Subgroups — #34304751

Order 20224.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764378	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764345	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763844	C₂	1	2	yes	maximal, complemented
6	#23763703	C₂	1	2	yes	maximal, complemented
7	#23763499	C₂	1	2	yes	maximal, complemented
8	#23763420	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14579088	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098322	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3475	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	C₂²	1	2	yes	—
13	C₂×D₄×Dic₇₉	—	2	1	no	—
14	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	—
15	#19098641	—	2	1	no	—
16	#19098635	—	2	2	no	—
17	D₄×C₇₉⋊C₈	—	2	1	no	—
18	#19098587	C₂²	1	1	yes	characteristic
19	C₂×#14579088	C₂²	1	1	yes	characteristic
20	C₂×#14579088	C₂²	1	1	yes	characteristic
21	C₂×#14579088	C₂²	1	2	yes	—
22	#19098527	C₂²	1	2	yes	—
23	C₄×#11929608	C₂²	1	1	yes	characteristic
24	C₄⋊C₄×Dic₇₉	—	2	1	no	—
25	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
26	C₂²⋊C₄×Dic₇₉	—	2	2	no	—
27	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
28	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
29	#19098322	C₂²	1	1	yes	characteristic
30	#19098322	C₂²	1	1	yes	characteristic
31	#19098322	C₂²	1	2	yes	—
32	#19098322	C₂²	1	2	yes	—
33	#19098322	C₂²	1	2	yes	—
34	#19098322	C₂²	1	2	yes	—
35	#19098322	C₂²	1	2	yes	—
36	#556×C₇₉	C₄	1	1	yes	characteristic, complemented
37	#555×C₇₉	C₄	1	1	yes	characteristic, complemented
38	#554×C₇₉	C₄	1	1	yes	characteristic, complemented
39	#553×C₇₉	C₄	1	2	yes	complemented
40	#552×C₇₉	—	2	1	no	—
41	#552×C₇₉	C₄	1	2	yes	complemented
42	#551×C₇₉	—	2	2	no	—
43	#547×C₇₉	C₄	1	1	yes	characteristic, complemented
44	#546×C₇₉	—	2	1	no	—
45	#533×C₇₉	C₂²	1	1	yes	characteristic
46	#529×C₇₉	—	2	2	no	—
47	#529×C₇₉	—	2	1	no	—
48	#525×C₇₉	C₂²	1	2	yes	—
49	C₄×#41×C₇₉	—	2	1	no	—
50	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₇₉	C₂²	1	2	yes	—
53	C₂³×Dic₇₉	—	2	2	no	—
54	C₂×#11929608	—	2	2	no	—
55	C₂×#11929608	—	2	4	no	—
56	C₂×#11929608	—	4	2	no	—
57	C₂×#11929608	C₂³	1	1	yes	characteristic
58	C₂×#11929608	C₂³	1	2	yes	—
59	C₂×#11929608	C₂³	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	—	2	2	no	—
61	D₄×Dic₇₉	—	2	8	no	—
62	C₂×C₄⋊Dic₇₉	—	2	1	no	—
63	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
64	C₂×C₄×Dic₇₉	—	2	1	no	—
65	C₂×C₄×Dic₇₉	—	2	4	no	—
66	C₂×C₄×Dic₇₉	—	2	1	no	—
67	C₂×C₄×Dic₇₉	—	2	2	no	—
68	C₂×C₄×Dic₇₉	—	4	2	no	—
69	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
71	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
72	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
74	#14579088	—	2	2	no	—
75	#14579088	—	2	2	no	—
76	#14579088	—	4	2	no	—
77	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
79	#14579072	—	2	1	no	—
80	C₄×C₇₉⋊C₈	—	2	1	no	—
81	C₇₉⋊#95	—	2	2	no	—
82	C₇₉⋊#95	—	2	1	no	—
83	C₂×#41×C₇₉	—	2	1	no	—
84	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
88	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
89	#126×C₇₉	—	2	2	no	—
90	#126×C₇₉	—	2	2	no	—
91	#126×C₇₉	—	2	2	no	—
92	#125×C₇₉	—	2	2	no	—
93	#125×C₇₉	—	2	1	no	—
94	#125×C₇₉	C₂×C₄	1	2	yes	complemented
95	#124×C₇₉	—	2	1	no	—
96	#124×C₇₉	—	2	2	no	—
97	#123×C₇₉	—	2	2	no	—
98	#123×C₇₉	—	2	2	no	—
99	#123×C₇₉	—	2	2	no	—
100	#123×C₇₉	—	2	2	no	—
101	C₂²⋊Q₈×C₇₉	—	2	1	no	—
102	C₂²⋊Q₈×C₇₉	—	2	1	no	—
103	C₂²⋊Q₈×C₇₉	—	2	1	no	—
104	C₂²⋊Q₈×C₇₉	—	2	2	no	—
105	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
106	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
107	#121×C₇₉	—	2	2	no	—
108	#121×C₇₉	—	2	1	no	—
109	#121×C₇₉	C₂×C₄	1	2	yes	complemented
110	#121×C₇₉	C₂×C₄	1	2	yes	complemented
111	#120×C₇₉	—	2	2	no	—
112	C₄×Q₈×C₇₉	—	2	1	no	—
113	C₄×Q₈×C₇₉	—	2	1	no	—
114	C₄×Q₈×C₇₉	—	2	1	no	—
115	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
116	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	—	2	2	no	—
119	C₄×D₄×C₇₉	—	2	1	no	—
120	C₄×D₄×C₇₉	—	2	1	no	—
121	C₄×D₄×C₇₉	—	2	2	no	—
122	C₄×D₄×C₇₉	—	2	2	no	—
123	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
127	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
128	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
129	C₄×D₄×C₇₉	D₄	1	2	yes	—
130	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
131	#117×C₇₉	—	2	2	no	—
132	#117×C₇₉	—	2	2	no	—
133	#117×C₇₉	—	2	1	no	—
134	#117×C₇₉	—	2	2	no	—
135	#117×C₇₉	—	2	1	no	—
136	#117×C₇₉	C₂×C₄	1	2	yes	complemented
137	#117×C₇₉	C₂×C₄	1	2	yes	complemented
138	#117×C₇₉	C₂³	1	1	yes	characteristic
139	#117×C₇₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	complemented
141	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	complemented
142	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
145	C₂×C₄²×C₇₉	—	2	2	no	—
146	C₂×C₄²×C₇₉	—	2	1	no	—
147	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₇₉	—	2	8	no	—
149	C₂²×Dic₇₉	—	2	1	no	—
150	C₂²×Dic₇₉	—	2	1	no	—
151	C₂²×Dic₇₉	—	2	2	no	—
152	C₂²×Dic₇₉	—	4	4	no	—
153	C₂²×Dic₇₉	—	4	4	no	—
154	#11929608	—	2	1	no	—
155	#11929608	—	2	2	no	—
156	#11929608	—	2	1	no	—
157	#11929608	—	2	2	no	—
158	#11929608	—	2	1	no	—
159	#11929608	—	4	4	no	—
160	#11929608	#41	1	2	yes	complemented
161	C₂×C₇₉⋊C₈	—	2	1	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	2	no	—
164	C₂×C₇₉⋊C₈	—	4	4	no	—
165	C₄⋊Dic₇₉	—	2	4	no	—
166	C₂²⋊Dic₇₉	—	2	8	no	—
167	C₄×Dic₇₉	—	2	4	no	—
168	C₄×Dic₇₉	—	2	1	no	—
169	C₄×Dic₇₉	—	2	2	no	—
170	C₄×Dic₇₉	—	2	1	no	—
171	C₄×Dic₇₉	—	2	2	no	—
172	C₄×Dic₇₉	—	2	1	no	—
173	C₄×Dic₇₉	—	4	4	no	—
174	C₄×Dic₇₉	—	4	2	no	—
175	C₄×Dic₇₉	#41	1	2	yes	complemented
176	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
177	#41×C₇₉	—	2	1	no	—
178	#41×C₇₉	—	2	1	no	—
179	#41×C₇₉	—	2	1	no	—
180	#41×C₇₉	—	2	1	no	—
181	#41×C₇₉	—	4	4	no	—
182	C₂×Q₈×C₇₉	—	2	1	no	—
183	C₂×Q₈×C₇₉	—	2	1	no	—
184	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×D₄×C₇₉	—	2	4	no	—
186	C₂×D₄×C₇₉	—	2	2	no	—
187	C₂×D₄×C₇₉	—	2	1	no	—
188	C₂×D₄×C₇₉	—	2	2	no	—
189	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
190	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
191	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	—	2	2	no	—
194	C₂²×C₄×C₇₉	—	2	2	no	—
195	C₂²×C₄×C₇₉	—	2	2	no	—
196	C₂²×C₄×C₇₉	—	2	2	no	—
197	C₂²×C₄×C₇₉	—	2	2	no	—
198	C₂²×C₄×C₇₉	—	2	2	no	—
199	C₂²×C₄×C₇₉	—	2	1	no	—
200	C₂²×C₄×C₇₉	—	2	1	no	—
201	C₂²×C₄×C₇₉	—	2	1	no	—
202	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
204	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₇₉	—	2	2	no	—
211	C₄⋊C₄×C₇₉	—	2	2	no	—
212	C₄⋊C₄×C₇₉	—	2	1	no	—
213	C₄⋊C₄×C₇₉	—	2	2	no	—
214	C₄⋊C₄×C₇₉	—	2	2	no	—
215	C₄⋊C₄×C₇₉	—	2	1	no	—
216	C₄⋊C₄×C₇₉	—	2	1	no	—
217	C₄⋊C₄×C₇₉	—	2	2	no	—
218	C₄⋊C₄×C₇₉	—	2	2	no	—
219	C₄⋊C₄×C₇₉	—	2	1	no	—
220	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
222	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
223	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
224	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
225	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
227	C₂²⋊C₄×C₇₉	—	2	2	no	—
228	C₂²⋊C₄×C₇₉	—	2	2	no	—
229	C₂²⋊C₄×C₇₉	—	2	2	no	—
230	C₂²⋊C₄×C₇₉	—	2	2	no	—
231	C₂²⋊C₄×C₇₉	—	2	1	no	—
232	C₂²⋊C₄×C₇₉	—	2	2	no	—
233	C₂²⋊C₄×C₇₉	—	2	2	no	—
234	C₂²⋊C₄×C₇₉	—	2	1	no	—
235	C₂²⋊C₄×C₇₉	—	2	1	no	—
236	C₂²⋊C₄×C₇₉	—	2	2	no	—
237	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
238	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
239	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
240	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
241	C₄²×C₇₉	—	2	2	no	—
242	C₄²×C₇₉	—	2	1	no	—
243	C₄²×C₇₉	—	2	2	no	—
244	C₄²×C₇₉	—	2	1	no	—
245	C₄²×C₇₉	—	2	1	no	—
246	C₄²×C₇₉	—	2	2	no	—
247	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
251	C₂³×C₇₉	—	2	2	no	—
252	C₂³×C₇₉	—	2	2	no	—
253	C₂³×C₇₉	—	2	4	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	4	2	no	—
256	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₇₉	—	2	1	no	—
260	Q₈×C₇₉	—	2	1	no	—
261	Q₈×C₇₉	—	4	2	no	—
262	Q₈×C₇₉	—	8	1	no	—
263	D₄×C₇₉	—	2	4	no	—
264	D₄×C₇₉	—	2	1	no	—
265	D₄×C₇₉	—	2	1	no	—
266	D₄×C₇₉	—	2	2	no	—
267	D₄×C₇₉	—	4	1	no	—
268	D₄×C₇₉	—	4	1	no	—
269	D₄×C₇₉	—	4	4	no	—
270	D₄×C₇₉	—	8	2	no	—
271	D₄×C₇₉	#104	1	4	yes	complemented
272	C₂×C₄×C₇₉	—	2	2	no	—
273	C₂×C₄×C₇₉	—	2	2	no	—
274	C₂×C₄×C₇₉	—	2	2	no	—
275	C₂×C₄×C₇₉	—	2	2	no	—
276	C₂×C₄×C₇₉	—	2	2	no	—
277	C₂×C₄×C₇₉	—	2	2	no	—
278	C₂×C₄×C₇₉	—	2	2	no	—
279	C₂×C₄×C₇₉	—	2	2	no	—
280	C₂×C₄×C₇₉	—	2	2	no	—
281	C₂×C₄×C₇₉	—	2	2	no	—
282	C₂×C₄×C₇₉	—	2	2	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	2	no	—
287	C₂×C₄×C₇₉	—	2	2	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	4	no	—
290	C₂×C₄×C₇₉	—	4	1	no	—
291	C₂×C₄×C₇₉	—	4	1	no	—
292	C₂×C₄×C₇₉	—	4	2	no	—
293	C₂×C₄×C₇₉	—	8	1	no	—
294	C₂×C₄×C₇₉	—	8	2	no	—
295	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
307	C₂×Dic₇₉	—	2	2	no	—
308	C₂×Dic₇₉	—	2	2	no	—
309	C₂×Dic₇₉	—	2	2	no	—
310	C₂×Dic₇₉	—	2	2	no	—
311	C₂×Dic₇₉	—	2	4	no	—
312	C₂×Dic₇₉	—	4	16	no	—
313	C₂×Dic₇₉	—	4	1	no	—
314	C₂×Dic₇₉	—	4	2	no	—
315	C₂×Dic₇₉	—	4	2	no	—
316	C₂×Dic₇₉	—	4	1	no	—
317	C₇₉⋊C₈	—	2	2	no	—
318	C₇₉⋊C₈	—	4	2	no	—
319	C₇₉⋊C₈	—	4	1	no	—
320	C₂²×C₇₉	—	2	2	no	—
321	C₂²×C₇₉	—	2	1	no	—
322	C₂²×C₇₉	—	2	1	no	—
323	C₂²×C₇₉	—	2	2	no	—
324	C₂²×C₇₉	—	2	2	no	—
325	C₂²×C₇₉	—	2	2	no	—
326	C₂²×C₇₉	—	2	2	no	—
327	C₂²×C₇₉	—	4	4	no	—
328	C₂²×C₇₉	—	4	4	no	—
329	C₂²×C₇₉	—	4	1	no	—
330	C₂²×C₇₉	—	4	1	no	—
331	C₂²×C₇₉	—	4	1	no	—
332	C₂²×C₇₉	C₂×#104	1	4	yes	—
333	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
334	C₂²×C₇₉	#546	1	1	yes	characteristic
335	C₂²×C₇₉	#547	1	1	yes	characteristic
336	C₄×C₇₉	—	2	2	no	—
337	C₄×C₇₉	—	2	2	no	—
338	C₄×C₇₉	—	2	1	no	—
339	C₄×C₇₉	—	2	1	no	—
340	C₄×C₇₉	—	2	1	no	—
341	C₄×C₇₉	—	4	1	no	—
342	C₄×C₇₉	—	4	1	no	—
343	C₄×C₇₉	—	4	2	no	—
344	C₄×C₇₉	—	4	1	no	—
345	C₄×C₇₉	—	4	2	no	—
346	C₄×C₇₉	C₂×#104	1	2	yes	—
347	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
348	C₄×C₇₉	#520	1	1	yes	characteristic
349	C₄×C₇₉	#546	1	1	yes	characteristic
350	C₄×C₇₉	#547	1	1	yes	characteristic
351	Dic₇₉	—	2	4	no	—
352	Dic₇₉	—	4	2	no	—
353	Dic₇₉	—	4	4	no	—
354	#22505	—	79	1	no	maximal, Sylow
355	C₂×C₇₉	—	2	1	no	—
356	C₂×C₇₉	—	2	1	no	—
357	C₂×C₇₉	—	2	4	no	—
358	C₂×C₇₉	—	4	2	no	—
359	C₂×C₇₉	—	8	1	no	—
360	C₂×C₇₉	#2339	1	1	yes	characteristic
361	C₂×C₇₉	C₂²×#104	1	1	yes	characteristic
362	C₂×C₇₉	#2901	1	1	yes	characteristic
363	#3475	D₇₉	1	1	yes	characteristic
364	D₄×M₁₆	—	79	1	no	—
365	C₄²×D₄	—	79	1	no	—
366	#1994	—	79	1	no	—
367	#1986	—	79	1	no	—
368	#1896	—	79	2	no	—
369	#1871	—	79	2	no	—
370	#1826	—	79	2	no	—
371	#1806	—	79	1	no	—
372	C₄×#104	—	79	1	no	—
373	C₂×#339	—	79	2	no	—
374	C₇₉	#22505	1	1	yes	characteristic, complemented, Sylow
375	C₂²×M₁₆	—	79	2	no	—
376	#556	Dic₇₉	1	1	yes	characteristic, complemented
377	#555	Dic₇₉	1	1	yes	characteristic, complemented
378	#554	Dic₇₉	1	1	yes	characteristic, complemented
379	#553	Dic₇₉	1	2	yes	complemented
380	#552	—	2	1	no	—
381	#552	Dic₇₉	1	2	yes	complemented
382	#551	—	2	2	no	—
383	#547	Dic₇₉	1	1	yes	characteristic, complemented
384	#546	—	2	1	no	—
385	#533	C₂×D₇₉	1	1	yes	characteristic
386	#529	—	2	2	no	—
387	#529	—	2	1	no	—
388	#525	C₂×D₇₉	1	2	yes	—
389	C₄×#41	—	2	1	no	—
390	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
391	C₂×C₄×D₄	—	158	1	no	—
392	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
393	C₂×#117	C₂×D₇₉	1	2	yes	—
394	C₂²×C₄²	—	79	2	no	—
395	#436	—	158	1	no	—
396	#435	—	158	2	no	—
397	C₈×D₄	—	158	1	no	—
398	#423	—	79	1	no	—
399	C₂×#104	—	79	2	no	—
400	C₂×#104	—	79	1	no	—
401	C₂×#104	—	79	1	no	—
402	#407	—	79	2	no	—
403	C₄×M₁₆	—	79	1	no	—
404	C₄×C₄⋊C₄	—	79	1	no	—
405	C₄×C₄⋊C₄	—	158	1	no	—
406	C₄×C₂²⋊C₄	—	79	2	no	—
407	C₄×C₂²⋊C₄	—	158	2	no	—
408	C₄³	—	79	1	no	—
409	#339	—	79	2	no	—
410	#339	—	79	1	no	—
411	#339	—	79	2	no	—
412	#339	—	79	2	no	—
413	#339	—	79	2	no	—
414	#339	—	79	2	no	—
415	#339	—	79	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
418	C₂²×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
419	C₂³×C₄	—	158	2	no	—
420	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
421	C₂×M₁₆	—	316	2	no	—
422	C₂×M₁₆	—	79	1	no	—
423	C₂×M₁₆	—	79	2	no	—
424	C₂×M₁₆	—	79	1	no	—
425	C₂×M₁₆	—	158	4	no	—
426	C₂×M₁₆	—	158	2	no	—
427	C₂²×C₈	—	158	2	no	—
428	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
429	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#125	—	2	2	no	—
434	#125	—	2	1	no	—
435	#125	C₂×Dic₇₉	1	2	yes	complemented
436	#124	—	2	1	no	—
437	#124	—	2	2	no	—
438	#123	—	2	2	no	—
439	#123	—	2	2	no	—
440	#123	—	2	2	no	—
441	#123	—	2	2	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	complemented
447	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	complemented
448	#121	—	2	2	no	—
449	#121	—	2	1	no	—
450	#121	C₂×Dic₇₉	1	2	yes	complemented
451	#121	C₂×Dic₇₉	1	2	yes	complemented
452	#120	—	2	2	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
457	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	158	8	no	—
465	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
466	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
467	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
468	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic, complemented
469	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic, complemented
470	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
471	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
472	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
473	#117	—	2	2	no	—
474	#117	—	2	2	no	—
475	#117	—	2	1	no	—
476	#117	—	2	2	no	—
477	#117	—	2	1	no	—
478	#117	C₂×Dic₇₉	1	2	yes	complemented
479	#117	C₂×Dic₇₉	1	2	yes	complemented
480	#117	C₂²×D₇₉	1	1	yes	characteristic
481	#117	C₂²×D₇₉	1	2	yes	—
482	C₂×C₄⋊C₄	—	158	1	no	—
483	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	complemented
484	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	complemented
485	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	—	2	2	no	—
487	C₂×C₂²⋊C₄	—	158	2	no	—
488	C₂×C₂²⋊C₄	C₂²⋊D₇₉	1	2	yes	—
489	C₂×C₄²	—	2	2	no	—
490	C₂×C₄²	—	2	1	no	—
491	C₂×C₄²	—	316	2	no	—
492	C₂×C₄²	—	79	1	no	—
493	C₂×C₄²	—	79	1	no	—
494	C₂×C₄²	—	79	2	no	—
495	C₂×C₄²	—	158	1	no	—
496	C₂×C₄²	—	158	2	no	—
497	C₂×C₄²	—	158	4	no	—
498	C₂×C₄²	—	158	1	no	—
499	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
500	C₄⋊C₈	—	158	1	no	—
501	C₄⋊C₈	—	158	1	no	—
502	#104	—	316	2	no	—
503	#104	—	158	2	no	—
504	#104	—	158	2	no	—
505	C₂²⋊C₈	—	158	2	no	—
506	C₂²⋊C₈	—	158	2	no	—
507	#97	—	158	1	no	—
508	C₄×C₈	—	158	1	no	—
509	#95	—	158	2	no	—
510	#95	—	158	1	no	—
511	C₂⁴	C₂×C₂²⋊D₇₉	1	2	yes	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	2	1	no	—
515	#41	—	2	1	no	—
516	#41	—	4	4	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
525	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
526	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
527	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	316	4	no	—
538	C₂²×C₄	—	316	4	no	—
539	C₂²×C₄	—	158	8	no	—
540	C₂²×C₄	—	158	1	no	—
541	C₂²×C₄	—	158	2	no	—
542	C₂²×C₄	—	158	1	no	—
543	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
544	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
545	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
546	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
548	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
549	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
550	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
551	M₁₆	—	316	4	no	—
552	M₁₆	—	79	2	no	—
553	M₁₆	—	158	1	no	—
554	M₁₆	—	158	2	no	—
555	M₁₆	—	158	2	no	—
556	M₁₆	—	158	1	no	—
557	M₁₆	—	158	1	no	—
558	C₂×C₈	—	316	4	no	—
559	C₂×C₈	—	158	1	no	—
560	C₂×C₈	—	158	2	no	—
561	C₂×C₈	—	158	1	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	158	4	no	—
573	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
574	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
575	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
576	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
577	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
578	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
579	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	158	8	no	—
591	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
592	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
593	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
594	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	316	4	no	—
602	C₄²	—	316	2	no	—
603	C₄²	—	79	2	no	—
604	C₄²	—	158	4	no	—
605	C₄²	—	158	1	no	—
606	C₄²	—	158	2	no	—
607	C₄²	—	158	2	no	—
608	C₄²	—	158	1	no	—
609	C₄²	—	158	1	no	—
610	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
611	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
612	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
613	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	4	2	no	—
619	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
620	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
621	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	4	2	no	—
625	Q₈	—	8	1	no	—
626	D₄	—	2	4	no	—
627	D₄	—	2	1	no	—
628	D₄	—	2	1	no	—
629	D₄	—	2	2	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	4	no	—
633	D₄	—	8	2	no	—
634	D₄	#14579088	1	4	yes	complemented
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	8	1	no	—
657	C₂×C₄	—	8	2	no	—
658	C₂×C₄	—	316	1	no	—
659	C₂×C₄	—	316	2	no	—
660	C₂×C₄	—	316	2	no	—
661	C₂×C₄	—	316	1	no	—
662	C₂×C₄	—	316	16	no	—
663	C₂×C₄	—	158	2	no	—
664	C₂×C₄	—	158	4	no	—
665	C₂×C₄	—	158	2	no	—
666	C₂×C₄	—	158	2	no	—
667	C₂×C₄	—	158	2	no	—
668	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
669	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
670	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
671	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
672	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
673	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
674	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
675	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
676	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
677	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
678	C₂×C₄	#14579207	1	1	yes	characteristic
679	C₂×C₄	#14579208	1	1	yes	characteristic
680	C₈	—	316	2	no	—
681	C₈	—	316	1	no	—
682	C₈	—	158	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	C₂×#14579088	1	4	yes	—
696	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
697	C₂²	#19099201	1	1	yes	characteristic
698	C₂²	#19099212	1	1	yes	characteristic
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	316	4	no	—
710	C₄	—	316	2	no	—
711	C₄	—	158	4	no	—
712	C₄	C₂×#14579088	1	2	yes	—
713	C₄	#41×Dic₇₉	1	1	yes	characteristic
714	C₄	#19099046	1	1	yes	characteristic
715	C₄	#19099201	1	1	yes	characteristic
716	C₄	#19099212	1	1	yes	characteristic
717	C₂	—	2	1	no	—
718	C₂	—	2	1	no	—
719	C₂	—	2	4	no	—
720	C₂	—	4	2	no	—
721	C₂	—	8	1	no	—
722	C₂	#23766230	1	1	yes	characteristic
723	C₂	C₂²×#14579088	1	1	yes	characteristic
724	C₂	#23771947	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, prime radical	C₇₉×#3475	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#3475	D₇₉
hypocenter	C₇₉	#22505
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. D₄×#11929608	C₂	semidirect
2. C₄×D₄×Dic₇₉	C₂	semidirect
3. #23764378	C₂	semidirect
4. #23764345	C₂	semidirect
5. #23763844	C₂	semidirect
6. #23763703	C₂	semidirect
7. #23763499	C₂	semidirect
8. #23763420	C₂	semidirect
9. C₄×#14579088	C₂	semidirect
10. C₂×#19098322	C₂	semidirect
36. #556×C₇₉	C₄	semidirect
37. #555×C₇₉	C₄	semidirect
38. #554×C₇₉	C₄	semidirect
39. #553×C₇₉	C₄	semidirect
41. #552×C₇₉	C₄	semidirect
43. #547×C₇₉	C₄	semidirect
87. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
88. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
94. #125×C₇₉	C₂×C₄	semidirect
105. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
106. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
109. #121×C₇₉	C₂×C₄	semidirect
110. #121×C₇₉	C₂×C₄	semidirect
115. C₄×Q₈×C₇₉	C₂×C₄	semidirect
116. C₄×Q₈×C₇₉	C₂×C₄	semidirect
126. C₄×D₄×C₇₉	C₂×C₄	semidirect
127. C₄×D₄×C₇₉	C₂×C₄	semidirect
136. #117×C₇₉	C₂×C₄	semidirect
137. #117×C₇₉	C₂×C₄	semidirect
140. C₂×C₄⋊C₄×C₇₉	C₂×C₄	semidirect
141. C₂×C₄⋊C₄×C₇₉	C₂×C₄	semidirect
160. #11929608	#41	semidirect
175. C₄×Dic₇₉	#41	semidirect
271. D₄×C₇₉	#104	semidirect
374. C₇₉	#22505	semidirect
376. #556	Dic₇₉	semidirect
377. #555	Dic₇₉	semidirect
378. #554	Dic₇₉	semidirect
379. #553	Dic₇₉	semidirect
381. #552	Dic₇₉	semidirect
383. #547	Dic₇₉	semidirect
428. C₄⋊Q₈	C₂×Dic₇₉	semidirect
429. C₄⋊Q₈	C₂×Dic₇₉	semidirect
435. #125	C₂×Dic₇₉	semidirect
446. C₂²⋊Q₈	C₂×Dic₇₉	semidirect
447. C₂²⋊Q₈	C₂×Dic₇₉	semidirect
450. #121	C₂×Dic₇₉	semidirect
451. #121	C₂×Dic₇₉	semidirect
456. C₄×Q₈	C₂×Dic₇₉	semidirect
457. C₄×Q₈	C₂×Dic₇₉	semidirect
468. C₄×D₄	C₂×Dic₇₉	semidirect
469. C₄×D₄	C₂×Dic₇₉	semidirect
478. #117	C₂×Dic₇₉	semidirect
479. #117	C₂×Dic₇₉	semidirect
483. C₂×C₄⋊C₄	C₂×Dic₇₉	semidirect
484. C₂×C₄⋊C₄	C₂×Dic₇₉	semidirect
634. D₄	#14579088	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11929608	2
C₄×D₄×Dic₇₉	2
#23764378	2
#23764345	2
#23763844	2
#23763703	2
#23763499	2
#23763420	2
C₄×#14579088	2
C₂×#19098322	2
C₇₉×#3475	2
#22505	79