Subgroups — #34182428

Order 20224.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic
2	#23763559	C₂	1	1	yes	maximal, characteristic, complemented
3	#23763397	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098290	C₂	1	1	yes	maximal, characteristic
5	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₁₆	—	2	1	no	—
9	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×D₇₉	—	2	1	no	—
11	C₂×#14579094	—	2	2	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#14579081	—	2	1	no	—
14	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	#19098461	—	2	1	no	—
16	#19098437	—	2	2	no	—
17	#19098433	C₂²	1	1	yes	characteristic
18	#19098420	—	2	1	no	—
19	#19098325	—	2	1	no	—
20	#19098290	C₄	1	4	yes	complemented
21	C₂×#107×C₇₉	—	2	1	no	—
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	#384×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
25	#340×C₇₉	—	2	1	no	—
26	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₇₉	—	2	1	no	—
28	C₂²×C₄×D₇₉	—	2	2	no	—
29	C₂²×C₇₉⋊C₈	—	2	1	no	—
30	C₂²×C₇₉⋊C₈	—	2	1	no	—
31	C₄×D₃₁₆	—	2	1	no	—
32	C₄×D₃₁₆	—	2	1	no	—
33	C₄×D₃₁₆	—	4	2	no	—
34	C₄×D₃₁₆	—	4	2	no	—
35	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
36	C₄×D₃₁₆	Q₈	1	2	yes	—
37	C₂×C₄⋊Dic₇₉	—	2	1	no	—
38	C₂×C₄⋊Dic₇₉	—	2	1	no	—
39	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
41	C₂×Dic₇₉⋊C₄	—	2	2	no	—
42	C₄⋊C₄×D₇₉	—	4	2	no	—
43	C₄⋊C₄×D₇₉	—	4	2	no	—
44	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
45	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
46	#14579094	—	4	4	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
49	#14579081	—	4	2	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	complemented
52	C₇₉⋊#95	—	2	2	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	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₉	—	2	1	no	—
60	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
61	#107×C₇₉	—	4	2	no	—
62	C₄⋊C₈×C₇₉	—	2	1	no	—
63	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
64	#95×C₇₉	—	2	1	no	—
65	C₂³×D₇₉	—	2	1	no	—
66	C₂×D₃₁₆	—	2	1	no	—
67	C₂×D₃₁₆	—	2	1	no	—
68	C₂×D₃₁₆	—	2	1	no	—
69	C₂×D₃₁₆	C₄⋊C₄	1	2	yes	—
70	C₂×D₃₁₆	D₈	1	2	yes	—
71	C₂×D₃₁₆	Q₁₆	1	2	yes	—
72	C₂²×Dic₇₉	—	2	1	no	—
73	C₂²×Dic₇₉	—	2	2	no	—
74	C₂×C₄×D₇₉	—	2	2	no	—
75	C₂×C₄×D₇₉	—	2	2	no	—
76	C₂×C₄×D₇₉	—	4	4	no	—
77	C₂×C₄×D₇₉	—	4	4	no	—
78	C₂×C₄×D₇₉	—	4	1	no	—
79	C₂×C₄×D₇₉	—	4	1	no	—
80	C₂×C₄×D₇₉	—	4	1	no	—
81	C₂×C₄×D₇₉	—	4	1	no	—
82	C₂×C₄×D₇₉	—	8	2	no	—
83	C₂×C₇₉⋊C₈	—	2	2	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	—	2	2	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	—	2	1	no	—
90	C₄⋊Dic₇₉	—	4	2	no	—
91	C₄⋊Dic₇₉	—	4	1	no	—
92	C₄⋊Dic₇₉	—	4	1	no	—
93	C₄⋊Dic₇₉	—	4	1	no	—
94	C₄⋊Dic₇₉	—	4	1	no	—
95	C₄⋊Dic₇₉	C₄⋊C₄	1	2	yes	—
96	Dic₇₉⋊C₄	—	4	4	no	—
97	(C₂×D₇₉)⋊C₄	—	2	2	no	—
98	(C₂×D₇₉)⋊C₄	—	2	2	no	—
99	(C₂×D₇₉)⋊C₄	—	4	4	no	—
100	C₂²×C₄×C₇₉	—	2	1	no	—
101	C₂²×C₄×C₇₉	—	2	1	no	—
102	C₂²×C₄×C₇₉	—	4	1	no	—
103	C₂²×C₄×C₇₉	C₂×D₄	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	—	2	2	no	—
107	C₂×C₈×C₇₉	—	4	1	no	—
108	C₂×C₈×C₇₉	—	4	1	no	—
109	C₄⋊C₄×C₇₉	—	2	1	no	—
110	C₄⋊C₄×C₇₉	—	2	1	no	—
111	C₄⋊C₄×C₇₉	—	2	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	C₄⋊C₄×C₇₉	D₈	1	2	yes	—
118	C₄²×C₇₉	—	4	1	no	—
119	C₄²×C₇₉	—	4	1	no	—
120	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₇₉	#41	1	1	yes	characteristic
123	C₄²×C₇₉	#41	1	1	yes	characteristic
124	C₂³×C₇₉	#120	1	1	yes	characteristic
125	C₂²×D₇₉	—	2	2	no	—
126	C₂²×D₇₉	—	2	2	no	—
127	C₂²×D₇₉	—	2	2	no	—
128	C₂²×D₇₉	—	4	1	no	—
129	C₂²×D₇₉	—	4	1	no	—
130	C₂²×D₇₉	—	4	1	no	—
131	C₂²×D₇₉	—	4	1	no	—
132	C₂×C₄×C₇₉	—	2	1	no	—
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	2	no	—
135	C₂×C₄×C₇₉	—	4	1	no	—
136	C₂×C₄×C₇₉	—	4	1	no	—
137	C₂×C₄×C₇₉	—	4	1	no	—
138	C₂×C₄×C₇₉	—	4	1	no	—
139	C₂×C₄×C₇₉	—	4	1	no	—
140	C₂×C₄×C₇₉	—	8	1	no	—
141	C₂×C₄×C₇₉	—	8	1	no	—
142	C₂×C₄×C₇₉	—	8	1	no	—
143	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
157	C₂×Dic₇₉	—	2	2	no	—
158	C₂×Dic₇₉	—	4	1	no	—
159	C₂×Dic₇₉	—	4	1	no	—
160	C₂×Dic₇₉	—	4	2	no	—
161	C₂×Dic₇₉	—	4	2	no	—
162	C₂×Dic₇₉	—	4	2	no	—
163	D₃₁₆	—	2	2	no	—
164	D₃₁₆	—	2	2	no	—
165	D₃₁₆	—	2	2	no	—
166	D₃₁₆	#107	1	4	yes	complemented
167	C₄×D₇₉	—	4	2	no	—
168	C₄×D₇₉	—	4	2	no	—
169	C₄×D₇₉	—	4	2	no	—
170	C₄×D₇₉	—	4	2	no	—
171	C₄×D₇₉	—	8	8	no	—
172	C₈×C₇₉	—	4	2	no	—
173	C₇₉⋊C₈	—	2	4	no	—
174	C₇₉⋊C₈	—	8	1	no	—
175	C₂²×C₇₉	#385	1	1	yes	characteristic
176	C₂²×C₇₉	#447	1	1	yes	characteristic
177	C₂²×C₇₉	#447	1	1	yes	characteristic
178	C₂²×C₇₉	#451	1	1	yes	characteristic
179	C₂²×C₇₉	#452	1	1	yes	characteristic
180	C₂²×C₇₉	#453	1	1	yes	characteristic
181	C₂²×C₇₉	#456	1	1	yes	characteristic
182	C₂×D₇₉	—	2	4	no	—
183	C₂×D₇₉	—	4	2	no	—
184	C₂×D₇₉	—	4	2	no	—
185	C₂×D₇₉	—	4	2	no	—
186	C₂×D₇₉	—	4	2	no	—
187	C₂×D₇₉	—	4	2	no	—
188	C₂×D₇₉	—	4	2	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	4	2	no	—
192	C₄×C₇₉	—	8	1	no	—
193	C₄×C₇₉	—	16	1	no	—
194	C₄×C₇₉	C₂×#107	1	1	yes	characteristic
195	C₄×C₇₉	#428	1	1	yes	characteristic
196	C₄×C₇₉	C₄×D₈	1	1	yes	characteristic
197	C₄×C₇₉	#440	1	1	yes	characteristic
198	C₄×C₇₉	#474	1	1	yes	characteristic
199	C₄×C₇₉	#478	1	1	yes	characteristic
200	C₄×C₇₉	#480	1	1	yes	characteristic
201	C₄×C₇₉	#484	1	1	yes	characteristic
202	Dic₇₉	—	4	2	no	—
203	Dic₇₉	—	8	2	no	—
204	#8882	—	79	1	no	maximal, Sylow
205	C₂×C₇₉	#1619	1	1	yes	characteristic
206	C₂×C₇₉	#1632	1	1	yes	characteristic
207	C₂×C₇₉	#1647	1	1	yes	characteristic
208	C₂×C₇₉	#1649	1	1	yes	characteristic
209	C₂×C₇₉	#1852	1	1	yes	characteristic
210	C₂×C₇₉	#1859	1	1	yes	characteristic
211	C₂×C₇₉	#1862	1	1	yes	characteristic
212	D₇₉	—	4	4	no	—
213	D₄×C₄⋊C₄	—	79	1	no	—
214	#1947	D₇₉	1	1	yes	characteristic, complemented
215	#1845	—	79	1	no	—
216	#1802	—	79	1	no	—
217	C₂×D₄⋊C₈	—	79	1	no	—
218	#1296	—	79	1	no	—
219	#1279	—	79	1	no	—
220	C₇₉	#8882	1	1	yes	characteristic, complemented, Sylow
221	C₂×C₄×D₄	—	79	1	no	—
222	C₂×C₄×D₄	—	158	1	no	—
223	C₂²×C₄⋊C₄	—	158	1	no	—
224	C₂×#107	—	2	1	no	—
225	C₂×#107	—	158	2	no	—
226	C₂×C₄⋊C₈	—	79	1	no	—
227	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
228	C₂×#102	—	158	1	no	—
229	C₂×C₄×C₈	—	79	1	no	—
230	#389	—	158	1	no	—
231	#385	—	158	2	no	—
232	#384	—	79	1	no	—
233	#384	C₂×D₇₉	1	1	yes	characteristic
234	#380	—	158	1	no	—
235	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
236	#340	—	2	1	no	—
237	#340	—	158	1	no	—
238	D₄⋊C₈	—	79	4	no	—
239	C₂²×D₄	—	79	1	no	—
240	C₂³×C₄	—	158	2	no	—
241	C₂³×C₄	—	158	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	158	1	no	—
244	C₂²×C₈	—	158	1	no	—
245	C₄×D₄	—	316	2	no	—
246	C₄×D₄	—	316	2	no	—
247	C₄×D₄	—	79	2	no	—
248	C₄×D₄	—	79	2	no	—
249	C₄×D₄	—	158	1	no	—
250	C₄×D₄	—	158	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	316	2	no	—
255	C₂×C₄⋊C₄	—	316	2	no	—
256	C₂×C₄⋊C₄	—	79	2	no	—
257	C₂×C₄⋊C₄	—	79	1	no	—
258	C₂×C₄⋊C₄	—	158	2	no	—
259	C₂×C₄⋊C₄	—	158	1	no	—
260	C₂×C₄⋊C₄	—	158	1	no	—
261	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	158	2	no	—
264	C₂×C₂²⋊C₄	—	158	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
267	#107	—	4	2	no	—
268	#107	—	316	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	158	1	no	—
271	C₄⋊C₈	—	158	1	no	—
272	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
273	#102	—	316	2	no	—
274	C₄×C₈	—	79	2	no	—
275	C₄×C₈	—	158	1	no	—
276	#95	—	2	1	no	—
277	#95	—	158	2	no	—
278	C₂⁴	—	158	1	no	—
279	C₂×D₄	—	79	2	no	—
280	C₂×D₄	—	79	2	no	—
281	C₂×D₄	—	79	2	no	—
282	C₂×D₄	—	158	1	no	—
283	C₂×D₄	—	158	1	no	—
284	C₂×D₄	—	158	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	316	4	no	—
289	C₂²×C₄	—	316	4	no	—
290	C₂²×C₄	—	316	1	no	—
291	C₂²×C₄	—	316	1	no	—
292	C₂²×C₄	—	316	1	no	—
293	C₂²×C₄	—	316	1	no	—
294	C₂²×C₄	—	632	2	no	—
295	C₂²×C₄	—	158	2	no	—
296	C₂²×C₄	—	158	1	no	—
297	C₂²×C₄	—	158	2	no	—
298	C₂²×C₄	—	158	2	no	—
299	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂×C₈	—	2	2	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	—	158	2	no	—
309	C₂×C₈	—	158	2	no	—
310	C₂×C₈	—	158	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	316	2	no	—
320	C₄⋊C₄	—	316	4	no	—
321	C₄⋊C₄	—	316	1	no	—
322	C₄⋊C₄	—	316	1	no	—
323	C₄⋊C₄	—	316	1	no	—
324	C₄⋊C₄	—	316	1	no	—
325	C₄⋊C₄	—	79	2	no	—
326	C₄⋊C₄	—	158	1	no	—
327	C₄⋊C₄	#11929609	1	2	yes	—
328	C₂²⋊C₄	—	316	4	no	—
329	C₂²⋊C₄	—	158	2	no	—
330	C₂²⋊C₄	—	158	2	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
334	C₄²	Q₈×D₇₉	1	1	yes	characteristic
335	C₄²	#11929624	1	1	yes	characteristic
336	C₄²	#11929625	1	1	yes	characteristic
337	C₂³	—	316	1	no	—
338	C₂³	—	316	1	no	—
339	C₂³	—	316	1	no	—
340	C₂³	—	316	1	no	—
341	C₂³	—	158	2	no	—
342	C₂³	—	158	2	no	—
343	C₂³	—	158	2	no	—
344	C₂³	#14579129	1	1	yes	characteristic
345	D₄	—	79	4	no	—
346	D₄	—	158	2	no	—
347	D₄	—	158	2	no	—
348	D₄	—	158	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	316	1	no	—
361	C₂×C₄	—	316	1	no	—
362	C₂×C₄	—	316	2	no	—
363	C₂×C₄	—	316	2	no	—
364	C₂×C₄	—	316	2	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	8	no	—
370	C₂×C₄	—	158	2	no	—
371	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
372	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
373	C₂×C₄	#14579123	1	1	yes	characteristic
374	C₂×C₄	#14579137	1	1	yes	characteristic
375	C₂×C₄	#14579139	1	1	yes	characteristic
376	C₂×C₄	#14579146	1	1	yes	characteristic
377	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
379	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
380	C₂×C₄	#14579181	1	1	yes	characteristic
381	C₂×C₄	#14579185	1	1	yes	characteristic
382	C₂×C₄	#14579186	1	1	yes	characteristic
383	C₂×C₄	#14579192	1	1	yes	characteristic
384	C₂×C₄	#14579193	1	1	yes	characteristic
385	C₈	—	4	2	no	—
386	C₈	—	632	1	no	—
387	C₈	—	158	4	no	—
388	C₂²	—	316	2	no	—
389	C₂²	—	316	2	no	—
390	C₂²	—	316	2	no	—
391	C₂²	—	316	2	no	—
392	C₂²	—	316	2	no	—
393	C₂²	—	316	2	no	—
394	C₂²	—	158	4	no	—
395	C₂²	#19098434	1	1	yes	characteristic
396	C₂²	#19098695	1	1	yes	characteristic
397	C₂²	#19098696	1	1	yes	characteristic
398	C₂²	#19098717	1	1	yes	characteristic
399	C₂²	#19098723	1	1	yes	characteristic
400	C₂²	#19098729	1	1	yes	characteristic
401	C₂²	#19098744	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	16	1	no	—
407	C₄	—	316	2	no	—
408	C₄	—	632	2	no	—
409	C₄	#107×D₇₉	1	1	yes	characteristic
410	C₄	#19098604	1	1	yes	characteristic
411	C₄	C₄×#11929609	1	1	yes	characteristic
412	C₄	#19098661	1	1	yes	characteristic
413	C₄	#19098840	1	1	yes	characteristic
414	C₄	#19098860	1	1	yes	characteristic
415	C₄	#19098878	1	1	yes	characteristic
416	C₄	#19098900	1	1	yes	characteristic
417	C₂	—	316	4	no	—
418	C₂	#23762453	1	1	yes	characteristic
419	C₂	#23762533	1	1	yes	characteristic
420	C₂	#23762634	1	1	yes	characteristic
421	C₂	#23762647	1	1	yes	characteristic
422	C₂	#23763586	1	1	yes	characteristic
423	C₂	#23763623	1	1	yes	characteristic
424	C₂	#23763646	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1947	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂²×D₃₁₆	D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1947	D₇₉
hypocenter	C₇₉	#8882
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
2. #23763559	C₂	semidirect
5. #23761284	C₂	semidirect
6. #23761241	C₂	semidirect
7. C₇₉×#1947	C₂	semidirect
20. #19098290	C₄	semidirect
51. C₄×C₇₉⋊C₈	C₂×C₄	semidirect
63. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
166. D₃₁₆	#107	semidirect
214. #1947	D₇₉	semidirect
220. C₇₉	#8882	semidirect
272. C₄⋊C₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×D₃₁₆	2
#23763559	2
#23763397	2
C₂×#19098290	2
#23761284	2
#23761241	2
C₇₉×#1947	2
#8882	79