₉	—	4	1	no	—
302	C₂×C₄×C₇₉	—	4	1	no	—
303	C₂×C₄×C₇₉	—	4	1	no	—
304	C₂×C₄×C₇₉	—	4	1	no	—
305	C₂×C₄×C₇₉	—	4	1	no	—
306	C₂×C₄×C₇₉	—	4	1	no	—
307	C₂×C₄×C₇₉	—	8	1	no	—
308	C₂×C₄×C₇₉	—	8	1	no	—
309	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
310	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
311	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
312	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
313	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
319	C₂×Dic₇₉	—	2	2	no	—
320	C₂×Dic₇₉	—	4	1	no	—
321	C₂×Dic₇₉	—	4	1	no	—
322	C₂×Dic₇₉	—	4	1	no	—
323	C₂×Dic₇₉	—	4	1	no	—
324	C₂×Dic₇₉	—	4	1	no	—
325	C₈×C₇₉	—	2	1	no	—
326	C₈×C₇₉	—	2	1	no	—
327	C₈×C₇₉	—	2	1	no	—
328	C₈×C₇₉	—	2	1	no	—
329	C₇₉⋊C₈	—	2	2	no	—
330	C₇₉⋊C₈	—	2	1	no	—
331	C₇₉⋊C₈	—	2	2	no	—
332	C₇₉⋊C₈	—	2	1	no	—
333	C₇₉⋊C₈	—	4	1	no	—
334	C₇₉⋊C₈	—	4	1	no	—
335	C₇₉⋊C₈	#121	1	2	yes	—
336	C₇₉⋊C₈	#121	1	2	yes	—
337	C₂²×C₇₉	—	2	1	no	—
338	C₂²×C₇₉	—	2	1	no	—
339	C₂²×C₇₉	—	2	2	no	—
340	C₂²×C₇₉	—	4	1	no	—
341	C₂²×C₇₉	—	4	1	no	—
342	C₂²×C₇₉	—	4	1	no	—
343	C₂²×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	4	1	no	—
345	C₂²×C₇₉	—	4	1	no	—
346	C₂²×C₇₉	—	4	1	no	—
347	C₂²×C₇₉	—	4	1	no	—
348	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
349	C₂²×C₇₉	#529	1	1	yes	characteristic
350	C₂²×C₇₉	#532	1	1	yes	characteristic
351	C₄×C₇₉	—	2	1	no	—
352	C₄×C₇₉	—	2	1	no	—
353	C₄×C₇₉	—	2	1	no	—
354	C₄×C₇₉	—	2	1	no	—
355	C₄×C₇₉	—	2	2	no	—
356	C₄×C₇₉	—	4	1	no	—
357	C₄×C₇₉	—	4	1	no	—
358	C₄×C₇₉	—	4	1	no	—
359	C₄×C₇₉	—	4	1	no	—
360	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
361	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
362	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
363	C₄×C₇₉	#525	1	1	yes	characteristic
364	Dic₇₉	—	4	2	no	—
365	Dic₇₉	—	8	1	no	—
366	#21519	—	79	1	no	maximal, Sylow
367	C₂×C₇₉	—	2	1	no	—
368	C₂×C₇₉	—	2	1	no	—
369	C₂×C₇₉	—	4	2	no	—
370	C₂×C₇₉	—	8	1	no	—
371	C₂×C₇₉	—	8	1	no	—
372	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
373	C₂×C₇₉	#2956	1	1	yes	characteristic
374	C₂×C₇₉	#2957	1	1	yes	characteristic
375	#3035	D₇₉	1	1	yes	characteristic
376	C₂×#444	—	79	1	no	—
377	C₂×#443	—	79	1	no	—
378	#2932	—	79	1	no	—
379	#2875	—	79	1	no	—
380	#1980	—	79	1	no	—
381	#1950	—	79	1	no	—
382	#1929	—	79	1	no	—
383	#1929	—	79	1	no	—
384	#1876	—	79	1	no	—
385	#1876	—	79	1	no	—
386	#1806	—	79	1	no	—
387	#1771	—	79	1	no	—
388	#1765	—	79	1	no	—
389	#1764	—	79	1	no	—
390	C₇₉	#21519	1	1	yes	characteristic, complemented, Sylow
391	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
392	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
393	C₂×#131	—	79	1	no	—
394	C₂×#131	—	79	1	no	—
395	C₂×#131	—	79	1	no	—
396	C₂×#131	—	79	1	no	—
397	#532	C₂×D₇₉	1	1	yes	characteristic
398	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
399	#464	Dic₇₉	1	1	yes	characteristic, complemented
400	#464	Dic₇₉	1	1	yes	characteristic, complemented
401	#463	Dic₇₉	1	1	yes	characteristic, complemented
402	#463	Dic₇₉	1	1	yes	characteristic, complemented
403	#462	Dic₇₉	1	1	yes	characteristic, complemented
404	#461	Dic₇₉	1	1	yes	characteristic, complemented
405	#460	Dic₇₉	1	1	yes	characteristic, complemented
406	#459	Dic₇₉	1	1	yes	characteristic, complemented
407	#444	—	158	4	no	—
408	#443	—	158	4	no	—
409	#435	—	158	1	no	—
410	#435	—	158	1	no	—
411	#435	—	158	1	no	—
412	#435	—	158	1	no	—
413	C₂×#108	—	79	1	no	—
414	C₂×#108	—	79	1	no	—
415	#423	—	79	1	no	—
416	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
417	C₂×#104	—	79	1	no	—
418	C₂×#104	—	79	1	no	—
419	C₂×#104	—	79	1	no	—
420	C₂×#104	—	79	1	no	—
421	C₂×#104	—	79	1	no	—
422	C₂×#104	—	79	1	no	—
423	#416	C₂×D₇₉	1	1	yes	characteristic
424	#416	C₂×D₇₉	1	1	yes	characteristic
425	#408	—	79	1	no	—
426	#408	—	79	1	no	—
427	#405	—	79	1	no	—
428	#405	—	79	1	no	—
429	#405	—	158	1	no	—
430	#405	—	158	1	no	—
431	C₄×M₁₆	—	79	1	no	—
432	C₄×M₁₆	—	158	1	no	—
433	C₂×#97	—	79	1	no	—
434	C₂×#97	—	79	1	no	—
435	C₂×#97	—	158	1	no	—
436	C₂×C₄×C₈	—	79	1	no	—
437	C₄×C₄⋊C₄	—	79	1	no	—
438	#341	—	79	1	no	—
439	#341	—	79	1	no	—
440	#339	—	79	1	no	—
441	#339	—	79	1	no	—
442	#336	—	79	1	no	—
443	#336	—	79	1	no	—
444	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
445	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
446	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
447	#135	—	2	2	no	—
448	#135	—	2	2	no	—
449	#135	—	2	2	no	—
450	#135	—	2	2	no	—
451	C₂×Q₁₆	C₂×Dic₇₉	1	1	yes	characteristic
452	C₂×Q₁₆	C₂×Dic₇₉	1	1	yes	characteristic
453	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
454	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
455	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
456	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
457	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
458	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
459	#131	—	79	4	no	—
460	#131	—	158	2	no	—
461	#131	—	158	2	no	—
462	#131	—	158	2	no	—
463	#131	—	158	2	no	—
464	#131	—	158	2	no	—
465	#131	—	158	2	no	—
466	#131	—	158	2	no	—
467	C₂×M₁₆	—	79	1	no	—
468	C₂×M₁₆	—	79	1	no	—
469	C₂×M₁₆	—	79	1	no	—
470	C₂×M₁₆	—	79	1	no	—
471	C₂×M₁₆	—	158	1	no	—
472	C₂×M₁₆	—	158	1	no	—
473	C₂×M₁₆	—	158	1	no	—
474	C₂×M₁₆	—	158	1	no	—
475	C₂²×C₈	—	79	1	no	—
476	C₂²×C₈	—	79	1	no	—
477	C₂²×C₈	—	158	1	no	—
478	C₂²×C₈	—	158	1	no	—
479	C₂²×C₈	—	158	1	no	—
480	C₂²×C₈	—	158	1	no	—
481	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
482	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
483	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
484	#127	C₂×Dic₇₉	1	1	yes	characteristic
485	#124	C₂×Dic₇₉	1	1	yes	characteristic
486	#124	C₂×Dic₇₉	1	1	yes	characteristic
487	#121	—	2	1	no	—
488	#121	—	2	1	no	—
489	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
490	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
496	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
497	#117	—	2	1	no	—
498	#117	C₂²×D₇₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	—	158	1	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂×C₄²	—	79	1	no	—
502	C₂×C₄²	—	79	1	no	—
503	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
504	#108	—	158	2	no	—
505	#108	—	158	2	no	—
506	C₄⋊C₈	—	158	1	no	—
507	C₄⋊C₈	—	158	1	no	—
508	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
509	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
510	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
511	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
512	#104	—	158	2	no	—
513	#104	—	158	2	no	—
514	#104	—	158	2	no	—
515	#104	—	158	2	no	—
516	#104	—	158	2	no	—
517	#104	—	158	2	no	—
518	#103	C₂×Dic₇₉	1	1	yes	characteristic
519	#103	C₂×Dic₇₉	1	1	yes	characteristic
520	#103	C₂×Dic₇₉	1	1	yes	characteristic
521	#103	C₂×Dic₇₉	1	1	yes	characteristic
522	#102	C₂×Dic₇₉	1	1	yes	characteristic
523	#102	C₂×Dic₇₉	1	1	yes	characteristic
524	#102	C₂×Dic₇₉	1	1	yes	characteristic
525	#102	C₂×Dic₇₉	1	1	yes	characteristic
526	C₂²⋊C₈	—	158	1	no	—
527	C₂²⋊C₈	—	158	1	no	—
528	C₂²⋊C₈	—	158	1	no	—
529	C₂²⋊C₈	—	158	1	no	—
530	#97	—	79	1	no	—
531	#97	—	79	1	no	—
532	#97	—	79	1	no	—
533	#97	—	79	1	no	—
534	#97	—	158	1	no	—
535	#97	—	158	1	no	—
536	#97	—	158	2	no	—
537	#97	—	158	1	no	—
538	C₄×C₈	—	158	1	no	—
539	C₄×C₈	—	158	1	no	—
540	C₄×C₈	—	158	2	no	—
541	C₄×C₈	—	158	1	no	—
542	#95	—	158	1	no	—
543	#41	—	2	1	no	—
544	#41	—	2	1	no	—
545	#41	—	2	1	no	—
546	#41	—	2	1	no	—
547	#41	—	2	1	no	—
548	#41	—	2	1	no	—
549	#41	—	2	1	no	—
550	#41	—	2	1	no	—
551	#41	—	2	1	no	—
552	#41	—	2	1	no	—
553	#41	D₄×D₇₉	1	2	yes	—
554	#41	#11929623	1	2	yes	—
555	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
556	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
557	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
564	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
565	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	158	1	no	—
572	C₂²×C₄	—	158	1	no	—
573	C₂²×C₄	#11929623	1	1	yes	characteristic
574	C₂²×C₄	#11929623	1	1	yes	characteristic
575	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
576	Q₁₆	—	2	2	no	—
577	Q₁₆	—	2	2	no	—
578	SD₁₆	—	2	2	no	—
579	SD₁₆	—	2	2	no	—
580	SD₁₆	—	2	2	no	—
581	SD₁₆	—	2	2	no	—
582	D₈	—	2	2	no	—
583	D₈	—	2	2	no	—
584	M₁₆	—	316	2	no	—
585	M₁₆	—	316	2	no	—
586	M₁₆	—	79	2	no	—
587	M₁₆	—	79	2	no	—
588	M₁₆	—	158	1	no	—
589	M₁₆	—	158	1	no	—
590	M₁₆	—	158	1	no	—
591	M₁₆	—	158	1	no	—
592	M₁₆	—	158	4	no	—
593	M₁₆	—	158	4	no	—
594	M₁₆	—	158	1	no	—
595	M₁₆	—	158	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	316	2	no	—
601	C₂×C₈	—	316	2	no	—
602	C₂×C₈	—	79	2	no	—
603	C₂×C₈	—	79	2	no	—
604	C₂×C₈	—	79	1	no	—
605	C₂×C₈	—	79	1	no	—
606	C₂×C₈	—	79	1	no	—
607	C₂×C₈	—	79	1	no	—
608	C₂×C₈	—	158	1	no	—
609	C₂×C₈	—	158	1	no	—
610	C₂×C₈	—	158	4	no	—
611	C₂×C₈	—	158	4	no	—
612	C₂×C₈	—	158	1	no	—
613	C₂×C₈	—	158	1	no	—
614	C₂×C₈	—	158	1	no	—
615	C₂×C₈	—	158	1	no	—
616	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
617	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
618	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
619	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	316	2	no	—
625	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	158	1	no	—
638	C₄²	—	158	1	no	—
639	C₄²	—	158	1	no	—
640	C₄²	—	158	1	no	—
641	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
642	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
643	C₄²	D₄×D₇₉	1	1	yes	characteristic
644	C₄²	D₄×D₇₉	1	1	yes	characteristic
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	C₂×#11929623	1	1	yes	characteristic
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	D₄×Dic₇₉	1	2	yes	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	2	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	8	1	no	—
667	D₄	—	8	1	no	—
668	D₄	D₄×Dic₇₉	1	2	yes	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	316	1	no	—
685	C₂×C₄	—	316	1	no	—
686	C₂×C₄	—	316	1	no	—
687	C₂×C₄	—	316	1	no	—
688	C₂×C₄	—	316	1	no	—
689	C₂×C₄	—	158	2	no	—
690	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
691	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
692	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
693	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
694	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
695	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
696	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
697	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
698	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
699	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	1	no	—
704	C₈	—	316	1	no	—
705	C₈	—	316	1	no	—
706	C₈	—	79	2	no	—
707	C₈	—	79	2	no	—
708	C₈	—	158	2	no	—
709	C₈	—	158	1	no	—
710	C₈	—	158	1	no	—
711	C₈	—	158	2	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
724	C₂²	#19099094	1	1	yes	characteristic
725	C₂²	#19099108	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	316	2	no	—
736	C₄	—	632	1	no	—
737	C₄	C₂×D₄×Dic₇₉	1	1	yes	characteristic
738	C₄	#41×Dic₇₉	1	1	yes	characteristic
739	C₄	#121×D₇₉	1	1	yes	characteristic
740	C₄	#19099073	1	1	yes	characteristic
741	C₂	—	2	1	no	—
742	C₂	—	2	1	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	1	no	—
746	C₂	#121×Dic₇₉	1	1	yes	characteristic
747	C₂	#23772310	1	1	yes	characteristic
748	C₂	#23772317	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting, prime radical	C₇₉×#3035	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#3035	D₇₉
hypocenter	C₇₉	#21519
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#19098685	C₂	semidirect
2. C₂×#19098680	C₂	semidirect
3. #23772118	C₂	semidirect
4. #23771828	C₂	semidirect
5. #23764320	C₂	semidirect
6. #23764176	C₂	semidirect
7. #23764050	C₂	semidirect
8. #23764050	C₂	semidirect
9. #23763729	C₂	semidirect
10. #23763729	C₂	semidirect
11. #23763420	C₂	semidirect
12. #23763277	C₂	semidirect
13. #23763247	C₂	semidirect
14. #23763240	C₂	semidirect
58. #464×C₇₉	C₄	semidirect
59. #464×C₇₉	C₄	semidirect
60. #463×C₇₉	C₄	semidirect
61. #463×C₇₉	C₄	semidirect
62. #462×C₇₉	C₄	semidirect
63. #461×C₇₉	C₄	semidirect
64. #460×C₇₉	C₄	semidirect
65. #459×C₇₉	C₄	semidirect
76. #14579168	D₄	semidirect
390. C₇₉	#21519	semidirect
399. #464	Dic₇₉	semidirect
400. #464	Dic₇₉	semidirect
401. #463	Dic₇₉	semidirect
402. #463	Dic₇₉	semidirect
403. #462	Dic₇₉	semidirect
404. #461	Dic₇₉	semidirect
405. #460	Dic₇₉	semidirect
406. #459	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098685	2
C₂×#19098680	2
#23772118	2
#23771828	2
#23764320	2
#23764176	2
#23764050	2
#23763729	2
#23763420	2
#23763277	2
#23763247	2
#23763240	2
C₇₉×#3035	2
#21519	79