Subgroups — #34181694

Order 20224.

514 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765805	C₂	1	1	yes	maximal, characteristic
2	#23763377	C₂	1	1	yes	maximal, characteristic
3	#23763377	C₂	1	1	yes	maximal, characteristic
4	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761283	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14579119	—	2	1	no	—
9	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
14	#19098433	C₂²	1	1	yes	characteristic
15	#19098428	—	2	1	no	—
16	#19098420	—	2	1	no	—
17	#19098420	C₄	1	2	yes	—
18	C₄⋊C₄×Dic₇₉	—	2	1	no	—
19	C₄⋊C₄×Dic₇₉	C₄	1	2	yes	—
20	#19098317	—	2	1	no	—
21	#19098317	—	2	1	no	—
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
24	#384×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
28	C₂²×C₇₉⋊C₈	—	2	1	no	—
29	C₂²×C₇₉⋊C₈	—	2	1	no	—
30	#14579119	—	4	2	no	—
31	#14579119	—	4	2	no	—
32	C₂×C₄⋊Dic₇₉	—	2	1	no	—
33	C₂×C₄⋊Dic₇₉	—	2	1	no	—
34	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
35	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
36	C₂×C₄×Dic₇₉	—	2	2	no	—
37	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
40	C₄²×D₇₉	—	2	1	no	—
41	C₄²×D₇₉	—	2	1	no	—
42	C₄²×D₇₉	—	2	1	no	—
43	C₄²×D₇₉	—	2	1	no	—
44	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	(C₂×D₇₉)⋊C₈	—	4	2	no	—
49	(C₂×D₇₉)⋊C₈	—	4	2	no	—
50	C₇₉⋊#95	—	2	2	no	—
51	C₇₉⋊#95	—	2	2	no	—
52	C₂²×C₈×C₇₉	—	2	1	no	—
53	C₂²×C₈×C₇₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₇₉	—	2	1	no	—
59	C₄⋊C₈×C₇₉	—	2	1	no	—
60	C₄⋊C₈×C₇₉	—	2	1	no	—
61	C₄⋊C₈×C₇₉	—	2	1	no	—
62	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×Dic₇₉	—	2	2	no	—
64	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×D₇₉	—	2	1	no	—
68	C₂×C₄×D₇₉	—	2	1	no	—
69	C₂×C₄×D₇₉	—	2	1	no	—
70	C₂×C₄×D₇₉	—	2	1	no	—
71	C₂×C₄×D₇₉	—	2	1	no	—
72	C₂×C₄×D₇₉	—	2	1	no	—
73	C₂×C₄×D₇₉	—	2	1	no	—
74	C₂×C₄×D₇₉	—	2	1	no	—
75	C₂×C₄×D₇₉	—	2	1	no	—
76	C₂×C₄×D₇₉	—	2	1	no	—
77	C₂×C₄×D₇₉	—	2	1	no	—
78	C₂×C₄×D₇₉	—	2	1	no	—
79	C₂×C₄×D₇₉	—	4	1	no	—
80	C₂×C₄×D₇₉	—	4	1	no	—
81	C₂×C₄×D₇₉	D₈	1	2	yes	—
82	C₂×C₄×D₇₉	SD₁₆	1	2	yes	—
83	C₂×C₇₉⋊C₈	—	4	1	no	—
84	C₂×C₇₉⋊C₈	—	4	1	no	—
85	C₂×C₇₉⋊C₈	—	4	1	no	—
86	C₂×C₇₉⋊C₈	—	4	1	no	—
87	C₂×C₇₉⋊C₈	—	4	1	no	—
88	C₂×C₇₉⋊C₈	—	4	1	no	—
89	C₄⋊Dic₇₉	—	4	2	no	—
90	C₄⋊Dic₇₉	—	4	1	no	—
91	C₄⋊Dic₇₉	—	4	1	no	—
92	C₄⋊Dic₇₉	—	4	1	no	—
93	C₄⋊Dic₇₉	—	4	1	no	—
94	(C₂×D₇₉)⋊C₄	—	4	4	no	—
95	C₄×Dic₇₉	—	2	1	no	—
96	C₄×Dic₇₉	—	2	1	no	—
97	C₄×Dic₇₉	—	2	1	no	—
98	C₄×Dic₇₉	—	2	1	no	—
99	C₄×Dic₇₉	—	2	1	no	—
100	C₄×Dic₇₉	—	2	1	no	—
101	C₄×Dic₇₉	—	4	4	no	—
102	C₂²×C₄×C₇₉	—	2	2	no	—
103	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₇₉	—	4	1	no	—
107	C₂×C₈×C₇₉	—	4	1	no	—
108	C₂×C₈×C₇₉	—	4	1	no	—
109	C₂×C₈×C₇₉	—	4	1	no	—
110	C₂×C₈×C₇₉	—	4	1	no	—
111	C₂×C₈×C₇₉	—	4	1	no	—
112	C₄⋊C₄×C₇₉	—	4	2	no	—
113	C₄⋊C₄×C₇₉	—	4	1	no	—
114	C₄⋊C₄×C₇₉	—	4	1	no	—
115	C₄⋊C₄×C₇₉	—	4	1	no	—
116	C₄⋊C₄×C₇₉	—	4	1	no	—
117	C₄²×C₇₉	#41	1	1	yes	characteristic
118	C₄²×C₇₉	#41	1	1	yes	characteristic
119	C₄²×C₇₉	#41	1	1	yes	characteristic
120	C₄²×C₇₉	#41	1	1	yes	characteristic
121	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×D₇₉	—	2	1	no	—
123	C₂²×D₇₉	—	2	1	no	—
124	C₂²×D₇₉	—	2	1	no	—
125	C₂²×D₇₉	—	2	1	no	—
126	C₂²×D₇₉	—	2	1	no	—
127	C₂²×D₇₉	—	2	1	no	—
128	C₂²×D₇₉	#102	1	2	yes	—
129	C₂×C₄×C₇₉	—	2	1	no	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	—	4	2	no	—
132	C₂×C₄×C₇₉	—	4	2	no	—
133	C₂×C₄×C₇₉	—	4	2	no	—
134	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
135	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
136	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
137	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
138	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
141	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
144	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
146	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
147	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
148	C₂×Dic₇₉	—	2	1	no	—
149	C₂×Dic₇₉	—	2	1	no	—
150	C₂×Dic₇₉	—	2	1	no	—
151	C₂×Dic₇₉	—	2	1	no	—
152	C₂×Dic₇₉	—	2	1	no	—
153	C₂×Dic₇₉	—	2	1	no	—
154	C₂×Dic₇₉	—	2	1	no	—
155	C₂×Dic₇₉	—	2	1	no	—
156	C₂×Dic₇₉	—	4	2	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₂×Dic₇₉	—	4	2	no	—
159	C₂×Dic₇₉	#102	1	2	yes	—
160	C₄×D₇₉	—	2	2	no	—
161	C₄×D₇₉	—	2	2	no	—
162	C₄×D₇₉	—	2	2	no	—
163	C₄×D₇₉	—	2	2	no	—
164	C₄×D₇₉	—	4	2	no	—
165	C₄×D₇₉	—	4	2	no	—
166	C₄×D₇₉	—	4	1	no	—
167	C₄×D₇₉	—	4	1	no	—
168	C₄×D₇₉	—	4	1	no	—
169	C₄×D₇₉	—	4	1	no	—
170	C₈×C₇₉	—	8	1	no	—
171	C₈×C₇₉	—	8	1	no	—
172	C₇₉⋊C₈	—	8	1	no	—
173	C₇₉⋊C₈	—	8	1	no	—
174	C₂²×C₇₉	#381	1	1	yes	characteristic
175	C₂²×C₇₉	#413	1	1	yes	characteristic
176	C₂²×C₇₉	#413	1	1	yes	characteristic
177	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
178	C₂²×C₇₉	#416	1	1	yes	characteristic
179	C₂²×C₇₉	#417	1	1	yes	characteristic
180	C₂²×C₇₉	#419	1	1	yes	characteristic
181	C₂×D₇₉	—	2	2	no	—
182	C₂×D₇₉	—	2	2	no	—
183	C₂×D₇₉	—	2	2	no	—
184	C₂×D₇₉	—	4	1	no	—
185	C₂×D₇₉	—	4	1	no	—
186	C₂×D₇₉	—	4	1	no	—
187	C₂×D₇₉	—	4	1	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	8	2	no	—
191	C₄×C₇₉	#480	1	1	yes	characteristic
192	C₄×C₇₉	#480	1	1	yes	characteristic
193	C₄×C₇₉	#482	1	1	yes	characteristic
194	C₄×C₇₉	#482	1	1	yes	characteristic
195	C₄×C₇₉	#483	1	1	yes	characteristic
196	C₄×C₇₉	#483	1	1	yes	characteristic
197	C₄×C₇₉	#485	1	1	yes	characteristic
198	C₄×C₇₉	#485	1	1	yes	characteristic
199	Dic₇₉	—	2	2	no	—
200	Dic₇₉	—	4	1	no	—
201	Dic₇₉	—	4	1	no	—
202	Dic₇₉	—	8	2	no	—
203	#8726	—	79	1	no	maximal, Sylow
204	C₂×C₇₉	#1540	1	1	yes	characteristic
205	C₂×C₇₉	#1547	1	1	yes	characteristic
206	C₂×C₇₉	#1554	1	1	yes	characteristic
207	C₂×C₇₉	#1559	1	1	yes	characteristic
208	C₂×C₇₉	#1822	1	1	yes	characteristic
209	C₂×C₇₉	#1823	1	1	yes	characteristic
210	C₂×C₇₉	#1825	1	1	yes	characteristic
211	D₇₉	—	4	2	no	—
212	#2285	—	79	1	no	—
213	#1797	—	79	1	no	—
214	#1797	—	79	1	no	—
215	#1296	—	79	1	no	—
216	#1296	—	79	1	no	—
217	#1296	—	79	1	no	—
218	#1296	D₇₉	1	1	yes	characteristic, complemented
219	C₇₉	#8726	1	1	yes	characteristic, complemented, Sylow
220	C₂×#117	—	158	1	no	—
221	C₂²×C₄²	—	79	1	no	—
222	C₂×C₄⋊C₈	—	79	1	no	—
223	C₂×C₄⋊C₈	—	79	1	no	—
224	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	158	1	no	—
227	C₂×C₂²⋊C₈	—	158	1	no	—
228	#384	—	79	1	no	—
229	#384	C₂×D₇₉	1	1	yes	characteristic
230	#382	—	158	1	no	—
231	#380	—	79	2	no	—
232	#380	—	158	1	no	—
233	C₄×C₄⋊C₄	—	79	2	no	—
234	C₄×C₄⋊C₄	—	158	1	no	—
235	#336	—	158	1	no	—
236	#336	—	158	1	no	—
237	C₂³×C₄	—	79	1	no	—
238	C₂³×C₄	—	79	1	no	—
239	C₂³×C₄	—	79	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	158	1	no	—
243	C₂²×C₈	—	158	1	no	—
244	#117	—	316	2	no	—
245	#117	—	316	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	79	2	no	—
249	C₂×C₄⋊C₄	—	158	1	no	—
250	C₂×C₄⋊C₄	—	158	1	no	—
251	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
252	C₂×C₂²⋊C₄	—	158	2	no	—
253	C₂×C₄²	—	79	1	no	—
254	C₂×C₄²	—	79	1	no	—
255	C₂×C₄²	—	79	1	no	—
256	C₂×C₄²	—	158	2	no	—
257	C₂×C₄²	—	158	1	no	—
258	C₂×C₄²	—	158	1	no	—
259	C₂×C₄²	—	158	1	no	—
260	C₂×C₄²	—	158	1	no	—
261	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	158	1	no	—
267	C₄⋊C₈	—	158	1	no	—
268	C₄⋊C₈	—	158	1	no	—
269	C₄⋊C₈	—	158	1	no	—
270	C₂²⋊C₈	—	316	2	no	—
271	C₂²⋊C₈	—	316	2	no	—
272	#95	—	158	2	no	—
273	#95	—	158	2	no	—
274	C₂⁴	—	79	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	316	1	no	—
277	C₂²×C₄	—	316	1	no	—
278	C₂²×C₄	—	79	1	no	—
279	C₂²×C₄	—	79	2	no	—
280	C₂²×C₄	—	79	2	no	—
281	C₂²×C₄	—	79	1	no	—
282	C₂²×C₄	—	79	1	no	—
283	C₂²×C₄	—	158	2	no	—
284	C₂²×C₄	—	158	1	no	—
285	C₂²×C₄	—	158	1	no	—
286	C₂²×C₄	—	158	1	no	—
287	C₂²×C₄	—	158	1	no	—
288	C₂²×C₄	—	158	1	no	—
289	C₂²×C₄	—	158	1	no	—
290	C₂²×C₄	—	158	1	no	—
291	C₂²×C₄	—	158	1	no	—
292	C₂²×C₄	—	158	1	no	—
293	C₂²×C₄	—	158	1	no	—
294	C₂²×C₄	—	158	1	no	—
295	C₂²×C₄	—	158	1	no	—
296	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	316	1	no	—
306	C₂×C₈	—	316	1	no	—
307	C₂×C₈	—	316	1	no	—
308	C₂×C₈	—	316	1	no	—
309	C₂×C₈	—	316	1	no	—
310	C₂×C₈	—	316	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	316	2	no	—
317	C₄⋊C₄	—	316	1	no	—
318	C₄⋊C₄	—	316	1	no	—
319	C₄⋊C₄	—	316	1	no	—
320	C₄⋊C₄	—	316	1	no	—
321	C₂²⋊C₄	—	316	4	no	—
322	C₄²	—	316	4	no	—
323	C₄²	—	158	1	no	—
324	C₄²	—	158	1	no	—
325	C₄²	—	158	1	no	—
326	C₄²	—	158	1	no	—
327	C₄²	—	158	1	no	—
328	C₄²	—	158	1	no	—
329	C₄²	#11929623	1	1	yes	characteristic
330	C₄²	#11929624	1	1	yes	characteristic
331	C₄²	#11929624	1	1	yes	characteristic
332	C₄²	#11929625	1	1	yes	characteristic
333	C₂³	—	79	2	no	—
334	C₂³	—	158	1	no	—
335	C₂³	—	158	1	no	—
336	C₂³	—	158	1	no	—
337	C₂³	—	158	1	no	—
338	C₂³	—	158	1	no	—
339	C₂³	—	158	1	no	—
340	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	316	2	no	—
347	C₂×C₄	—	316	2	no	—
348	C₂×C₄	—	316	1	no	—
349	C₂×C₄	—	316	1	no	—
350	C₂×C₄	—	316	1	no	—
351	C₂×C₄	—	316	1	no	—
352	C₂×C₄	—	316	2	no	—
353	C₂×C₄	—	316	2	no	—
354	C₂×C₄	—	316	2	no	—
355	C₂×C₄	—	79	2	no	—
356	C₂×C₄	—	158	1	no	—
357	C₂×C₄	—	158	1	no	—
358	C₂×C₄	—	158	1	no	—
359	C₂×C₄	—	158	1	no	—
360	C₂×C₄	—	158	1	no	—
361	C₂×C₄	—	158	1	no	—
362	C₂×C₄	—	158	1	no	—
363	C₂×C₄	—	158	1	no	—
364	C₂×C₄	—	158	2	no	—
365	C₂×C₄	—	158	2	no	—
366	C₂×C₄	—	158	2	no	—
367	C₂×C₄	—	158	2	no	—
368	C₂×C₄	#14579118	1	1	yes	characteristic
369	C₂×C₄	#14579119	1	1	yes	characteristic
370	C₂×C₄	#14579143	1	1	yes	characteristic
371	C₂×C₄	#14579143	1	1	yes	characteristic
372	C₂×C₄	#14579146	1	1	yes	characteristic
373	C₂×C₄	#14579146	1	1	yes	characteristic
374	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
375	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
376	C₂×C₄	#14579180	1	1	yes	characteristic
377	C₂×C₄	#14579182	1	1	yes	characteristic
378	C₂×C₄	#14579188	1	1	yes	characteristic
379	C₂×C₄	#14579190	1	1	yes	characteristic
380	C₂×C₄	#14579193	1	1	yes	characteristic
381	C₂×C₄	#14579193	1	1	yes	characteristic
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₈	—	632	1	no	—
385	C₈	—	632	1	no	—
386	C₂²	—	316	1	no	—
387	C₂²	—	316	1	no	—
388	C₂²	—	316	1	no	—
389	C₂²	—	316	1	no	—
390	C₂²	—	158	2	no	—
391	C₂²	—	158	2	no	—
392	C₂²	—	158	2	no	—
393	C₂²	#19098425	1	1	yes	characteristic
394	C₂²	#19098544	1	1	yes	characteristic
395	C₂²	#19098546	1	1	yes	characteristic
396	C₂²	#102×D₇₉	1	1	yes	characteristic
397	C₂²	#19098556	1	1	yes	characteristic
398	C₂²	#19098563	1	1	yes	characteristic
399	C₂²	#19098570	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	316	1	no	—
404	C₄	—	316	1	no	—
405	C₄	—	632	2	no	—
406	C₄	—	158	2	no	—
407	C₄	#19098875	1	1	yes	characteristic
408	C₄	#19098878	1	1	yes	characteristic
409	C₄	#19098885	1	1	yes	characteristic
410	C₄	#19098889	1	1	yes	characteristic
411	C₄	#19098892	1	1	yes	characteristic
412	C₄	#19098895	1	1	yes	characteristic
413	C₄	#19098902	1	1	yes	characteristic
414	C₄	#19098906	1	1	yes	characteristic
415	C₂	—	316	2	no	—
416	C₂	#23762046	1	1	yes	characteristic
417	C₂	#23762076	1	1	yes	characteristic
418	C₂	#23762107	1	1	yes	characteristic
419	C₂	#23762127	1	1	yes	characteristic
420	C₂	#23763482	1	1	yes	characteristic
421	C₂	#23763485	1	1	yes	characteristic
422	C₂	#23763493	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1296	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1296	D₇₉
hypocenter	C₇₉	#8726
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #23761284	C₂	semidirect
5. #23761284	C₂	semidirect
6. #23761283	C₂	semidirect
7. C₇₉×#1296	C₂	semidirect
218. #1296	D₇₉	semidirect
219. C₇₉	#8726	semidirect

Maximal subgroups

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

subgroup	index
#23765805	2
#23763377	2
#23761284	2
#23761283	2
C₇₉×#1296	2
#8726	79