Subgroups — #34314734

Order 20224.

622 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766668	C₂	1	1	yes	maximal, characteristic
2	#23764338	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764334	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764122	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764122	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764016	C₂	1	1	yes	maximal, characteristic
7	#23764016	C₂	1	1	yes	maximal, characteristic
8	#23764010	C₂	1	1	yes	maximal, characteristic
9	#23764003	C₂	1	1	yes	maximal, characteristic
10	#23763967	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763965	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763965	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763960	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763384	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#1818	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×#14579071	C₂²	1	1	yes	characteristic
26	C₂×#14579071	C₂²	1	1	yes	characteristic
27	C₂×#14579071	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
29	#19098502	C₄	1	1	yes	characteristic
30	#19098499	C₄	1	1	yes	characteristic
31	#19098496	C₄	1	1	yes	characteristic
32	#19098496	C₄	1	1	yes	characteristic
33	#19098486	C₄	1	1	yes	characteristic
34	#19098486	C₄	1	1	yes	characteristic
35	#19098483	C₄	1	1	yes	characteristic
36	#19098475	C₄	1	1	yes	characteristic
37	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098317	C₂²	1	1	yes	characteristic
45	#19098317	C₂²	1	1	yes	characteristic
46	#19098317	C₂²	1	1	yes	characteristic
47	#19098317	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	#19098317	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
55	#336×C₇₉	C₂²	1	1	yes	characteristic
56	#336×C₇₉	C₂²	1	1	yes	characteristic
57	#336×C₇₉	C₂²	1	1	yes	characteristic
58	#336×C₇₉	C₂²	1	1	yes	characteristic
59	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×Dic₁₅₈	—	4	1	no	—
65	C₄×Dic₁₅₈	—	4	1	no	—
66	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
84	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
85	Dic₇₉⋊C₈	—	4	1	no	—
86	Dic₇₉⋊C₈	—	4	1	no	—
87	Dic₇₉⋊C₈	—	4	1	no	—
88	Dic₇₉⋊C₈	—	4	1	no	—
89	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
91	#14579071	—	4	1	no	—
92	#14579071	—	4	1	no	—
93	#14579071	—	4	1	no	—
94	C₈×Dic₇₉	—	4	1	no	—
95	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
96	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
110	#117×C₇₉	—	4	1	no	—
111	#117×C₇₉	—	4	1	no	—
112	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₈×C₇₉	—	4	1	no	—
119	C₂²⋊C₈×C₇₉	—	4	1	no	—
120	C₂×Dic₁₅₈	—	2	2	no	—
121	C₂×Dic₁₅₈	—	4	1	no	—
122	C₂×Dic₁₅₈	—	4	1	no	—
123	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₇₉⋊C₈	—	2	1	no	—
132	C₂×C₇₉⋊C₈	—	2	1	no	—
133	C₂×C₇₉⋊C₈	—	2	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	1	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₄⋊Dic₇₉	—	4	1	no	—
144	C₄⋊Dic₇₉	—	4	1	no	—
145	C₄⋊Dic₇₉	—	4	1	no	—
146	Dic₇₉⋊C₄	—	2	2	no	—
147	Dic₇₉⋊C₄	—	4	1	no	—
148	Dic₇₉⋊C₄	—	4	1	no	—
149	Dic₇₉⋊C₄	—	4	1	no	—
150	Dic₇₉⋊C₄	—	4	1	no	—
151	Dic₇₉⋊C₄	—	4	1	no	—
152	C₂²⋊Dic₇₉	—	2	2	no	—
153	C₂²⋊Dic₇₉	—	4	1	no	—
154	C₂²⋊Dic₇₉	—	4	1	no	—
155	C₂²⋊Dic₇₉	—	4	1	no	—
156	C₄×Dic₇₉	—	2	1	no	—
157	C₄×Dic₇₉	—	2	1	no	—
158	C₄×Dic₇₉	—	2	1	no	—
159	C₄×Dic₇₉	—	2	1	no	—
160	C₄×Dic₇₉	—	2	1	no	—
161	C₄×Dic₇₉	—	2	1	no	—
162	C₄×Dic₇₉	—	2	1	no	—
163	C₄×Dic₇₉	—	2	1	no	—
164	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	—	2	1	no	—
166	C₂²×C₄×C₇₉	—	2	1	no	—
167	C₂²×C₄×C₇₉	—	2	1	no	—
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₇₉	—	2	1	no	—
178	C₂×C₈×C₇₉	—	2	1	no	—
179	C₂×C₈×C₇₉	—	2	1	no	—
180	C₂×C₈×C₇₉	—	2	1	no	—
181	C₂×C₈×C₇₉	—	2	1	no	—
182	C₂×C₈×C₇₉	—	2	1	no	—
183	C₂×C₈×C₇₉	—	2	1	no	—
184	C₂×C₈×C₇₉	—	2	1	no	—
185	C₂×C₈×C₇₉	—	2	1	no	—
186	C₂×C₈×C₇₉	—	2	1	no	—
187	C₂×C₈×C₇₉	—	2	1	no	—
188	C₂×C₈×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	—	4	1	no	—
190	C₄⋊C₄×C₇₉	—	4	1	no	—
191	C₂²⋊C₄×C₇₉	—	4	1	no	—
192	C₂²⋊C₄×C₇₉	—	4	1	no	—
193	C₄²×C₇₉	—	2	1	no	—
194	C₄²×C₇₉	—	2	1	no	—
195	C₄²×C₇₉	—	2	1	no	—
196	C₄²×C₇₉	—	2	1	no	—
197	C₂³×C₇₉	—	2	1	no	—
198	C₂³×C₇₉	—	2	1	no	—
199	C₂³×C₇₉	—	2	1	no	—
200	C₂³×C₇₉	—	2	1	no	—
201	C₂³×C₇₉	—	2	1	no	—
202	C₂³×C₇₉	—	2	1	no	—
203	C₂³×C₇₉	—	2	1	no	—
204	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	1	no	—
207	C₂×C₄×C₇₉	—	2	1	no	—
208	C₂×C₄×C₇₉	—	2	1	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	1	no	—
211	C₂×C₄×C₇₉	—	2	1	no	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	1	no	—
215	C₂×C₄×C₇₉	—	2	1	no	—
216	C₂×C₄×C₇₉	—	2	1	no	—
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	no	—
224	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
228	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
229	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
230	C₂×Dic₇₉	—	2	1	no	—
231	C₂×Dic₇₉	—	2	1	no	—
232	C₂×Dic₇₉	—	2	1	no	—
233	C₂×Dic₇₉	—	2	1	no	—
234	C₂×Dic₇₉	—	2	1	no	—
235	C₂×Dic₇₉	—	2	1	no	—
236	C₂×Dic₇₉	—	2	1	no	—
237	C₂×Dic₇₉	—	2	1	no	—
238	C₂×Dic₇₉	—	2	1	no	—
239	C₂×Dic₇₉	—	2	1	no	—
240	C₂×Dic₇₉	—	2	1	no	—
241	C₂×Dic₇₉	—	2	1	no	—
242	C₂×Dic₇₉	—	2	1	no	—
243	C₂×Dic₇₉	—	2	1	no	—
244	C₂×Dic₇₉	—	2	1	no	—
245	C₂×Dic₇₉	—	2	1	no	—
246	C₂×Dic₇₉	—	2	1	no	—
247	C₂×Dic₇₉	—	2	1	no	—
248	C₂×Dic₇₉	—	2	1	no	—
249	C₂×Dic₇₉	—	2	1	no	—
250	C₂×Dic₇₉	—	2	1	no	—
251	C₂×Dic₇₉	—	2	1	no	—
252	C₂×Dic₇₉	—	2	1	no	—
253	C₂×Dic₇₉	#131	1	2	yes	—
254	Dic₁₅₈	—	4	4	no	—
255	C₈×C₇₉	—	4	1	no	—
256	C₈×C₇₉	—	4	1	no	—
257	C₈×C₇₉	—	4	1	no	—
258	C₈×C₇₉	—	4	1	no	—
259	C₇₉⋊C₈	—	4	1	no	—
260	C₇₉⋊C₈	—	4	1	no	—
261	C₇₉⋊C₈	—	4	1	no	—
262	C₇₉⋊C₈	—	4	1	no	—
263	C₂²×C₇₉	—	4	1	no	—
264	C₂²×C₇₉	—	4	1	no	—
265	C₂²×C₇₉	—	4	1	no	—
266	C₂²×C₇₉	—	4	1	no	—
267	C₂²×C₇₉	—	4	1	no	—
268	C₂²×C₇₉	—	4	1	no	—
269	C₂²×C₇₉	—	4	1	no	—
270	C₂²×C₇₉	#518	1	1	yes	characteristic
271	C₂²×C₇₉	#519	1	1	yes	characteristic
272	C₂²×C₇₉	#520	1	1	yes	characteristic
273	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
274	C₂²×C₇₉	#568	1	1	yes	characteristic
275	C₂²×C₇₉	#568	1	1	yes	characteristic
276	C₂²×C₇₉	#568	1	1	yes	characteristic
277	C₄×C₇₉	—	4	1	no	—
278	C₄×C₇₉	—	4	1	no	—
279	C₄×C₇₉	—	4	1	no	—
280	C₄×C₇₉	—	4	1	no	—
281	C₄×C₇₉	—	4	1	no	—
282	C₄×C₇₉	#562	1	1	yes	characteristic
283	C₄×C₇₉	#562	1	1	yes	characteristic
284	C₄×C₇₉	#563	1	1	yes	characteristic
285	C₄×C₇₉	#563	1	1	yes	characteristic
286	Dic₇₉	—	2	2	no	—
287	Dic₇₉	—	4	1	no	—
288	Dic₇₉	—	4	1	no	—
289	Dic₇₉	—	4	1	no	—
290	Dic₇₉	—	4	1	no	—
291	Dic₇₉	—	4	1	no	—
292	Dic₇₉	—	4	1	no	—
293	Dic₇₉	—	4	1	no	—
294	#23345	—	79	1	no	maximal, Sylow
295	C₂×C₇₉	—	8	1	no	—
296	C₂×C₇₉	#2378	1	1	yes	characteristic
297	C₂×C₇₉	#2976	1	1	yes	characteristic
298	C₂×C₇₉	#2980	1	1	yes	characteristic
299	C₂×C₇₉	#2985	1	1	yes	characteristic
300	C₂×C₇₉	#2987	1	1	yes	characteristic
301	C₂×C₇₉	#2993	1	1	yes	characteristic
302	C₂×C₇₉	#2995	1	1	yes	characteristic
303	#2396	—	79	1	no	—
304	#1985	—	79	1	no	—
305	#1984	—	79	1	no	—
306	#1940	—	79	1	no	—
307	#1940	—	79	1	no	—
308	#1924	—	79	1	no	—
309	#1924	—	79	1	no	—
310	#1924	—	79	1	no	—
311	#1923	—	79	1	no	—
312	#1917	—	79	1	no	—
313	#1917	—	79	1	no	—
314	#1917	—	79	1	no	—
315	#1916	—	79	1	no	—
316	#1818	D₇₉	1	1	yes	characteristic
317	#1798	—	79	1	no	—
318	C₇₉	#23345	1	1	yes	characteristic, complemented, Sylow
319	C₂×C₄×Q₈	—	79	1	no	—
320	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
321	C₂×C₄⋊C₈	—	79	1	no	—
322	C₂×C₄⋊C₈	—	79	1	no	—
323	C₂×C₄⋊C₈	—	79	1	no	—
324	C₂×C₄⋊C₈	—	79	1	no	—
325	C₂×C₄⋊C₈	—	79	1	no	—
326	C₂×C₄⋊C₈	—	79	1	no	—
327	C₂×C₂²⋊C₈	—	79	1	no	—
328	C₂×C₂²⋊C₈	—	79	1	no	—
329	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
331	C₂×#97	—	79	1	no	—
332	C₂×#97	—	79	1	no	—
333	C₂×#97	—	79	1	no	—
334	C₂×C₄×C₈	—	79	1	no	—
335	#400	—	79	1	no	—
336	#399	—	79	1	no	—
337	#398	—	79	1	no	—
338	#398	—	79	1	no	—
339	#396	—	79	1	no	—
340	#396	—	79	1	no	—
341	#395	—	79	1	no	—
342	#393	—	79	1	no	—
343	C₄×C₄⋊C₄	—	79	1	no	—
344	C₄×C₄⋊C₄	—	79	1	no	—
345	C₄×C₄⋊C₄	—	79	1	no	—
346	C₄×C₂²⋊C₄	—	79	1	no	—
347	C₄×C₂²⋊C₄	—	79	1	no	—
348	#336	—	79	1	no	—
349	#336	—	79	1	no	—
350	#336	—	79	1	no	—
351	#336	—	79	1	no	—
352	#336	—	79	1	no	—
353	#336	—	79	1	no	—
354	#336	—	79	1	no	—
355	#336	—	79	1	no	—
356	#336	—	79	1	no	—
357	#336	—	79	1	no	—
358	#336	C₂×D₇₉	1	1	yes	characteristic
359	#336	C₂×D₇₉	1	1	yes	characteristic
360	#336	C₂×D₇₉	1	1	yes	characteristic
361	#336	C₂×D₇₉	1	1	yes	characteristic
362	C₂²×Q₈	—	79	1	no	—
363	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
364	C₂²×C₈	—	79	1	no	—
365	C₂²×C₈	—	79	1	no	—
366	C₂²×C₈	—	79	1	no	—
367	C₂²×C₈	—	79	1	no	—
368	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
369	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
370	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
371	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
372	C₄×Q₈	—	316	1	no	—
373	C₄×Q₈	—	316	1	no	—
374	#117	—	4	1	no	—
375	#117	—	4	1	no	—
376	C₂×C₄⋊C₄	—	79	1	no	—
377	C₂×C₄⋊C₄	—	79	1	no	—
378	C₂×C₄⋊C₄	—	79	1	no	—
379	C₂×C₄⋊C₄	—	79	1	no	—
380	C₂×C₄⋊C₄	—	79	1	no	—
381	C₂×C₄⋊C₄	—	79	1	no	—
382	C₂×C₄⋊C₄	—	79	1	no	—
383	C₂×C₄⋊C₄	—	79	1	no	—
384	C₂×C₄⋊C₄	—	79	1	no	—
385	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	79	1	no	—
388	C₂×C₂²⋊C₄	—	79	1	no	—
389	C₂×C₂²⋊C₄	—	79	1	no	—
390	C₂×C₂²⋊C₄	—	79	1	no	—
391	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
393	C₂×C₄²	—	79	1	no	—
394	C₂×C₄²	—	79	1	no	—
395	C₂×C₄²	—	79	1	no	—
396	C₂×C₄²	—	79	1	no	—
397	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
398	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
399	C₄⋊C₈	—	316	1	no	—
400	C₄⋊C₈	—	316	1	no	—
401	C₄⋊C₈	—	316	1	no	—
402	C₄⋊C₈	—	316	1	no	—
403	C₄⋊C₈	—	316	1	no	—
404	C₄⋊C₈	—	316	1	no	—
405	C₂²⋊C₈	—	4	1	no	—
406	C₂²⋊C₈	—	4	1	no	—
407	C₂²⋊C₈	—	316	1	no	—
408	C₂²⋊C₈	—	316	1	no	—
409	#97	—	316	1	no	—
410	#97	—	316	1	no	—
411	#97	—	316	1	no	—
412	C₄×C₈	—	316	1	no	—
413	#95	—	79	1	no	—
414	#95	—	79	1	no	—
415	#95	—	79	1	no	—
416	#95	—	79	1	no	—
417	#95	—	79	1	no	—
418	#95	—	79	1	no	—
419	#95	—	79	1	no	—
420	#95	—	79	1	no	—
421	#95	—	79	1	no	—
422	#95	—	79	1	no	—
423	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
424	C₂×Q₈	—	316	1	no	—
425	C₂×Q₈	—	316	1	no	—
426	C₂×Q₈	—	158	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	79	1	no	—
434	C₂²×C₄	—	79	1	no	—
435	C₂²×C₄	—	79	1	no	—
436	C₂²×C₄	—	79	1	no	—
437	C₂²×C₄	—	79	1	no	—
438	C₂²×C₄	—	79	1	no	—
439	C₂²×C₄	—	79	1	no	—
440	C₂²×C₄	—	79	1	no	—
441	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	158	1	no	—
460	C₂×C₈	—	158	1	no	—
461	C₂×C₈	—	158	1	no	—
462	C₂×C₈	—	158	1	no	—
463	C₂×C₈	—	158	1	no	—
464	C₂×C₈	—	158	1	no	—
465	C₂×C₈	—	158	1	no	—
466	C₂×C₈	—	158	1	no	—
467	C₂×C₈	—	158	1	no	—
468	C₂×C₈	—	158	1	no	—
469	C₂×C₈	—	158	1	no	—
470	C₂×C₈	—	158	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	316	1	no	—
474	C₄⋊C₄	—	316	1	no	—
475	C₄⋊C₄	—	316	1	no	—
476	C₄⋊C₄	—	316	1	no	—
477	C₄⋊C₄	—	316	1	no	—
478	C₄⋊C₄	—	316	1	no	—
479	C₄⋊C₄	—	316	1	no	—
480	C₄⋊C₄	—	316	1	no	—
481	C₄⋊C₄	—	158	2	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	316	1	no	—
485	C₂²⋊C₄	—	316	1	no	—
486	C₂²⋊C₄	—	316	1	no	—
487	C₂²⋊C₄	—	158	2	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	158	1	no	—
493	C₄²	—	158	1	no	—
494	C₄²	—	158	1	no	—
495	C₄²	—	158	1	no	—
496	C₄²	—	158	1	no	—
497	C₄²	—	158	1	no	—
498	C₄²	—	158	1	no	—
499	C₄²	—	158	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
508	Q₈	—	316	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	79	2	no	—
529	C₂×C₄	—	158	1	no	—
530	C₂×C₄	—	158	1	no	—
531	C₂×C₄	—	158	1	no	—
532	C₂×C₄	—	158	1	no	—
533	C₂×C₄	—	158	1	no	—
534	C₂×C₄	—	158	1	no	—
535	C₂×C₄	—	158	1	no	—
536	C₂×C₄	—	158	1	no	—
537	C₂×C₄	—	158	1	no	—
538	C₂×C₄	—	158	1	no	—
539	C₂×C₄	—	158	1	no	—
540	C₂×C₄	—	158	1	no	—
541	C₂×C₄	—	158	1	no	—
542	C₂×C₄	—	158	1	no	—
543	C₂×C₄	—	158	1	no	—
544	C₂×C₄	—	158	1	no	—
545	C₂×C₄	—	158	1	no	—
546	C₂×C₄	—	158	1	no	—
547	C₂×C₄	—	158	1	no	—
548	C₂×C₄	—	158	1	no	—
549	C₂×C₄	—	158	1	no	—
550	C₂×C₄	—	158	1	no	—
551	C₂×C₄	—	158	1	no	—
552	C₂×C₄	#14579206	1	1	yes	characteristic
553	C₂×C₄	#14579206	1	1	yes	characteristic
554	C₂×C₄	#14579207	1	1	yes	characteristic
555	C₂×C₄	#14579208	1	1	yes	characteristic
556	C₂×C₄	#14579208	1	1	yes	characteristic
557	C₂×C₄	#14579208	1	1	yes	characteristic
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	316	1	no	—
563	C₈	—	316	1	no	—
564	C₈	—	316	1	no	—
565	C₈	—	316	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	#19099036	1	1	yes	characteristic
574	C₂²	#19099040	1	1	yes	characteristic
575	C₂²	#19099043	1	1	yes	characteristic
576	C₂²	#131×D₇₉	1	1	yes	characteristic
577	C₂²	#19099328	1	1	yes	characteristic
578	C₂²	#19099328	1	1	yes	characteristic
579	C₂²	#19099328	1	1	yes	characteristic
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	316	1	no	—
586	C₄	—	316	1	no	—
587	C₄	—	316	1	no	—
588	C₄	—	316	1	no	—
589	C₄	—	316	1	no	—
590	C₄	—	316	1	no	—
591	C₄	—	316	1	no	—
592	C₄	—	158	2	no	—
593	C₄	#19099310	1	1	yes	characteristic
594	C₄	#19099310	1	1	yes	characteristic
595	C₄	#19099316	1	1	yes	characteristic
596	C₄	#19099316	1	1	yes	characteristic
597	C₂	—	8	1	no	—
598	C₂	#23766568	1	1	yes	characteristic
599	C₂	#23772443	1	1	yes	characteristic
600	C₂	#23772469	1	1	yes	characteristic
601	C₂	#23772492	1	1	yes	characteristic
602	C₂	#23772504	1	1	yes	characteristic
603	C₂	#23772543	1	1	yes	characteristic
604	C₂	#23772565	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1818	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1818	D₇₉
hypocenter	C₇₉	#23345
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1818

Complements

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

N	H ≅ G/N	type
2. #23764338	C₂	semidirect
3. #23764334	C₂	semidirect
4. #23764122	C₂	semidirect
5. #23764122	C₂	semidirect
10. #23763967	C₂	semidirect
11. #23763965	C₂	semidirect
12. #23763965	C₂	semidirect
13. #23763960	C₂	semidirect
318. C₇₉	#23345	semidirect

Maximal subgroups

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

subgroup	index
#23766668	2
#23764338	2
#23764334	2
#23764122	2
#23764016	2
#23764010	2
#23764003	2
#23763967	2
#23763965	2
#23763960	2
#23763384	2
C₇₉×#1818	2
#23345	79