Subgroups — #34181624

Order 20224.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579119	C₂	1	1	yes	maximal, characteristic
2	#23763377	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₇₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761240	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14579119	C₄	1	1	yes	characteristic
9	C₂×#14579119	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₇₉	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	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
16	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
18	C₄×(C₂×D₇₉)⋊C₄	—	2	1	no	—
19	#19098410	—	2	1	no	—
20	#19098408	—	2	1	no	—
21	C₄²×Dic₇₉	—	2	1	no	—
22	#19098317	—	2	1	no	—
23	#19098317	—	2	1	no	—
24	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
30	C₂²×C₇₉⋊C₈	—	2	1	no	—
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	#14579119	—	2	2	no	—
33	#14579119	—	2	2	no	—
34	#14579119	—	2	2	no	—
35	#14579119	C₈	1	4	yes	complemented
36	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
38	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
39	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₇₉	—	2	1	no	—
41	C₂×C₄×Dic₇₉	—	2	1	no	—
42	C₂×C₄×Dic₇₉	—	2	1	no	—
43	C₂×C₄×Dic₇₉	—	2	1	no	—
44	C₂×C₄×Dic₇₉	—	2	1	no	—
45	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
48	C₄²×D₇₉	—	2	1	no	—
49	C₄²×D₇₉	—	2	1	no	—
50	C₄²×D₇₉	—	2	1	no	—
51	C₄²×D₇₉	—	2	1	no	—
52	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
54	(C₂×D₇₉)⋊C₈	—	2	4	no	—
55	(C₂×D₇₉)⋊C₈	—	4	2	no	—
56	C₄×C₇₉⋊C₈	—	2	1	no	—
57	C₄×C₇₉⋊C₈	—	2	1	no	—
58	C₇₉⋊#95	—	2	1	no	—
59	C₇₉⋊#95	—	2	1	no	—
60	C₇₉⋊#95	—	2	1	no	—
61	C₂²×C₈×C₇₉	—	2	1	no	—
62	C₂²×C₈×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₉	—	2	1	no	—
66	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₇₉	—	2	1	no	—
68	C₄⋊C₈×C₇₉	—	2	1	no	—
69	C₄×C₈×C₇₉	—	2	1	no	—
70	C₄×C₈×C₇₉	—	2	1	no	—
71	#95×C₇₉	—	2	1	no	—
72	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₇₉	—	2	1	no	—
74	C₂²×Dic₇₉	—	2	1	no	—
75	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₇₉	—	2	2	no	—
79	C₂×C₄×D₇₉	—	2	1	no	—
80	C₂×C₄×D₇₉	—	2	1	no	—
81	C₂×C₄×D₇₉	—	2	1	no	—
82	C₂×C₄×D₇₉	—	2	1	no	—
83	C₂×C₄×D₇₉	—	2	1	no	—
84	C₂×C₄×D₇₉	—	2	1	no	—
85	C₂×C₄×D₇₉	—	2	1	no	—
86	C₂×C₄×D₇₉	—	2	1	no	—
87	C₂×C₄×D₇₉	—	2	1	no	—
88	C₂×C₄×D₇₉	—	2	1	no	—
89	C₂×C₄×D₇₉	—	2	1	no	—
90	C₂×C₄×D₇₉	—	2	1	no	—
91	C₂×C₄×D₇₉	—	4	1	no	—
92	C₂×C₄×D₇₉	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₇₉	M₁₆	1	2	yes	—
94	C₂×C₇₉⋊C₈	—	2	2	no	—
95	C₂×C₇₉⋊C₈	—	4	1	no	—
96	C₂×C₇₉⋊C₈	—	4	1	no	—
97	C₂×C₇₉⋊C₈	—	4	1	no	—
98	C₂×C₇₉⋊C₈	—	4	1	no	—
99	C₂×C₇₉⋊C₈	—	4	1	no	—
100	C₄⋊Dic₇₉	—	2	1	no	—
101	C₄⋊Dic₇₉	—	2	1	no	—
102	C₄⋊Dic₇₉	C₂×C₈	1	2	yes	—
103	C₄⋊Dic₇₉	M₁₆	1	2	yes	—
104	(C₂×D₇₉)⋊C₄	—	2	4	no	—
105	(C₂×D₇₉)⋊C₄	—	2	4	no	—
106	C₄×Dic₇₉	—	2	4	no	—
107	C₄×Dic₇₉	—	2	4	no	—
108	C₄×Dic₇₉	—	2	1	no	—
109	C₄×Dic₇₉	—	2	1	no	—
110	C₄×Dic₇₉	—	2	1	no	—
111	C₄×Dic₇₉	—	2	1	no	—
112	C₄×Dic₇₉	—	2	1	no	—
113	C₄×Dic₇₉	—	2	1	no	—
114	C₄×Dic₇₉	—	4	2	no	—
115	C₄×Dic₇₉	—	4	2	no	—
116	C₄×Dic₇₉	—	4	1	no	—
117	C₄×Dic₇₉	—	4	1	no	—
118	C₂²×C₄×C₇₉	—	2	1	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₇₉	—	2	2	no	—
124	C₂×C₈×C₇₉	—	4	1	no	—
125	C₂×C₈×C₇₉	—	4	1	no	—
126	C₂×C₈×C₇₉	—	4	1	no	—
127	C₂×C₈×C₇₉	—	4	1	no	—
128	C₂×C₈×C₇₉	—	4	1	no	—
129	C₄⋊C₄×C₇₉	—	2	1	no	—
130	C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	—
132	C₄⋊C₄×C₇₉	M₁₆	1	2	yes	—
133	C₄²×C₇₉	—	4	1	no	—
134	C₄²×C₇₉	—	4	1	no	—
135	C₄²×C₇₉	#41	1	1	yes	characteristic
136	C₄²×C₇₉	#41	1	1	yes	characteristic
137	C₄²×C₇₉	#41	1	1	yes	characteristic
138	C₄²×C₇₉	#41	1	1	yes	characteristic
139	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×D₇₉	—	2	1	no	—
141	C₂²×D₇₉	—	2	1	no	—
142	C₂²×D₇₉	—	2	1	no	—
143	C₂²×D₇₉	—	2	1	no	—
144	C₂²×D₇₉	—	2	1	no	—
145	C₂²×D₇₉	—	2	1	no	—
146	C₂²×D₇₉	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	4	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	1	no	—
171	C₂×Dic₇₉	—	2	1	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	2	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	C₂×Dic₇₉	—	2	1	no	—
178	C₂×Dic₇₉	—	4	1	no	—
179	C₂×Dic₇₉	—	4	1	no	—
180	C₂×Dic₇₉	—	4	1	no	—
181	C₂×Dic₇₉	—	4	1	no	—
182	C₂×Dic₇₉	C₂²⋊C₈	1	2	yes	—
183	C₂×Dic₇₉	#104	1	2	yes	—
184	C₄×D₇₉	—	2	2	no	—
185	C₄×D₇₉	—	2	2	no	—
186	C₄×D₇₉	—	2	2	no	—
187	C₄×D₇₉	—	2	2	no	—
188	C₄×D₇₉	—	4	2	no	—
189	C₄×D₇₉	—	4	2	no	—
190	C₄×D₇₉	—	4	1	no	—
191	C₄×D₇₉	—	4	1	no	—
192	C₄×D₇₉	—	4	1	no	—
193	C₄×D₇₉	—	4	1	no	—
194	C₈×C₇₉	—	4	2	no	—
195	C₈×C₇₉	—	8	1	no	—
196	C₇₉⋊C₈	—	4	2	no	—
197	C₇₉⋊C₈	—	8	1	no	—
198	C₂²×C₇₉	#381	1	1	yes	characteristic
199	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
200	C₂²×C₇₉	#407	1	1	yes	characteristic
201	C₂²×C₇₉	#416	1	1	yes	characteristic
202	C₂²×C₇₉	#417	1	1	yes	characteristic
203	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
204	C₂²×C₇₉	#421	1	1	yes	characteristic
205	C₂×D₇₉	—	2	2	no	—
206	C₂×D₇₉	—	2	2	no	—
207	C₂×D₇₉	—	2	2	no	—
208	C₂×D₇₉	—	4	1	no	—
209	C₂×D₇₉	—	4	1	no	—
210	C₂×D₇₉	—	4	1	no	—
211	C₂×D₇₉	—	4	1	no	—
212	C₄×C₇₉	—	2	1	no	—
213	C₄×C₇₉	—	2	1	no	—
214	C₄×C₇₉	—	4	2	no	—
215	C₄×C₇₉	—	4	2	no	—
216	C₄×C₇₉	#431	1	1	yes	characteristic
217	C₄×C₇₉	#431	1	1	yes	characteristic
218	C₄×C₇₉	#432	1	1	yes	characteristic
219	C₄×C₇₉	#432	1	1	yes	characteristic
220	C₄×C₇₉	#482	1	1	yes	characteristic
221	C₄×C₇₉	#482	1	1	yes	characteristic
222	C₄×C₇₉	#485	1	1	yes	characteristic
223	C₄×C₇₉	#485	1	1	yes	characteristic
224	Dic₇₉	—	2	2	no	—
225	Dic₇₉	—	2	2	no	—
226	Dic₇₉	—	4	1	no	—
227	Dic₇₉	—	4	2	no	—
228	Dic₇₉	—	4	2	no	—
229	#8708	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	#1476	1	1	yes	characteristic
231	C₂×C₇₉	#1477	1	1	yes	characteristic
232	C₂×C₇₉	#1488	1	1	yes	characteristic
233	C₂×C₇₉	#1489	1	1	yes	characteristic
234	C₂×C₇₉	#1817	1	1	yes	characteristic
235	C₂×C₇₉	#1825	1	1	yes	characteristic
236	C₂×C₇₉	#1826	1	1	yes	characteristic
237	D₇₉	—	4	2	no	—
238	C₄×#117	—	79	1	no	—
239	#1797	—	79	1	no	—
240	C₄×C₂²⋊C₈	—	79	1	no	—
241	#1279	—	79	1	no	—
242	#1279	—	79	1	no	—
243	#1279	—	79	1	no	—
244	#1279	D₇₉	1	1	yes	characteristic, complemented
245	C₇₉	#8708	1	1	yes	characteristic, complemented, Sylow
246	C₂×#117	—	79	1	no	—
247	C₂×#117	—	79	1	no	—
248	C₂²×C₄²	—	79	1	no	—
249	C₂×C₄⋊C₈	—	79	1	no	—
250	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	—	158	1	no	—
252	C₂×C₂²⋊C₈	—	158	1	no	—
253	C₂×C₄×C₈	—	79	1	no	—
254	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	79	1	no	—
256	C₄×C₄⋊C₄	—	79	1	no	—
257	C₄×C₄⋊C₄	—	79	1	no	—
258	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	—	158	1	no	—
260	C₄×C₂²⋊C₄	—	158	1	no	—
261	#376	—	158	1	no	—
262	C₄³	—	158	1	no	—
263	#336	—	158	1	no	—
264	#336	—	158	1	no	—
265	C₂³×C₄	—	79	1	no	—
266	C₂³×C₄	—	79	1	no	—
267	C₂³×C₄	—	79	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	158	1	no	—
271	C₂²×C₈	—	158	1	no	—
272	#117	—	79	4	no	—
273	#117	—	158	2	no	—
274	#117	—	158	2	no	—
275	#117	—	158	2	no	—
276	C₂×C₄⋊C₄	—	79	1	no	—
277	C₂×C₄⋊C₄	—	79	1	no	—
278	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	158	1	no	—
281	C₂×C₂²⋊C₄	—	158	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	158	1	no	—
287	C₂×C₄²	—	158	1	no	—
288	C₂×C₄²	—	158	1	no	—
289	C₂×C₄²	—	158	1	no	—
290	C₂×C₄²	—	158	1	no	—
291	C₂×C₄²	—	158	1	no	—
292	C₂×C₄²	—	158	1	no	—
293	C₂×C₄²	—	158	1	no	—
294	C₂×C₄²	—	158	1	no	—
295	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	158	1	no	—
299	C₄⋊C₈	—	158	1	no	—
300	C₂²⋊C₈	—	316	2	no	—
301	C₂²⋊C₈	—	158	4	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	158	1	no	—
305	C₄×C₈	—	158	1	no	—
306	#95	—	2	1	no	—
307	#95	—	158	1	no	—
308	#95	—	158	1	no	—
309	#95	—	158	1	no	—
310	C₂⁴	—	79	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	316	1	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	2	no	—
317	C₂²×C₄	—	79	2	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	158	2	no	—
320	C₂²×C₄	—	158	1	no	—
321	C₂²×C₄	—	158	1	no	—
322	C₂²×C₄	—	158	1	no	—
323	C₂²×C₄	—	158	1	no	—
324	C₂²×C₄	—	158	1	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	—	158	1	no	—
327	C₂²×C₄	—	158	1	no	—
328	C₂²×C₄	—	158	1	no	—
329	C₂²×C₄	—	158	1	no	—
330	C₂²×C₄	—	158	1	no	—
331	C₂²×C₄	—	158	1	no	—
332	C₂²×C₄	—	158	1	no	—
333	C₂²×C₄	—	158	1	no	—
334	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	316	1	no	—
344	C₂×C₈	—	316	1	no	—
345	C₂×C₈	—	316	1	no	—
346	C₂×C₈	—	316	1	no	—
347	C₂×C₈	—	316	1	no	—
348	C₂×C₈	—	158	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	79	2	no	—
352	C₄⋊C₄	—	79	2	no	—
353	C₄⋊C₄	—	158	1	no	—
354	C₄⋊C₄	—	158	1	no	—
355	C₄⋊C₄	C₈×D₇₉	1	2	yes	—
356	C₄⋊C₄	#11929607	1	2	yes	—
357	C₂²⋊C₄	—	158	4	no	—
358	C₂²⋊C₄	—	158	4	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	316	2	no	—
362	C₄²	—	316	2	no	—
363	C₄²	—	316	1	no	—
364	C₄²	—	316	1	no	—
365	C₄²	—	158	4	no	—
366	C₄²	—	158	4	no	—
367	C₄²	—	158	1	no	—
368	C₄²	—	158	1	no	—
369	C₄²	—	158	1	no	—
370	C₄²	—	158	1	no	—
371	C₄²	—	158	1	no	—
372	C₄²	—	158	1	no	—
373	C₄²	#11929623	1	1	yes	characteristic
374	C₄²	#11929624	1	1	yes	characteristic
375	C₄²	#11929624	1	1	yes	characteristic
376	C₄²	#11929625	1	1	yes	characteristic
377	C₂³	—	79	2	no	—
378	C₂³	—	158	1	no	—
379	C₂³	—	158	1	no	—
380	C₂³	—	158	1	no	—
381	C₂³	—	158	1	no	—
382	C₂³	—	158	1	no	—
383	C₂³	—	158	1	no	—
384	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	316	2	no	—
394	C₂×C₄	—	316	2	no	—
395	C₂×C₄	—	316	1	no	—
396	C₂×C₄	—	316	1	no	—
397	C₂×C₄	—	316	1	no	—
398	C₂×C₄	—	316	1	no	—
399	C₂×C₄	—	316	1	no	—
400	C₂×C₄	—	316	1	no	—
401	C₂×C₄	—	316	1	no	—
402	C₂×C₄	—	316	1	no	—
403	C₂×C₄	—	79	2	no	—
404	C₂×C₄	—	79	2	no	—
405	C₂×C₄	—	158	1	no	—
406	C₂×C₄	—	158	2	no	—
407	C₂×C₄	—	158	2	no	—
408	C₂×C₄	—	158	1	no	—
409	C₂×C₄	—	158	1	no	—
410	C₂×C₄	—	158	1	no	—
411	C₂×C₄	—	158	1	no	—
412	C₂×C₄	—	158	1	no	—
413	C₂×C₄	—	158	1	no	—
414	C₂×C₄	—	158	2	no	—
415	C₂×C₄	—	158	2	no	—
416	C₂×C₄	—	158	2	no	—
417	C₂×C₄	—	158	2	no	—
418	C₂×C₄	#14579118	1	1	yes	characteristic
419	C₂×C₄	#14579119	1	1	yes	characteristic
420	C₂×C₄	#14579143	1	1	yes	characteristic
421	C₂×C₄	#14579143	1	1	yes	characteristic
422	C₂×C₄	#14579146	1	1	yes	characteristic
423	C₂×C₄	#14579146	1	1	yes	characteristic
424	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
425	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
426	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#11929607	1	1	yes	characteristic
428	C₂×C₄	#14579182	1	1	yes	characteristic
429	C₂×C₄	#14579184	1	1	yes	characteristic
430	C₂×C₄	#14579185	1	1	yes	characteristic
431	C₂×C₄	#14579190	1	1	yes	characteristic
432	C₈	—	4	2	no	—
433	C₈	—	8	1	no	—
434	C₈	—	316	2	no	—
435	C₈	—	632	1	no	—
436	C₂²	—	316	1	no	—
437	C₂²	—	316	1	no	—
438	C₂²	—	316	1	no	—
439	C₂²	—	316	1	no	—
440	C₂²	—	158	2	no	—
441	C₂²	—	158	2	no	—
442	C₂²	—	158	2	no	—
443	C₂²	#19098425	1	1	yes	characteristic
444	C₂²	C₂²⋊C₈×D₇₉	1	1	yes	characteristic
445	C₂²	#19098525	1	1	yes	characteristic
446	C₂²	#19098558	1	1	yes	characteristic
447	C₂²	#19098561	1	1	yes	characteristic
448	C₂²	#104×D₇₉	1	1	yes	characteristic
449	C₂²	#19098578	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	316	1	no	—
455	C₄	—	316	2	no	—
456	C₄	—	316	2	no	—
457	C₄	—	158	2	no	—
458	C₄	—	158	2	no	—
459	C₄	#19098614	1	1	yes	characteristic
460	C₄	#19098615	1	1	yes	characteristic
461	C₄	#19098618	1	1	yes	characteristic
462	C₄	#19098619	1	1	yes	characteristic
463	C₄	#19098886	1	1	yes	characteristic
464	C₄	#19098890	1	1	yes	characteristic
465	C₄	#19098903	1	1	yes	characteristic
466	C₄	#19098907	1	1	yes	characteristic
467	C₂	—	316	2	no	—
468	C₂	#23761781	1	1	yes	characteristic
469	C₂	#23761784	1	1	yes	characteristic
470	C₂	#23761833	1	1	yes	characteristic
471	C₂	#23761836	1	1	yes	characteristic
472	C₂	#23763467	1	1	yes	characteristic
473	C₂	#23763494	1	1	yes	characteristic
474	C₂	#23763498	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1279	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1279	D₇₉
hypocenter	C₇₉	#8708
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #23761241	C₂	semidirect
5. #23761240	C₂	semidirect
6. #23761239	C₂	semidirect
7. C₇₉×#1279	C₂	semidirect
35. #14579119	C₈	semidirect
244. #1279	D₇₉	semidirect
245. C₇₉	#8708	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579119	2
#23763377	2
C₄×(C₂×D₇₉)⋊C₈	2
#23761241	2
#23761240	2
#23761239	2
C₇₉×#1279	2
#8708	79