Subgroups — C₂×#23777536 #35195158

Order 20224.

7418 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777536	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099313	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099312	C₂	1	2	yes	maximal, complemented
4	C₂×#19099308	C₂	1	4	yes	maximal, complemented
5	C₂×#19099307	C₂	1	2	yes	maximal, complemented
6	C₂×#19099305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19099301	C₂	1	4	yes	maximal, complemented
8	C₂×#19099300	C₂	1	2	yes	maximal, complemented
9	C₂×#19099109	C₂	1	2	yes	maximal, complemented
10	C₂×#19099097	C₂	1	2	yes	maximal, complemented
11	C₂×#19099093	C₂	1	4	yes	maximal, complemented
12	C₂×#19099072	C₂	1	4	yes	maximal, complemented
13	C₂×#19099070	C₂	1	2	yes	maximal, complemented
14	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#11929624	C₂²	1	2	yes	—
16	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
17	#19099313	C₂²	1	16	yes	complemented
18	#19099312	C₂²	1	32	yes	complemented
19	#19099308	C₂²	1	64	yes	complemented
20	#19099307	C₂²	1	32	yes	complemented
21	#19099305	C₂²	1	16	yes	complemented
22	#19099301	C₂²	1	64	yes	complemented
23	#19099300	C₂²	1	32	yes	complemented
24	#19099109	C₂²	1	32	yes	complemented
25	C₂×#14579159	C₂²	1	2	yes	complemented
26	C₂×#14579157	C₂²	1	2	yes	—
27	#19099097	C₂²	1	32	yes	complemented
28	#19099093	C₂²	1	64	yes	complemented
29	C₂×#14579156	C₂²	1	4	yes	complemented
30	C₂×#14579155	C₂²	1	4	yes	complemented
31	C₂×#14579154	C₂²	1	4	yes	complemented
32	C₂×#14579153	C₂²	1	2	yes	complemented
33	C₂×#14579151	C₂²	1	4	yes	complemented
34	C₂×#14579150	C₂²	1	2	yes	—
35	C₂×#14579149	C₂²	1	2	yes	—
36	C₂×#14579148	C₂²	1	2	yes	complemented
37	C₂×#14579147	C₂²	1	4	yes	—
38	#19099072	C₂²	1	64	yes	complemented
39	#19099070	C₂²	1	32	yes	complemented
40	C₂×#14579146	C₂²	1	4	yes	—
41	C₂×#14579145	C₂²	1	4	yes	complemented
42	C₂×#14579144	C₂²	1	4	yes	complemented
43	C₂×#14579143	C₂²	1	4	yes	complemented
44	C₂×#14579142	C₂²	1	2	yes	—
45	C₂×#14579142	C₂²	1	2	yes	complemented
46	C₂×#14579142	C₂²	1	4	yes	complemented
47	C₂×#14579140	C₂²	1	2	yes	complemented
48	C₂×#14579139	C₂²	1	4	yes	complemented
49	C₂×#14579138	C₂²	1	4	yes	complemented
50	C₂×#14579138	C₂²	1	4	yes	complemented
51	C₂×#14579137	C₂²	1	4	yes	complemented
52	C₂×#14579135	C₂²	1	2	yes	—
53	C₂×#14579134	C₂²	1	4	yes	—
54	C₂×#14579133	C₂²	1	4	yes	—
55	C₂×#14579133	C₂²	1	4	yes	—
56	C₂×#14579133	C₂²	1	4	yes	complemented
57	C₂×#14579133	C₂²	1	4	yes	complemented
58	C₂×#14579132	C₂²	1	4	yes	—
59	C₂×#14579131	C₂²	1	4	yes	—
60	C₂×#14579129	C₂²	1	2	yes	—
61	C₂×#14579129	C₂²	1	2	yes	complemented
62	C₂×#14579129	C₂²	1	4	yes	complemented
63	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
64	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
65	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	—
66	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
67	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
68	C₂×#14579120	C₂²	1	2	yes	complemented
69	C₂×#14579118	C₂²	1	4	yes	complemented
70	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	complemented
71	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
72	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
73	#532×C₇₉	C₂²	1	16	yes	complemented
74	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
75	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
76	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
77	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
78	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
81	C₂⁴×D₇₉	C₂³	1	2	yes	—
82	C₂×#11929624	—	4	8	no	—
83	C₂×#11929624	C₂³	1	16	yes	—
84	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
85	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
86	C₂²×D₃₁₆	C₂³	1	2	yes	—
87	C₂²×D₃₁₆	C₂³	1	2	yes	—
88	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
89	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
90	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
91	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
92	C₂³×Dic₇₉	C₂³	1	4	yes	—
93	C₂³×Dic₇₉	C₂³	1	2	yes	—
94	C₂²×C₄×D₇₉	—	4	8	no	—
95	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
96	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
97	C₂²×C₄×D₇₉	C₂³	1	16	yes	complemented
98	#14579159	C₂³	1	16	yes	complemented
99	#14579157	C₂³	1	16	yes	—
100	#14579156	C₂³	1	32	yes	complemented
101	#14579155	C₂³	1	32	yes	complemented
102	#14579154	C₂³	1	32	yes	complemented
103	#14579153	C₂³	1	16	yes	complemented
104	#14579151	C₂³	1	32	yes	complemented
105	#14579150	C₂³	1	16	yes	—
106	#14579149	C₂³	1	16	yes	—
107	#14579148	C₂³	1	16	yes	complemented
108	#14579147	C₂³	1	32	yes	—
109	#14579146	C₂³	1	32	yes	—
110	#14579145	C₂³	1	32	yes	complemented
111	#14579144	C₂³	1	32	yes	complemented
112	#14579143	C₂³	1	32	yes	complemented
113	#14579142	C₂³	1	16	yes	—
114	#14579142	C₂³	1	32	yes	complemented
115	#14579142	C₂³	1	16	yes	complemented
116	#14579140	C₂³	1	16	yes	complemented
117	#14579139	C₂³	1	32	yes	complemented
118	#14579138	C₂³	1	32	yes	complemented
119	#14579138	C₂³	1	32	yes	complemented
120	#14579137	C₂³	1	32	yes	complemented
121	#14579135	C₂³	1	16	yes	—
122	#14579134	C₂³	1	32	yes	—
123	#14579133	C₂³	1	32	yes	—
124	#14579133	C₂³	1	32	yes	—
125	#14579133	C₂³	1	32	yes	complemented
126	#14579133	C₂³	1	32	yes	complemented
127	#14579132	C₂³	1	32	yes	—
128	#14579131	C₂³	1	32	yes	—
129	#14579129	C₂³	1	16	yes	—
130	#14579129	C₂³	1	32	yes	complemented
131	#14579129	C₂³	1	16	yes	complemented
132	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
133	C₄×D₃₁₆	C₂³	1	16	yes	—
134	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	—
135	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
136	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
137	#14579120	C₂³	1	16	yes	complemented
138	#14579118	C₂³	1	32	yes	complemented
139	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
140	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
141	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
142	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
143	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
144	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
145	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
146	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
147	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
148	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₇₉	C₂³	1	4	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×C₄×Dic₇₉	C₂³	1	4	yes	—
160	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
161	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
162	C₂×C₄×Dic₇₉	C₂³	1	16	yes	complemented
163	C₂×#41×C₇₉	—	4	4	no	—
164	C₂×#41×C₇₉	—	4	4	no	—
165	C₂×#41×C₇₉	C₂³	1	8	yes	—
166	C₂×#41×C₇₉	C₂³	1	8	yes	complemented
167	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
168	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
170	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
171	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
172	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
175	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
176	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
177	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
178	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
179	#127×C₇₉	C₂³	1	8	yes	—
180	#124×C₇₉	C₂³	1	8	yes	—
181	#124×C₇₉	C₂³	1	8	yes	complemented
182	#121×C₇₉	C₂³	1	32	yes	complemented
183	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
184	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
186	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
187	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₉	C₂³	1	8	yes	complemented
191	C₂³×D₇₉	—	4	8	no	—
192	C₂³×D₇₉	—	4	4	no	—
193	C₂³×D₇₉	C₂⁴	1	4	yes	—
194	C₂³×D₇₉	C₂⁴	1	8	yes	—
195	#11929624	—	4	32	no	—
196	C₂×Dic₁₅₈	—	4	4	no	—
197	C₂×Dic₁₅₈	—	4	4	no	—
198	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
199	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
200	C₂×D₃₁₆	—	4	4	no	—
201	C₂×D₃₁₆	—	4	4	no	—
202	C₂×D₃₁₆	C₂⁴	1	8	yes	—
203	C₂×D₃₁₆	C₂⁴	1	8	yes	—
204	C₂×C₂²⋊D₇₉	—	4	8	no	—
205	C₂×C₂²⋊D₇₉	—	4	8	no	—
206	C₂×C₂²⋊D₇₉	—	4	8	no	—
207	C₂×C₂²⋊D₇₉	—	4	8	no	—
208	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
209	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
210	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
211	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
212	C₂²×Dic₇₉	—	4	4	no	—
213	C₂²×Dic₇₉	—	4	8	no	—
214	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
215	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
216	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
217	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
218	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
219	C₂×C₄×D₇₉	—	2	16	no	—
220	C₂×C₄×D₇₉	—	4	8	no	—
221	C₂×C₄×D₇₉	—	4	32	no	—
222	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
223	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
224	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
225	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
226	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
227	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
228	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
229	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
230	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
231	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
232	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
233	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
234	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
235	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
236	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
237	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
238	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
239	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
240	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
241	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
242	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
243	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
244	C₄×Dic₇₉	C₂⁴	1	16	yes	—
245	C₄×Dic₇₉	C₂⁴	1	8	yes	—
246	C₄×Dic₇₉	C₂⁴	1	8	yes	—
247	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
248	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
249	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
250	#41×C₇₉	—	4	16	no	—
251	#41×C₇₉	—	4	16	no	—
252	C₂×Q₈×C₇₉	—	4	2	no	—
253	C₂×Q₈×C₇₉	—	4	2	no	—
254	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
255	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
256	C₂×D₄×C₇₉	—	4	8	no	—
257	C₂×D₄×C₇₉	—	4	4	no	—
258	C₂×D₄×C₇₉	—	4	4	no	—
259	C₂×D₄×C₇₉	—	4	2	no	—
260	C₂×D₄×C₇₉	—	4	2	no	—
261	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
262	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
263	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
264	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
265	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₇₉	—	2	8	no	—
267	C₂²×C₄×C₇₉	—	2	4	no	—
268	C₂²×C₄×C₇₉	—	2	8	no	—
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	8	yes	—
273	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
280	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
281	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
282	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
283	C₄²×C₇₉	C₂⁴	1	8	yes	—
284	C₄²×C₇₉	C₂⁴	1	4	yes	—
285	C₄²×C₇₉	C₂⁴	1	4	yes	—
286	C₂³×C₇₉	—	2	4	no	—
287	C₂³×C₇₉	—	2	4	no	—
288	C₂³×C₇₉	—	2	2	no	—
289	C₂³×C₇₉	—	2	8	no	—
290	C₂³×C₇₉	—	2	4	no	—
291	C₂³×C₇₉	—	2	8	no	—
292	C₂³×C₇₉	C₂⁵	1	4	yes	—
293	C₂³×C₇₉	C₂⁵	1	2	yes	—
294	C₂³×C₇₉	C₂⁵	1	4	yes	—
295	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
296	C₂²×D₇₉	—	2	8	no	—
297	C₂²×D₇₉	—	2	8	no	—
298	C₂²×D₇₉	—	2	8	no	—
299	C₂²×D₇₉	—	4	8	no	—
300	C₂²×D₇₉	—	4	16	no	—
301	C₂²×D₇₉	—	4	32	no	—
302	C₂²×D₇₉	C₂⁵	1	8	yes	—
303	Q₈×C₇₉	—	4	4	no	—
304	Q₈×C₇₉	—	4	4	no	—
305	D₄×C₇₉	—	4	16	no	—
306	D₄×C₇₉	—	4	4	no	—
307	D₄×C₇₉	—	4	4	no	—
308	D₄×C₇₉	—	4	8	no	—
309	D₄×C₇₉	—	4	8	no	—
310	C₂×C₄×C₇₉	—	2	4	no	—
311	C₂×C₄×C₇₉	—	2	4	no	—
312	C₂×C₄×C₇₉	—	2	2	no	—
313	C₂×C₄×C₇₉	—	2	4	no	—
314	C₂×C₄×C₇₉	—	2	4	no	—
315	C₂×C₄×C₇₉	—	2	16	no	—
316	C₂×C₄×C₇₉	—	2	16	no	—
317	C₂×C₄×C₇₉	—	2	8	no	—
318	C₂×C₄×C₇₉	—	4	8	no	—
319	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
321	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
322	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
323	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
324	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
325	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
326	C₂²⋊D₇₉	—	4	16	no	—
327	C₂²⋊D₇₉	—	4	16	no	—
328	C₂²⋊D₇₉	—	4	16	no	—
329	C₂²⋊D₇₉	—	4	16	no	—
330	C₂×Dic₇₉	—	2	8	no	—
331	C₂×Dic₇₉	—	2	8	no	—
332	C₂×Dic₇₉	—	2	8	no	—
333	C₂×Dic₇₉	—	4	8	no	—
334	C₂×Dic₇₉	—	4	16	no	—
335	C₂×Dic₇₉	C₂⁵	1	8	yes	—
336	C₂×Dic₇₉	C₂⁵	1	8	yes	—
337	C₂×Dic₇₉	C₂⁵	1	8	yes	—
338	D₃₁₆	—	4	8	no	—
339	D₃₁₆	—	4	8	no	—
340	C₄×D₇₉	—	2	32	no	—
341	C₄×D₇₉	—	4	16	no	—
342	Dic₁₅₈	—	4	8	no	—
343	Dic₁₅₈	—	4	8	no	—
344	C₂²×C₇₉	—	2	4	no	—
345	C₂²×C₇₉	—	2	2	no	—
346	C₂²×C₇₉	—	2	4	no	—
347	C₂²×C₇₉	—	2	4	no	—
348	C₂²×C₇₉	—	2	8	no	—
349	C₂²×C₇₉	—	2	8	no	—
350	C₂²×C₇₉	—	4	8	no	—
351	C₂²×C₇₉	—	4	8	no	—
352	C₂²×C₇₉	—	4	4	no	—
353	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
354	C₂²×C₇₉	#585	1	4	yes	—
355	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
356	C₂×D₇₉	—	2	8	no	—
357	C₂×D₇₉	—	2	8	no	—
358	C₂×D₇₉	—	2	8	no	—
359	C₂×D₇₉	—	4	32	no	—
360	C₂×D₇₉	—	4	16	no	—
361	C₄×C₇₉	—	2	2	no	—
362	C₄×C₇₉	—	2	4	no	—
363	C₄×C₇₉	—	2	4	no	—
364	C₄×C₇₉	—	2	4	no	—
365	C₄×C₇₉	—	2	4	no	—
366	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
367	Dic₇₉	—	2	8	no	—
368	Dic₇₉	—	2	8	no	—
369	Dic₇₉	—	2	8	no	—
370	C₂×#3529	—	79	1	no	maximal, Sylow
371	C₂×C₇₉	—	4	4	no	—
372	C₂×C₇₉	—	4	4	no	—
373	C₂×C₇₉	—	4	2	no	—
374	C₂×C₇₉	#3529	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	—	4	8	no	—
378	#3529	—	79	32	no	—
379	C₂×#563	—	79	2	no	—
380	C₂×#563	—	79	1	no	—
381	C₂×#562	—	79	2	no	—
382	C₂×#562	—	79	4	no	—
383	C₂×H(3,𝔽₄)	—	79	1	no	—
384	C₂×#560	—	79	2	no	—
385	C₂×#560	—	79	4	no	—
386	C₂×#532	—	79	2	no	—
387	C₂×#532	D₇₉	1	1	yes	characteristic, complemented
388	C₂×#529	—	79	2	no	—
389	C₂×#529	—	79	4	no	—
390	C₂×#525	—	79	2	no	—
391	C₂×#525	—	79	4	no	—
392	C₇₉	C₂×#3529	1	1	yes	characteristic, complemented, Sylow
393	C₂²×#41	—	79	2	no	—
394	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
395	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
396	C₂⁴×C₄	—	79	2	no	—
397	#563	—	79	32	no	—
398	#563	—	79	16	no	—
399	#562	—	79	32	no	—
400	#562	—	79	64	no	—
401	H(3,𝔽₄)	—	79	16	no	—
402	#560	—	79	32	no	—
403	#560	—	79	64	no	—
404	#532	—	79	32	no	—
405	#532	C₂×D₇₉	1	16	yes	complemented
406	C₂×C₄⋊Q₈	—	79	2	no	—
407	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
408	C₂×#127	—	79	2	no	—
409	C₂×#127	C₂×D₇₉	1	1	yes	characteristic
410	#529	—	79	64	no	—
411	#529	—	79	32	no	—
412	C₂×#126	—	79	4	no	—
413	C₂×#126	—	79	4	no	—
414	C₂×#126	—	79	4	no	—
415	C₂×#125	—	79	4	no	—
416	C₂×#125	—	79	2	no	—
417	C₂×#124	—	79	2	no	—
418	C₂×#124	—	79	2	no	—
419	C₂×#124	—	79	4	no	—
420	C₂×#124	—	79	2	no	—
421	C₂×#124	C₂×D₇₉	1	1	yes	characteristic
422	C₂×#124	C₂×D₇₉	1	1	yes	characteristic, complemented
423	#525	—	79	32	no	—
424	#525	—	79	64	no	—
425	C₂×#123	—	79	2	no	—
426	C₂×#123	—	79	2	no	—
427	C₂×#123	—	79	4	no	—
428	C₂×#123	—	79	4	no	—
429	C₂×#123	—	79	4	no	—
430	C₂×#123	—	79	4	no	—
431	C₂×#123	—	79	4	no	—
432	C₂×C₂²⋊Q₈	—	79	4	no	—
433	C₂×C₂²⋊Q₈	—	79	2	no	—
434	C₂×C₂²⋊Q₈	—	79	4	no	—
435	C₂×C₂²⋊Q₈	—	79	4	no	—
436	C₂×C₂²⋊Q₈	—	79	4	no	—
437	C₂×#121	—	79	4	no	—
438	C₂×#121	—	79	4	no	—
439	C₂×#121	—	79	4	no	—
440	C₂×#121	—	79	4	no	—
441	C₂×#121	—	79	4	no	—
442	C₂×#121	—	79	2	no	—
443	C₂×#121	—	79	4	no	—
444	C₂×#121	C₂×D₇₉	1	4	yes	complemented
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	4	no	—
452	C₂×C₄×D₄	—	79	4	no	—
453	C₂×C₄×D₄	—	79	2	no	—
454	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
455	C₂×#117	—	79	2	no	—
456	C₂×#117	—	79	4	no	—
457	C₂²×C₄²	—	79	2	no	—
458	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
459	C₂⁵	—	79	2	no	—
460	C₂×#41	—	4	4	no	—
461	C₂×#41	—	4	4	no	—
462	C₂×#41	—	316	8	no	—
463	C₂×#41	—	79	16	no	—
464	C₂×#41	C₂²×D₇₉	1	8	yes	—
465	C₂×#41	C₂²×D₇₉	1	8	yes	complemented
466	C₂²×Q₈	—	79	2	no	—
467	C₂²×Q₈	—	79	2	no	—
468	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
469	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
470	C₂²×D₄	—	79	4	no	—
471	C₂²×D₄	—	79	4	no	—
472	C₂²×D₄	—	79	4	no	—
473	C₂²×D₄	—	79	4	no	—
474	C₂²×D₄	—	79	2	no	—
475	C₂²×D₄	—	79	2	no	—
476	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
477	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
478	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
479	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
480	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
481	C₂³×C₄	—	316	8	no	—
482	C₂³×C₄	—	79	4	no	—
483	C₂³×C₄	—	79	2	no	—
484	C₂³×C₄	—	79	4	no	—
485	C₂³×C₄	—	79	16	no	—
486	C₂³×C₄	—	79	4	no	—
487	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
488	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
489	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
490	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
491	C₄⋊Q₈	—	79	16	no	—
492	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
493	#127	—	79	16	no	—
494	#127	C₂²×D₇₉	1	8	yes	—
495	#126	—	79	32	no	—
496	#126	—	79	32	no	—
497	#126	—	79	32	no	—
498	#125	—	79	32	no	—
499	#125	—	79	16	no	—
500	#124	—	79	16	no	—
501	#124	—	79	16	no	—
502	#124	—	79	32	no	—
503	#124	—	79	16	no	—
504	#124	C₂²×D₇₉	1	8	yes	—
505	#124	C₂²×D₇₉	1	8	yes	complemented
506	#123	—	79	16	no	—
507	#123	—	79	16	no	—
508	#123	—	79	32	no	—
509	#123	—	79	32	no	—
510	#123	—	79	32	no	—
511	#123	—	79	32	no	—
512	#123	—	79	32	no	—
513	C₂²⋊Q₈	—	79	32	no	—
514	C₂²⋊Q₈	—	79	16	no	—
515	C₂²⋊Q₈	—	79	32	no	—
516	C₂²⋊Q₈	—	79	32	no	—
517	C₂²⋊Q₈	—	79	32	no	—
518	#121	—	79	32	no	—
519	#121	—	79	32	no	—
520	#121	—	79	32	no	—
521	#121	—	79	32	no	—
522	#121	—	79	32	no	—
523	#121	—	79	16	no	—
524	#121	—	79	32	no	—
525	#121	C₂²×D₇₉	1	32	yes	complemented
526	#120	—	79	16	no	—
527	#120	—	79	32	no	—
528	#120	—	79	16	no	—
529	#120	—	79	32	no	—
530	C₄×Q₈	—	79	16	no	—
531	C₄×D₄	—	79	32	no	—
532	C₄×D₄	—	79	32	no	—
533	C₄×D₄	—	79	32	no	—
534	C₄×D₄	—	79	16	no	—
535	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
536	#117	—	79	16	no	—
537	#117	—	79	32	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	—	79	4	no	—
542	C₂×C₄⋊C₄	—	79	4	no	—
543	C₂×C₄⋊C₄	—	79	4	no	—
544	C₂×C₄⋊C₄	—	79	2	no	—
545	C₂×C₄⋊C₄	—	79	4	no	—
546	C₂×C₄⋊C₄	—	79	2	no	—
547	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
548	C₂×C₂²⋊C₄	—	79	2	no	—
549	C₂×C₂²⋊C₄	—	79	2	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	4	no	—
559	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
561	C₂×C₄²	—	79	2	no	—
562	C₂×C₄²	—	79	2	no	—
563	C₂×C₄²	—	79	16	no	—
564	C₂×C₄²	—	79	4	no	—
565	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
566	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
567	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
568	C₂×C₄²	C₂²×D₇₉	1	8	yes	complemented
569	C₂⁴	—	316	4	no	—
570	C₂⁴	—	316	8	no	—
571	C₂⁴	—	79	8	no	—
572	C₂⁴	—	79	4	no	—
573	C₂⁴	C₂³×D₇₉	1	2	yes	—
574	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
575	C₂⁴	C₂³×D₇₉	1	2	yes	—
576	#41	—	4	16	no	—
577	#41	—	4	16	no	—
578	#41	—	316	32	no	—
579	C₂×Q₈	—	4	2	no	—
580	C₂×Q₈	—	4	2	no	—
581	C₂×Q₈	—	316	4	no	—
582	C₂×Q₈	—	316	4	no	—
583	C₂×Q₈	—	79	8	no	—
584	C₂×Q₈	—	79	8	no	—
585	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
586	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	—	4	8	no	—
592	C₂×D₄	—	316	4	no	—
593	C₂×D₄	—	316	4	no	—
594	C₂×D₄	—	316	8	no	—
595	C₂×D₄	—	316	8	no	—
596	C₂×D₄	—	316	8	no	—
597	C₂×D₄	—	316	8	no	—
598	C₂×D₄	—	79	16	no	—
599	C₂×D₄	—	79	16	no	—
600	C₂×D₄	—	79	16	no	—
601	C₂×D₄	—	79	16	no	—
602	C₂×D₄	—	79	8	no	—
603	C₂×D₄	—	79	8	no	—
604	C₂×D₄	C₂³×D₇₉	1	16	yes	—
605	C₂×D₄	C₂³×D₇₉	1	4	yes	—
606	C₂×D₄	C₂³×D₇₉	1	8	yes	—
607	C₂×D₄	C₂³×D₇₉	1	4	yes	—
608	C₂×D₄	C₂³×D₇₉	1	8	yes	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	4	4	no	—
613	C₂²×C₄	—	316	8	no	—
614	C₂²×C₄	—	316	32	no	—
615	C₂²×C₄	—	316	4	no	—
616	C₂²×C₄	—	316	8	no	—
617	C₂²×C₄	—	79	16	no	—
618	C₂²×C₄	—	79	8	no	—
619	C₂²×C₄	—	79	16	no	—
620	C₂²×C₄	—	79	4	no	—
621	C₂²×C₄	—	79	4	no	—
622	C₂²×C₄	—	79	4	no	—
623	C₂²×C₄	—	79	16	no	—
624	C₂²×C₄	—	158	16	no	—
625	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
626	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
627	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
628	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
629	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
630	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
631	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
632	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
633	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
634	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
635	C₄⋊C₄	—	79	16	no	—
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	—	79	16	no	—
641	C₄⋊C₄	—	79	16	no	—
642	C₄⋊C₄	—	79	8	no	—
643	C₄⋊C₄	—	79	8	no	—
644	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
645	C₂²⋊C₄	—	79	8	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	C₂³×D₇₉	1	16	yes	—
657	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
658	C₄²	—	79	16	no	—
659	C₄²	—	79	8	no	—
660	C₄²	—	79	8	no	—
661	C₄²	C₂³×D₇₉	1	8	yes	—
662	C₄²	C₂³×D₇₉	1	4	yes	—
663	C₄²	C₂³×D₇₉	1	4	yes	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	8	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	316	8	no	—
671	C₂³	—	316	16	no	—
672	C₂³	—	316	32	no	—
673	C₂³	—	79	8	no	—
674	C₂³	—	158	8	no	—
675	C₂³	—	158	8	no	—
676	C₂³	—	158	8	no	—
677	C₂³	C₂⁴×D₇₉	1	4	yes	—
678	C₂³	C₂⁴×D₇₉	1	2	yes	—
679	C₂³	C₂⁴×D₇₉	1	4	yes	—
680	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	316	8	no	—
684	Q₈	—	316	8	no	—
685	D₄	—	4	16	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	8	no	—
690	D₄	—	316	8	no	—
691	D₄	—	316	8	no	—
692	D₄	—	316	16	no	—
693	D₄	—	316	16	no	—
694	D₄	—	316	16	no	—
695	D₄	—	316	16	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	8	no	—
703	C₂×C₄	—	2	16	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	316	16	no	—
706	C₂×C₄	—	316	8	no	—
707	C₂×C₄	—	316	16	no	—
708	C₂×C₄	—	79	8	no	—
709	C₂×C₄	—	79	8	no	—
710	C₂×C₄	—	79	8	no	—
711	C₂×C₄	—	158	8	no	—
712	C₂×C₄	—	158	8	no	—
713	C₂×C₄	—	158	8	no	—
714	C₂×C₄	—	158	32	no	—
715	C₂×C₄	#14579206	1	4	yes	—
716	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
717	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
718	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
719	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
720	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
721	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	4	8	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	8	no	—
731	C₂²	—	316	32	no	—
732	C₂²	—	316	16	no	—
733	C₂²	—	158	8	no	—
734	C₂²	—	158	8	no	—
735	C₂²	—	158	8	no	—
736	C₂²	C₂×#14579206	1	2	yes	—
737	C₂²	#19099399	1	4	yes	—
738	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	4	no	—
744	C₄	—	158	8	no	—
745	C₄	—	158	8	no	—
746	C₄	—	158	8	no	—
747	C₄	C₂×#14579206	1	4	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	2	no	—
750	C₂	—	4	4	no	—
751	C₂	—	316	8	no	—
752	C₂	#23777536	1	4	yes	direct product factor
753	C₂	C₂²×#14579206	1	1	yes	characteristic
754	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#532×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#532	D₇₉
hypocenter	C₇₉	C₂×#3529
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #23777536	C₂	direct (N × H)
2. C₂×#19099313	C₂	semidirect
3. C₂×#19099312	C₂	semidirect
4. C₂×#19099308	C₂	semidirect
5. C₂×#19099307	C₂	semidirect
6. C₂×#19099305	C₂	semidirect
7. C₂×#19099301	C₂	semidirect
8. C₂×#19099300	C₂	semidirect
9. C₂×#19099109	C₂	semidirect
10. C₂×#19099097	C₂	semidirect
11. C₂×#19099093	C₂	semidirect
12. C₂×#19099072	C₂	semidirect
13. C₂×#19099070	C₂	semidirect
14. C₂×#532×C₇₉	C₂	semidirect
16. C₂³×C₄×D₇₉	C₂²	semidirect
17. #19099313	C₂²	semidirect
18. #19099312	C₂²	semidirect
19. #19099308	C₂²	semidirect
20. #19099307	C₂²	semidirect
21. #19099305	C₂²	semidirect
22. #19099301	C₂²	semidirect
23. #19099300	C₂²	semidirect
24. #19099109	C₂²	semidirect
25. C₂×#14579159	C₂²	semidirect
27. #19099097	C₂²	semidirect
28. #19099093	C₂²	semidirect
29. C₂×#14579156	C₂²	semidirect
30. C₂×#14579155	C₂²	semidirect
31. C₂×#14579154	C₂²	semidirect
32. C₂×#14579153	C₂²	semidirect
33. C₂×#14579151	C₂²	semidirect
36. C₂×#14579148	C₂²	semidirect
38. #19099072	C₂²	semidirect
39. #19099070	C₂²	semidirect
41. C₂×#14579145	C₂²	semidirect
42. C₂×#14579144	C₂²	semidirect
43. C₂×#14579143	C₂²	semidirect
45. C₂×#14579142	C₂²	semidirect
46. C₂×#14579142	C₂²	semidirect
47. C₂×#14579140	C₂²	semidirect
48. C₂×#14579139	C₂²	semidirect
49. C₂×#14579138	C₂²	semidirect
50. C₂×#14579138	C₂²	semidirect
51. C₂×#14579137	C₂²	semidirect
56. C₂×#14579133	C₂²	semidirect
57. C₂×#14579133	C₂²	semidirect
61. C₂×#14579129	C₂²	semidirect
62. C₂×#14579129	C₂²	semidirect
63. C₂×C₄×Dic₁₅₈	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
67. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
68. C₂×#14579120	C₂²	semidirect
69. C₂×#14579118	C₂²	semidirect
70. C₂²×C₄×Dic₇₉	C₂²	semidirect
72. C₂²×#41×C₇₉	C₂²	semidirect
73. #532×C₇₉	C₂²	semidirect
74. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
77. C₂×#124×C₇₉	C₂²	semidirect
78. C₂×#121×C₇₉	C₂²	semidirect
79. C₂×C₄×D₄×C₇₉	C₂²	semidirect
80. C₂²×C₄²×C₇₉	C₂²	semidirect
97. C₂²×C₄×D₇₉	C₂³	semidirect
98. #14579159	C₂³	semidirect
100. #14579156	C₂³	semidirect
101. #14579155	C₂³	semidirect
102. #14579154	C₂³	semidirect
103. #14579153	C₂³	semidirect
104. #14579151	C₂³	semidirect
107. #14579148	C₂³	semidirect
110. #14579145	C₂³	semidirect
111. #14579144	C₂³	semidirect
112. #14579143	C₂³	semidirect
114. #14579142	C₂³	semidirect
115. #14579142	C₂³	semidirect
116. #14579140	C₂³	semidirect
117. #14579139	C₂³	semidirect
118. #14579138	C₂³	semidirect
119. #14579138	C₂³	semidirect
120. #14579137	C₂³	semidirect
125. #14579133	C₂³	semidirect
126. #14579133	C₂³	semidirect
130. #14579129	C₂³	semidirect
131. #14579129	C₂³	semidirect
132. C₄×Dic₁₅₈	C₂³	semidirect
135. C₄×C₂²⋊D₇₉	C₂³	semidirect
136. C₄×C₂²⋊D₇₉	C₂³	semidirect
137. #14579120	C₂³	semidirect
138. #14579118	C₂³	semidirect
162. C₂×C₄×Dic₇₉	C₂³	semidirect
166. C₂×#41×C₇₉	C₂³	semidirect
178. C₄⋊Q₈×C₇₉	C₂³	semidirect
181. #124×C₇₉	C₂³	semidirect
182. #121×C₇₉	C₂³	semidirect
183. C₄×D₄×C₇₉	C₂³	semidirect
190. C₂×C₄²×C₇₉	C₂³	semidirect
374. C₂×C₇₉	#3529	semidirect
387. C₂×#532	D₇₉	semidirect
392. C₇₉	C₂×#3529	semidirect
395. C₂²×#41	C₂×D₇₉	semidirect
405. #532	C₂×D₇₉	semidirect
407. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
422. C₂×#124	C₂×D₇₉	semidirect
444. C₂×#121	C₂×D₇₉	semidirect
454. C₂×C₄×D₄	C₂×D₇₉	semidirect
458. C₂²×C₄²	C₂×D₇₉	semidirect
465. C₂×#41	C₂²×D₇₉	semidirect
492. C₄⋊Q₈	C₂²×D₇₉	semidirect
505. #124	C₂²×D₇₉	semidirect
525. #121	C₂²×D₇₉	semidirect
535. C₄×D₄	C₂²×D₇₉	semidirect
568. C₂×C₄²	C₂²×D₇₉	semidirect
752. C₂	#23777536	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777536	2
C₂×#19099313	2
C₂×#19099312	2
C₂×#19099308	2
C₂×#19099307	2
C₂×#19099305	2
C₂×#19099301	2
C₂×#19099300	2
C₂×#19099109	2
C₂×#19099097	2
C₂×#19099093	2
C₂×#19099072	2
C₂×#19099070	2
C₂×#532×C₇₉	2
C₂×#3529	79

Subgroups — C2×#23777536 #35195158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777536 #35195158