Subgroups — #34184419

Order 20224.

610 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098765	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098628	C₂	1	1	yes	maximal, characteristic
3	#23764362	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763401	C₂	1	1	yes	maximal, characteristic
5	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#332×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929611	—	2	1	no	—
9	C₂²×C₈×D₇₉	—	2	1	no	—
10	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
11	#19098765	—	2	2	no	—
12	#19098765	C₄	1	4	yes	complemented
13	#19098628	—	2	2	no	—
14	#19098628	—	2	2	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14579085	—	2	1	no	—
17	C₂×#14579083	—	2	1	no	—
18	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
19	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#19098433	C₂²	1	1	yes	characteristic
21	#19098326	—	2	1	no	—
22	#19098325	—	2	1	no	—
23	#19098325	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	#332×C₇₉	—	2	2	no	—
28	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₇₉	—	2	1	no	—
30	C₂×#11929611	—	2	4	no	—
31	C₂×#11929611	—	4	2	no	—
32	C₂×#11929611	—	4	2	no	—
33	C₂²×C₇₉⋊C₈	—	2	1	no	—
34	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
35	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
36	C₂×C₈×D₇₉	—	2	4	no	—
37	C₂×C₈×D₇₉	—	4	2	no	—
38	C₂×C₈×D₇₉	—	4	2	no	—
39	C₄×D₃₁₆	—	2	1	no	—
40	C₄×D₃₁₆	—	2	1	no	—
41	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
42	C₄×D₃₁₆	D₄	1	2	yes	—
43	C₂×C₄⋊Dic₇₉	—	2	1	no	—
44	C₂×C₄⋊Dic₇₉	—	2	1	no	—
45	C₂×C₄⋊Dic₇₉	—	2	1	no	—
46	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
47	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
48	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
50	#14579085	—	2	4	no	—
51	#14579083	—	4	2	no	—
52	(C₂×D₇₉)⋊C₈	—	2	4	no	—
53	C₄×C₇₉⋊C₈	—	2	1	no	—
54	C₄×C₇₉⋊C₈	—	2	1	no	—
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂²×C₈×C₇₉	—	2	1	no	—
57	C₂²×C₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₇₉	—	2	1	no	—
66	C₄⋊C₈×C₇₉	—	2	1	no	—
67	C₄⋊C₈×C₇₉	—	2	1	no	—
68	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
69	C₂³×D₇₉	—	2	1	no	—
70	C₂×D₃₁₆	—	2	1	no	—
71	C₂×D₃₁₆	—	2	1	no	—
72	C₂×D₃₁₆	—	2	1	no	—
73	C₂×D₃₁₆	C₂²⋊C₄	1	2	yes	—
74	C₂×D₃₁₆	D₈	1	2	yes	—
75	C₂×D₃₁₆	SD₁₆	1	2	yes	—
76	C₂²×Dic₇₉	—	2	1	no	—
77	C₂²×Dic₇₉	—	4	1	no	—
78	C₂×C₄×D₇₉	—	2	2	no	—
79	C₂×C₄×D₇₉	—	2	2	no	—
80	C₂×C₄×D₇₉	—	4	1	no	—
81	C₂×C₄×D₇₉	—	4	1	no	—
82	C₂×C₄×D₇₉	—	4	1	no	—
83	C₂×C₄×D₇₉	—	4	1	no	—
84	#11929611	—	4	8	no	—
85	C₂×C₇₉⋊C₈	—	2	2	no	—
86	C₂×C₇₉⋊C₈	—	2	1	no	—
87	C₂×C₇₉⋊C₈	—	2	1	no	—
88	C₂×C₇₉⋊C₈	—	2	1	no	—
89	C₂×C₇₉⋊C₈	—	2	1	no	—
90	C₂×C₇₉⋊C₈	—	2	1	no	—
91	C₂×C₇₉⋊C₈	—	4	1	no	—
92	C₂×C₇₉⋊C₈	—	4	1	no	—
93	C₂×C₇₉⋊C₈	SD₁₆	1	2	yes	complemented
94	C₈×D₇₉	—	4	8	no	—
95	C₄⋊Dic₇₉	—	2	1	no	—
96	C₄⋊Dic₇₉	—	4	1	no	—
97	C₄⋊Dic₇₉	—	4	1	no	—
98	C₄⋊Dic₇₉	—	4	1	no	—
99	C₄⋊Dic₇₉	—	4	1	no	—
100	C₄⋊Dic₇₉	—	8	1	no	—
101	C₄⋊Dic₇₉	C₂²⋊C₄	1	2	yes	—
102	(C₂×D₇₉)⋊C₄	—	2	2	no	—
103	(C₂×D₇₉)⋊C₄	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	2	2	no	—
105	C₂×Q₈×C₇₉	—	4	1	no	—
106	C₂×Q₈×C₇₉	—	4	1	no	—
107	C₂×Q₈×C₇₉	—	4	1	no	—
108	C₂×Q₈×C₇₉	—	4	1	no	—
109	C₂×Q₈×C₇₉	—	4	1	no	—
110	C₂²×C₄×C₇₉	—	4	1	no	—
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
114	C₂×C₈×C₇₉	—	2	2	no	—
115	C₂×C₈×C₇₉	—	4	1	no	—
116	C₂×C₈×C₇₉	—	4	1	no	—
117	C₂×C₈×C₇₉	—	4	1	no	—
118	C₂×C₈×C₇₉	—	4	1	no	—
119	C₂×C₈×C₇₉	—	4	1	no	—
120	C₄⋊C₄×C₇₉	—	2	2	no	—
121	C₄⋊C₄×C₇₉	—	2	2	no	—
122	C₄⋊C₄×C₇₉	—	4	1	no	—
123	C₄⋊C₄×C₇₉	—	4	1	no	—
124	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₉	#41	1	1	yes	characteristic
128	C₂³×C₇₉	#121	1	1	yes	characteristic
129	C₂²×D₇₉	—	2	2	no	—
130	C₂²×D₇₉	—	2	2	no	—
131	C₂²×D₇₉	—	2	2	no	—
132	C₂²×D₇₉	—	4	1	no	—
133	C₂²×D₇₉	—	4	1	no	—
134	C₂²×D₇₉	—	4	1	no	—
135	C₂²×D₇₉	—	4	1	no	—
136	Q₈×C₇₉	—	4	2	no	—
137	Q₈×C₇₉	—	4	2	no	—
138	Q₈×C₇₉	—	8	1	no	—
139	Q₈×C₇₉	—	8	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	4	2	no	—
143	C₂×C₄×C₇₉	—	8	1	no	—
144	C₂×C₄×C₇₉	—	8	1	no	—
145	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	4	1	no	—
161	C₂×Dic₇₉	—	4	1	no	—
162	C₂×Dic₇₉	—	8	1	no	—
163	C₂×Dic₇₉	—	8	1	no	—
164	C₂×Dic₇₉	—	8	1	no	—
165	D₃₁₆	—	2	2	no	—
166	D₃₁₆	—	2	2	no	—
167	D₃₁₆	—	2	2	no	—
168	D₃₁₆	#102	1	4	yes	—
169	C₄×D₇₉	—	4	2	no	—
170	C₄×D₇₉	—	4	2	no	—
171	C₄×D₇₉	—	4	2	no	—
172	C₄×D₇₉	—	4	2	no	—
173	C₈×C₇₉	—	4	2	no	—
174	C₈×C₇₉	—	8	1	no	—
175	C₇₉⋊C₈	—	2	2	no	—
176	C₇₉⋊C₈	—	4	2	no	—
177	C₇₉⋊C₈	—	4	1	no	—
178	C₂²×C₇₉	#386	1	1	yes	characteristic
179	C₂²×C₇₉	#461	1	1	yes	characteristic
180	C₂²×C₇₉	#463	1	1	yes	characteristic
181	C₂²×C₇₉	#465	1	1	yes	characteristic
182	C₂²×C₇₉	#466	1	1	yes	characteristic
183	C₂²×C₇₉	#471	1	1	yes	characteristic
184	C₂²×C₇₉	#473	1	1	yes	characteristic
185	C₂×D₇₉	—	2	4	no	—
186	C₂×D₇₉	—	4	2	no	—
187	C₂×D₇₉	—	4	2	no	—
188	C₂×D₇₉	—	4	2	no	—
189	C₂×D₇₉	—	4	2	no	—
190	C₂×D₇₉	—	4	2	no	—
191	C₂×D₇₉	—	4	2	no	—
192	C₄×C₇₉	—	2	1	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	8	2	no	—
195	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
196	C₄×C₇₉	#416	1	1	yes	characteristic
197	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
198	C₄×C₇₉	#440	1	1	yes	characteristic
199	C₄×C₇₉	#450	1	1	yes	characteristic
200	C₄×C₇₉	#452	1	1	yes	characteristic
201	C₄×C₇₉	#465	1	1	yes	characteristic
202	C₄×C₇₉	#466	1	1	yes	characteristic
203	Dic₇₉	—	4	2	no	—
204	Dic₇₉	—	16	1	no	—
205	#9217	—	79	1	no	maximal, Sylow
206	C₂×C₇₉	#1671	1	1	yes	characteristic
207	C₂×C₇₉	#1673	1	1	yes	characteristic
208	C₂×C₇₉	#1679	1	1	yes	characteristic
209	C₂×C₇₉	#1681	1	1	yes	characteristic
210	C₂×C₇₉	#1877	1	1	yes	characteristic
211	C₂×C₇₉	#1893	1	1	yes	characteristic
212	C₂×C₇₉	#1908	1	1	yes	characteristic
213	D₇₉	—	4	4	no	—
214	C₂×#461	—	79	1	no	—
215	C₂×C₈×D₄	—	79	1	no	—
216	#1990	—	79	1	no	—
217	#1802	—	79	1	no	—
218	C₂×#332	D₇₉	1	1	yes	characteristic, complemented
219	#1296	—	79	1	no	—
220	#1277	—	79	1	no	—
221	C₇₉	#9217	1	1	yes	characteristic, complemented, Sylow
222	C₂²×SD₁₆	—	158	1	no	—
223	C₂³×C₈	—	158	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
225	C₂×C₄×D₄	—	79	1	no	—
226	#461	—	79	4	no	—
227	#461	—	158	2	no	—
228	C₈×D₄	—	158	2	no	—
229	C₈×D₄	—	158	2	no	—
230	C₂×C₄⋊C₈	—	79	1	no	—
231	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
233	C₂×#103	—	158	1	no	—
234	C₂×#102	—	158	1	no	—
235	C₂×C₂²⋊C₈	—	158	1	no	—
236	C₂×C₄×C₈	—	79	1	no	—
237	#384	—	79	1	no	—
238	#340	—	158	1	no	—
239	#340	—	158	1	no	—
240	#340	—	158	1	no	—
241	#332	—	2	2	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	79	1	no	—
244	C₂³×C₄	—	158	1	no	—
245	C₂×SD₁₆	—	316	2	no	—
246	C₂×SD₁₆	—	316	2	no	—
247	C₂×SD₁₆	—	158	4	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	316	2	no	—
251	C₂²×C₈	—	316	2	no	—
252	C₂²×C₈	—	79	1	no	—
253	C₂²×C₈	—	79	1	no	—
254	C₂²×C₈	—	158	4	no	—
255	C₂²×C₈	—	158	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	C₄×D₇₉	1	2	yes	—
260	C₄×D₄	—	79	2	no	—
261	C₄×D₄	—	79	2	no	—
262	C₄×D₄	—	158	1	no	—
263	C₄×D₄	—	158	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	79	1	no	—
267	C₂×C₄⋊C₄	—	158	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	C₂×C₄⋊C₄	—	158	1	no	—
270	C₂×C₂²⋊C₄	—	158	1	no	—
271	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	79	2	no	—
276	C₄⋊C₈	—	158	1	no	—
277	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
278	#103	—	158	4	no	—
279	#102	—	316	2	no	—
280	C₂²⋊C₈	—	158	4	no	—
281	C₄×C₈	—	158	1	no	—
282	C₄×C₈	—	158	1	no	—
283	C₂⁴	—	158	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	79	2	no	—
291	C₂×D₄	—	79	2	no	—
292	C₂×D₄	—	79	2	no	—
293	C₂×D₄	—	158	1	no	—
294	C₂×D₄	—	158	1	no	—
295	C₂×D₄	—	158	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	316	1	no	—
298	C₂²×C₄	—	316	1	no	—
299	C₂²×C₄	—	316	1	no	—
300	C₂²×C₄	—	316	1	no	—
301	C₂²×C₄	—	316	1	no	—
302	C₂²×C₄	—	158	1	no	—
303	C₂²×C₄	—	158	2	no	—
304	C₂²×C₄	—	158	2	no	—
305	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
307	C₂²×C₄	#11929624	1	1	yes	characteristic
308	SD₁₆	—	316	8	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	316	8	no	—
316	C₂×C₈	—	316	1	no	—
317	C₂×C₈	—	316	1	no	—
318	C₂×C₈	—	79	2	no	—
319	C₂×C₈	—	158	2	no	—
320	C₂×C₈	—	158	1	no	—
321	C₂×C₈	—	158	1	no	—
322	C₂×C₈	—	158	1	no	—
323	C₂×C₈	—	158	1	no	—
324	C₂×C₈	—	158	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	316	1	no	—
330	C₄⋊C₄	—	316	1	no	—
331	C₄⋊C₄	—	316	1	no	—
332	C₄⋊C₄	—	316	1	no	—
333	C₄⋊C₄	—	79	2	no	—
334	C₄⋊C₄	—	632	1	no	—
335	C₄⋊C₄	—	158	1	no	—
336	C₂²⋊C₄	—	158	2	no	—
337	C₂²⋊C₄	—	158	2	no	—
338	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
339	C₄²	D₄×D₇₉	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
341	C₄²	#11929623	1	1	yes	characteristic
342	C₂³	—	316	1	no	—
343	C₂³	—	316	1	no	—
344	C₂³	—	316	1	no	—
345	C₂³	—	316	1	no	—
346	C₂³	—	158	2	no	—
347	C₂³	—	158	2	no	—
348	C₂³	—	158	2	no	—
349	C₂³	#14579134	1	1	yes	characteristic
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	1	no	—
353	Q₈	—	8	1	no	—
354	D₄	—	79	4	no	—
355	D₄	—	158	2	no	—
356	D₄	—	158	2	no	—
357	D₄	—	158	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	—	316	1	no	—
364	C₂×C₄	—	316	1	no	—
365	C₂×C₄	—	316	2	no	—
366	C₂×C₄	—	316	2	no	—
367	C₂×C₄	—	316	2	no	—
368	C₂×C₄	—	316	2	no	—
369	C₂×C₄	—	632	1	no	—
370	C₂×C₄	—	632	1	no	—
371	C₂×C₄	—	632	1	no	—
372	C₂×C₄	—	158	2	no	—
373	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
374	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
376	C₂×C₄	#14579129	1	1	yes	characteristic
377	C₂×C₄	#14579132	1	1	yes	characteristic
378	C₂×C₄	#14579143	1	1	yes	characteristic
379	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
380	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
381	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
382	C₂×C₄	#14579180	1	1	yes	characteristic
383	C₂×C₄	#14579182	1	1	yes	characteristic
384	C₂×C₄	#14579184	1	1	yes	characteristic
385	C₂×C₄	#14579188	1	1	yes	characteristic
386	C₂×C₄	#14579193	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	8	1	no	—
389	C₈	—	316	1	no	—
390	C₈	—	316	2	no	—
391	C₈	—	158	2	no	—
392	C₂²	—	316	2	no	—
393	C₂²	—	316	2	no	—
394	C₂²	—	316	2	no	—
395	C₂²	—	316	2	no	—
396	C₂²	—	316	2	no	—
397	C₂²	—	316	2	no	—
398	C₂²	—	158	4	no	—
399	C₂²	#19098439	1	1	yes	characteristic
400	C₂²	#19098767	1	1	yes	characteristic
401	C₂²	#19098781	1	1	yes	characteristic
402	C₂²	#19098791	1	1	yes	characteristic
403	C₂²	#19098798	1	1	yes	characteristic
404	C₂²	#19098829	1	1	yes	characteristic
405	C₂²	#19098837	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	2	no	—
409	C₄	—	316	2	no	—
410	C₄	—	1264	1	no	—
411	C₄	#102×D₇₉	1	1	yes	characteristic
412	C₄	#19098556	1	1	yes	characteristic
413	C₄	#19098648	1	1	yes	characteristic
414	C₄	#19098666	1	1	yes	characteristic
415	C₄	#19098712	1	1	yes	characteristic
416	C₄	#19098724	1	1	yes	characteristic
417	C₄	#19098789	1	1	yes	characteristic
418	C₄	#19098796	1	1	yes	characteristic
419	C₂	—	316	4	no	—
420	C₂	#23762774	1	1	yes	characteristic
421	C₂	#23762788	1	1	yes	characteristic
422	C₂	#23762826	1	1	yes	characteristic
423	C₂	#23762840	1	1	yes	characteristic
424	C₂	#23763731	1	1	yes	characteristic
425	C₂	#23763825	1	1	yes	characteristic
426	C₂	#23763912	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579134
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#332×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₃₁₆	D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×#332	D₇₉
hypocenter	C₇₉	#9217
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
3. #23764362	C₂	semidirect
5. #23761284	C₂	semidirect
6. #23761234	C₂	semidirect
7. C₂×#332×C₇₉	C₂	semidirect
12. #19098765	C₄	semidirect
93. C₂×C₇₉⋊C₈	SD₁₆	semidirect
218. C₂×#332	D₇₉	semidirect
221. C₇₉	#9217	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098765	2
C₂×#19098628	2
#23764362	2
#23763401	2
#23761284	2
#23761234	2
C₂×#332×C₇₉	2
#9217	79