Subgroups — C₂×#23777758 #35196029

Order 20224.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777758	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099311	C₂	1	2	yes	maximal, complemented
3	C₂×#19099305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099279	C₂	1	2	yes	maximal, complemented
5	C₂×#19099241	C₂	1	2	yes	maximal, complemented
6	C₂×#19099238	C₂	1	4	yes	maximal, complemented
7	C₂×#19099204	C₂	1	4	yes	maximal, complemented
8	C₂×#19099183	C₂	1	4	yes	maximal, complemented
9	C₂×#19099152	C₂	1	4	yes	maximal, complemented
10	C₂×#19099138	C₂	1	2	yes	maximal, complemented
11	C₂×#19099124	C₂	1	2	yes	maximal, complemented
12	C₂×#19099098	C₂	1	2	yes	maximal, complemented
13	C₂×#124×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#563×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#11929625	C₂²	1	2	yes	—
16	C₂²×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
18	C₂²×D₄×D₇₉	C₂²	1	1	yes	characteristic
19	#19099311	C₂²	1	32	yes	complemented
20	#19099305	C₂²	1	16	yes	complemented
21	#19099279	C₂²	1	32	yes	complemented
22	#19099241	C₂²	1	32	yes	complemented
23	#19099238	C₂²	1	64	yes	complemented
24	#19099204	C₂²	1	64	yes	complemented
25	#19099183	C₂²	1	64	yes	complemented
26	#19099152	C₂²	1	64	yes	complemented
27	#19099138	C₂²	1	32	yes	complemented
28	#19099124	C₂²	1	32	yes	complemented
29	C₂×#14579159	C₂²	1	2	yes	complemented
30	#19099098	C₂²	1	32	yes	complemented
31	C₂×#14579156	C₂²	1	4	yes	complemented
32	C₂×#14579154	C₂²	1	4	yes	complemented
33	C₂×#14579150	C₂²	1	4	yes	complemented
34	C₂×#14579150	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14579150	C₂²	1	2	yes	complemented
36	C₂×#14579149	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14579149	C₂²	1	2	yes	complemented
38	C₂×#14579149	C₂²	1	2	yes	complemented
39	C₂×#14579148	C₂²	1	1	yes	characteristic
40	C₂×#14579147	C₂²	1	4	yes	complemented
41	C₂×#14579147	C₂²	1	4	yes	complemented
42	#124×D₇₉	C₂²	1	16	yes	complemented
43	C₂×#14579146	C₂²	1	4	yes	complemented
44	C₂×#14579146	C₂²	1	4	yes	complemented
45	C₂×#14579146	C₂²	1	4	yes	complemented
46	C₂×#14579146	C₂²	1	4	yes	complemented
47	C₂×#14579144	C₂²	1	2	yes	complemented
48	C₂×#14579143	C₂²	1	4	yes	complemented
49	C₂×#14579141	C₂²	1	2	yes	complemented
50	C₂×#14579139	C₂²	1	4	yes	complemented
51	C₂×#14579139	C₂²	1	4	yes	complemented
52	C₂×#14579139	C₂²	1	4	yes	complemented
53	C₂×#14579136	C₂²	1	2	yes	—
54	C₂×#14579136	C₂²	1	4	yes	complemented
55	C₂×#14579136	C₂²	1	4	yes	complemented
56	C₂×#14579136	C₂²	1	4	yes	complemented
57	C₂×#14579134	C₂²	1	4	yes	—
58	C₂×#14579131	C₂²	1	4	yes	—
59	C₂×#14579131	C₂²	1	4	yes	complemented
60	C₂×#14579131	C₂²	1	2	yes	complemented
61	C₂×#14579129	C₂²	1	2	yes	—
62	C₂×#14579126	C₂²	1	2	yes	complemented
63	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
64	C₂×#14579123	C₂²	1	4	yes	complemented
65	C₂×#14579123	C₂²	1	2	yes	complemented
66	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
67	C₂×#14579119	C₂²	1	4	yes	complemented
68	C₂×#14579119	C₂²	1	4	yes	complemented
69	C₂×#14579118	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
73	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
74	#563×C₇₉	C₂²	1	16	yes	complemented
75	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
76	C₂×#126×C₇₉	C₂²	1	4	yes	complemented
77	C₂×#125×C₇₉	C₂²	1	2	yes	complemented
78	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
79	C₂×#123×C₇₉	C₂²	1	2	yes	—
80	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	4	yes	complemented
81	C₂⁴×D₇₉	C₂³	1	2	yes	—
82	C₂⁴×D₇₉	C₂³	1	2	yes	—
83	C₂×#11929625	—	4	8	no	—
84	C₂×#11929625	C₂³	1	16	yes	—
85	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
86	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
88	C₂×Q₈×D₇₉	—	4	4	no	—
89	C₂×Q₈×D₇₉	C₂³	1	8	yes	complemented
90	C₂²×D₃₁₆	—	4	8	no	—
91	C₂²×D₃₁₆	C₂³	1	4	yes	—
92	C₂²×D₃₁₆	C₂³	1	2	yes	—
93	C₂²×D₃₁₆	C₂³	1	4	yes	—
94	C₂²×D₃₁₆	C₂³	1	2	yes	—
95	C₂²×D₃₁₆	C₂³	1	4	yes	—
96	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
97	C₂²×D₃₁₆	C₂³	1	16	yes	complemented
98	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
99	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
100	C₂×D₄×D₇₉	—	4	4	no	—
101	C₂×D₄×D₇₉	C₂³	1	8	yes	—
102	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
104	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
105	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
106	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
107	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
108	#14579159	C₂³	1	16	yes	complemented
109	#14579156	C₂³	1	32	yes	complemented
110	#14579154	C₂³	1	32	yes	complemented
111	#14579150	C₂³	1	16	yes	complemented
112	#14579150	C₂³	1	32	yes	complemented
113	#14579150	C₂³	1	8	yes	complemented
114	#14579149	C₂³	1	16	yes	complemented
115	#14579149	C₂³	1	16	yes	complemented
116	#14579149	C₂³	1	8	yes	complemented
117	#14579148	C₂³	1	8	yes	—
118	#14579147	C₂³	1	32	yes	complemented
119	#14579147	C₂³	1	32	yes	complemented
120	#14579146	C₂³	1	32	yes	complemented
121	#14579146	C₂³	1	32	yes	complemented
122	#14579146	C₂³	1	32	yes	complemented
123	#14579146	C₂³	1	32	yes	complemented
124	#14579144	C₂³	1	16	yes	complemented
125	#14579143	C₂³	1	32	yes	complemented
126	#14579141	C₂³	1	16	yes	complemented
127	#14579139	C₂³	1	32	yes	complemented
128	#14579139	C₂³	1	32	yes	complemented
129	#14579139	C₂³	1	32	yes	complemented
130	#14579136	C₂³	1	16	yes	—
131	#14579136	C₂³	1	32	yes	complemented
132	#14579136	C₂³	1	32	yes	complemented
133	#14579136	C₂³	1	32	yes	complemented
134	#14579134	C₂³	1	32	yes	—
135	#14579131	C₂³	1	32	yes	—
136	#14579131	C₂³	1	16	yes	complemented
137	#14579131	C₂³	1	32	yes	complemented
138	#14579129	C₂³	1	16	yes	—
139	#14579126	C₂³	1	16	yes	complemented
140	C₄×D₃₁₆	C₂³	1	32	yes	complemented
141	#14579123	C₂³	1	16	yes	complemented
142	#14579123	C₂³	1	32	yes	complemented
143	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
144	#14579119	C₂³	1	32	yes	complemented
145	#14579119	C₂³	1	32	yes	complemented
146	#14579118	C₂³	1	16	yes	complemented
147	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
148	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
149	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
150	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
151	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
153	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
154	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
155	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
156	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
157	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
159	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
160	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
161	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
162	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
163	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
164	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
165	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
166	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
168	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
169	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
170	C₄²×D₇₉	C₂³	1	8	yes	complemented
171	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
172	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₇₉	C₂³	1	16	yes	complemented
176	#126×C₇₉	C₂³	1	32	yes	complemented
177	#125×C₇₉	C₂³	1	16	yes	complemented
178	#124×C₇₉	C₂³	1	8	yes	—
179	#123×C₇₉	C₂³	1	16	yes	—
180	C₂²⋊Q₈×C₇₉	C₂³	1	32	yes	complemented
181	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
187	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
188	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
191	C₂³×D₇₉	—	2	8	no	—
192	C₂³×D₇₉	—	4	8	no	—
193	C₂³×D₇₉	—	4	8	no	—
194	C₂³×D₇₉	—	4	4	no	—
195	C₂³×D₇₉	C₂⁴	1	4	yes	—
196	C₂³×D₇₉	C₂⁴	1	2	yes	—
197	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
198	C₂³×D₇₉	C₂⁴	1	8	yes	—
199	C₂³×D₇₉	C₂⁴	1	8	yes	—
200	#11929625	—	4	32	no	—
201	C₂×Dic₁₅₈	—	4	2	no	—
202	C₂×Dic₁₅₈	—	4	4	no	—
203	C₂×Dic₁₅₈	—	4	4	no	—
204	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
205	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
206	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
207	Q₈×D₇₉	—	4	16	no	—
208	C₂×D₃₁₆	—	2	16	no	—
209	C₂×D₃₁₆	—	4	4	no	—
210	C₂×D₃₁₆	—	4	2	no	—
211	C₂×D₃₁₆	—	4	8	no	—
212	C₂×D₃₁₆	—	4	8	no	—
213	C₂×D₃₁₆	—	4	4	no	—
214	C₂×D₃₁₆	—	4	32	no	—
215	C₂×D₃₁₆	C₂⁴	1	16	yes	—
216	C₂×D₃₁₆	C₂⁴	1	8	yes	—
217	C₂×D₃₁₆	C₂⁴	1	8	yes	—
218	C₂×D₃₁₆	C₂⁴	1	16	yes	—
219	C₂×D₃₁₆	C₂⁴	1	16	yes	—
220	C₂×D₃₁₆	C₂⁴	1	4	yes	—
221	C₂×C₂²⋊D₇₉	—	4	4	no	—
222	C₂×C₂²⋊D₇₉	—	4	8	no	—
223	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
224	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
225	D₄×D₇₉	—	4	16	no	—
226	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
227	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
228	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
229	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
230	C₂×C₄×D₇₉	—	2	8	no	—
231	C₂×C₄×D₇₉	—	2	4	no	—
232	C₂×C₄×D₇₉	—	4	8	no	—
233	C₂×C₄×D₇₉	—	4	8	no	—
234	C₂×C₄×D₇₉	—	4	8	no	—
235	C₂×C₄×D₇₉	—	4	4	no	—
236	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
237	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
238	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
239	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
240	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
241	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
242	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
243	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
244	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
245	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
246	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
247	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
248	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
249	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
250	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
251	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
252	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
253	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
254	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
255	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
256	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
257	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
258	C₄×Dic₇₉	C₂⁴	1	4	yes	—
259	C₄×Dic₇₉	C₂⁴	1	8	yes	—
260	C₄×Dic₇₉	C₂⁴	1	8	yes	—
261	C₄×Dic₇₉	C₂⁴	1	16	yes	—
262	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
263	C₂×Q₈×C₇₉	—	4	2	no	—
264	C₂×Q₈×C₇₉	—	4	4	no	—
265	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
266	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
267	C₂×D₄×C₇₉	—	4	2	no	—
268	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₇₉	—	4	4	no	—
270	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
276	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
278	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
280	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
281	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
282	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
283	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
284	C₄²×C₇₉	C₂⁴	1	4	yes	—
285	C₄²×C₇₉	C₂⁴	1	8	yes	—
286	C₂³×C₇₉	—	2	4	no	—
287	C₂³×C₇₉	—	2	8	no	—
288	C₂³×C₇₉	C₂⁵	1	4	yes	—
289	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
290	C₂²×D₇₉	—	2	4	no	—
291	C₂²×D₇₉	—	2	8	no	—
292	C₂²×D₇₉	—	2	4	no	—
293	C₂²×D₇₉	—	2	8	no	—
294	C₂²×D₇₉	—	2	8	no	—
295	C₂²×D₇₉	—	2	8	no	—
296	C₂²×D₇₉	—	2	16	no	—
297	C₂²×D₇₉	—	4	8	no	—
298	C₂²×D₇₉	—	4	16	no	—
299	C₂²×D₇₉	—	4	16	no	—
300	C₂²×D₇₉	—	8	16	no	—
301	C₂²×D₇₉	—	8	16	no	—
302	C₂²×D₇₉	H(5,𝔽₂)	1	4	yes	—
303	C₂²×D₇₉	C₂⁵	1	4	yes	—
304	C₂²×D₇₉	C₂⁵	1	8	yes	—
305	C₂²×D₇₉	C₂⁵	1	2	yes	—
306	Q₈×C₇₉	—	4	4	no	—
307	Q₈×C₇₉	—	4	8	no	—
308	D₄×C₇₉	—	4	4	no	—
309	C₂×C₄×C₇₉	—	2	2	no	—
310	C₂×C₄×C₇₉	—	2	4	no	—
311	C₂×C₄×C₇₉	—	2	8	no	—
312	C₂×C₄×C₇₉	—	2	8	no	—
313	C₂×C₄×C₇₉	—	2	4	no	—
314	C₂×C₄×C₇₉	—	4	8	no	—
315	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
316	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
317	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
318	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
319	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
320	C₂²⋊D₇₉	—	4	8	no	—
321	C₂²⋊D₇₉	—	4	16	no	—
322	C₂×Dic₇₉	—	2	4	no	—
323	C₂×Dic₇₉	—	2	2	no	—
324	C₂×Dic₇₉	—	2	4	no	—
325	C₂×Dic₇₉	—	2	8	no	—
326	C₂×Dic₇₉	C₂⁵	1	4	yes	—
327	C₂×Dic₇₉	C₂⁵	1	8	yes	—
328	C₂×Dic₇₉	C₂⁵	1	2	yes	—
329	C₂×Dic₇₉	C₂⁵	1	4	yes	—
330	D₃₁₆	—	2	32	no	—
331	D₃₁₆	—	4	4	no	—
332	D₃₁₆	—	4	16	no	—
333	D₃₁₆	—	4	8	no	—
334	D₃₁₆	—	4	16	no	—
335	D₃₁₆	—	4	8	no	—
336	C₄×D₇₉	—	2	8	no	—
337	C₄×D₇₉	—	2	16	no	—
338	C₄×D₇₉	—	4	16	no	—
339	C₄×D₇₉	—	4	8	no	—
340	C₄×D₇₉	—	4	16	no	—
341	C₄×D₇₉	—	4	16	no	—
342	Dic₁₅₈	—	4	8	no	—
343	Dic₁₅₈	—	4	4	no	—
344	Dic₁₅₈	—	4	8	no	—
345	C₂²×C₇₉	—	2	4	no	—
346	C₂²×C₇₉	—	2	8	no	—
347	C₂²×C₇₉	—	4	8	no	—
348	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂²×C₇₉	#585	1	4	yes	—
350	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
351	C₂×D₇₉	—	2	4	no	—
352	C₂×D₇₉	—	2	8	no	—
353	C₂×D₇₉	—	2	4	no	—
354	C₂×D₇₉	—	2	8	no	—
355	C₂×D₇₉	—	2	8	no	—
356	C₂×D₇₉	—	2	8	no	—
357	C₂×D₇₉	—	2	8	no	—
358	C₂×D₇₉	—	4	16	no	—
359	C₂×D₇₉	—	4	8	no	—
360	C₂×D₇₉	—	8	16	no	—
361	C₂×D₇₉	—	8	16	no	—
362	C₂×D₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
363	C₄×C₇₉	—	2	8	no	—
364	C₄×C₇₉	—	2	2	no	—
365	C₄×C₇₉	—	2	4	no	—
366	C₄×C₇₉	—	2	4	no	—
367	C₄×C₇₉	—	2	8	no	—
368	Dic₇₉	—	2	2	no	—
369	Dic₇₉	—	2	4	no	—
370	Dic₇₉	—	2	8	no	—
371	Dic₇₉	—	2	4	no	—
372	C₂×#3545	—	79	1	no	maximal, Sylow
373	C₂×C₇₉	—	4	4	no	—
374	C₂×C₇₉	#3545	1	4	yes	complemented
375	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₇₉	C₂×#585	1	2	yes	—
377	D₇₉	—	2	4	no	—
378	D₇₉	—	4	4	no	—
379	D₇₉	—	4	8	no	—
380	#3545	—	79	32	no	—
381	C₂×#563	D₇₉	1	1	yes	characteristic, complemented
382	C₂×#562	—	79	2	no	—
383	C₂×H(3,𝔽₄)	—	79	1	no	—
384	C₂×#555	—	79	2	no	—
385	C₂×#551	—	79	4	no	—
386	C₂×#551	—	79	2	no	—
387	C₂×#546	—	79	4	no	—
388	C₂×#542	—	79	4	no	—
389	C₂×#538	—	79	4	no	—
390	C₂×#536	—	79	2	no	—
391	C₂×#534	—	79	2	no	—
392	C₂×#529	—	79	2	no	—
393	C₂²×#124	—	79	1	no	—
394	C₇₉	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
395	C₂²×#41	—	79	2	no	—
396	C₂³×Q₈	—	79	1	no	—
397	C₂³×D₄	—	79	1	no	—
398	C₂³×D₄	—	79	2	no	—
399	#563	C₂×D₇₉	1	16	yes	complemented
400	#562	—	79	32	no	—
401	H(3,𝔽₄)	—	79	16	no	—
402	#555	—	79	32	no	—
403	#551	—	79	64	no	—
404	#551	—	79	32	no	—
405	#546	—	79	64	no	—
406	#542	—	79	64	no	—
407	#538	—	79	64	no	—
408	#536	—	79	32	no	—
409	#534	—	79	32	no	—
410	C₂×C₄⋊Q₈	—	79	2	no	—
411	C₂×C₄⋊Q₈	C₂×D₇₉	1	2	yes	complemented
412	#529	—	79	32	no	—
413	C₂×#126	—	79	4	no	—
414	C₂×#126	—	79	4	no	—
415	C₂×#126	C₂×D₇₉	1	4	yes	complemented
416	C₂×#125	C₂×D₇₉	1	2	yes	complemented
417	C₂×#124	—	79	1	no	—
418	C₂×#124	—	79	2	no	—
419	C₂×#124	—	79	4	no	—
420	C₂×#124	—	79	1	no	—
421	C₂×#124	—	79	16	no	—
422	C₂×#124	—	79	4	no	—
423	C₂×#124	—	79	4	no	—
424	C₂×#124	—	79	1	no	—
425	C₂×#124	—	79	2	no	—
426	C₂×#124	—	79	2	no	—
427	C₂×#124	C₂×D₇₉	1	1	yes	characteristic
428	C₂×#123	—	79	2	no	—
429	C₂×#123	—	79	4	no	—
430	C₂×#123	—	79	4	no	—
431	C₂×#123	—	79	4	no	—
432	C₂×#123	—	79	4	no	—
433	C₂×#123	—	79	4	no	—
434	C₂×#123	C₂×D₇₉	1	2	yes	—
435	C₂×C₂²⋊Q₈	—	79	2	no	—
436	C₂×C₂²⋊Q₈	—	79	4	no	—
437	C₂×C₂²⋊Q₈	—	79	4	no	—
438	C₂×C₂²⋊Q₈	—	79	4	no	—
439	C₂×C₂²⋊Q₈	C₂×D₇₉	1	4	yes	complemented
440	C₂×#121	—	79	2	no	—
441	C₂×#121	—	79	4	no	—
442	C₂×#121	—	79	4	no	—
443	C₂×#121	—	79	4	no	—
444	C₂×#121	—	79	4	no	—
445	C₂×#120	—	79	2	no	—
446	C₂×#120	—	79	2	no	—
447	C₂×#120	—	79	4	no	—
448	C₂×#120	—	79	4	no	—
449	C₂×C₄×Q₈	—	79	2	no	—
450	C₂×C₄×D₄	—	79	4	no	—
451	C₂×C₄×D₄	—	79	2	no	—
452	C₂×C₄×D₄	—	79	4	no	—
453	C₂×C₄×D₄	—	79	4	no	—
454	C₂×#117	—	79	4	no	—
455	C₂×#117	—	79	4	no	—
456	C₂×#117	—	79	2	no	—
457	C₂²×C₂²⋊C₄	—	79	4	no	—
458	C₂²×C₂²⋊C₄	—	79	2	no	—
459	C₂²×C₂²⋊C₄	—	79	4	no	—
460	C₂²×C₄²	—	79	1	no	—
461	C₂⁵	—	79	2	no	—
462	C₂⁵	—	79	2	no	—
463	C₂×#41	—	316	8	no	—
464	C₂×#41	—	79	16	no	—
465	C₂²×Q₈	—	316	4	no	—
466	C₂²×Q₈	—	79	8	no	—
467	C₂²×Q₈	—	79	2	no	—
468	C₂²×Q₈	—	79	1	no	—
469	C₂²×Q₈	—	79	2	no	—
470	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
471	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
472	C₂²×D₄	—	316	8	no	—
473	C₂²×D₄	—	316	4	no	—
474	C₂²×D₄	—	79	4	no	—
475	C₂²×D₄	—	79	2	no	—
476	C₂²×D₄	—	79	8	no	—
477	C₂²×D₄	—	79	4	no	—
478	C₂²×D₄	—	79	2	no	—
479	C₂²×D₄	—	79	2	no	—
480	C₂²×D₄	—	79	4	no	—
481	C₂²×D₄	—	79	1	no	—
482	C₂²×D₄	—	79	16	no	—
483	C₂²×D₄	—	79	4	no	—
484	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
485	C₂³×C₄	—	79	2	no	—
486	C₂³×C₄	—	79	4	no	—
487	C₂³×C₄	—	79	4	no	—
488	C₂³×C₄	—	79	4	no	—
489	C₂³×C₄	—	79	2	no	—
490	C₂³×C₄	—	79	1	no	—
491	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
492	C₄⋊Q₈	—	79	16	no	—
493	C₄⋊Q₈	C₂²×D₇₉	1	16	yes	complemented
494	#126	—	79	32	no	—
495	#126	—	79	32	no	—
496	#126	C₂²×D₇₉	1	32	yes	complemented
497	#125	C₂²×D₇₉	1	16	yes	complemented
498	#124	—	79	8	no	—
499	#124	—	79	16	no	—
500	#124	—	79	32	no	—
501	#124	—	79	8	no	—
502	#124	—	79	32	no	—
503	#124	—	79	32	no	—
504	#124	—	79	8	no	—
505	#124	—	79	16	no	—
506	#124	—	79	16	no	—
507	#124	C₂²×D₇₉	1	8	yes	—
508	#123	—	79	16	no	—
509	#123	—	79	32	no	—
510	#123	—	79	32	no	—
511	#123	—	79	32	no	—
512	#123	—	79	32	no	—
513	#123	—	79	32	no	—
514	#123	C₂²×D₇₉	1	16	yes	—
515	C₂²⋊Q₈	—	79	16	no	—
516	C₂²⋊Q₈	—	79	32	no	—
517	C₂²⋊Q₈	—	79	32	no	—
518	C₂²⋊Q₈	—	79	32	no	—
519	C₂²⋊Q₈	C₂²×D₇₉	1	32	yes	complemented
520	#121	—	79	16	no	—
521	#121	—	79	32	no	—
522	#121	—	79	32	no	—
523	#121	—	79	32	no	—
524	#121	—	79	32	no	—
525	#120	—	79	16	no	—
526	#120	—	79	16	no	—
527	#120	—	79	32	no	—
528	#120	—	79	32	no	—
529	C₄×Q₈	—	79	16	no	—
530	C₄×D₄	—	79	32	no	—
531	C₄×D₄	—	79	16	no	—
532	C₄×D₄	—	79	32	no	—
533	C₄×D₄	—	79	32	no	—
534	#117	—	79	32	no	—
535	#117	—	79	32	no	—
536	#117	—	79	16	no	—
537	C₂×C₄⋊C₄	—	79	4	no	—
538	C₂×C₄⋊C₄	—	79	4	no	—
539	C₂×C₄⋊C₄	—	79	4	no	—
540	C₂×C₄⋊C₄	—	79	4	no	—
541	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
543	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
546	C₂×C₂²⋊C₄	—	79	4	no	—
547	C₂×C₂²⋊C₄	—	79	2	no	—
548	C₂×C₂²⋊C₄	—	79	4	no	—
549	C₂×C₂²⋊C₄	—	79	4	no	—
550	C₂×C₂²⋊C₄	—	79	4	no	—
551	C₂×C₂²⋊C₄	—	79	4	no	—
552	C₂×C₂²⋊C₄	—	79	4	no	—
553	C₂×C₂²⋊C₄	—	79	4	no	—
554	C₂×C₂²⋊C₄	—	79	4	no	—
555	C₂×C₂²⋊C₄	—	79	4	no	—
556	C₂×C₂²⋊C₄	—	79	4	no	—
557	C₂×C₂²⋊C₄	—	79	4	no	—
558	C₂×C₂²⋊C₄	—	79	32	no	—
559	C₂×C₂²⋊C₄	—	79	16	no	—
560	C₂×C₂²⋊C₄	—	79	32	no	—
561	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
564	C₂×C₄²	—	79	1	no	—
565	C₂×C₄²	—	79	2	no	—
566	C₂×C₄²	—	79	4	no	—
567	C₂×C₄²	—	79	2	no	—
568	C₂×C₄²	—	79	8	no	—
569	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
570	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
571	C₂⁴	—	316	4	no	—
572	C₂⁴	—	316	8	no	—
573	C₂⁴	—	316	8	no	—
574	C₂⁴	—	79	8	no	—
575	C₂⁴	—	79	8	no	—
576	C₂⁴	—	79	1	no	—
577	C₂⁴	—	79	4	no	—
578	C₂⁴	—	79	2	no	—
579	C₂⁴	—	158	8	no	—
580	C₂⁴	C₂³×D₇₉	1	2	yes	—
581	#41	—	316	32	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	316	2	no	—
585	C₂×Q₈	—	316	4	no	—
586	C₂×Q₈	—	316	4	no	—
587	C₂×Q₈	—	316	16	no	—
588	C₂×Q₈	—	79	8	no	—
589	C₂×Q₈	—	79	4	no	—
590	C₂×Q₈	—	79	8	no	—
591	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
592	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	316	8	no	—
595	C₂×D₄	—	316	2	no	—
596	C₂×D₄	—	316	8	no	—
597	C₂×D₄	—	316	4	no	—
598	C₂×D₄	—	316	4	no	—
599	C₂×D₄	—	316	32	no	—
600	C₂×D₄	—	316	16	no	—
601	C₂×D₄	—	316	4	no	—
602	C₂×D₄	—	316	8	no	—
603	C₂×D₄	—	79	16	no	—
604	C₂×D₄	—	79	8	no	—
605	C₂×D₄	—	79	16	no	—
606	C₂×D₄	—	79	8	no	—
607	C₂×D₄	—	79	8	no	—
608	C₂×D₄	—	79	16	no	—
609	C₂×D₄	—	79	4	no	—
610	C₂×D₄	—	79	16	no	—
611	C₂×D₄	—	158	16	no	—
612	C₂×D₄	C₂³×D₇₉	1	4	yes	—
613	C₂²×C₄	—	4	4	no	—
614	C₂²×C₄	—	316	8	no	—
615	C₂²×C₄	—	316	8	no	—
616	C₂²×C₄	—	316	4	no	—
617	C₂²×C₄	—	316	8	no	—
618	C₂²×C₄	—	79	8	no	—
619	C₂²×C₄	—	79	16	no	—
620	C₂²×C₄	—	79	16	no	—
621	C₂²×C₄	—	79	16	no	—
622	C₂²×C₄	—	79	2	no	—
623	C₂²×C₄	—	79	4	no	—
624	C₂²×C₄	—	79	1	no	—
625	C₂²×C₄	—	79	2	no	—
626	C₂²×C₄	—	79	4	no	—
627	C₂²×C₄	—	79	8	no	—
628	C₂²×C₄	—	158	4	no	—
629	C₂²×C₄	—	158	8	no	—
630	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
631	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
632	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
633	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
634	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
635	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
636	C₄⋊C₄	—	79	16	no	—
637	C₄⋊C₄	—	79	16	no	—
638	C₄⋊C₄	—	79	16	no	—
639	C₄⋊C₄	—	79	16	no	—
640	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
641	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
642	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
643	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
644	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
645	C₂²⋊C₄	—	79	16	no	—
646	C₂²⋊C₄	—	79	8	no	—
647	C₂²⋊C₄	—	79	16	no	—
648	C₂²⋊C₄	—	79	16	no	—
649	C₂²⋊C₄	—	79	16	no	—
650	C₂²⋊C₄	—	79	16	no	—
651	C₂²⋊C₄	—	79	16	no	—
652	C₂²⋊C₄	—	79	16	no	—
653	C₂²⋊C₄	—	79	16	no	—
654	C₂²⋊C₄	—	79	16	no	—
655	C₂²⋊C₄	—	79	16	no	—
656	C₂²⋊C₄	—	79	16	no	—
657	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
658	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
659	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
660	C₄²	—	79	4	no	—
661	C₄²	—	79	8	no	—
662	C₄²	—	79	8	no	—
663	C₄²	—	79	16	no	—
664	C₄²	C₂³×D₇₉	1	4	yes	—
665	C₄²	C₂³×D₇₉	1	8	yes	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	316	8	no	—
669	C₂³	—	316	16	no	—
670	C₂³	—	316	16	no	—
671	C₂³	—	79	4	no	—
672	C₂³	—	79	2	no	—
673	C₂³	—	79	8	no	—
674	C₂³	—	79	4	no	—
675	C₂³	—	632	16	no	—
676	C₂³	—	632	16	no	—
677	C₂³	—	158	16	no	—
678	C₂³	—	158	8	no	—
679	C₂³	—	158	4	no	—
680	C₂³	—	158	8	no	—
681	C₂³	—	158	8	no	—
682	C₂³	—	158	8	no	—
683	C₂³	—	158	4	no	—
684	C₂³	C₂⁴×D₇₉	1	4	yes	—
685	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	316	4	no	—
689	Q₈	—	316	8	no	—
690	Q₈	—	316	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	316	16	no	—
693	D₄	—	316	4	no	—
694	D₄	—	316	8	no	—
695	D₄	—	316	16	no	—
696	D₄	—	316	8	no	—
697	D₄	—	316	8	no	—
698	D₄	—	316	16	no	—
699	D₄	—	158	32	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	316	16	no	—
707	C₂×C₄	—	316	16	no	—
708	C₂×C₄	—	316	16	no	—
709	C₂×C₄	—	316	8	no	—
710	C₂×C₄	—	79	4	no	—
711	C₂×C₄	—	79	8	no	—
712	C₂×C₄	—	79	2	no	—
713	C₂×C₄	—	79	4	no	—
714	C₂×C₄	—	158	8	no	—
715	C₂×C₄	—	158	16	no	—
716	C₂×C₄	—	158	4	no	—
717	C₂×C₄	—	158	2	no	—
718	C₂×C₄	—	158	4	no	—
719	C₂×C₄	—	158	8	no	—
720	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
721	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
722	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
723	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
724	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	4	8	no	—
728	C₂²	—	316	16	no	—
729	C₂²	—	316	8	no	—
730	C₂²	—	79	4	no	—
731	C₂²	—	632	16	no	—
732	C₂²	—	632	16	no	—
733	C₂²	—	158	8	no	—
734	C₂²	—	158	4	no	—
735	C₂²	—	158	8	no	—
736	C₂²	—	158	8	no	—
737	C₂²	—	158	8	no	—
738	C₂²	—	158	4	no	—
739	C₂²	—	158	8	no	—
740	C₂²	H(5,𝔽₂)×D₇₉	1	2	yes	—
741	C₂²	#19099400	1	4	yes	—
742	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
743	C₄	—	2	8	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	8	no	—
747	C₄	—	2	4	no	—
748	C₄	—	158	4	no	—
749	C₄	—	158	2	no	—
750	C₄	—	158	4	no	—
751	C₄	—	158	8	no	—
752	C₂	—	4	4	no	—
753	C₂	—	316	8	no	—
754	C₂	—	316	4	no	—
755	C₂	—	158	4	no	—
756	C₂	#23777758	1	4	yes	direct product factor
757	C₂	C₂×H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
758	C₂	C₂×#19099400	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#563×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#563	D₇₉
hypocenter	C₇₉	C₂×#3545
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#563

Complements

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

N	H ≅ G/N	type
1. #23777758	C₂	direct (N × H)
2. C₂×#19099311	C₂	semidirect
3. C₂×#19099305	C₂	semidirect
4. C₂×#19099279	C₂	semidirect
5. C₂×#19099241	C₂	semidirect
6. C₂×#19099238	C₂	semidirect
7. C₂×#19099204	C₂	semidirect
8. C₂×#19099183	C₂	semidirect
9. C₂×#19099152	C₂	semidirect
10. C₂×#19099138	C₂	semidirect
11. C₂×#19099124	C₂	semidirect
12. C₂×#19099098	C₂	semidirect
13. C₂×#124×D₇₉	C₂	semidirect
14. C₂×#563×C₇₉	C₂	semidirect
16. C₂²×Q₈×D₇₉	C₂²	semidirect
17. C₂³×D₃₁₆	C₂²	semidirect
19. #19099311	C₂²	semidirect
20. #19099305	C₂²	semidirect
21. #19099279	C₂²	semidirect
22. #19099241	C₂²	semidirect
23. #19099238	C₂²	semidirect
24. #19099204	C₂²	semidirect
25. #19099183	C₂²	semidirect
26. #19099152	C₂²	semidirect
27. #19099138	C₂²	semidirect
28. #19099124	C₂²	semidirect
29. C₂×#14579159	C₂²	semidirect
30. #19099098	C₂²	semidirect
31. C₂×#14579156	C₂²	semidirect
32. C₂×#14579154	C₂²	semidirect
33. C₂×#14579150	C₂²	semidirect
34. C₂×#14579150	C₂²	semidirect
35. C₂×#14579150	C₂²	semidirect
36. C₂×#14579149	C₂²	semidirect
37. C₂×#14579149	C₂²	semidirect
38. C₂×#14579149	C₂²	semidirect
40. C₂×#14579147	C₂²	semidirect
41. C₂×#14579147	C₂²	semidirect
42. #124×D₇₉	C₂²	semidirect
43. C₂×#14579146	C₂²	semidirect
44. C₂×#14579146	C₂²	semidirect
45. C₂×#14579146	C₂²	semidirect
46. C₂×#14579146	C₂²	semidirect
47. C₂×#14579144	C₂²	semidirect
48. C₂×#14579143	C₂²	semidirect
49. C₂×#14579141	C₂²	semidirect
50. C₂×#14579139	C₂²	semidirect
51. C₂×#14579139	C₂²	semidirect
52. C₂×#14579139	C₂²	semidirect
54. C₂×#14579136	C₂²	semidirect
55. C₂×#14579136	C₂²	semidirect
56. C₂×#14579136	C₂²	semidirect
59. C₂×#14579131	C₂²	semidirect
60. C₂×#14579131	C₂²	semidirect
62. C₂×#14579126	C₂²	semidirect
63. C₂×C₄×D₃₁₆	C₂²	semidirect
64. C₂×#14579123	C₂²	semidirect
65. C₂×#14579123	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
67. C₂×#14579119	C₂²	semidirect
68. C₂×#14579119	C₂²	semidirect
69. C₂×#14579118	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
72. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
73. C₂×C₄²×D₇₉	C₂²	semidirect
74. #563×C₇₉	C₂²	semidirect
75. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
76. C₂×#126×C₇₉	C₂²	semidirect
77. C₂×#125×C₇₉	C₂²	semidirect
80. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
89. C₂×Q₈×D₇₉	C₂³	semidirect
97. C₂²×D₃₁₆	C₂³	semidirect
108. #14579159	C₂³	semidirect
109. #14579156	C₂³	semidirect
110. #14579154	C₂³	semidirect
111. #14579150	C₂³	semidirect
112. #14579150	C₂³	semidirect
113. #14579150	C₂³	semidirect
114. #14579149	C₂³	semidirect
115. #14579149	C₂³	semidirect
116. #14579149	C₂³	semidirect
118. #14579147	C₂³	semidirect
119. #14579147	C₂³	semidirect
120. #14579146	C₂³	semidirect
121. #14579146	C₂³	semidirect
122. #14579146	C₂³	semidirect
123. #14579146	C₂³	semidirect
124. #14579144	C₂³	semidirect
125. #14579143	C₂³	semidirect
126. #14579141	C₂³	semidirect
127. #14579139	C₂³	semidirect
128. #14579139	C₂³	semidirect
129. #14579139	C₂³	semidirect
131. #14579136	C₂³	semidirect
132. #14579136	C₂³	semidirect
133. #14579136	C₂³	semidirect
136. #14579131	C₂³	semidirect
137. #14579131	C₂³	semidirect
139. #14579126	C₂³	semidirect
140. C₄×D₃₁₆	C₂³	semidirect
141. #14579123	C₂³	semidirect
142. #14579123	C₂³	semidirect
143. C₄×C₂²⋊D₇₉	C₂³	semidirect
144. #14579119	C₂³	semidirect
145. #14579119	C₂³	semidirect
146. #14579118	C₂³	semidirect
163. C₂²⋊C₄×D₇₉	C₂³	semidirect
164. C₂²⋊C₄×D₇₉	C₂³	semidirect
165. C₂²⋊C₄×D₇₉	C₂³	semidirect
170. C₄²×D₇₉	C₂³	semidirect
175. C₄⋊Q₈×C₇₉	C₂³	semidirect
176. #126×C₇₉	C₂³	semidirect
177. #125×C₇₉	C₂³	semidirect
180. C₂²⋊Q₈×C₇₉	C₂³	semidirect
374. C₂×C₇₉	#3545	semidirect
381. C₂×#563	D₇₉	semidirect
394. C₇₉	C₂×#3545	semidirect
399. #563	C₂×D₇₉	semidirect
411. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
415. C₂×#126	C₂×D₇₉	semidirect
416. C₂×#125	C₂×D₇₉	semidirect
439. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
493. C₄⋊Q₈	C₂²×D₇₉	semidirect
496. #126	C₂²×D₇₉	semidirect
497. #125	C₂²×D₇₉	semidirect
519. C₂²⋊Q₈	C₂²×D₇₉	semidirect
756. C₂	#23777758	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777758	2
C₂×#19099311	2
C₂×#19099305	2
C₂×#19099279	2
C₂×#19099241	2
C₂×#19099238	2
C₂×#19099204	2
C₂×#19099183	2
C₂×#19099152	2
C₂×#19099138	2
C₂×#19099124	2
C₂×#19099098	2
C₂×#124×D₇₉	2
C₂×#563×C₇₉	2
C₂×#3545	79

Subgroups — C2×#23777758 #35196029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777758 #35196029