Subgroups — #34196527

Order 20224.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098433	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098325	C₂	1	2	yes	maximal
3	C₂×#19098325	C₂	1	2	yes	maximal
4	C₂×#19098318	C₂	1	1	yes	maximal, characteristic
5	C₇₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₇₉	—	2	1	no	—
8	C₂²×C₄⋊Dic₇₉	—	2	1	no	—
9	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	#19098433	—	2	4	no	—
11	#19098325	—	2	4	no	—
12	#19098325	—	2	4	no	—
13	#19098318	C₄	1	4	yes	complemented
14	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#95×C₇₉	—	2	1	no	—
18	C₂×#95×C₇₉	—	2	1	no	—
19	C₂³×Dic₇₉	—	2	2	no	—
20	C₂²×C₇₉⋊C₈	—	2	2	no	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	2	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	2	no	—
25	C₂²×C₇₉⋊C₈	—	2	2	no	—
26	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊Dic₇₉	—	2	2	no	—
28	C₂×C₄⋊Dic₇₉	—	2	2	no	—
29	C₂×C₄⋊Dic₇₉	—	2	2	no	—
30	C₂×C₄⋊Dic₇₉	—	2	2	no	—
31	C₂×C₄⋊Dic₇₉	—	2	4	no	—
32	C₂×C₄⋊Dic₇₉	—	2	4	no	—
33	C₂×C₄⋊Dic₇₉	—	2	2	no	—
34	C₂×C₄⋊Dic₇₉	—	4	2	no	—
35	C₂×C₄⋊Dic₇₉	—	4	2	no	—
36	C₂×C₄⋊Dic₇₉	—	4	2	no	—
37	C₂×C₄⋊Dic₇₉	—	4	2	no	—
38	C₂×C₄⋊Dic₇₉	D₄	1	4	yes	—
39	C₂³×C₄×C₇₉	—	2	1	no	—
40	C₂³×C₄×C₇₉	—	2	1	no	—
41	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₇₉	Q₈	1	2	yes	—
52	C₂×C₄²×C₇₉	—	2	2	no	—
53	C₂×C₄²×C₇₉	—	2	2	no	—
54	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₇₉	Q₈	1	2	yes	—
56	#95×C₇₉	—	4	2	no	—
57	#95×C₇₉	—	4	2	no	—
58	C₂²×Dic₇₉	—	2	4	no	—
59	C₂²×Dic₇₉	—	4	2	no	—
60	C₂²×Dic₇₉	—	4	2	no	—
61	C₂²×Dic₇₉	—	4	2	no	—
62	C₂²×Dic₇₉	—	4	2	no	—
63	C₂²×Dic₇₉	—	4	2	no	—
64	C₂²×Dic₇₉	—	4	2	no	—
65	C₂×C₇₉⋊C₈	—	2	4	no	—
66	C₂×C₇₉⋊C₈	—	2	4	no	—
67	C₂×C₇₉⋊C₈	—	2	4	no	—
68	C₂×C₇₉⋊C₈	—	4	2	no	—
69	C₂×C₇₉⋊C₈	—	4	2	no	—
70	C₂×C₇₉⋊C₈	—	4	2	no	—
71	C₂×C₇₉⋊C₈	—	4	2	no	—
72	C₄⋊Dic₇₉	—	2	4	no	—
73	C₄⋊Dic₇₉	—	2	4	no	—
74	C₄⋊Dic₇₉	—	4	8	no	—
75	C₄⋊Dic₇₉	—	4	8	no	—
76	C₄⋊Dic₇₉	—	4	2	no	—
77	C₄⋊Dic₇₉	—	4	2	no	—
78	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₉	—	2	1	no	—
80	C₂²×C₄×C₇₉	—	2	1	no	—
81	C₂²×C₄×C₇₉	—	2	1	no	—
82	C₂²×C₄×C₇₉	—	2	1	no	—
83	C₂²×C₄×C₇₉	—	2	1	no	—
84	C₂²×C₄×C₇₉	—	2	1	no	—
85	C₂²×C₄×C₇₉	—	2	1	no	—
86	C₂²×C₄×C₇₉	—	2	1	no	—
87	C₂²×C₄×C₇₉	—	2	2	no	—
88	C₂²×C₄×C₇₉	—	2	2	no	—
89	C₂²×C₄×C₇₉	—	4	1	no	—
90	C₂²×C₄×C₇₉	—	4	1	no	—
91	C₂²×C₄×C₇₉	—	4	1	no	—
92	C₂²×C₄×C₇₉	—	4	1	no	—
93	C₂²×C₄×C₇₉	—	4	1	no	—
94	C₂²×C₄×C₇₉	—	4	1	no	—
95	C₂²×C₄×C₇₉	—	4	1	no	—
96	C₂²×C₄×C₇₉	—	4	1	no	—
97	C₂²×C₄×C₇₉	—	4	1	no	—
98	C₂²×C₄×C₇₉	—	4	1	no	—
99	C₂²×C₄×C₇₉	—	4	1	no	—
100	C₂²×C₄×C₇₉	—	4	1	no	—
101	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₇₉	D₈	1	2	yes	—
104	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
105	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
106	C₂²×C₄×C₇₉	Q₁₆	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	#41	1	2	yes	—
113	C₂²×C₄×C₇₉	#41	1	2	yes	—
114	C₂²×C₄×C₇₉	#41	1	2	yes	—
115	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
117	C₄⋊C₄×C₇₉	—	2	4	no	—
118	C₄⋊C₄×C₇₉	—	2	4	no	—
119	C₄⋊C₄×C₇₉	—	4	2	no	—
120	C₄⋊C₄×C₇₉	—	4	2	no	—
121	C₄²×C₇₉	—	2	4	no	—
122	C₄²×C₇₉	—	2	4	no	—
123	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₇₉	#120	1	1	yes	characteristic
125	C₂³×C₇₉	#121	1	1	yes	characteristic
126	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₇₉	#123	1	1	yes	characteristic
128	C₂³×C₇₉	#124	1	1	yes	characteristic
129	C₂³×C₇₉	#124	1	1	yes	characteristic
130	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₇₉	#137	1	1	yes	characteristic
137	C₂³×C₇₉	#137	1	1	yes	characteristic
138	C₂×C₄×C₇₉	—	2	2	no	—
139	C₂×C₄×C₇₉	—	2	2	no	—
140	C₂×C₄×C₇₉	—	2	2	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	2	2	no	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	4	2	no	—
151	C₂×C₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	4	2	no	—
154	C₂×C₄×C₇₉	—	4	2	no	—
155	C₂×C₄×C₇₉	—	4	2	no	—
156	C₂×C₄×C₇₉	—	8	1	no	—
157	C₂×C₄×C₇₉	—	8	1	no	—
158	C₂×C₄×C₇₉	—	8	1	no	—
159	C₂×C₄×C₇₉	—	8	1	no	—
160	C₂×C₄×C₇₉	—	8	1	no	—
161	C₂×C₄×C₇₉	—	8	1	no	—
162	C₂×C₄×C₇₉	—	8	1	no	—
163	C₂×C₄×C₇₉	—	8	1	no	—
164	C₂×C₄×C₇₉	#106	1	4	yes	—
165	C₂×C₄×C₇₉	#107	1	4	yes	—
166	C₂×C₄×C₇₉	#117	1	2	yes	—
167	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₇₉	#121	1	2	yes	—
171	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₇₉	#123	1	2	yes	—
174	C₂×C₄×C₇₉	#123	1	2	yes	—
175	C₂×C₄×C₇₉	#124	1	2	yes	—
176	C₂×C₄×C₇₉	#125	1	2	yes	—
177	C₂×C₄×C₇₉	#125	1	2	yes	—
178	C₂×C₄×C₇₉	#125	1	1	yes	characteristic
179	C₂×C₄×C₇₉	#126	1	2	yes	—
180	C₂×C₄×C₇₉	#126	1	2	yes	—
181	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×Dic₇₉	—	4	4	no	—
183	C₂×Dic₇₉	—	4	4	no	—
184	C₂×Dic₇₉	—	4	4	no	—
185	C₂×Dic₇₉	—	8	2	no	—
186	C₂×Dic₇₉	—	8	2	no	—
187	C₂×Dic₇₉	—	8	2	no	—
188	C₂×Dic₇₉	—	8	2	no	—
189	C₇₉⋊C₈	—	4	4	no	—
190	C₂²×C₇₉	#382	1	1	yes	characteristic
191	C₂²×C₇₉	#385	1	1	yes	characteristic
192	C₂²×C₇₉	#389	1	1	yes	characteristic
193	C₂²×C₇₉	#393	1	1	yes	characteristic
194	C₂²×C₇₉	#394	1	1	yes	characteristic
195	C₂²×C₇₉	#397	1	1	yes	characteristic
196	C₂²×C₇₉	#400	1	1	yes	characteristic
197	C₂²×C₇₉	C₂×#106	1	1	yes	characteristic
198	C₂²×C₇₉	C₂×#107	1	1	yes	characteristic
199	C₂²×C₇₉	#428	1	1	yes	characteristic
200	C₂²×C₇₉	#428	1	1	yes	characteristic
201	C₂²×C₇₉	#447	1	1	yes	characteristic
202	C₂²×C₇₉	#448	1	1	yes	characteristic
203	C₂²×C₇₉	#450	1	1	yes	characteristic
204	C₂²×C₇₉	#451	1	1	yes	characteristic
205	C₂²×C₇₉	#459	1	1	yes	characteristic
206	C₂²×C₇₉	#460	1	1	yes	characteristic
207	C₂²×C₇₉	#461	1	1	yes	characteristic
208	C₂²×C₇₉	#462	1	1	yes	characteristic
209	C₂²×C₇₉	#474	1	1	yes	characteristic
210	C₂²×C₇₉	#475	1	1	yes	characteristic
211	C₂²×C₇₉	#476	1	1	yes	characteristic
212	C₂²×C₇₉	#477	1	1	yes	characteristic
213	C₂²×C₇₉	#480	1	1	yes	characteristic
214	C₂²×C₇₉	#481	1	1	yes	characteristic
215	C₂²×C₇₉	#483	1	1	yes	characteristic
216	C₂²×C₇₉	#484	1	1	yes	characteristic
217	C₂²×C₇₉	#486	1	1	yes	characteristic
218	C₂²×C₇₉	#486	1	1	yes	characteristic
219	C₂²×C₇₉	#487	1	1	yes	characteristic
220	C₂²×C₇₉	#487	1	1	yes	characteristic
221	C₂²×C₇₉	#489	1	1	yes	characteristic
222	C₂²×C₇₉	#489	1	1	yes	characteristic
223	C₂²×C₇₉	#490	1	1	yes	characteristic
224	C₂²×C₇₉	#491	1	1	yes	characteristic
225	C₄×C₇₉	—	2	4	no	—
226	C₄×C₇₉	—	2	4	no	—
227	C₄×C₇₉	—	8	2	no	—
228	C₄×C₇₉	—	8	2	no	—
229	C₄×C₇₉	#387	1	2	yes	—
230	C₄×C₇₉	#388	1	2	yes	—
231	C₄×C₇₉	#398	1	2	yes	—
232	C₄×C₇₉	#400	1	2	yes	—
233	Dic₇₉	—	8	4	no	—
234	#11267	—	79	1	no	maximal, Sylow
235	C₂×C₇₉	#1442	1	1	yes	characteristic
236	C₂×C₇₉	#1834	1	1	yes	characteristic
237	C₂×C₇₉	#1836	1	1	yes	characteristic
238	C₂×C₇₉	#1852	1	1	yes	characteristic
239	C₂×C₇₉	#1853	1	1	yes	characteristic
240	C₂×C₇₉	#1947	1	1	yes	characteristic
241	C₂×C₇₉	#1948	1	1	yes	characteristic
242	C₂×C₇₉	#2023	1	1	yes	characteristic
243	C₂×C₇₉	#2024	1	1	yes	characteristic
244	C₂×C₇₉	#2041	1	1	yes	characteristic
245	C₂×C₇₉	#2043	1	1	yes	characteristic
246	C₂×C₇₉	#2071	1	1	yes	characteristic
247	C₂×C₇₉	#2072	1	1	yes	characteristic
248	C₂×C₇₉	#2099	1	1	yes	characteristic
249	C₂×C₇₉	#2100	1	1	yes	characteristic
250	C₂×#384	—	79	1	no	—
251	C₂×#340	—	79	2	no	—
252	C₂×#340	—	79	2	no	—
253	C₂×#336	—	79	1	no	—
254	C₄⋊#95	D₇₉	1	1	yes	characteristic
255	C₇₉	#11267	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₈	—	79	2	no	—
257	C₂²×C₄⋊C₄	—	79	2	no	—
258	C₂²×C₄⋊C₄	—	158	1	no	—
259	C₂²×C₄⋊C₄	—	158	1	no	—
260	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
262	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
263	#384	—	158	4	no	—
264	C₂×#95	—	2	1	no	—
265	C₂×#95	—	2	1	no	—
266	#340	—	158	4	no	—
267	#340	—	158	4	no	—
268	#336	—	79	4	no	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	158	2	no	—
272	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
273	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
275	C₂²×C₈	—	79	4	no	—
276	C₂²×C₈	—	158	2	no	—
277	C₂²×C₈	—	158	2	no	—
278	C₂²×C₈	—	158	2	no	—
279	C₂²×C₈	—	158	2	no	—
280	C₂²×C₈	—	158	2	no	—
281	C₂²×C₈	—	158	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	316	2	no	—
289	C₂×C₄⋊C₄	—	316	2	no	—
290	C₂×C₄⋊C₄	—	316	2	no	—
291	C₂×C₄⋊C₄	—	316	2	no	—
292	C₂×C₄⋊C₄	—	79	4	no	—
293	C₂×C₄⋊C₄	—	158	4	no	—
294	C₂×C₄⋊C₄	—	158	4	no	—
295	C₂×C₄⋊C₄	—	158	2	no	—
296	C₂×C₄⋊C₄	—	158	2	no	—
297	C₂×C₄⋊C₄	—	158	2	no	—
298	C₂×C₄⋊C₄	—	158	2	no	—
299	C₂×C₄⋊C₄	—	158	2	no	—
300	C₂×C₄⋊C₄	Dic₁₅₈	1	2	yes	—
301	C₂×C₄⋊C₄	D₃₁₆	1	2	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	Dic₁₅₈	1	2	yes	—
305	C₂×C₄²	C₄×D₇₉	1	2	yes	—
306	#95	—	4	2	no	—
307	#95	—	4	2	no	—
308	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	316	2	no	—
332	C₂²×C₄	—	316	2	no	—
333	C₂²×C₄	—	316	2	no	—
334	C₂²×C₄	—	316	2	no	—
335	C₂²×C₄	—	316	2	no	—
336	C₂²×C₄	—	316	2	no	—
337	C₂²×C₄	—	158	4	no	—
338	C₂²×C₄	Dic₇₉⋊C₄	1	2	yes	—
339	C₂²×C₄	Dic₇₉⋊C₄	1	2	yes	—
340	C₂²×C₄	#11929609	1	2	yes	—
341	C₂²×C₄	#11929611	1	2	yes	—
342	C₂²×C₄	#11929612	1	2	yes	—
343	C₂²×C₄	#11929614	1	2	yes	—
344	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₇₉	1	2	yes	—
346	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
347	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
348	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
349	C₂²×C₄	#11929623	1	2	yes	—
350	C₂²×C₄	#11929623	1	2	yes	—
351	C₂²×C₄	#11929624	1	1	yes	characteristic
352	C₂²×C₄	#11929624	1	1	yes	characteristic
353	C₂²×C₄	#11929625	1	2	yes	—
354	C₂×C₈	—	316	2	no	—
355	C₂×C₈	—	316	2	no	—
356	C₂×C₈	—	316	2	no	—
357	C₂×C₈	—	316	2	no	—
358	C₂×C₈	—	158	4	no	—
359	C₂×C₈	—	158	4	no	—
360	C₂×C₈	—	158	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	316	8	no	—
366	C₄⋊C₄	—	316	8	no	—
367	C₄⋊C₄	—	316	2	no	—
368	C₄⋊C₄	—	316	2	no	—
369	C₄⋊C₄	—	158	4	no	—
370	C₄⋊C₄	—	158	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
374	C₂³	#14579129	1	1	yes	characteristic
375	C₂³	#14579135	1	1	yes	characteristic
376	C₂³	#14579140	1	1	yes	characteristic
377	C₂³	#14579142	1	1	yes	characteristic
378	C₂³	#14579148	1	1	yes	characteristic
379	C₂³	#14579150	1	1	yes	characteristic
380	C₂³	C₂×#11929609	1	1	yes	characteristic
381	C₂³	C₂×#11929611	1	1	yes	characteristic
382	C₂³	C₂×#11929612	1	1	yes	characteristic
383	C₂³	C₂×#11929614	1	1	yes	characteristic
384	C₂³	#14579186	1	1	yes	characteristic
385	C₂³	#14579186	1	1	yes	characteristic
386	C₂³	#14579191	1	1	yes	characteristic
387	C₂³	#14579191	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	1	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	316	4	no	—
415	C₂×C₄	—	316	4	no	—
416	C₂×C₄	—	316	4	no	—
417	C₂×C₄	—	632	2	no	—
418	C₂×C₄	—	632	2	no	—
419	C₂×C₄	—	632	2	no	—
420	C₂×C₄	—	632	2	no	—
421	C₂×C₄	#14579092	1	4	yes	—
422	C₂×C₄	#14579094	1	4	yes	—
423	C₂×C₄	#14579119	1	2	yes	—
424	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
425	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
426	C₂×C₄	C₄×Dic₁₅₈	1	1	yes	characteristic
427	C₂×C₄	#14579136	1	2	yes	—
428	C₂×C₄	#14579138	1	2	yes	—
429	C₂×C₄	#14579138	1	2	yes	—
430	C₂×C₄	#14579145	1	2	yes	—
431	C₂×C₄	#14579146	1	2	yes	—
432	C₂×C₄	#14579147	1	2	yes	—
433	C₂×C₄	#14579152	1	2	yes	—
434	C₂×C₄	#14579152	1	2	yes	—
435	C₂×C₄	#14579153	1	1	yes	characteristic
436	C₂×C₄	#14579154	1	2	yes	—
437	C₂×C₄	#14579156	1	2	yes	—
438	C₂×C₄	#14579161	1	1	yes	characteristic
439	C₈	—	316	4	no	—
440	C₂²	#19098428	1	1	yes	characteristic
441	C₂²	#19098435	1	1	yes	characteristic
442	C₂²	#19098461	1	1	yes	characteristic
443	C₂²	#19098475	1	1	yes	characteristic
444	C₂²	#19098480	1	1	yes	characteristic
445	C₂²	#19098488	1	1	yes	characteristic
446	C₂²	#19098502	1	1	yes	characteristic
447	C₂²	C₂×#14579092	1	1	yes	characteristic
448	C₂²	C₂×#14579094	1	1	yes	characteristic
449	C₂²	#19098606	1	1	yes	characteristic
450	C₂²	#19098606	1	1	yes	characteristic
451	C₂²	#19098696	1	1	yes	characteristic
452	C₂²	#19098701	1	1	yes	characteristic
453	C₂²	#19098713	1	1	yes	characteristic
454	C₂²	#19098718	1	1	yes	characteristic
455	C₂²	#19098758	1	1	yes	characteristic
456	C₂²	#19098763	1	1	yes	characteristic
457	C₂²	#19098768	1	1	yes	characteristic
458	C₂²	#19098773	1	1	yes	characteristic
459	C₂²	#19098843	1	1	yes	characteristic
460	C₂²	#19098848	1	1	yes	characteristic
461	C₂²	#19098853	1	1	yes	characteristic
462	C₂²	#19098858	1	1	yes	characteristic
463	C₂²	#19098874	1	1	yes	characteristic
464	C₂²	#19098879	1	1	yes	characteristic
465	C₂²	#19098891	1	1	yes	characteristic
466	C₂²	#19098896	1	1	yes	characteristic
467	C₂²	#19098909	1	1	yes	characteristic
468	C₂²	#19098911	1	1	yes	characteristic
469	C₂²	#19098913	1	1	yes	characteristic
470	C₂²	#19098915	1	1	yes	characteristic
471	C₂²	#19098922	1	1	yes	characteristic
472	C₂²	#19098922	1	1	yes	characteristic
473	C₂²	#19098929	1	1	yes	characteristic
474	C₂²	#19098933	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	—	632	4	no	—
480	C₄	#19098450	1	2	yes	—
481	C₄	#19098455	1	2	yes	—
482	C₄	#19098495	1	2	yes	—
483	C₄	#19098505	1	2	yes	—
484	C₂	#23761656	1	1	yes	characteristic
485	C₂	#23763527	1	1	yes	characteristic
486	C₂	#23763533	1	1	yes	characteristic
487	C₂	#23763587	1	1	yes	characteristic
488	C₂	#23763592	1	1	yes	characteristic
489	C₂	#23764158	1	1	yes	characteristic
490	C₂	#23764163	1	1	yes	characteristic
491	C₂	#23764536	1	1	yes	characteristic
492	C₂	#23764541	1	1	yes	characteristic
493	C₂	#23764634	1	1	yes	characteristic
494	C₂	#23764646	1	1	yes	characteristic
495	C₂	#23764803	1	1	yes	characteristic
496	C₂	#23764808	1	1	yes	characteristic
497	C₂	#23764958	1	1	yes	characteristic
498	C₂	#23764963	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₇₉×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₄⋊#95	D₇₉
hypocenter	C₇₉	#11267
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
13. #19098318	C₄	semidirect
255. C₇₉	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098433	2
C₂×#19098325	2
C₂×#19098318	2
C₇₉×C₄⋊#95	2
#11267	79