Subgroups — #34295119

Order 20224.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773006	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098683	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×M₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764287	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764145	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764114	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764110	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763844	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763841	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763440	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763285	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763239	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579181	C₂²	1	1	yes	characteristic
17	C₂×#14579167	C₂²	1	1	yes	characteristic
18	C₂²×#11929608	C₂²	1	1	yes	characteristic
19	#19099074	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
21	#19098819	C₄	1	2	yes	complemented
22	#19098814	C₄	1	2	yes	complemented
23	#19098811	C₄	1	2	yes	complemented
24	#19098807	C₄	1	2	yes	complemented
25	#19098683	—	2	4	no	—
26	#19098639	—	2	2	no	—
27	#19098632	—	2	2	no	—
28	C₂×#14579096	C₂²	1	1	yes	characteristic
29	C₂×#14579096	C₂²	1	1	yes	characteristic
30	#19098599	C₂²	1	1	yes	characteristic
31	#19098589	C₂²	1	1	yes	characteristic
32	C₂×#14579088	C₂²	1	1	yes	characteristic
33	C₂×#14579088	C₂²	1	1	yes	characteristic
34	C₂×#14579087	C₂²	1	1	yes	characteristic
35	C₂×#14579087	C₂²	1	1	yes	characteristic
36	#19098559	C₂²	1	1	yes	characteristic
37	#19098557	C₂²	1	1	yes	characteristic
38	#19098529	C₂²	1	1	yes	characteristic
39	#19098527	C₂²	1	1	yes	characteristic
40	#19098518	C₂²	1	1	yes	characteristic
41	M₁₆×Dic₇₉	—	2	4	no	—
42	C₂×#14579071	C₂²	1	1	yes	characteristic
43	C₂×#14579071	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
46	#19098327	C₂²	1	1	yes	characteristic
47	#19098327	C₂²	1	1	yes	characteristic
48	#19098324	C₂²	1	1	yes	characteristic
49	#19098324	C₂²	1	1	yes	characteristic
50	#19098322	C₂²	1	1	yes	characteristic
51	#19098322	C₂²	1	1	yes	characteristic
52	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
53	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
54	#525×C₇₉	C₂²	1	1	yes	characteristic
55	#436×C₇₉	—	2	2	no	—
56	#435×C₇₉	—	2	2	no	—
57	#424×C₇₉	C₂²	1	1	yes	characteristic
58	#408×C₇₉	C₂²	1	1	yes	characteristic
59	#407×C₇₉	C₂²	1	1	yes	characteristic
60	#405×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#11929624	C₂³	1	1	yes	characteristic
62	C₂³×Dic₇₉	—	2	1	no	—
63	#14579181	—	2	2	no	—
64	#14579181	—	2	2	no	—
65	C₂×#11929614	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×#11929612	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#11929611	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×#11929609	C₂×C₄	1	1	yes	characteristic, complemented
69	#14579167	—	2	2	no	—
70	#14579167	—	2	2	no	—
71	C₂×#11929608	—	2	2	no	—
72	C₂×#11929608	—	2	2	no	—
73	C₂×#11929608	C₂×C₄	1	2	yes	—
74	C₂×#11929608	C₂×C₄	1	2	yes	—
75	C₂×#11929608	C₂³	1	1	yes	characteristic
76	C₂×#11929608	C₂³	1	1	yes	characteristic
77	C₂×#11929607	—	2	1	no	—
78	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₇₉	—	2	1	no	—
81	#14579144	—	2	1	no	—
82	#14579140	C₂×C₄	1	2	yes	—
83	#14579135	C₂×C₄	1	2	yes	—
84	#14579130	—	2	1	no	—
85	C₄×C₂²⋊D₇₉	—	2	2	no	—
86	#14579120	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₇₉	—	2	1	no	—
88	C₂×C₄×Dic₇₉	—	2	2	no	—
89	C₂×C₄×Dic₇₉	—	2	2	no	—
90	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
92	#14579096	—	2	2	no	—
93	#14579096	—	2	2	no	—
94	#14579094	C₂×C₄	1	2	yes	complemented
95	#14579092	C₂×C₄	1	2	yes	complemented
96	Dic₇₉⋊C₈	—	2	2	no	—
97	#14579088	—	2	2	no	—
98	#14579088	—	2	2	no	—
99	#14579087	—	2	2	no	—
100	#14579087	—	2	2	no	—
101	#14579085	C₂×C₄	1	2	yes	complemented
102	#14579084	C₂×C₄	1	2	yes	complemented
103	#14579082	C₂×C₄	1	2	yes	complemented
104	#14579081	C₂×C₄	1	2	yes	complemented
105	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
106	(C₂×D₇₉)⋊C₈	—	2	2	no	—
107	#14579071	—	2	1	no	—
108	#14579071	—	2	2	no	—
109	#14579071	D₄	1	4	yes	complemented
110	C₈×Dic₇₉	—	2	1	no	—
111	C₈×Dic₇₉	—	2	2	no	—
112	C₈×Dic₇₉	—	2	2	no	—
113	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
115	#131×C₇₉	—	2	2	no	—
116	#131×C₇₉	—	2	2	no	—
117	C₂×M₁₆×C₇₉	—	2	2	no	—
118	C₂×M₁₆×C₇₉	—	2	1	no	—
119	C₂×M₁₆×C₇₉	—	2	2	no	—
120	C₂×M₁₆×C₇₉	D₄	1	2	yes	—
121	C₂×M₁₆×C₇₉	D₄	1	2	yes	—
122	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₇₉	—	2	1	no	—
125	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	#123×C₇₉	—	2	1	no	—
128	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
129	#121×C₇₉	C₂×C₄	1	2	yes	—
130	#120×C₇₉	—	2	1	no	—
131	C₄×D₄×C₇₉	—	2	2	no	—
132	#117×C₇₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₇₉	—	2	2	no	—
134	C₂²⋊C₈×C₇₉	—	2	2	no	—
135	C₂²⋊C₈×C₇₉	—	2	2	no	—
136	#97×C₇₉	—	2	1	no	—
137	C₄×C₈×C₇₉	—	2	1	no	—
138	#11929624	—	2	1	no	—
139	#11929624	—	2	1	no	—
140	#11929624	—	2	1	no	—
141	#11929624	—	2	1	no	—
142	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊D₇₉	—	2	1	no	—
145	C₂×C₂²⋊D₇₉	—	2	2	no	—
146	C₂²×Dic₇₉	—	2	4	no	—
147	C₂²×Dic₇₉	—	2	1	no	—
148	C₂²×Dic₇₉	—	2	1	no	—
149	C₂²×Dic₇₉	—	4	4	no	—
150	C₂×C₄×D₇₉	—	2	1	no	—
151	#11929614	—	2	2	no	—
152	#11929612	—	2	2	no	—
153	#11929611	—	2	2	no	—
154	#11929609	—	2	2	no	—
155	#11929608	—	2	4	no	—
156	#11929608	—	2	4	no	—
157	#11929608	—	2	1	no	—
158	#11929608	—	2	1	no	—
159	#11929608	—	2	1	no	—
160	#11929608	—	2	1	no	—
161	#11929607	—	4	2	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	1	no	—
164	C₂×C₇₉⋊C₈	—	2	1	no	—
165	C₂×C₇₉⋊C₈	—	2	1	no	—
166	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×C₇₉⋊C₈	#41	1	2	yes	—
171	C₈×D₇₉	—	4	2	no	—
172	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
173	Dic₇₉⋊C₄	—	2	2	no	—
174	C₂²⋊Dic₇₉	—	2	2	no	—
175	C₂²⋊Dic₇₉	—	2	1	no	—
176	(C₂×D₇₉)⋊C₄	—	2	2	no	—
177	C₄×Dic₇₉	—	2	4	no	—
178	C₄×Dic₇₉	—	2	1	no	—
179	C₄×Dic₇₉	—	2	1	no	—
180	C₄×Dic₇₉	—	2	1	no	—
181	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
182	C₄×Dic₇₉	#41	1	2	yes	—
183	C₂⁴×C₇₉	#41	1	1	yes	characteristic
184	#41×C₇₉	—	2	1	no	—
185	#41×C₇₉	—	2	1	no	—
186	#41×C₇₉	—	2	1	no	—
187	#41×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×D₄×C₇₉	—	2	1	no	—
190	C₂×D₄×C₇₉	—	2	2	no	—
191	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₉	—	2	1	no	—
193	C₂²×C₄×C₇₉	—	2	1	no	—
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
201	M₁₆×C₇₉	—	2	4	no	—
202	M₁₆×C₇₉	—	2	4	no	—
203	M₁₆×C₇₉	—	2	1	no	—
204	M₁₆×C₇₉	—	2	1	no	—
205	M₁₆×C₇₉	—	2	1	no	—
206	M₁₆×C₇₉	—	2	1	no	—
207	M₁₆×C₇₉	—	4	2	no	—
208	C₂×C₈×C₇₉	—	2	1	no	—
209	C₂×C₈×C₇₉	—	2	1	no	—
210	C₂×C₈×C₇₉	—	2	1	no	—
211	C₂×C₈×C₇₉	—	2	1	no	—
212	C₂×C₈×C₇₉	—	4	2	no	—
213	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
215	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
217	C₂×C₈×C₇₉	#41	1	2	yes	—
218	C₄⋊C₄×C₇₉	—	2	2	no	—
219	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
220	C₂²⋊C₄×C₇₉	—	2	2	no	—
221	C₂²⋊C₄×C₇₉	—	2	1	no	—
222	C₂²⋊C₄×C₇₉	—	2	2	no	—
223	C₄²×C₇₉	—	2	1	no	—
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	—	2	1	no	—
226	C₂³×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	—	4	2	no	—
228	C₂³×C₇₉	C₄×D₄	1	2	yes	—
229	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
230	C₂²×D₇₉	—	2	1	no	—
231	Q₈×C₇₉	—	2	1	no	—
232	Q₈×C₇₉	—	2	1	no	—
233	D₄×C₇₉	—	2	1	no	—
234	D₄×C₇₉	—	2	1	no	—
235	D₄×C₇₉	—	4	1	no	—
236	D₄×C₇₉	—	4	1	no	—
237	D₄×C₇₉	—	8	2	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	2	2	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
255	C₂²⋊D₇₉	—	4	1	no	—
256	C₂²⋊D₇₉	—	4	1	no	—
257	C₂²⋊D₇₉	—	8	2	no	—
258	C₂×Dic₇₉	—	2	4	no	—
259	C₂×Dic₇₉	—	2	2	no	—
260	C₂×Dic₇₉	—	2	2	no	—
261	C₂×Dic₇₉	—	2	1	no	—
262	C₂×Dic₇₉	—	2	2	no	—
263	C₂×Dic₇₉	—	4	8	no	—
264	C₂×Dic₇₉	—	4	2	no	—
265	D₃₁₆	—	2	1	no	—
266	D₃₁₆	—	2	1	no	—
267	C₄×D₇₉	—	4	1	no	—
268	C₄×D₇₉	—	4	1	no	—
269	Dic₁₅₈	—	2	1	no	—
270	Dic₁₅₈	—	2	1	no	—
271	C₈×C₇₉	—	2	2	no	—
272	C₈×C₇₉	—	4	1	no	—
273	C₈×C₇₉	—	4	1	no	—
274	C₈×C₇₉	#121	1	2	yes	—
275	C₈×C₇₉	#121	1	2	yes	—
276	C₇₉⋊C₈	—	2	2	no	—
277	C₇₉⋊C₈	—	4	1	no	—
278	C₇₉⋊C₈	—	4	1	no	—
279	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
280	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
281	C₂²×C₇₉	—	2	2	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	—	2	2	no	—
284	C₂²×C₇₉	—	2	2	no	—
285	C₂²×C₇₉	—	4	2	no	—
286	C₂²×C₇₉	—	4	2	no	—
287	C₂²×C₇₉	—	4	2	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₇₉	#525	1	1	yes	characteristic
291	C₂²×C₇₉	#529	1	1	yes	characteristic
292	C₂×D₇₉	—	4	2	no	—
293	C₂×D₇₉	—	4	1	no	—
294	C₄×C₇₉	—	2	2	no	—
295	C₄×C₇₉	—	4	2	no	—
296	C₄×C₇₉	—	4	1	no	—
297	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
298	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
299	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
300	C₄×C₇₉	#532	1	1	yes	characteristic
301	Dic₇₉	—	2	4	no	—
302	Dic₇₉	—	4	2	no	—
303	Dic₇₉	—	4	2	no	—
304	Dic₇₉	—	4	1	no	—
305	#21551	—	79	1	no	maximal, Sylow
306	C₂×C₇₉	—	2	1	no	—
307	C₂×C₇₉	—	2	1	no	—
308	C₂×C₇₉	—	4	2	no	—
309	C₂×C₇₉	—	8	1	no	—
310	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
311	C₂×C₇₉	#2956	1	2	yes	—
312	D₇₉	—	8	1	no	—
313	#3054	—	79	1	no	—
314	C₂×#444	—	79	1	no	—
315	#2930	—	79	1	no	—
316	#2930	D₇₉	1	1	yes	characteristic, complemented
317	C₂×C₄×M₁₆	—	79	1	no	—
318	#1974	—	79	1	no	—
319	#1945	—	79	1	no	—
320	#1938	—	79	1	no	—
321	#1938	—	79	1	no	—
322	#1896	—	79	1	no	—
323	#1896	—	79	1	no	—
324	#1811	—	79	1	no	—
325	#1773	—	79	1	no	—
326	#1764	—	79	1	no	—
327	#1764	—	79	1	no	—
328	C₇₉	#21551	1	1	yes	characteristic, complemented, Sylow
329	C₂×#135	—	79	1	no	—
330	C₂×#131	—	79	1	no	—
331	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
332	C₂²×M₁₆	—	79	1	no	—
333	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
334	#525	—	79	1	no	—
335	#525	C₂×D₇₉	1	1	yes	characteristic
336	C₂²×C₄²	—	79	1	no	—
337	#470	—	79	2	no	—
338	#469	—	79	2	no	—
339	#468	—	79	2	no	—
340	#468	—	79	2	no	—
341	#444	—	158	4	no	—
342	#436	—	2	2	no	—
343	#436	—	158	2	no	—
344	#435	—	2	2	no	—
345	#435	—	158	2	no	—
346	C₂×#108	—	79	1	no	—
347	C₂×#108	—	79	1	no	—
348	#427	—	79	1	no	—
349	#424	—	79	1	no	—
350	#424	C₂×D₇₉	1	1	yes	characteristic
351	C₂×#104	—	79	1	no	—
352	C₂×#104	—	79	1	no	—
353	C₂×#104	—	79	1	no	—
354	C₂×#104	—	79	1	no	—
355	#416	—	79	1	no	—
356	#416	—	79	1	no	—
357	#408	—	79	1	no	—
358	#408	C₂×D₇₉	1	1	yes	characteristic
359	#407	—	79	1	no	—
360	#407	C₂×D₇₉	1	1	yes	characteristic
361	#405	—	79	1	no	—
362	#405	C₂×D₇₉	1	1	yes	characteristic
363	C₄×M₁₆	—	158	4	no	—
364	C₂×#97	—	79	1	no	—
365	C₂×#97	—	79	1	no	—
366	C₂×C₄×C₈	—	79	1	no	—
367	C₂×C₄×C₈	—	79	1	no	—
368	#341	—	79	1	no	—
369	#341	—	79	1	no	—
370	#339	—	79	1	no	—
371	#339	—	79	1	no	—
372	#339	—	79	1	no	—
373	#339	—	79	1	no	—
374	C₂×#41	—	79	1	no	—
375	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
376	C₂³×C₄	—	158	1	no	—
377	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
378	#135	—	158	2	no	—
379	#135	—	158	2	no	—
380	C₂×Q₁₆	—	79	1	no	—
381	C₂×SD₁₆	—	79	1	no	—
382	C₂×SD₁₆	—	79	1	no	—
383	C₂×D₈	—	79	1	no	—
384	#131	—	2	2	no	—
385	#131	—	2	2	no	—
386	#131	—	158	2	no	—
387	#131	—	158	2	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	79	2	no	—
392	C₂×M₁₆	—	79	2	no	—
393	C₂×M₁₆	—	79	1	no	—
394	C₂×M₁₆	—	79	1	no	—
395	C₂×M₁₆	—	158	2	no	—
396	C₂×M₁₆	—	158	2	no	—
397	C₂×M₁₆	—	158	1	no	—
398	C₂×M₁₆	C₂²⋊D₇₉	1	2	yes	—
399	C₂×M₁₆	C₂²⋊D₇₉	1	2	yes	—
400	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
401	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	79	1	no	—
404	C₂²×C₈	—	79	1	no	—
405	C₂²×C₈	—	158	1	no	—
406	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
407	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
408	#123	—	2	1	no	—
409	#123	—	158	1	no	—
410	C₂²⋊Q₈	—	79	2	no	—
411	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
412	#121	—	79	2	no	—
413	#121	C₄×D₇₉	1	2	yes	—
414	#120	—	2	1	no	—
415	#120	—	158	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	158	2	no	—
418	#117	—	79	1	no	—
419	#117	C₂²×D₇₉	1	1	yes	characteristic
420	C₂×C₄²	—	79	1	no	—
421	C₂×C₄²	—	79	1	no	—
422	C₂×C₄²	—	158	2	no	—
423	C₂×C₄²	—	158	2	no	—
424	C₂×C₄²	—	158	1	no	—
425	#108	—	158	2	no	—
426	#108	—	158	2	no	—
427	#107	—	79	2	no	—
428	#106	—	79	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	158	2	no	—
431	#104	—	158	2	no	—
432	#104	—	158	2	no	—
433	#104	—	158	2	no	—
434	#104	—	158	2	no	—
435	#103	—	79	2	no	—
436	#103	—	79	2	no	—
437	#102	—	79	2	no	—
438	#102	—	79	2	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	C₂²⋊C₈	—	158	2	no	—
442	C₂²⋊C₈	—	158	2	no	—
443	#97	—	2	1	no	—
444	#97	—	79	4	no	—
445	#97	—	158	2	no	—
446	#97	—	158	1	no	—
447	C₄×C₈	—	2	1	no	—
448	C₄×C₈	—	158	2	no	—
449	C₄×C₈	—	158	2	no	—
450	C₄×C₈	—	158	1	no	—
451	C₂⁴	#11929624	1	1	yes	characteristic
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	158	1	no	—
457	#41	—	158	1	no	—
458	#41	—	158	1	no	—
459	#41	—	158	1	no	—
460	C₂×Q₈	—	79	1	no	—
461	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	79	1	no	—
465	C₂×D₄	—	158	1	no	—
466	C₂×D₄	—	158	2	no	—
467	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	316	4	no	—
474	C₂²×C₄	—	158	4	no	—
475	C₂²×C₄	—	158	1	no	—
476	C₂²×C₄	—	158	1	no	—
477	C₂²×C₄	—	158	1	no	—
478	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
479	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
480	C₂²×C₄	#11929624	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
482	Q₁₆	—	158	2	no	—
483	SD₁₆	—	158	2	no	—
484	SD₁₆	—	158	2	no	—
485	D₈	—	158	2	no	—
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	4	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	2	1	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	4	2	no	—
493	M₁₆	—	316	2	no	—
494	M₁₆	—	158	1	no	—
495	M₁₆	—	158	1	no	—
496	M₁₆	—	158	1	no	—
497	M₁₆	—	158	1	no	—
498	M₁₆	—	158	4	no	—
499	M₁₆	—	158	4	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	4	2	no	—
505	C₂×C₈	—	316	2	no	—
506	C₂×C₈	—	79	2	no	—
507	C₂×C₈	—	79	1	no	—
508	C₂×C₈	—	79	1	no	—
509	C₂×C₈	—	79	2	no	—
510	C₂×C₈	—	79	2	no	—
511	C₂×C₈	—	158	1	no	—
512	C₂×C₈	—	158	1	no	—
513	C₂×C₈	—	158	1	no	—
514	C₂×C₈	—	158	1	no	—
515	C₂×C₈	D₄×D₇₉	1	2	yes	—
516	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
517	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
518	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
519	C₂×C₈	#11929623	1	2	yes	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	79	2	no	—
522	C₄⋊C₄	—	158	2	no	—
523	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	158	1	no	—
528	C₂²⋊C₄	—	158	2	no	—
529	C₂²⋊C₄	—	158	2	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	79	2	no	—
532	C₄²	—	79	2	no	—
533	C₄²	—	158	4	no	—
534	C₄²	—	158	1	no	—
535	C₄²	—	158	1	no	—
536	C₄²	—	158	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	158	1	no	—
542	C₂³	C₄×C₂²⋊D₇₉	1	2	yes	—
543	C₂³	C₂×#11929624	1	1	yes	characteristic
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	158	1	no	—
547	Q₈	—	158	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	316	1	no	—
554	D₄	—	316	1	no	—
555	D₄	—	632	2	no	—
556	D₄	—	158	1	no	—
557	D₄	—	158	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	316	2	no	—
569	C₂×C₄	—	316	8	no	—
570	C₂×C₄	—	316	1	no	—
571	C₂×C₄	—	316	1	no	—
572	C₂×C₄	—	158	2	no	—
573	C₂×C₄	—	158	1	no	—
574	C₂×C₄	—	158	2	no	—
575	C₂×C₄	—	158	4	no	—
576	C₂×C₄	—	158	2	no	—
577	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
578	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
580	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
581	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
582	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
583	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	316	1	no	—
588	C₈	—	316	1	no	—
589	C₈	—	79	2	no	—
590	C₈	—	79	2	no	—
591	C₈	—	158	2	no	—
592	C₈	#14579133	1	2	yes	—
593	C₈	#14579133	1	2	yes	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	316	2	no	—
603	C₂²	—	316	1	no	—
604	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
605	C₂²	#19099072	1	1	yes	characteristic
606	C₂²	#19099093	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	316	2	no	—
611	C₄	—	316	2	no	—
612	C₄	—	316	1	no	—
613	C₄	—	158	4	no	—
614	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
615	C₄	C₄×#11929623	1	1	yes	characteristic
616	C₄	C₂×#14579133	1	1	yes	characteristic
617	C₄	#19099109	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	4	2	no	—
621	C₂	—	8	1	no	—
622	C₂	—	632	1	no	—
623	C₂	C₄×#14579133	1	1	yes	characteristic
624	C₂	#23772307	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2930	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773006	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2930	D₇₉
hypocenter	C₇₉	#21551
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ #2930

Complements

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

N	H ≅ G/N	type
2. C₂×#19098683	C₂	semidirect
3. #23772103	C₂	semidirect
4. C₂×M₁₆×Dic₇₉	C₂	semidirect
5. #23764287	C₂	semidirect
6. #23764145	C₂	semidirect
7. #23764114	C₂	semidirect
8. #23764110	C₂	semidirect
9. #23763844	C₂	semidirect
10. #23763841	C₂	semidirect
11. #23763440	C₂	semidirect
12. #23763285	C₂	semidirect
13. #23763239	C₂	semidirect
14. #23763235	C₂	semidirect
15. C₇₉×#2930	C₂	semidirect
21. #19098819	C₄	semidirect
22. #19098814	C₄	semidirect
23. #19098811	C₄	semidirect
24. #19098807	C₄	semidirect
65. C₂×#11929614	C₂×C₄	semidirect
66. C₂×#11929612	C₂×C₄	semidirect
67. C₂×#11929611	C₂×C₄	semidirect
68. C₂×#11929609	C₂×C₄	semidirect
94. #14579094	C₂×C₄	semidirect
95. #14579092	C₂×C₄	semidirect
101. #14579085	C₂×C₄	semidirect
102. #14579084	C₂×C₄	semidirect
103. #14579082	C₂×C₄	semidirect
104. #14579081	C₂×C₄	semidirect
109. #14579071	D₄	semidirect
316. #2930	D₇₉	semidirect
328. C₇₉	#21551	semidirect

Maximal subgroups

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

subgroup	index
#23773006	2
C₂×#19098683	2
#23772103	2
C₂×M₁₆×Dic₇₉	2
#23764287	2
#23764145	2
#23764114	2
#23764110	2
#23763844	2
#23763841	2
#23763440	2
#23763285	2
#23763239	2
#23763235	2
C₇₉×#2930	2
#21551	79