Subgroups — #34196876

Order 20224.

974 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579093	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14579092	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098432	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098325	C₂	1	1	yes	maximal, characteristic
5	C₂×#19098317	C₂	1	1	yes	maximal, characteristic
6	#23761629	C₂	1	1	yes	maximal, characteristic
7	C₂×#340×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₇₉⋊C₄	—	2	2	no	—
12	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂×#14579093	—	2	2	no	—
14	C₂×#14579093	—	2	2	no	—
15	C₂×#14579093	—	2	2	no	—
16	C₂×#14579092	—	2	2	no	—
17	C₂×#14579092	—	2	2	no	—
18	C₂×#14579092	—	2	2	no	—
19	#19098432	—	2	2	no	—
20	#19098432	—	2	2	no	—
21	C₂×C₇₉⋊#95	—	2	2	no	—
22	#19098325	—	2	2	no	—
23	#19098317	C₄	1	4	yes	complemented
24	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
27	#340×C₇₉	—	2	2	no	—
28	C₂³×Dic₇₉	—	2	1	no	—
29	C₂³×Dic₇₉	—	2	1	no	—
30	C₂³×Dic₇₉	D₄	1	2	yes	—
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	C₂²×C₇₉⋊C₈	—	2	1	no	—
33	C₂²×C₇₉⋊C₈	—	2	1	no	—
34	C₂²×C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
37	C₂²×C₇₉⋊C₈	Q₈	1	2	yes	—
38	C₂×C₄⋊Dic₇₉	—	2	1	no	—
39	C₂×C₄⋊Dic₇₉	—	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	—	2	1	no	—
46	C₂×C₄⋊Dic₇₉	—	2	1	no	—
47	C₂×C₄⋊Dic₇₉	—	2	1	no	—
48	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
49	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
50	C₂×Dic₇₉⋊C₄	—	2	8	no	—
51	C₂×Dic₇₉⋊C₄	—	4	4	no	—
52	C₂×Dic₇₉⋊C₄	—	4	4	no	—
53	C₂×C₄×Dic₇₉	—	2	1	no	—
54	C₂×C₄×Dic₇₉	—	2	1	no	—
55	C₂×C₄×Dic₇₉	—	2	1	no	—
56	C₂×C₄×Dic₇₉	—	2	1	no	—
57	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₇₉	Q₈	1	2	yes	—
59	#14579093	—	2	8	no	—
60	#14579092	—	2	8	no	—
61	C₇₉⋊#95	—	4	4	no	—
62	C₂³×C₄×C₇₉	—	2	1	no	—
63	C₂³×C₄×C₇₉	—	2	1	no	—
64	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₇₉	—	2	1	no	—
66	C₂²×C₈×C₇₉	—	2	1	no	—
67	C₂²×C₈×C₇₉	—	2	1	no	—
68	C₂²×C₈×C₇₉	—	2	1	no	—
69	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₇₉	D₄	1	2	yes	—
71	C₂²×C₈×C₇₉	Q₈	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₉	Q₈	1	2	yes	—
84	C₂²×Dic₇₉	—	2	2	no	—
85	C₂²×Dic₇₉	—	2	2	no	—
86	C₂²×Dic₇₉	—	2	2	no	—
87	C₂²×Dic₇₉	—	2	2	no	—
88	C₂²×Dic₇₉	—	2	2	no	—
89	C₂²×Dic₇₉	—	2	2	no	—
90	C₂²×Dic₇₉	—	4	1	no	—
91	C₂²×Dic₇₉	—	4	1	no	—
92	C₂²×Dic₇₉	—	4	1	no	—
93	C₂²×Dic₇₉	—	4	1	no	—
94	C₂²×Dic₇₉	—	4	2	no	—
95	C₂²×Dic₇₉	—	4	2	no	—
96	C₂²×Dic₇₉	—	4	2	no	—
97	C₂²×Dic₇₉	—	4	2	no	—
98	C₂²×Dic₇₉	C₄⋊C₄	1	4	yes	—
99	C₂²×Dic₇₉	SD₁₆	1	4	yes	—
100	C₂²×Dic₇₉	SD₁₆	1	4	yes	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	2	no	—
106	C₂×C₇₉⋊C₈	—	2	2	no	—
107	C₂×C₇₉⋊C₈	C₄⋊C₄	1	4	yes	complemented
108	C₄⋊Dic₇₉	—	2	2	no	—
109	C₄⋊Dic₇₉	—	2	2	no	—
110	C₄⋊Dic₇₉	—	2	2	no	—
111	C₄⋊Dic₇₉	—	2	2	no	—
112	C₄⋊Dic₇₉	—	4	1	no	—
113	C₄⋊Dic₇₉	—	4	1	no	—
114	C₄⋊Dic₇₉	—	4	1	no	—
115	C₄⋊Dic₇₉	—	4	1	no	—
116	Dic₇₉⋊C₄	—	4	16	no	—
117	C₄×Dic₇₉	—	2	2	no	—
118	C₄×Dic₇₉	—	2	2	no	—
119	C₄×Dic₇₉	—	2	2	no	—
120	C₄×Dic₇₉	—	2	2	no	—
121	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	4	1	no	—
125	C₂²×C₄×C₇₉	—	4	1	no	—
126	C₂²×C₄×C₇₉	—	4	1	no	—
127	C₂²×C₄×C₇₉	—	4	1	no	—
128	C₂²×C₄×C₇₉	—	4	2	no	—
129	C₂²×C₄×C₇₉	—	4	2	no	—
130	C₂²×C₄×C₇₉	—	4	2	no	—
131	C₂²×C₄×C₇₉	—	4	2	no	—
132	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₇₉	—	2	2	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	C₄⋊C₄	1	4	yes	complemented
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	4	1	no	—
158	C₄⋊C₄×C₇₉	—	4	1	no	—
159	C₄⋊C₄×C₇₉	—	4	1	no	—
160	C₄⋊C₄×C₇₉	—	4	1	no	—
161	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂³×C₇₉	#120	1	1	yes	characteristic
163	C₂³×C₇₉	#121	1	1	yes	characteristic
164	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂³×C₇₉	#123	1	1	yes	characteristic
166	C₂³×C₇₉	#127	1	1	yes	characteristic
167	C₂³×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
168	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
169	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
170	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂³×C₇₉	#137	1	2	yes	—
172	C₂×C₄×C₇₉	—	4	2	no	—
173	C₂×C₄×C₇₉	—	4	2	no	—
174	C₂×C₄×C₇₉	—	4	4	no	—
175	C₂×C₄×C₇₉	—	4	4	no	—
176	C₂×C₄×C₇₉	—	8	2	no	—
177	C₂×C₄×C₇₉	—	8	2	no	—
178	C₂×C₄×C₇₉	—	8	1	no	—
179	C₂×C₄×C₇₉	—	8	1	no	—
180	C₂×C₄×C₇₉	—	8	1	no	—
181	C₂×C₄×C₇₉	—	8	1	no	—
182	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×C₄⋊C₄	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	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
189	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
190	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
201	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
202	C₂×C₄×C₇₉	#125	1	1	yes	characteristic
203	C₂×C₄×C₇₉	#125	1	1	yes	characteristic
204	C₂×C₄×C₇₉	#125	1	1	yes	characteristic
205	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
210	C₂×Dic₇₉	—	2	4	no	—
211	C₂×Dic₇₉	—	2	4	no	—
212	C₂×Dic₇₉	—	2	4	no	—
213	C₂×Dic₇₉	—	2	4	no	—
214	C₂×Dic₇₉	—	2	4	no	—
215	C₂×Dic₇₉	—	2	4	no	—
216	C₂×Dic₇₉	—	4	2	no	—
217	C₂×Dic₇₉	—	4	2	no	—
218	C₂×Dic₇₉	—	4	4	no	—
219	C₂×Dic₇₉	—	4	4	no	—
220	C₂×Dic₇₉	—	8	2	no	—
221	C₂×Dic₇₉	—	8	2	no	—
222	C₂×Dic₇₉	—	8	1	no	—
223	C₂×Dic₇₉	—	8	1	no	—
224	C₂×Dic₇₉	—	8	1	no	—
225	C₂×Dic₇₉	—	8	1	no	—
226	C₂×Dic₇₉	#106	1	8	yes	complemented
227	C₈×C₇₉	—	2	4	no	—
228	C₇₉⋊C₈	—	2	4	no	—
229	C₂²×C₇₉	#384	1	1	yes	characteristic
230	C₂²×C₇₉	#385	1	1	yes	characteristic
231	C₂²×C₇₉	#389	1	1	yes	characteristic
232	C₂²×C₇₉	#392	1	1	yes	characteristic
233	C₂²×C₇₉	#395	1	1	yes	characteristic
234	C₂²×C₇₉	#398	1	1	yes	characteristic
235	C₂²×C₇₉	#399	1	1	yes	characteristic
236	C₂²×C₇₉	C₂×#106	1	2	yes	—
237	C₂²×C₇₉	#428	1	2	yes	—
238	C₂²×C₇₉	#448	1	2	yes	—
239	C₂²×C₇₉	#450	1	2	yes	—
240	C₂²×C₇₉	#460	1	2	yes	—
241	C₂²×C₇₉	#461	1	2	yes	—
242	C₂²×C₇₉	#475	1	2	yes	—
243	C₂²×C₇₉	#476	1	2	yes	—
244	C₂²×C₇₉	#481	1	2	yes	—
245	C₂²×C₇₉	#483	1	2	yes	—
246	C₂²×C₇₉	#492	1	1	yes	characteristic
247	C₂²×C₇₉	#492	1	1	yes	characteristic
248	C₂²×C₇₉	#496	1	1	yes	characteristic
249	C₂²×C₇₉	#497	1	1	yes	characteristic
250	C₂²×C₇₉	#498	1	2	yes	—
251	C₂²×C₇₉	#501	1	2	yes	—
252	C₄×C₇₉	—	8	2	no	—
253	C₄×C₇₉	—	8	2	no	—
254	C₄×C₇₉	#385	1	1	yes	characteristic
255	C₄×C₇₉	#385	1	1	yes	characteristic
256	C₄×C₇₉	#389	1	1	yes	characteristic
257	C₄×C₇₉	#389	1	1	yes	characteristic
258	C₄×C₇₉	#395	1	1	yes	characteristic
259	C₄×C₇₉	#395	1	1	yes	characteristic
260	C₄×C₇₉	#398	1	1	yes	characteristic
261	C₄×C₇₉	#398	1	1	yes	characteristic
262	Dic₇₉	—	2	8	no	—
263	Dic₇₉	—	8	2	no	—
264	Dic₇₉	—	8	2	no	—
265	#11323	—	79	1	no	maximal, Sylow
266	C₂×C₇₉	#1444	1	1	yes	characteristic
267	C₂×C₇₉	#1844	1	1	yes	characteristic
268	C₂×C₇₉	#1847	1	1	yes	characteristic
269	C₂×C₇₉	#1853	1	2	yes	—
270	C₂×C₇₉	#1948	1	2	yes	—
271	C₂×C₇₉	#2013	1	1	yes	characteristic
272	C₂×C₇₉	#2014	1	1	yes	characteristic
273	C₂×C₇₉	#2058	1	2	yes	—
274	C₂×C₇₉	#2084	1	2	yes	—
275	C₂×C₇₉	#2094	1	1	yes	characteristic
276	C₂×C₇₉	#2096	1	1	yes	characteristic
277	C₂²×#106	—	79	1	no	—
278	C₂²×#106	—	79	1	no	—
279	C₂×#384	—	79	1	no	—
280	C₂×#340	—	79	1	no	—
281	C₂×#340	D₇₉	1	1	yes	characteristic
282	C₂×#336	—	79	1	no	—
283	C₄⋊#95	—	79	1	no	—
284	C₇₉	#11323	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₈	—	79	1	no	—
286	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	—	79	1	no	—
288	C₂²×C₄⋊C₄	—	79	1	no	—
289	C₂²×C₄⋊C₄	—	158	2	no	—
290	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
292	C₂²×C₄²	—	79	1	no	—
293	C₂×#106	—	158	2	no	—
294	C₂×#106	—	158	2	no	—
295	C₂×#106	—	158	2	no	—
296	C₂×#106	—	158	2	no	—
297	C₂×#106	—	158	2	no	—
298	C₂×#106	—	158	2	no	—
299	#384	—	158	2	no	—
300	#384	—	158	2	no	—
301	C₂×#95	—	158	2	no	—
302	#340	—	2	2	no	—
303	#340	—	158	2	no	—
304	#336	—	79	4	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	79	2	no	—
308	C₂³×C₄	—	158	1	no	—
309	C₂³×C₄	—	158	1	no	—
310	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	79	2	no	—
316	C₂²×C₈	—	79	2	no	—
317	C₂²×C₈	—	79	2	no	—
318	C₂²×C₈	—	158	1	no	—
319	C₂²×C₈	—	158	1	no	—
320	C₂²×C₈	—	158	1	no	—
321	C₂²×C₈	—	158	1	no	—
322	C₂²×C₈	Dic₁₅₈	1	2	yes	—
323	C₂²×C₈	C₄×D₇₉	1	2	yes	—
324	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	316	4	no	—
336	C₂×C₄⋊C₄	—	316	4	no	—
337	C₂×C₄⋊C₄	—	79	2	no	—
338	C₂×C₄⋊C₄	—	79	2	no	—
339	C₂×C₄⋊C₄	—	158	8	no	—
340	C₂×C₄⋊C₄	—	158	1	no	—
341	C₂×C₄⋊C₄	—	158	1	no	—
342	C₂×C₄⋊C₄	—	158	1	no	—
343	C₂×C₄⋊C₄	—	158	1	no	—
344	C₂×C₄⋊C₄	—	158	1	no	—
345	C₂×C₄⋊C₄	—	158	1	no	—
346	C₂×C₄⋊C₄	—	158	1	no	—
347	C₂×C₄⋊C₄	—	158	1	no	—
348	C₂×C₄⋊C₄	—	158	1	no	—
349	C₂×C₄⋊C₄	—	158	1	no	—
350	C₂×C₄⋊C₄	Dic₁₅₈	1	2	yes	—
351	C₂×C₄⋊C₄	D₃₁₆	1	2	yes	—
352	C₂×C₄²	—	79	2	no	—
353	C₂×C₄²	—	79	2	no	—
354	C₂×C₄²	—	158	1	no	—
355	C₂×C₄²	—	158	1	no	—
356	C₂×C₄²	—	158	1	no	—
357	C₂×C₄²	—	158	1	no	—
358	#106	—	158	8	no	—
359	#106	—	158	8	no	—
360	#95	—	316	4	no	—
361	C₂⁴	D₄×D₇₉	1	1	yes	characteristic
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	316	1	no	—
373	C₂²×C₄	—	316	1	no	—
374	C₂²×C₄	—	316	1	no	—
375	C₂²×C₄	—	316	1	no	—
376	C₂²×C₄	—	316	2	no	—
377	C₂²×C₄	—	316	2	no	—
378	C₂²×C₄	—	316	2	no	—
379	C₂²×C₄	—	316	2	no	—
380	C₂²×C₄	—	79	4	no	—
381	C₂²×C₄	—	79	4	no	—
382	C₂²×C₄	—	79	4	no	—
383	C₂²×C₄	—	158	2	no	—
384	C₂²×C₄	—	158	2	no	—
385	C₂²×C₄	—	158	2	no	—
386	C₂²×C₄	—	158	2	no	—
387	C₂²×C₄	—	158	2	no	—
388	C₂²×C₄	—	158	2	no	—
389	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
390	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
391	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
392	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
395	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
396	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
398	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
399	C₂²×C₄	#11929623	1	1	yes	characteristic
400	C₂²×C₄	#11929623	1	1	yes	characteristic
401	C₂²×C₄	#11929624	1	1	yes	characteristic
402	C₂²×C₄	#11929624	1	1	yes	characteristic
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	79	4	no	—
410	C₂×C₈	—	158	2	no	—
411	C₂×C₈	—	158	2	no	—
412	C₂×C₈	—	158	2	no	—
413	C₂×C₈	—	158	2	no	—
414	C₂×C₈	—	158	2	no	—
415	C₂×C₈	—	158	2	no	—
416	C₂×C₈	Dic₇₉⋊C₄	1	4	yes	complemented
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	316	16	no	—
426	C₄⋊C₄	—	316	1	no	—
427	C₄⋊C₄	—	316	1	no	—
428	C₄⋊C₄	—	316	1	no	—
429	C₄⋊C₄	—	316	1	no	—
430	C₄⋊C₄	—	158	2	no	—
431	C₄⋊C₄	—	158	2	no	—
432	C₄⋊C₄	—	158	2	no	—
433	C₄⋊C₄	—	158	2	no	—
434	C₄²	—	158	2	no	—
435	C₄²	—	158	2	no	—
436	C₄²	—	158	2	no	—
437	C₄²	—	158	2	no	—
438	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
439	C₂³	#14579131	1	1	yes	characteristic
440	C₂³	#14579134	1	1	yes	characteristic
441	C₂³	#14579138	1	1	yes	characteristic
442	C₂³	#14579143	1	1	yes	characteristic
443	C₂³	#14579157	1	1	yes	characteristic
444	C₂³	#14579160	1	1	yes	characteristic
445	C₂³	SD₁₆×D₇₉	1	2	yes	—
446	C₂³	SD₁₆×D₇₉	1	2	yes	—
447	C₂³	#14579185	1	2	yes	—
448	C₂³	#14579193	1	2	yes	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	316	4	no	—
460	C₂×C₄	—	316	2	no	—
461	C₂×C₄	—	316	2	no	—
462	C₂×C₄	—	316	4	no	—
463	C₂×C₄	—	79	8	no	—
464	C₂×C₄	—	632	1	no	—
465	C₂×C₄	—	632	1	no	—
466	C₂×C₄	—	632	1	no	—
467	C₂×C₄	—	632	1	no	—
468	C₂×C₄	—	632	2	no	—
469	C₂×C₄	—	632	2	no	—
470	C₂×C₄	—	158	4	no	—
471	C₂×C₄	—	158	4	no	—
472	C₂×C₄	—	158	4	no	—
473	C₂×C₄	—	158	4	no	—
474	C₂×C₄	—	158	4	no	—
475	C₂×C₄	—	158	4	no	—
476	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
477	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
478	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
479	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
481	C₂×C₄	C₄×Dic₁₅₈	1	1	yes	characteristic
482	C₂×C₄	#14579129	1	1	yes	characteristic
483	C₂×C₄	#14579131	1	1	yes	characteristic
484	C₂×C₄	#14579134	1	1	yes	characteristic
485	C₂×C₄	#14579135	1	1	yes	characteristic
486	C₂×C₄	#14579138	1	1	yes	characteristic
487	C₂×C₄	#14579138	1	1	yes	characteristic
488	C₂×C₄	#14579138	1	1	yes	characteristic
489	C₂×C₄	#14579139	1	1	yes	characteristic
490	C₂×C₄	#14579139	1	1	yes	characteristic
491	C₂×C₄	#14579140	1	1	yes	characteristic
492	C₂×C₄	#14579141	1	1	yes	characteristic
493	C₂×C₄	#14579141	1	1	yes	characteristic
494	C₂×C₄	#14579142	1	1	yes	characteristic
495	C₂×C₄	#14579143	1	1	yes	characteristic
496	C₂×C₄	#14579151	1	1	yes	characteristic
497	C₂×C₄	#14579151	1	1	yes	characteristic
498	C₂×C₄	#14579153	1	1	yes	characteristic
499	C₂×C₄	#14579159	1	1	yes	characteristic
500	C₂×C₄	#14579160	1	1	yes	characteristic
501	C₂×C₄	#14579160	1	1	yes	characteristic
502	C₂×C₄	#14579160	1	1	yes	characteristic
503	C₂×C₄	#14579161	1	1	yes	characteristic
504	C₈	—	2	4	no	—
505	C₈	—	158	4	no	—
506	C₂²	#19098432	1	1	yes	characteristic
507	C₂²	#19098437	1	1	yes	characteristic
508	C₂²	#19098460	1	1	yes	characteristic
509	C₂²	#19098472	1	1	yes	characteristic
510	C₂²	#19098484	1	1	yes	characteristic
511	C₂²	#19098497	1	1	yes	characteristic
512	C₂²	#19098499	1	1	yes	characteristic
513	C₂²	#106×D₇₉	1	2	yes	—
514	C₂²	#19098604	1	2	yes	—
515	C₂²	#19098703	1	2	yes	—
516	C₂²	#19098715	1	2	yes	—
517	C₂²	#19098762	1	2	yes	—
518	C₂²	#19098767	1	2	yes	—
519	C₂²	#19098846	1	2	yes	—
520	C₂²	#19098851	1	2	yes	—
521	C₂²	#19098880	1	2	yes	—
522	C₂²	#19098892	1	2	yes	—
523	C₂²	#19098934	1	1	yes	characteristic
524	C₂²	#19098934	1	1	yes	characteristic
525	C₂²	#19098951	1	1	yes	characteristic
526	C₂²	#19098956	1	1	yes	characteristic
527	C₂²	#19098960	1	2	yes	—
528	C₂²	#19098971	1	2	yes	—
529	C₄	—	8	2	no	—
530	C₄	—	8	2	no	—
531	C₄	—	632	2	no	—
532	C₄	—	632	2	no	—
533	C₄	—	158	8	no	—
534	C₄	#19098435	1	1	yes	characteristic
535	C₄	#19098437	1	1	yes	characteristic
536	C₄	#19098460	1	1	yes	characteristic
537	C₄	#19098461	1	1	yes	characteristic
538	C₄	#19098483	1	1	yes	characteristic
539	C₄	#19098484	1	1	yes	characteristic
540	C₄	#19098493	1	1	yes	characteristic
541	C₄	#19098497	1	1	yes	characteristic
542	C₂	#23761664	1	1	yes	characteristic
543	C₂	#23763555	1	1	yes	characteristic
544	C₂	#23763567	1	1	yes	characteristic
545	C₂	#23763594	1	2	yes	—
546	C₂	#23764162	1	2	yes	—
547	C₂	#23764484	1	1	yes	characteristic
548	C₂	#23764489	1	1	yes	characteristic
549	C₂	#23764732	1	2	yes	—
550	C₂	#23764880	1	2	yes	—
551	C₂	#23764931	1	1	yes	characteristic
552	C₂	#23764941	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₂×#340×C₇₉	C₂
socle, prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₂×#340	D₇₉
hypocenter	C₇₉	#11323
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
23. #19098317	C₄	semidirect
107. C₂×C₇₉⋊C₈	C₄⋊C₄	semidirect
152. C₂×C₈×C₇₉	C₄⋊C₄	semidirect
226. C₂×Dic₇₉	#106	semidirect
284. C₇₉	#11323	semidirect
416. C₂×C₈	Dic₇₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579093	2
C₂²×#14579092	2
C₂×#19098432	2
C₂×#19098325	2
C₂×#19098317	2
#23761629	2
C₂×#340×C₇₉	2
#11323	79