Subgroups — #34258259

Order 20224.

700 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773454	C₂	1	1	yes	maximal, characteristic
2	C₈×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762276	C₂	1	2	yes	maximal, complemented
4	#23762262	C₂	1	2	yes	maximal, complemented
5	C₈×#11929612	C₂	1	2	yes	maximal, complemented
6	C₈×#11929609	C₂	1	2	yes	maximal, complemented
7	#23762191	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761837	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11929624	C₂²	1	1	yes	characteristic
13	#19098884	C₄	1	2	yes	—
14	#19098855	C₄	1	1	yes	characteristic
15	#19098850	C₄	1	1	yes	characteristic
16	#19098760	C₄	1	1	yes	characteristic
17	#19098755	C₄	1	1	yes	characteristic
18	#19098706	C₄	1	2	yes	—
19	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
21	C₄×#11929612	C₂²	1	2	yes	—
22	C₄×#11929609	C₂²	1	2	yes	—
23	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
24	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₇₉	—	2	1	no	—
26	C₈×C₂²⋊D₇₉	—	2	1	no	—
27	#19098616	C₂²	1	1	yes	characteristic
28	#19098616	C₂²	1	1	yes	characteristic
29	#19098614	—	2	1	no	—
30	C₄×#11929608	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₇₉	—	2	1	no	—
32	#19098315	C₂²	1	2	yes	—
33	#19098313	C₂²	1	2	yes	—
34	#19098293	C₂²	1	2	yes	—
35	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
37	#19098290	C₂²	1	2	yes	—
38	#19098285	C₂²	1	2	yes	—
39	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
40	C₂×#131×C₇₉	—	2	1	no	—
41	#532×C₇₉	C₂²	1	1	yes	characteristic
42	#436×C₇₉	—	2	1	no	—
43	#436×C₇₉	C₂²	1	2	yes	—
44	C₈×D₄×C₇₉	—	2	1	no	—
45	C₈×D₄×C₇₉	C₂²	1	2	yes	—
46	#423×C₇₉	C₂²	1	1	yes	characteristic
47	#408×C₇₉	—	2	1	no	—
48	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#11929624	C₂×C₄	1	1	yes	characteristic
50	C₂×#11929612	C₂×C₄	1	2	yes	—
51	C₂×#11929609	C₂×C₄	1	2	yes	—
52	C₂×#11929608	—	2	1	no	—
53	C₂×C₈×D₇₉	—	2	1	no	—
54	C₂×C₈×D₇₉	—	2	1	no	—
55	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
57	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
58	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
59	C₄×C₂²⋊D₇₉	—	2	1	no	—
60	C₄×C₂²⋊D₇₉	—	2	1	no	—
61	#14579120	C₂×C₄	1	1	yes	characteristic
62	#14579118	—	2	1	no	—
63	C₄²×D₇₉	—	2	1	no	—
64	#14579094	C₂×C₄	1	2	yes	—
65	#14579092	C₂×C₄	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₇₉⋊C₈	—	2	1	no	—
71	Dic₇₉⋊C₈	—	2	1	no	—
72	#14579084	C₂×C₄	1	2	yes	—
73	#14579082	C₂×C₄	1	2	yes	—
74	#14579082	C₂×C₄	1	2	yes	—
75	#14579081	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
77	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
78	(C₂×D₇₉)⋊C₈	—	2	1	no	—
79	(C₂×D₇₉)⋊C₈	—	2	1	no	—
80	#14579072	—	2	1	no	—
81	C₄×C₇₉⋊C₈	—	2	1	no	—
82	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
83	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₇₉	—	2	1	no	—
85	C₈×Dic₇₉	—	2	1	no	—
86	C₂×#41×C₇₉	—	2	1	no	—
87	#131×C₇₉	—	4	4	no	—
88	C₂×M₁₆×C₇₉	—	2	1	no	—
89	C₂×M₁₆×C₇₉	—	2	2	no	—
90	C₂²×C₈×C₇₉	—	2	2	no	—
91	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
94	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
95	#124×C₇₉	—	2	1	no	—
96	#121×C₇₉	—	2	1	no	—
97	#121×C₇₉	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₇₉	—	2	1	no	—
99	C₄×D₄×C₇₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₇₉	—	2	1	no	—
102	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
103	C₂²⋊C₈×C₇₉	—	2	2	no	—
104	C₂²⋊C₈×C₇₉	—	2	2	no	—
105	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
109	#11929624	—	2	2	no	—
110	#11929624	—	2	2	no	—
111	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₇₉	—	2	1	no	—
114	C₂×C₄×D₇₉	—	2	1	no	—
115	C₂×C₄×D₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	#11929612	—	2	4	no	—
118	#11929609	—	2	4	no	—
119	#11929608	—	2	4	no	—
120	C₂×C₇₉⋊C₈	—	2	1	no	—
121	C₂×C₇₉⋊C₈	—	2	1	no	—
122	C₂×C₇₉⋊C₈	—	2	2	no	—
123	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
125	C₈×D₇₉	—	4	2	no	—
126	C₈×D₇₉	—	4	2	no	—
127	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	Dic₇₉⋊C₄	—	2	1	no	—
130	Dic₇₉⋊C₄	—	2	1	no	—
131	C₂²⋊Dic₇₉	—	2	1	no	—
132	(C₂×D₇₉)⋊C₄	—	2	1	no	—
133	(C₂×D₇₉)⋊C₄	—	2	1	no	—
134	C₄×Dic₇₉	—	2	1	no	—
135	C₄×Dic₇₉	—	2	1	no	—
136	C₄×Dic₇₉	—	2	1	no	—
137	#41×C₇₉	—	4	2	no	—
138	#41×C₇₉	—	4	2	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×D₄×C₇₉	—	2	2	no	—
141	C₂×D₄×C₇₉	—	2	1	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
148	M₁₆×C₇₉	—	4	2	no	—
149	M₁₆×C₇₉	—	4	4	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	4	1	no	—
153	C₂×C₈×C₇₉	—	4	4	no	—
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₇₉	—	2	1	no	—
159	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
160	C₂²⋊C₄×C₇₉	—	2	2	no	—
161	C₂²⋊C₄×C₇₉	—	2	2	no	—
162	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇₉	#41	1	1	yes	characteristic
165	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
166	C₂³×C₇₉	—	2	2	no	—
167	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₇₉	—	2	1	no	—
169	Q₈×C₇₉	—	4	2	no	—
170	D₄×C₇₉	—	2	2	no	—
171	D₄×C₇₉	—	2	2	no	—
172	D₄×C₇₉	—	4	2	no	—
173	D₄×C₇₉	—	4	4	no	—
174	D₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	—	2	1	no	—
176	C₂×C₄×C₇₉	—	2	1	no	—
177	C₂×C₄×C₇₉	—	2	1	no	—
178	C₂×C₄×C₇₉	—	2	1	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	4	2	no	—
182	C₂×C₄×C₇₉	—	4	2	no	—
183	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₇₉	—	2	4	no	—
190	C₂×Dic₇₉	—	2	1	no	—
191	C₂×Dic₇₉	—	2	1	no	—
192	C₂×Dic₇₉	—	2	1	no	—
193	D₃₁₆	—	2	1	no	—
194	D₃₁₆	#131	1	2	yes	complemented
195	C₄×D₇₉	—	2	4	no	—
196	C₄×D₇₉	—	4	1	no	—
197	C₄×D₇₉	—	4	1	no	—
198	C₄×D₇₉	—	4	2	no	—
199	Dic₁₅₈	—	2	1	no	—
200	Dic₁₅₈	#131	1	2	yes	complemented
201	C₈×C₇₉	—	2	1	no	—
202	C₈×C₇₉	—	2	1	no	—
203	C₈×C₇₉	—	2	1	no	—
204	C₈×C₇₉	—	4	2	no	—
205	C₈×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
206	C₇₉⋊C₈	—	2	4	no	—
207	C₇₉⋊C₈	—	2	2	no	—
208	C₇₉⋊C₈	—	2	2	no	—
209	C₇₉⋊C₈	—	4	1	no	—
210	C₇₉⋊C₈	—	4	1	no	—
211	C₂²×C₇₉	—	2	1	no	—
212	C₂²×C₇₉	—	2	1	no	—
213	C₂²×C₇₉	—	2	1	no	—
214	C₂²×C₇₉	—	4	2	no	—
215	C₂²×C₇₉	—	4	2	no	—
216	C₂²×C₇₉	—	4	2	no	—
217	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂×D₇₉	—	2	2	no	—
219	C₂×D₇₉	—	4	1	no	—
220	C₂×D₇₉	—	4	1	no	—
221	C₄×C₇₉	—	2	1	no	—
222	C₄×C₇₉	—	2	1	no	—
223	C₄×C₇₉	—	2	1	no	—
224	C₄×C₇₉	—	4	2	no	—
225	C₄×C₇₉	#443	1	2	yes	—
226	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
227	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
228	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₇₉	#575	1	1	yes	characteristic
230	Dic₇₉	—	2	2	no	—
231	Dic₇₉	—	4	1	no	—
232	Dic₇₉	—	4	1	no	—
233	#17912	—	79	1	no	maximal, Sylow
234	C₂×C₇₉	—	4	1	no	—
235	C₂×C₇₉	—	8	2	no	—
236	C₂×C₇₉	#2929	1	1	yes	characteristic
237	C₂×C₇₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
239	D₇₉	—	4	2	no	—
240	#3106	—	79	1	no	—
241	C₈×#41	—	79	1	no	—
242	#2931	D₇₉	1	1	yes	characteristic, complemented
243	#1588	—	79	2	no	—
244	#1586	—	79	2	no	—
245	C₈×SD₁₆	—	79	2	no	—
246	C₈×D₈	—	79	2	no	—
247	#1574	—	79	1	no	—
248	#1489	—	79	1	no	—
249	#1484	—	79	1	no	—
250	C₈×M₁₆	—	79	1	no	—
251	C₇₉	#17912	1	1	yes	characteristic, complemented, Sylow
252	C₂×#131	—	2	1	no	—
253	#532	C₂×D₇₉	1	1	yes	characteristic
254	C₄×#41	—	79	1	no	—
255	#482	—	79	2	no	—
256	#477	—	79	1	no	—
257	#476	—	79	1	no	—
258	#460	—	79	1	no	—
259	#459	—	79	1	no	—
260	#449	—	79	2	no	—
261	C₈×Q₈	—	79	1	no	—
262	C₈×Q₈	—	79	1	no	—
263	C₄×SD₁₆	—	79	2	no	—
264	C₄×D₈	—	79	2	no	—
265	#436	—	2	1	no	—
266	#436	C₂×D₇₉	1	2	yes	—
267	C₈×D₄	—	2	1	no	—
268	C₈×D₄	—	79	1	no	—
269	C₈×D₄	—	79	1	no	—
270	C₈×D₄	—	158	1	no	—
271	C₈×D₄	—	158	1	no	—
272	C₈×D₄	C₂×D₇₉	1	2	yes	—
273	#431	—	79	1	no	—
274	#431	—	79	1	no	—
275	#431	—	158	1	no	—
276	#423	C₂×D₇₉	1	1	yes	characteristic
277	#408	—	2	1	no	—
278	C₄×M₁₆	—	79	1	no	—
279	C₂×C₄×C₈	—	158	1	no	—
280	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
281	#335	—	79	2	no	—
282	#334	—	79	2	no	—
283	Q₈⋊C₈	—	79	2	no	—
284	D₄⋊C₈	—	79	2	no	—
285	D₄⋊C₈	—	79	2	no	—
286	D₄⋊C₈	—	79	2	no	—
287	#322	—	79	2	no	—
288	C₈²	—	79	2	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	79	1	no	—
291	C₂×SD₁₆	—	79	2	no	—
292	C₂×D₈	—	79	2	no	—
293	#131	—	4	4	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	158	1	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	158	1	no	—
299	C₂²×C₈	—	158	1	no	—
300	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
303	#127	C₄×D₇₉	1	1	yes	characteristic
304	#124	—	2	1	no	—
305	#121	—	2	1	no	—
306	#121	C₄×D₇₉	1	2	yes	—
307	C₄×Q₈	—	79	1	no	—
308	C₄×Q₈	—	79	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	79	1	no	—
311	C₄×D₄	—	79	1	no	—
312	C₄×D₄	—	158	1	no	—
313	C₄×D₄	—	158	1	no	—
314	C₄×D₄	C₂²×D₇₉	1	2	yes	—
315	#117	—	79	1	no	—
316	#117	—	158	1	no	—
317	C₂×C₄²	—	158	1	no	—
318	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
319	#107	—	79	2	no	—
320	#106	—	79	2	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	79	1	no	—
323	C₄⋊C₈	—	79	1	no	—
324	C₄⋊C₈	—	79	1	no	—
325	C₄⋊C₈	—	79	1	no	—
326	C₄⋊C₈	—	158	1	no	—
327	C₄⋊C₈	—	158	1	no	—
328	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
329	#103	—	79	2	no	—
330	#102	—	79	2	no	—
331	#102	—	79	2	no	—
332	#102	—	79	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	79	2	no	—
336	C₂²⋊C₈	—	158	1	no	—
337	C₂²⋊C₈	—	158	1	no	—
338	C₂²⋊C₈	—	158	1	no	—
339	#97	—	158	1	no	—
340	C₄×C₈	—	79	2	no	—
341	C₄×C₈	—	79	2	no	—
342	C₄×C₈	—	158	1	no	—
343	C₄×C₈	—	158	1	no	—
344	C₄×C₈	—	158	1	no	—
345	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
346	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	#41	—	158	2	no	—
352	#41	—	158	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	79	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	79	1	no	—
359	C₂×D₄	—	158	1	no	—
360	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	158	1	no	—
363	C₂²×C₄	—	158	1	no	—
364	C₂²×C₄	—	158	1	no	—
365	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
367	C₂²×C₄	#11929624	1	1	yes	characteristic
368	SD₁₆	—	158	4	no	—
369	D₈	—	158	4	no	—
370	M₁₆	—	4	4	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	158	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	316	2	no	—
378	C₂×C₈	—	316	2	no	—
379	C₂×C₈	—	79	2	no	—
380	C₂×C₈	—	79	2	no	—
381	C₂×C₈	—	158	1	no	—
382	C₂×C₈	—	158	1	no	—
383	C₂×C₈	—	158	2	no	—
384	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	79	1	no	—
390	C₄⋊C₄	—	79	1	no	—
391	C₄⋊C₄	—	158	1	no	—
392	C₄⋊C₄	—	158	1	no	—
393	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	158	1	no	—
397	C₂²⋊C₄	—	158	1	no	—
398	C₂²⋊C₄	—	158	1	no	—
399	C₄²	—	158	1	no	—
400	C₄²	—	158	1	no	—
401	C₄²	—	158	1	no	—
402	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
403	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
404	C₄²	#11929624	1	1	yes	characteristic
405	C₄²	C₂³×D₇₉	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	—	158	1	no	—
408	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
409	Q₈	—	4	2	no	—
410	Q₈	—	79	2	no	—
411	Q₈	—	158	1	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	2	no	—
417	D₄	—	79	2	no	—
418	D₄	—	158	4	no	—
419	D₄	—	158	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	316	2	no	—
429	C₂×C₄	—	316	1	no	—
430	C₂×C₄	—	316	1	no	—
431	C₂×C₄	—	158	4	no	—
432	C₂×C₄	—	158	1	no	—
433	C₂×C₄	—	158	1	no	—
434	C₂×C₄	—	158	1	no	—
435	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
437	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	4	2	no	—
445	C₈	—	316	1	no	—
446	C₈	—	316	1	no	—
447	C₈	—	158	4	no	—
448	C₈	—	158	2	no	—
449	C₈	—	158	2	no	—
450	C₈	#14579187	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	316	1	no	—
458	C₂²	—	316	1	no	—
459	C₂²	—	158	2	no	—
460	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	316	1	no	—
466	C₄	—	316	1	no	—
467	C₄	—	158	2	no	—
468	C₄	#19098678	1	2	yes	—
469	C₄	#131×D₇₉	1	1	yes	characteristic
470	C₄	#131×D₇₉	1	1	yes	characteristic
471	C₄	C₂×#14579187	1	1	yes	characteristic
472	C₄	#19099361	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	8	2	no	—
475	C₂	—	316	2	no	—
476	C₂	#23772092	1	1	yes	characteristic
477	C₂	C₄×#14579187	1	1	yes	characteristic
478	C₂	C₂×#19098678	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#2931	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773454	C₂
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#2931	D₇₉
hypocenter	C₇₉	#17912
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. C₈×#11929624	C₂	semidirect
3. #23762276	C₂	semidirect
4. #23762262	C₂	semidirect
5. C₈×#11929612	C₂	semidirect
6. C₈×#11929609	C₂	semidirect
7. #23762191	C₂	semidirect
8. #23761837	C₂	semidirect
9. #23761817	C₂	semidirect
10. C₈×#11929608	C₂	semidirect
11. C₇₉×#2931	C₂	semidirect
194. D₃₁₆	#131	semidirect
200. Dic₁₅₈	#131	semidirect
242. #2931	D₇₉	semidirect
251. C₇₉	#17912	semidirect

Maximal subgroups

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

subgroup	index
#23773454	2
C₈×#11929624	2
#23762276	2
#23762262	2
C₈×#11929612	2
C₈×#11929609	2
#23762191	2
#23761837	2
#23761817	2
C₈×#11929608	2
C₇₉×#2931	2
#17912	79