Subgroups — #34294357

Order 20224.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098641	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098635	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764199	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764124	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764008	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764008	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763275	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#121×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂²×#11929608	C₂²	1	1	yes	characteristic
18	C₂²×#11929608	C₂²	1	1	yes	characteristic
19	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#19098641	—	2	4	no	—
21	#19098635	—	2	4	no	—
22	#19098635	—	2	4	no	—
23	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	C₄×#11929608	—	2	4	no	—
36	C₂×#14579072	C₂²	1	1	yes	characteristic
37	C₂×#14579072	C₂²	1	1	yes	characteristic
38	C₂×#14579072	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098318	C₂²	1	1	yes	characteristic
45	#19098318	C₂²	1	1	yes	characteristic
46	#19098318	C₂²	1	1	yes	characteristic
47	#19098318	C₂²	1	1	yes	characteristic
48	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
49	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
53	#390×C₇₉	C₄	1	1	yes	characteristic
54	#389×C₇₉	C₄	1	1	yes	characteristic
55	#388×C₇₉	C₄	1	1	yes	characteristic
56	#388×C₇₉	C₄	1	1	yes	characteristic
57	#386×C₇₉	C₄	1	1	yes	characteristic
58	#386×C₇₉	C₄	1	1	yes	characteristic
59	#380×C₇₉	C₄	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
63	C₂×#11929608	—	2	2	no	—
64	C₂×#11929608	—	2	2	no	—
65	C₂×#11929608	—	2	2	no	—
66	C₂×#11929608	—	2	2	no	—
67	C₂×#11929608	—	2	2	no	—
68	C₂×#11929608	—	2	2	no	—
69	C₂×#11929608	—	2	2	no	—
70	C₂×#11929608	—	2	2	no	—
71	C₂×#11929608	D₄	1	4	yes	complemented
72	C₂²×C₇₉⋊C₈	—	2	2	no	—
73	C₂²×C₇₉⋊C₈	—	2	2	no	—
74	C₂²×C₇₉⋊C₈	—	2	2	no	—
75	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
84	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
85	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
86	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
89	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
92	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
94	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
95	#14579072	—	2	2	no	—
96	#14579072	—	2	2	no	—
97	#14579072	D₄	1	4	yes	complemented
98	C₄×C₇₉⋊C₈	—	2	2	no	—
99	C₄×C₇₉⋊C₈	—	2	2	no	—
100	C₄×C₇₉⋊C₈	—	2	2	no	—
101	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
109	#121×C₇₉	—	2	4	no	—
110	C₄×D₄×C₇₉	—	2	2	no	—
111	C₄×D₄×C₇₉	—	2	2	no	—
112	C₄×D₄×C₇₉	—	2	2	no	—
113	C₄×D₄×C₇₉	—	2	2	no	—
114	C₄×D₄×C₇₉	—	2	2	no	—
115	C₄×D₄×C₇₉	—	2	2	no	—
116	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₇₉	—	2	2	no	—
132	C₂×C₄²×C₇₉	—	2	2	no	—
133	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
139	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
140	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
141	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
142	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
143	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
144	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
145	#11929608	—	2	8	no	—
146	#11929608	—	2	8	no	—
147	#11929608	—	4	4	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	1	no	—
151	C₂×C₇₉⋊C₈	—	2	1	no	—
152	C₂×C₇₉⋊C₈	—	2	1	no	—
153	C₂×C₇₉⋊C₈	—	2	1	no	—
154	C₂×C₇₉⋊C₈	—	2	1	no	—
155	C₂×C₇₉⋊C₈	—	2	1	no	—
156	C₂×C₇₉⋊C₈	—	2	1	no	—
157	C₂×C₇₉⋊C₈	—	2	1	no	—
158	C₂×C₇₉⋊C₈	—	2	1	no	—
159	C₂×C₇₉⋊C₈	—	2	1	no	—
160	C₂×C₇₉⋊C₈	—	2	1	no	—
161	C₂×C₇₉⋊C₈	—	2	1	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	1	no	—
164	C₂×C₇₉⋊C₈	—	2	1	no	—
165	C₂×C₇₉⋊C₈	—	2	1	no	—
166	C₂×C₇₉⋊C₈	—	4	4	no	—
167	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
168	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
171	C₂×C₇₉⋊C₈	#41	1	2	yes	—
172	C₂×C₇₉⋊C₈	#41	1	2	yes	—
173	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×D₄×C₇₉	—	2	2	no	—
177	C₂×D₄×C₇₉	—	2	2	no	—
178	C₂×D₄×C₇₉	—	2	2	no	—
179	C₂×D₄×C₇₉	—	2	2	no	—
180	C₂×D₄×C₇₉	—	2	2	no	—
181	C₂×D₄×C₇₉	—	2	2	no	—
182	C₂×D₄×C₇₉	—	4	1	no	—
183	C₂×D₄×C₇₉	—	4	1	no	—
184	C₂×D₄×C₇₉	—	4	1	no	—
185	C₂²×C₄×C₇₉	—	2	1	no	—
186	C₂²×C₄×C₇₉	—	2	1	no	—
187	C₂²×C₄×C₇₉	—	2	1	no	—
188	C₂²×C₄×C₇₉	—	2	1	no	—
189	C₂²×C₄×C₇₉	—	2	2	no	—
190	C₂²×C₄×C₇₉	—	2	2	no	—
191	C₂²×C₄×C₇₉	—	2	2	no	—
192	C₂²×C₄×C₇₉	—	2	2	no	—
193	C₂²×C₄×C₇₉	—	2	1	no	—
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	1	no	—
198	C₂²×C₄×C₇₉	—	2	1	no	—
199	C₂²×C₄×C₇₉	—	2	1	no	—
200	C₂²×C₄×C₇₉	—	2	1	no	—
201	C₂²×C₄×C₇₉	—	2	1	no	—
202	C₂²×C₄×C₇₉	—	2	1	no	—
203	C₂²×C₄×C₇₉	—	2	1	no	—
204	C₂²×C₄×C₇₉	—	2	1	no	—
205	C₂²×C₄×C₇₉	—	4	1	no	—
206	C₂²×C₄×C₇₉	—	4	1	no	—
207	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₇₉	#41	1	2	yes	—
220	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₇₉	—	2	2	no	—
222	C₄⋊C₄×C₇₉	—	2	2	no	—
223	C₄⋊C₄×C₇₉	—	2	2	no	—
224	C₄⋊C₄×C₇₉	—	2	2	no	—
225	C₄⋊C₄×C₇₉	—	4	1	no	—
226	C₂²⋊C₄×C₇₉	—	2	2	no	—
227	C₂²⋊C₄×C₇₉	—	2	2	no	—
228	C₂²⋊C₄×C₇₉	—	2	2	no	—
229	C₂²⋊C₄×C₇₉	—	2	2	no	—
230	C₂²⋊C₄×C₇₉	—	2	2	no	—
231	C₂²⋊C₄×C₇₉	—	2	2	no	—
232	C₂²⋊C₄×C₇₉	—	2	2	no	—
233	C₂²⋊C₄×C₇₉	—	2	2	no	—
234	C₂²⋊C₄×C₇₉	—	2	2	no	—
235	C₂²⋊C₄×C₇₉	M₁₆	1	4	yes	complemented
236	C₄²×C₇₉	—	2	2	no	—
237	C₄²×C₇₉	—	2	2	no	—
238	C₄²×C₇₉	—	2	1	no	—
239	C₄²×C₇₉	—	2	1	no	—
240	C₄²×C₇₉	—	2	1	no	—
241	C₄²×C₇₉	—	2	1	no	—
242	C₄²×C₇₉	—	2	1	no	—
243	C₄²×C₇₉	—	2	1	no	—
244	C₄²×C₇₉	C₂×D₄	1	2	yes	—
245	C₄²×C₇₉	#41	1	2	yes	—
246	C₂³×C₇₉	—	2	1	no	—
247	C₂³×C₇₉	—	2	1	no	—
248	C₂³×C₇₉	—	2	1	no	—
249	C₂³×C₇₉	—	2	1	no	—
250	C₂³×C₇₉	—	2	1	no	—
251	C₂³×C₇₉	—	2	1	no	—
252	C₂³×C₇₉	—	2	1	no	—
253	C₂³×C₇₉	—	2	1	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	2	1	no	—
256	C₂³×C₇₉	—	2	1	no	—
257	C₂³×C₇₉	—	2	1	no	—
258	C₂³×C₇₉	—	2	1	no	—
259	C₂³×C₇₉	—	2	1	no	—
260	C₂³×C₇₉	—	2	1	no	—
261	C₂³×C₇₉	—	2	1	no	—
262	C₂³×C₇₉	—	2	1	no	—
263	C₂³×C₇₉	—	2	1	no	—
264	C₂³×C₇₉	—	2	1	no	—
265	C₂³×C₇₉	C₄×D₄	1	2	yes	—
266	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
267	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
268	D₄×C₇₉	—	4	4	no	—
269	D₄×C₇₉	—	4	4	no	—
270	D₄×C₇₉	—	4	4	no	—
271	C₂×C₄×C₇₉	—	2	1	no	—
272	C₂×C₄×C₇₉	—	2	1	no	—
273	C₂×C₄×C₇₉	—	2	1	no	—
274	C₂×C₄×C₇₉	—	2	1	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	2	1	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	2	1	no	—
280	C₂×C₄×C₇₉	—	2	1	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	2	no	—
284	C₂×C₄×C₇₉	—	2	2	no	—
285	C₂×C₄×C₇₉	—	2	2	no	—
286	C₂×C₄×C₇₉	—	2	2	no	—
287	C₂×C₄×C₇₉	—	2	1	no	—
288	C₂×C₄×C₇₉	—	2	1	no	—
289	C₂×C₄×C₇₉	—	2	1	no	—
290	C₂×C₄×C₇₉	—	2	1	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	1	no	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	1	no	—
296	C₂×C₄×C₇₉	—	2	1	no	—
297	C₂×C₄×C₇₉	—	2	1	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	1	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	4	4	no	—
303	C₂×C₄×C₇₉	—	4	4	no	—
304	C₂×C₄×C₇₉	—	4	1	no	—
305	C₂×C₄×C₇₉	—	4	1	no	—
306	C₂×C₄×C₇₉	—	4	1	no	—
307	C₂×C₄×C₇₉	—	4	1	no	—
308	C₂×C₄×C₇₉	—	4	1	no	—
309	C₂×C₄×C₇₉	—	4	1	no	—
310	C₂×C₄×C₇₉	—	4	1	no	—
311	C₂×C₄×C₇₉	—	4	1	no	—
312	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
313	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
314	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
316	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
317	C₂×C₄×C₇₉	#131	1	2	yes	—
318	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
324	C₇₉⋊C₈	—	2	2	no	—
325	C₇₉⋊C₈	—	2	2	no	—
326	C₇₉⋊C₈	—	2	2	no	—
327	C₇₉⋊C₈	—	4	1	no	—
328	C₇₉⋊C₈	—	4	1	no	—
329	C₇₉⋊C₈	—	4	1	no	—
330	C₇₉⋊C₈	—	4	1	no	—
331	C₇₉⋊C₈	#121	1	4	yes	complemented
332	C₂²×C₇₉	—	2	2	no	—
333	C₂²×C₇₉	—	2	2	no	—
334	C₂²×C₇₉	—	2	2	no	—
335	C₂²×C₇₉	—	2	2	no	—
336	C₂²×C₇₉	—	2	2	no	—
337	C₂²×C₇₉	—	2	2	no	—
338	C₂²×C₇₉	—	4	1	no	—
339	C₂²×C₇₉	—	4	1	no	—
340	C₂²×C₇₉	—	4	1	no	—
341	C₂²×C₇₉	—	4	1	no	—
342	C₂²×C₇₉	—	4	1	no	—
343	C₂²×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	4	1	no	—
345	C₂²×C₇₉	—	4	1	no	—
346	C₂²×C₇₉	—	4	1	no	—
347	C₂²×C₇₉	—	4	1	no	—
348	C₂²×C₇₉	—	4	1	no	—
349	C₂²×C₇₉	—	4	1	no	—
350	C₂²×C₇₉	—	4	1	no	—
351	C₂²×C₇₉	—	4	1	no	—
352	C₂²×C₇₉	—	4	1	no	—
353	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
354	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
356	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
357	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
358	C₂²×C₇₉	#568	1	1	yes	characteristic
359	C₂²×C₇₉	#568	1	1	yes	characteristic
360	C₄×C₇₉	—	2	2	no	—
361	C₄×C₇₉	—	2	2	no	—
362	C₄×C₇₉	—	2	2	no	—
363	C₄×C₇₉	—	2	2	no	—
364	C₄×C₇₉	—	2	2	no	—
365	C₄×C₇₉	—	2	2	no	—
366	C₄×C₇₉	—	4	1	no	—
367	C₄×C₇₉	—	4	1	no	—
368	C₄×C₇₉	—	4	1	no	—
369	C₄×C₇₉	—	4	1	no	—
370	C₄×C₇₉	—	4	1	no	—
371	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
372	C₄×C₇₉	#525	1	1	yes	characteristic
373	C₄×C₇₉	#529	1	1	yes	characteristic
374	C₄×C₇₉	#532	1	1	yes	characteristic
375	#21490	—	79	1	no	maximal, Sylow
376	C₂×C₇₉	—	4	2	no	—
377	C₂×C₇₉	—	4	2	no	—
378	C₂×C₇₉	—	8	1	no	—
379	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
380	C₂×C₇₉	#2933	1	1	yes	characteristic
381	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
382	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
383	C₂×C₇₉	#2935	1	1	yes	characteristic
384	C₂×C₇₉	#2965	1	1	yes	characteristic
385	C₂×C₇₉	#2967	1	1	yes	characteristic
386	C₂×#436	—	79	1	no	—
387	C₂×#435	—	79	1	no	—
388	C₂×#435	—	79	1	no	—
389	C₂×C₄×M₁₆	—	79	1	no	—
390	C₄×#121	D₇₉	1	1	yes	characteristic
391	#1955	—	79	1	no	—
392	#1940	—	79	1	no	—
393	#1923	—	79	1	no	—
394	#1923	—	79	1	no	—
395	#1870	—	79	1	no	—
396	#1870	—	79	1	no	—
397	#1797	—	79	1	no	—
398	#1771	—	79	1	no	—
399	#1753	—	79	1	no	—
400	C₈×C₂²⋊C₄	—	79	1	no	—
401	C₇₉	#21490	1	1	yes	characteristic, complemented, Sylow
402	C₂²×M₁₆	—	79	1	no	—
403	C₂²×M₁₆	—	79	1	no	—
404	C₂²×M₁₆	—	79	1	no	—
405	C₂³×C₈	—	79	1	no	—
406	C₂×#121	Dic₇₉	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
410	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
411	#436	—	158	4	no	—
412	#435	—	158	4	no	—
413	#435	—	158	4	no	—
414	C₂×C₄⋊C₈	—	79	1	no	—
415	C₂×C₄⋊C₈	—	79	1	no	—
416	C₂×C₄⋊C₈	—	79	1	no	—
417	C₂×C₄⋊C₈	—	79	1	no	—
418	C₂×C₂²⋊C₈	—	79	1	no	—
419	C₂×C₂²⋊C₈	—	79	1	no	—
420	C₂×C₂²⋊C₈	—	79	1	no	—
421	C₂×C₂²⋊C₈	—	79	1	no	—
422	C₂×C₂²⋊C₈	—	79	1	no	—
423	C₂×C₂²⋊C₈	—	79	1	no	—
424	C₂×C₂²⋊C₈	—	79	1	no	—
425	C₂×C₂²⋊C₈	—	79	1	no	—
426	C₄×M₁₆	—	158	4	no	—
427	C₂×#97	—	79	1	no	—
428	C₂×#97	—	79	1	no	—
429	C₂×#97	—	79	1	no	—
430	C₂×C₄×C₈	—	79	1	no	—
431	C₂×C₄×C₈	—	79	1	no	—
432	C₂×C₄×C₈	—	79	1	no	—
433	#390	Dic₇₉	1	1	yes	characteristic
434	#389	Dic₇₉	1	1	yes	characteristic
435	#388	Dic₇₉	1	1	yes	characteristic
436	#388	Dic₇₉	1	1	yes	characteristic
437	#386	Dic₇₉	1	1	yes	characteristic
438	#386	Dic₇₉	1	1	yes	characteristic
439	#380	Dic₇₉	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
443	#336	—	79	1	no	—
444	#336	—	79	1	no	—
445	#336	—	79	1	no	—
446	#336	—	79	1	no	—
447	#336	—	79	1	no	—
448	#336	—	79	1	no	—
449	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
450	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
451	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
452	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
453	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
454	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
455	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
456	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
457	C₂×M₁₆	—	79	4	no	—
458	C₂×M₁₆	—	158	2	no	—
459	C₂×M₁₆	—	158	2	no	—
460	C₂×M₁₆	—	158	2	no	—
461	C₂×M₁₆	—	158	2	no	—
462	C₂×M₁₆	—	158	2	no	—
463	C₂×M₁₆	—	158	2	no	—
464	C₂×M₁₆	—	158	2	no	—
465	C₂×M₁₆	—	158	2	no	—
466	C₂²×C₈	—	79	1	no	—
467	C₂²×C₈	—	79	1	no	—
468	C₂²×C₈	—	79	1	no	—
469	C₂²×C₈	—	79	1	no	—
470	C₂²×C₈	—	79	1	no	—
471	C₂²×C₈	—	79	1	no	—
472	C₂²×C₈	—	79	1	no	—
473	C₂²×C₈	—	79	1	no	—
474	C₂²×C₈	—	158	2	no	—
475	C₂²×C₈	—	158	2	no	—
476	C₂²×C₈	—	158	2	no	—
477	#121	—	2	4	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
499	C₂×C₄²	—	2	2	no	—
500	C₂×C₄²	—	2	2	no	—
501	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
502	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
503	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
504	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
505	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
506	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
507	C₄⋊C₈	—	158	2	no	—
508	C₄⋊C₈	—	158	2	no	—
509	C₄⋊C₈	—	158	2	no	—
510	C₄⋊C₈	—	158	2	no	—
511	C₂²⋊C₈	—	158	2	no	—
512	C₂²⋊C₈	—	158	2	no	—
513	C₂²⋊C₈	—	158	2	no	—
514	C₂²⋊C₈	—	158	2	no	—
515	C₂²⋊C₈	—	158	2	no	—
516	C₂²⋊C₈	—	158	2	no	—
517	C₂²⋊C₈	—	158	2	no	—
518	C₂²⋊C₈	—	158	2	no	—
519	#97	—	79	4	no	—
520	#97	—	158	2	no	—
521	#97	—	158	2	no	—
522	C₄×C₈	—	158	2	no	—
523	C₄×C₈	—	158	2	no	—
524	C₄×C₈	—	158	2	no	—
525	#95	C₂×Dic₇₉	1	1	yes	characteristic
526	#95	C₂×Dic₇₉	1	1	yes	characteristic
527	#95	C₂×Dic₇₉	1	1	yes	characteristic
528	#95	C₂×Dic₇₉	1	1	yes	characteristic
529	#95	C₂×Dic₇₉	1	1	yes	characteristic
530	#95	C₂×Dic₇₉	1	1	yes	characteristic
531	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
532	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
533	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	1	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
566	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
569	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
570	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
571	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
572	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
573	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
574	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
575	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
576	C₂²×C₄	D₄×D₇₉	1	2	yes	—
577	C₂²×C₄	#11929623	1	2	yes	—
578	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
579	M₁₆	—	316	4	no	—
580	M₁₆	—	158	8	no	—
581	M₁₆	—	158	8	no	—
582	C₂×C₈	—	316	4	no	—
583	C₂×C₈	—	79	2	no	—
584	C₂×C₈	—	79	2	no	—
585	C₂×C₈	—	79	2	no	—
586	C₂×C₈	—	79	2	no	—
587	C₂×C₈	—	79	2	no	—
588	C₂×C₈	—	79	2	no	—
589	C₂×C₈	—	158	1	no	—
590	C₂×C₈	—	158	1	no	—
591	C₂×C₈	—	158	1	no	—
592	C₂×C₈	—	158	1	no	—
593	C₂×C₈	—	158	1	no	—
594	C₂×C₈	—	158	1	no	—
595	C₂×C₈	—	158	1	no	—
596	C₂×C₈	—	158	1	no	—
597	C₂×C₈	—	158	1	no	—
598	C₂×C₈	—	158	1	no	—
599	C₂×C₈	—	158	1	no	—
600	C₂×C₈	—	158	1	no	—
601	C₂×C₈	—	158	1	no	—
602	C₂×C₈	—	158	1	no	—
603	C₂×C₈	—	158	1	no	—
604	C₂×C₈	—	158	1	no	—
605	C₂×C₈	—	158	1	no	—
606	C₂×C₈	—	158	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	#11929608	1	4	yes	complemented
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	D₄×D₇₉	1	2	yes	—
631	C₄²	#11929623	1	2	yes	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	D₄×Dic₇₉	1	2	yes	—
652	C₂³	C₂×#11929608	1	2	yes	—
653	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
654	D₄	—	4	4	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
699	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
700	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
701	C₂×C₄	C₂×#11929608	1	2	yes	—
702	C₂×C₄	C₂×#11929608	1	2	yes	—
703	C₂×C₄	#14579168	1	2	yes	—
704	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
705	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
706	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
707	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
708	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
709	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
710	C₈	—	316	1	no	—
711	C₈	—	316	1	no	—
712	C₈	—	316	1	no	—
713	C₈	—	316	1	no	—
714	C₈	—	79	4	no	—
715	C₈	—	158	2	no	—
716	C₈	—	158	2	no	—
717	C₈	—	158	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
740	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
741	C₂²	#41×Dic₇₉	1	1	yes	characteristic
742	C₂²	C₂²×#11929608	1	1	yes	characteristic
743	C₂²	C₂×#14579168	1	1	yes	characteristic
744	C₂²	#19099330	1	1	yes	characteristic
745	C₂²	#19099330	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	#121×D₇₉	1	1	yes	characteristic
758	C₄	#19099073	1	1	yes	characteristic
759	C₄	#19099094	1	1	yes	characteristic
760	C₄	#19099108	1	1	yes	characteristic
761	C₂	—	4	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	1	no	—
764	C₂	#121×Dic₇₉	1	1	yes	characteristic
765	C₂	#23772127	1	1	yes	characteristic
766	C₂	D₄×#11929608	1	1	yes	characteristic
767	C₂	D₄×#11929608	1	1	yes	characteristic
768	C₂	#23772144	1	1	yes	characteristic
769	C₂	#23772367	1	1	yes	characteristic
770	C₂	#23772387	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₄×#121×C₇₉	C₂
prime radical	C₂×#121×C₇₉	C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#121	D₇₉
hypocenter	C₇₉	#21490
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#19098641	C₂	semidirect
2. C₂×#19098635	C₂	semidirect
3. C₂×#19098635	C₂	semidirect
4. C₂×C₄×#11929608	C₂	semidirect
5. #23764199	C₂	semidirect
6. #23764124	C₂	semidirect
7. #23764008	C₂	semidirect
8. #23764008	C₂	semidirect
9. #23763698	C₂	semidirect
10. #23763698	C₂	semidirect
11. #23763380	C₂	semidirect
12. #23763275	C₂	semidirect
13. #23763184	C₂	semidirect
14. C₂²⋊C₄×C₇₉⋊C₈	C₂	semidirect
71. C₂×#11929608	D₄	semidirect
97. #14579072	D₄	semidirect
235. C₂²⋊C₄×C₇₉	M₁₆	semidirect
331. C₇₉⋊C₈	#121	semidirect
401. C₇₉	#21490	semidirect
621. C₂²⋊C₄	#11929608	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098641	2
C₂×#19098635	2
C₂×C₄×#11929608	2
#23764199	2
#23764124	2
#23764008	2
#23763698	2
#23763380	2
#23763275	2
#23763184	2
C₂²⋊C₄×C₇₉⋊C₈	2
C₄×#121×C₇₉	2
#21490	79