Subgroups — #34257914

Order 20224.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772511	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14579186	C₂	1	1	yes	maximal, characteristic
4	#23762275	C₂	1	2	yes	maximal, complemented
5	#23762261	C₂	1	2	yes	maximal, complemented
6	#23762240	C₂	1	2	yes	maximal, complemented
7	#23762226	C₂	1	2	yes	maximal, complemented
8	#23762153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19098292	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761689	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579186	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
14	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
15	#19098673	C₄	1	2	yes	—
16	#19098661	C₄	1	2	yes	—
17	C₄×#11929611	C₂²	1	2	yes	—
18	C₄×#11929609	C₂²	1	2	yes	—
19	#19098642	—	2	1	no	—
20	#19098642	—	2	1	no	—
21	#19098640	C₂²	1	2	yes	—
22	#19098640	C₂²	1	2	yes	—
23	D₄×C₇₉⋊C₈	—	2	2	no	—
24	D₄×C₇₉⋊C₈	C₂²	1	2	yes	complemented
25	#19098616	—	2	1	no	—
26	#19098616	C₂²	1	1	yes	characteristic
27	#19098606	C₄	1	1	yes	characteristic
28	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
29	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	#19098567	C₄	1	1	yes	characteristic
31	#19098564	C₄	1	1	yes	characteristic
32	#19098525	—	2	2	no	—
33	C₄×#11929608	C₂²	1	1	yes	characteristic
34	#19098315	C₂²	1	2	yes	complemented
35	#19098313	C₂²	1	2	yes	complemented
36	#19098292	C₂²	1	2	yes	—
37	#19098292	C₂²	1	2	yes	—
38	#19098285	C₂²	1	2	yes	complemented
39	#19098284	C₂²	1	2	yes	complemented
40	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
41	#431×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	Q₈⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	C₂²×D₃₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₉	—	2	1	no	—
49	#14579186	—	2	4	no	—
50	C₂×#11929611	C₂×C₄	1	2	yes	—
51	C₂×#11929609	C₂×C₄	1	2	yes	—
52	C₂×#11929608	C₂×C₄	1	1	yes	characteristic
53	C₂×#11929608	C₂×C₄	1	1	yes	characteristic
54	C₂×#11929607	—	2	2	no	—
55	C₂×#11929607	—	2	2	no	—
56	C₂²×C₇₉⋊C₈	—	2	1	no	—
57	C₂²×C₇₉⋊C₈	—	2	2	no	—
58	C₄×D₃₁₆	—	2	1	no	—
59	C₄×D₃₁₆	—	2	1	no	—
60	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
61	C₄×D₃₁₆	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
64	#14579094	C₂×C₄	1	2	yes	—
65	#14579092	C₂×C₄	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
68	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
69	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
70	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
71	#14579085	C₂×C₄	1	2	yes	—
72	#14579082	C₂×C₄	1	2	yes	—
73	#14579081	C₂×C₄	1	2	yes	—
74	#14579081	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
77	(C₂×D₇₉)⋊C₈	—	2	2	no	—
78	(C₂×D₇₉)⋊C₈	—	2	2	no	—
79	#14579072	C₂×C₄	1	2	yes	—
80	C₄×C₇₉⋊C₈	—	2	2	no	—
81	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
82	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
83	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₉	—	2	1	no	—
85	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
91	#117×C₇₉	—	2	1	no	—
92	#117×C₇₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂²⋊C₈×C₇₉	—	2	1	no	—
98	C₄×C₈×C₇₉	—	2	1	no	—
99	C₄×C₈×C₇₉	—	2	1	no	—
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	C₂³×D₇₉	—	2	1	no	—
103	C₂×D₃₁₆	—	2	1	no	—
104	C₂×D₃₁₆	—	2	2	no	—
105	C₂×D₃₁₆	—	2	2	no	—
106	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₇₉	—	2	1	no	—
108	C₂×C₄×D₇₉	—	2	2	no	—
109	C₂×C₄×D₇₉	—	2	2	no	—
110	C₂×C₄×D₇₉	—	8	1	no	—
111	C₂×C₄×D₇₉	—	8	1	no	—
112	#11929611	—	2	4	no	—
113	#11929609	—	2	4	no	—
114	#11929608	—	2	2	no	—
115	#11929608	—	2	2	no	—
116	#11929607	—	8	2	no	—
117	#11929607	—	8	2	no	—
118	C₂×C₇₉⋊C₈	—	2	2	no	—
119	C₂×C₇₉⋊C₈	—	8	1	no	—
120	C₂×C₇₉⋊C₈	—	8	2	no	—
121	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
122	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
124	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
125	C₄⋊Dic₇₉	—	2	1	no	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
127	(C₂×D₇₉)⋊C₄	—	2	2	no	—
128	(C₂×D₇₉)⋊C₄	—	2	2	no	—
129	#41×C₇₉	—	2	2	no	—
130	#41×C₇₉	M₁₆	1	4	yes	complemented
131	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₇₉	—	2	1	no	—
133	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₇₉	—	2	1	no	—
141	C₂×C₈×C₇₉	—	2	1	no	—
142	C₂×C₈×C₇₉	—	2	1	no	—
143	C₂×C₈×C₇₉	—	2	1	no	—
144	C₂×C₈×C₇₉	—	4	2	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₇₉	—	2	1	no	—
150	C₂²⋊C₄×C₇₉	—	2	1	no	—
151	C₂²⋊C₄×C₇₉	—	2	1	no	—
152	C₄²×C₇₉	—	2	1	no	—
153	C₄²×C₇₉	—	2	1	no	—
154	C₄²×C₇₉	—	2	1	no	—
155	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₉	#41	1	1	yes	characteristic
158	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₇₉	—	2	1	no	—
160	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₇₉	—	2	2	no	—
162	C₂²×D₇₉	—	4	2	no	—
163	C₂²×D₇₉	—	8	1	no	—
164	C₂²×D₇₉	—	8	1	no	—
165	Q₈×C₇₉	—	2	1	no	—
166	Q₈×C₇₉	C₂×M₁₆	1	2	yes	—
167	D₄×C₇₉	—	2	4	no	—
168	D₄×C₇₉	—	2	1	no	—
169	D₄×C₇₉	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	1	no	—
173	C₂×C₄×C₇₉	—	2	4	no	—
174	C₂×C₄×C₇₉	—	2	1	no	—
175	C₂×C₄×C₇₉	—	2	1	no	—
176	C₂×C₄×C₇₉	—	4	1	no	—
177	C₂×C₄×C₇₉	—	4	1	no	—
178	C₂×C₄×C₇₉	—	4	1	no	—
179	C₂×C₄×C₇₉	—	8	1	no	—
180	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₇₉	#131	1	2	yes	—
185	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₇₉	—	2	2	no	—
189	C₂×Dic₇₉	—	8	1	no	—
190	D₃₁₆	—	2	2	no	—
191	D₃₁₆	—	2	2	no	—
192	D₃₁₆	—	4	2	no	—
193	C₄×D₇₉	—	4	2	no	—
194	C₄×D₇₉	—	4	2	no	—
195	C₄×D₇₉	—	8	2	no	—
196	C₈×C₇₉	—	2	2	no	—
197	C₈×C₇₉	—	4	1	no	—
198	C₈×C₇₉	—	4	1	no	—
199	C₈×C₇₉	—	4	1	no	—
200	C₇₉⋊C₈	—	2	2	no	—
201	C₇₉⋊C₈	—	2	2	no	—
202	C₇₉⋊C₈	—	2	2	no	—
203	C₇₉⋊C₈	—	2	2	no	—
204	C₇₉⋊C₈	—	4	2	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	2	2	no	—
208	C₂²×C₇₉	—	4	1	no	—
209	C₂²×C₇₉	—	4	1	no	—
210	C₂²×C₇₉	#435	1	2	yes	—
211	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₇₉	—	4	2	no	—
213	C₂×D₇₉	—	4	2	no	—
214	C₂×D₇₉	—	4	2	no	—
215	C₂×D₇₉	—	8	4	no	—
216	C₄×C₇₉	—	2	2	no	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	—	2	1	no	—
219	C₄×C₇₉	—	2	1	no	—
220	C₄×C₇₉	—	4	1	no	—
221	C₄×C₇₉	—	4	1	no	—
222	C₄×C₇₉	#435	1	2	yes	—
223	C₄×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
224	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
225	C₄×C₇₉	#576	1	1	yes	characteristic
226	C₄×C₇₉	#577	1	1	yes	characteristic
227	Dic₇₉	—	4	2	no	—
228	#17875	—	79	1	no	maximal, Sylow
229	C₂×C₇₉	—	2	2	no	—
230	C₂×C₇₉	—	4	2	no	—
231	C₂×C₇₉	C₂×#435	1	1	yes	characteristic
232	C₂×C₇₉	#2946	1	1	yes	characteristic
233	C₂×C₇₉	#2956	1	1	yes	characteristic
234	D₇₉	—	8	2	no	—
235	#2988	—	79	1	no	—
236	#2975	—	79	1	no	—
237	C₄×AGL(1,ℤ/8)	—	79	1	no	—
238	#1588	—	79	2	no	—
239	#1586	—	79	2	no	—
240	#1583	—	79	2	no	—
241	#1581	—	79	2	no	—
242	#1565	—	79	1	no	—
243	#1476	D₇₉	1	1	yes	characteristic, complemented
244	C₂×D₄⋊C₈	—	79	1	no	—
245	#1451	—	79	1	no	—
246	C₇₉	#17875	1	1	yes	characteristic, complemented, Sylow
247	C₂×AGL(1,ℤ/8)	—	79	1	no	—
248	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
249	C₂×C₄×D₄	—	79	1	no	—
250	C₈×Q₈	—	79	2	no	—
251	#442	—	79	2	no	—
252	#440	—	79	2	no	—
253	C₄×SD₁₆	—	79	2	no	—
254	C₄×D₈	—	79	2	no	—
255	#436	—	79	2	no	—
256	#436	—	79	2	no	—
257	#436	—	158	1	no	—
258	#436	—	158	1	no	—
259	C₈×D₄	—	79	2	no	—
260	C₈×D₄	—	158	2	no	—
261	#431	—	79	1	no	—
262	#431	—	158	1	no	—
263	#431	C₂×D₇₉	1	1	yes	characteristic
264	#428	—	79	1	no	—
265	C₂×C₄⋊C₈	—	79	1	no	—
266	C₂×C₄⋊C₈	—	158	1	no	—
267	#418	—	79	1	no	—
268	#417	—	79	1	no	—
269	#407	—	158	2	no	—
270	C₄×M₁₆	—	79	1	no	—
271	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
272	#335	—	79	2	no	—
273	#334	—	79	2	no	—
274	Q₈⋊C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
275	Q₈⋊C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
276	D₄⋊C₈	—	79	2	no	—
277	D₄⋊C₈	—	79	2	no	—
278	D₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
279	D₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
280	#322	—	79	2	no	—
281	#322	—	79	2	no	—
282	C₂×#41	C₄×D₇₉	1	1	yes	characteristic
283	C₂²×D₄	—	79	1	no	—
284	C₂³×C₄	—	158	1	no	—
285	AGL(1,ℤ/8)	—	158	4	no	—
286	C₂×SD₁₆	—	79	2	no	—
287	C₂×D₈	—	79	2	no	—
288	C₂×M₁₆	—	79	1	no	—
289	C₂×M₁₆	—	79	1	no	—
290	C₂×M₁₆	—	158	2	no	—
291	C₂×M₁₆	—	158	2	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	158	2	no	—
294	C₂²×C₈	—	158	1	no	—
295	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	79	2	no	—
300	C₄×D₄	—	79	2	no	—
301	C₄×D₄	—	158	1	no	—
302	C₄×D₄	—	158	1	no	—
303	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
304	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₄×D₇₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	79	1	no	—
308	C₂×C₂²⋊C₄	—	158	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
311	#107	—	79	2	no	—
312	#106	—	79	2	no	—
313	C₄⋊C₈	—	79	1	no	—
314	C₄⋊C₈	—	79	1	no	—
315	C₄⋊C₈	—	79	2	no	—
316	C₄⋊C₈	—	158	2	no	—
317	C₄⋊C₈	—	158	1	no	—
318	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
320	#103	—	79	2	no	—
321	#102	—	79	2	no	—
322	#102	—	79	2	no	—
323	#102	—	79	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	79	2	no	—
326	C₂²⋊C₈	—	158	2	no	—
327	C₂²⋊C₈	—	158	2	no	—
328	C₂²⋊C₈	—	158	2	no	—
329	#97	—	79	2	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	79	2	no	—
333	C₄×C₈	—	79	2	no	—
334	C₄×C₈	—	158	2	no	—
335	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
337	C₂⁴	—	158	1	no	—
338	#41	—	2	2	no	—
339	#41	#11929607	1	4	yes	complemented
340	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	79	2	no	—
343	C₂×D₄	—	158	1	no	—
344	C₂×D₄	—	158	2	no	—
345	C₂×D₄	—	158	2	no	—
346	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	632	1	no	—
351	C₂²×C₄	—	632	1	no	—
352	C₂²×C₄	—	158	2	no	—
353	C₂²×C₄	—	158	1	no	—
354	C₂²×C₄	—	158	2	no	—
355	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
357	C₂²×C₄	#11929623	1	1	yes	characteristic
358	SD₁₆	—	158	4	no	—
359	D₈	—	158	4	no	—
360	M₁₆	—	632	2	no	—
361	M₁₆	—	632	2	no	—
362	M₁₆	—	158	2	no	—
363	M₁₆	—	158	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	79	2	no	—
370	C₂×C₈	—	79	2	no	—
371	C₂×C₈	—	79	2	no	—
372	C₂×C₈	—	79	2	no	—
373	C₂×C₈	—	632	1	no	—
374	C₂×C₈	—	632	2	no	—
375	C₂×C₈	—	158	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	79	2	no	—
379	C₄⋊C₄	—	158	1	no	—
380	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	158	2	no	—
386	C₂²⋊C₄	—	158	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
391	C₄²	D₄×D₇₉	1	1	yes	characteristic
392	C₄²	#11929623	1	1	yes	characteristic
393	C₄²	C₂³×D₇₉	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	316	2	no	—
396	C₂³	—	632	1	no	—
397	C₂³	—	632	1	no	—
398	C₂³	—	158	2	no	—
399	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×#11929607	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	316	2	no	—
405	D₄	—	158	2	no	—
406	D₄	—	158	2	no	—
407	D₄	C₂×#11929607	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	316	2	no	—
419	C₂×C₄	—	316	2	no	—
420	C₂×C₄	—	632	2	no	—
421	C₂×C₄	—	632	1	no	—
422	C₂×C₄	—	158	2	no	—
423	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
424	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
426	C₂×C₄	C₂×#11929607	1	2	yes	—
427	C₂×C₄	#14579169	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	316	2	no	—
436	C₈	—	158	2	no	—
437	C₈	—	158	2	no	—
438	C₈	—	158	2	no	—
439	C₈	—	158	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	316	2	no	—
446	C₂²	—	316	2	no	—
447	C₂²	—	316	2	no	—
448	C₂²	—	632	4	no	—
449	C₂²	#19098631	1	2	yes	—
450	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	316	2	no	—
458	C₄	#19098631	1	2	yes	—
459	C₄	C₂²×#11929607	1	1	yes	characteristic
460	C₄	C₂×#14579169	1	1	yes	characteristic
461	C₄	#19099365	1	1	yes	characteristic
462	C₄	#19099370	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	632	2	no	—
466	C₂	C₂×#19098631	1	1	yes	characteristic
467	C₂	#23772235	1	1	yes	characteristic
468	C₂	#23772306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1476	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579186	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1476	D₇₉
hypocenter	C₇₉	#17875
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
1. #23772511	C₂	semidirect
2. #23772440	C₂	semidirect
4. #23762275	C₂	semidirect
5. #23762261	C₂	semidirect
6. #23762240	C₂	semidirect
7. #23762226	C₂	semidirect
8. #23762153	C₂	semidirect
9. C₂×#19098292	C₂	semidirect
10. #23761689	C₂	semidirect
11. C₇₉×#1476	C₂	semidirect
14. Q₈×C₇₉⋊C₈	C₂²	semidirect
24. D₄×C₇₉⋊C₈	C₂²	semidirect
34. #19098315	C₂²	semidirect
35. #19098313	C₂²	semidirect
38. #19098285	C₂²	semidirect
39. #19098284	C₂²	semidirect
43. Q₈⋊C₈×C₇₉	C₂²	semidirect
44. Q₈⋊C₈×C₇₉	C₂²	semidirect
45. D₄⋊C₈×C₇₉	C₂²	semidirect
46. D₄⋊C₈×C₇₉	C₂²	semidirect
130. #41×C₇₉	M₁₆	semidirect
243. #1476	D₇₉	semidirect
246. C₇₉	#17875	semidirect
274. Q₈⋊C₈	C₂×D₇₉	semidirect
275. Q₈⋊C₈	C₂×D₇₉	semidirect
278. D₄⋊C₈	C₂×D₇₉	semidirect
279. D₄⋊C₈	C₂×D₇₉	semidirect
339. #41	#11929607	semidirect

Maximal subgroups

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

subgroup	index
#23772511	2
#23772440	2
C₄×#14579186	2
#23762275	2
#23762261	2
#23762240	2
#23762226	2
#23762153	2
C₂×#19098292	2
#23761689	2
C₇₉×#1476	2
#17875	79