Subgroups — C₂×#23776729 #35195106

Order 20224.

11662 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
2	#23776729	C₂	1	32	yes	maximal, direct product factor
3	C₂×#19099141	C₂	1	4	yes	maximal, complemented
4	C₂×#19099137	C₂	1	2	yes	maximal, complemented
5	C₂×#19099134	C₂	1	2	yes	maximal, complemented
6	C₂×#19099130	C₂	1	2	yes	maximal, complemented
7	C₂×#19099127	C₂	1	2	yes	maximal, complemented
8	C₂×#19099122	C₂	1	4	yes	maximal, complemented
9	C₂×#19099109	C₂	1	4	yes	maximal, complemented
10	C₂×#19099074	C₂	1	4	yes	maximal, complemented
11	C₂×#19099070	C₂	1	4	yes	maximal, complemented
12	C₂²×#14579120	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×#41×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#11929624	—	2	16	no	—
15	C₂²×#11929624	C₂²	1	2	yes	—
16	C₂²×#11929624	C₂²	1	2	yes	—
17	C₂²×#11929624	C₂²	1	2	yes	complemented
18	C₂²×#11929624	C₂²	1	2	yes	complemented
19	C₂²×#11929624	C₂²	1	16	yes	complemented
20	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	—
23	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
24	#19099141	C₂²	1	64	yes	complemented
25	#19099137	C₂²	1	32	yes	complemented
26	#19099134	C₂²	1	32	yes	complemented
27	#19099130	C₂²	1	32	yes	complemented
28	#19099127	C₂²	1	32	yes	complemented
29	#19099122	C₂²	1	64	yes	complemented
30	#19099109	C₂²	1	64	yes	complemented
31	C₂×#14579159	C₂²	1	4	yes	complemented
32	C₂×#14579157	C₂²	1	4	yes	complemented
33	C₂×#14579150	C₂²	1	4	yes	complemented
34	C₂×#14579148	C₂²	1	4	yes	complemented
35	#19099074	C₂²	1	64	yes	complemented
36	#19099070	C₂²	1	64	yes	complemented
37	C₂×#14579144	C₂²	1	8	yes	complemented
38	C₂×#14579142	C₂²	1	8	yes	complemented
39	C₂×#14579140	C₂²	1	8	yes	complemented
40	C₂×#14579137	C₂²	1	8	yes	complemented
41	C₂×#14579135	C₂²	1	8	yes	complemented
42	C₂×#14579133	C₂²	1	16	yes	complemented
43	C₂×#14579132	C₂²	1	8	yes	complemented
44	C₂×#14579130	C₂²	1	8	yes	complemented
45	C₂×#14579129	C₂²	1	8	yes	complemented
46	C₂×C₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
47	C₂×#14579120	C₂²	1	2	yes	complemented
48	C₂×#14579120	C₂²	1	2	yes	complemented
49	C₂×#14579120	C₂²	1	2	yes	complemented
50	C₂×#14579120	C₂²	1	2	yes	complemented
51	C₂×#14579120	C₂²	1	16	yes	complemented
52	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
53	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
54	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	complemented
55	C₂²×#41×C₇₉	—	2	16	no	—
56	C₂²×#41×C₇₉	C₂²	1	2	yes	—
57	C₂²×#41×C₇₉	C₂²	1	2	yes	—
58	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
59	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
60	C₂²×#41×C₇₉	C₂²	1	16	yes	complemented
61	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	C₂³×D₄×C₇₉	C₂²	1	2	yes	—
63	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
65	C₂⁴×C₄×C₇₉	C₂²	1	2	yes	complemented
66	C₂⁴×D₇₉	C₂³	1	2	yes	—
67	C₂×#11929624	—	2	16	no	—
68	C₂×#11929624	—	2	16	no	—
69	C₂×#11929624	—	2	16	no	—
70	C₂×#11929624	—	2	16	no	—
71	C₂×#11929624	—	2	128	no	—
72	C₂×#11929624	C₂³	1	16	yes	—
73	C₂×#11929624	C₂³	1	16	yes	—
74	C₂×#11929624	C₂³	1	16	yes	complemented
75	C₂×#11929624	C₂³	1	16	yes	complemented
76	C₂²×Dic₁₅₈	—	2	8	no	—
77	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
78	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
79	C₂²×Dic₁₅₈	C₂³	1	8	yes	complemented
80	C₂²×D₃₁₆	—	2	8	no	—
81	C₂²×D₃₁₆	C₂³	1	2	yes	—
82	C₂²×D₃₁₆	C₂³	1	2	yes	—
83	C₂²×D₃₁₆	C₂³	1	8	yes	complemented
84	C₂²×C₂²⋊D₇₉	—	2	16	no	—
85	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
86	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
87	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
88	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
89	C₂³×Dic₇₉	C₂³	1	2	yes	—
90	C₂³×Dic₇₉	C₂³	1	4	yes	—
91	C₂²×C₄×D₇₉	—	2	16	no	—
92	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
93	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
94	C₂²×C₄×D₇₉	C₂³	1	16	yes	complemented
95	#14579159	C₂³	1	32	yes	complemented
96	#14579157	C₂³	1	32	yes	complemented
97	#14579150	C₂³	1	32	yes	complemented
98	#14579148	C₂³	1	32	yes	complemented
99	#14579144	C₂³	1	64	yes	complemented
100	#14579142	C₂³	1	64	yes	complemented
101	#14579140	C₂³	1	64	yes	complemented
102	#14579137	C₂³	1	64	yes	complemented
103	#14579135	C₂³	1	64	yes	complemented
104	#14579133	C₂³	1	128	yes	complemented
105	#14579132	C₂³	1	64	yes	complemented
106	#14579130	C₂³	1	64	yes	complemented
107	#14579129	C₂³	1	64	yes	complemented
108	C₄×C₂²⋊D₇₉	C₂³	1	128	yes	complemented
109	#14579120	C₂³	1	16	yes	complemented
110	#14579120	C₂³	1	16	yes	complemented
111	#14579120	C₂³	1	16	yes	complemented
112	#14579120	C₂³	1	16	yes	complemented
113	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
114	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
115	C₂×C₄⋊Dic₇₉	C₂³	1	16	yes	complemented
116	C₂×Dic₇₉⋊C₄	C₂³	1	16	yes	—
117	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	—
120	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	—
121	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
122	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
123	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
124	C₂×C₄×Dic₇₉	C₂³	1	16	yes	complemented
125	C₂⁵×C₇₉	C₂³	1	2	yes	—
126	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
127	C₂×#41×C₇₉	—	2	16	no	—
128	C₂×#41×C₇₉	—	2	16	no	—
129	C₂×#41×C₇₉	—	2	16	no	—
130	C₂×#41×C₇₉	—	2	16	no	—
131	C₂×#41×C₇₉	—	2	128	no	—
132	C₂×#41×C₇₉	C₂³	1	16	yes	—
133	C₂×#41×C₇₉	C₂³	1	16	yes	—
134	C₂×#41×C₇₉	C₂³	1	16	yes	complemented
135	C₂×#41×C₇₉	C₂³	1	16	yes	complemented
136	C₂²×Q₈×C₇₉	—	2	8	no	—
137	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₇₉	C₂³	1	8	yes	complemented
140	C₂²×D₄×C₇₉	—	2	16	no	—
141	C₂²×D₄×C₇₉	—	2	8	no	—
142	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
143	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
144	C₂²×D₄×C₇₉	C₂³	1	16	yes	—
145	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
146	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
147	C₂²×D₄×C₇₉	C₂³	1	8	yes	complemented
148	C₂³×C₄×C₇₉	—	2	16	no	—
149	C₂³×C₄×C₇₉	D₄	1	16	yes	complemented
150	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
151	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
153	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₇₉	C₂³	1	8	yes	—
160	C₂³×C₄×C₇₉	C₂³	1	16	yes	complemented
161	C₂³×D₇₉	—	2	8	no	—
162	C₂³×D₇₉	—	4	8	no	—
163	C₂³×D₇₉	C₂⁴	1	4	yes	—
164	C₂³×D₇₉	C₂⁴	1	8	yes	—
165	#11929624	—	2	64	no	—
166	#11929624	—	2	64	no	—
167	#11929624	—	2	64	no	—
168	#11929624	—	2	64	no	—
169	C₂×Dic₁₅₈	—	2	8	no	—
170	C₂×Dic₁₅₈	—	2	8	no	—
171	C₂×Dic₁₅₈	—	2	32	no	—
172	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
173	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
174	C₂×D₃₁₆	—	2	8	no	—
175	C₂×D₃₁₆	—	2	8	no	—
176	C₂×D₃₁₆	—	2	32	no	—
177	C₂×D₃₁₆	C₂⁴	1	8	yes	—
178	C₂×D₃₁₆	C₂⁴	1	8	yes	—
179	C₂×C₂²⋊D₇₉	—	2	16	no	—
180	C₂×C₂²⋊D₇₉	—	2	16	no	—
181	C₂×C₂²⋊D₇₉	—	2	64	no	—
182	C₂×C₂²⋊D₇₉	—	4	32	no	—
183	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
184	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
185	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	—
186	C₂²×Dic₇₉	—	2	8	no	—
187	C₂²×Dic₇₉	—	4	8	no	—
188	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
189	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
190	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
191	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
192	C₂×C₄×D₇₉	—	2	16	no	—
193	C₂×C₄×D₇₉	—	2	16	no	—
194	C₂×C₄×D₇₉	—	2	64	no	—
195	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
196	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
197	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
198	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
199	Dic₇₉⋊C₄	C₂⁴	1	64	yes	—
200	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
201	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
202	C₂²⋊Dic₇₉	C₂⁴	1	64	yes	—
203	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	—
204	C₄×Dic₇₉	C₂⁴	1	16	yes	—
205	C₄×Dic₇₉	C₂⁴	1	16	yes	—
206	C₂⁴×C₇₉	—	2	8	no	—
207	C₂⁴×C₇₉	—	4	4	no	—
208	C₂⁴×C₇₉	—	4	8	no	—
209	C₂⁴×C₇₉	C₂×D₄	1	8	yes	—
210	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
211	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
215	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
216	#41×C₇₉	—	2	64	no	—
217	#41×C₇₉	—	2	64	no	—
218	#41×C₇₉	—	2	64	no	—
219	#41×C₇₉	—	2	64	no	—
220	C₂×Q₈×C₇₉	—	2	8	no	—
221	C₂×Q₈×C₇₉	—	2	8	no	—
222	C₂×Q₈×C₇₉	—	2	32	no	—
223	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
224	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
225	C₂×D₄×C₇₉	—	2	16	no	—
226	C₂×D₄×C₇₉	—	2	16	no	—
227	C₂×D₄×C₇₉	—	2	64	no	—
228	C₂×D₄×C₇₉	—	2	8	no	—
229	C₂×D₄×C₇₉	—	2	8	no	—
230	C₂×D₄×C₇₉	—	2	32	no	—
231	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
232	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
233	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
234	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
235	C₂²×C₄×C₇₉	—	2	8	no	—
236	C₂²×C₄×C₇₉	—	2	16	no	—
237	C₂²×C₄×C₇₉	—	2	16	no	—
238	C₂²×C₄×C₇₉	—	2	64	no	—
239	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
240	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
241	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
242	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
243	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
244	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
245	C₂²×C₄×C₇₉	C₂×D₄	1	64	yes	complemented
246	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
249	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
250	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
260	C₂³×C₇₉	—	2	4	no	—
261	C₂³×C₇₉	—	2	4	no	—
262	C₂³×C₇₉	—	2	4	no	—
263	C₂³×C₇₉	—	2	16	no	—
264	C₂³×C₇₉	—	2	8	no	—
265	C₂³×C₇₉	—	2	16	no	—
266	C₂³×C₇₉	—	4	16	no	—
267	C₂³×C₇₉	—	4	8	no	—
268	C₂³×C₇₉	—	4	16	no	—
269	C₂³×C₇₉	—	4	32	no	—
270	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
271	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
272	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
273	C₂³×C₇₉	C₂²×D₄	1	16	yes	—
274	C₂³×C₇₉	C₂⁵	1	8	yes	—
275	C₂³×C₇₉	C₂⁵	1	2	yes	—
276	C₂³×C₇₉	C₂⁵	1	2	yes	—
277	C₂³×C₇₉	C₂⁵	1	2	yes	—
278	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
279	C₂²×D₇₉	—	2	16	no	—
280	C₂²×D₇₉	—	2	8	no	—
281	C₂²×D₇₉	—	2	16	no	—
282	C₂²×D₇₉	—	4	16	no	—
283	C₂²×D₇₉	—	4	32	no	—
284	C₂²×D₇₉	C₂⁵	1	8	yes	—
285	Q₈×C₇₉	—	2	16	no	—
286	Q₈×C₇₉	—	2	16	no	—
287	D₄×C₇₉	—	2	32	no	—
288	D₄×C₇₉	—	2	32	no	—
289	D₄×C₇₉	—	2	16	no	—
290	D₄×C₇₉	—	2	16	no	—
291	C₂×C₄×C₇₉	—	2	16	no	—
292	C₂×C₄×C₇₉	—	2	8	no	—
293	C₂×C₄×C₇₉	—	2	32	no	—
294	C₂×C₄×C₇₉	—	2	32	no	—
295	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
298	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
301	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
302	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
303	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
304	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	—
305	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
306	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
307	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
308	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
309	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
310	C₂²⋊D₇₉	—	2	32	no	—
311	C₂²⋊D₇₉	—	2	32	no	—
312	C₂²⋊D₇₉	—	4	64	no	—
313	C₂×Dic₇₉	—	2	16	no	—
314	C₂×Dic₇₉	—	2	8	no	—
315	C₂×Dic₇₉	—	2	16	no	—
316	C₂×Dic₇₉	—	4	16	no	—
317	C₂×Dic₇₉	C₂⁵	1	16	yes	—
318	C₂×Dic₇₉	C₂⁵	1	8	yes	—
319	D₃₁₆	—	2	16	no	—
320	D₃₁₆	—	2	16	no	—
321	C₄×D₇₉	—	2	32	no	—
322	C₄×D₇₉	—	2	32	no	—
323	Dic₁₅₈	—	2	16	no	—
324	Dic₁₅₈	—	2	16	no	—
325	C₂²×C₇₉	—	2	4	no	—
326	C₂²×C₇₉	—	2	4	no	—
327	C₂²×C₇₉	—	2	4	no	—
328	C₂²×C₇₉	—	2	8	no	—
329	C₂²×C₇₉	—	2	8	no	—
330	C₂²×C₇₉	—	2	8	no	—
331	C₂²×C₇₉	—	2	8	no	—
332	C₂²×C₇₉	—	2	16	no	—
333	C₂²×C₇₉	—	4	16	no	—
334	C₂²×C₇₉	—	4	32	no	—
335	C₂²×C₇₉	—	4	16	no	—
336	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
337	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
338	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
339	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
340	C₂²×C₇₉	#585	1	4	yes	—
341	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
342	C₂×D₇₉	—	2	8	no	—
343	C₂×D₇₉	—	2	16	no	—
344	C₂×D₇₉	—	4	32	no	—
345	C₂×D₇₉	—	4	16	no	—
346	C₄×C₇₉	—	2	8	no	—
347	C₄×C₇₉	C₂³×D₄	1	4	yes	—
348	C₄×C₇₉	C₂³×D₄	1	4	yes	—
349	C₄×C₇₉	C₂³×D₄	1	4	yes	—
350	C₄×C₇₉	C₂³×D₄	1	4	yes	—
351	Dic₇₉	—	2	8	no	—
352	Dic₇₉	—	2	16	no	—
353	C₂×#3449	—	79	1	no	maximal, Sylow
354	C₂×C₇₉	—	2	4	no	—
355	C₂×C₇₉	—	2	4	no	—
356	C₂×C₇₉	—	2	4	no	—
357	C₂×C₇₉	—	4	8	no	—
358	C₂×C₇₉	#3449	1	4	yes	complemented
359	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
360	C₂×C₇₉	C₂×#585	1	2	yes	—
361	D₇₉	—	4	8	no	—
362	C₂³×#41	—	79	1	no	—
363	C₂³×#41	D₇₉	1	1	yes	characteristic, complemented
364	#3449	—	79	32	no	—
365	C₂×#537	—	79	4	no	—
366	C₂×#536	—	79	2	no	—
367	C₂×#536	—	79	2	no	—
368	C₂×#535	—	79	2	no	—
369	C₂×#535	—	79	2	no	—
370	C₂×#534	—	79	4	no	—
371	C₂×#532	—	79	4	no	—
372	C₂×#525	—	79	4	no	—
373	C₂×#525	—	79	4	no	—
374	C₂²×#117	—	79	1	no	—
375	C₇₉	C₂×#3449	1	1	yes	characteristic, complemented, Sylow
376	C₂²×#41	—	2	16	no	—
377	C₂²×#41	—	79	2	no	—
378	C₂²×#41	—	79	2	no	—
379	C₂²×#41	—	79	2	no	—
380	C₂²×#41	—	79	2	no	—
381	C₂²×#41	—	79	16	no	—
382	C₂²×#41	—	158	16	no	—
383	C₂²×#41	C₂×D₇₉	1	2	yes	—
384	C₂²×#41	C₂×D₇₉	1	2	yes	—
385	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
386	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
387	C₂²×#41	C₂×D₇₉	1	16	yes	complemented
388	C₂³×Q₈	—	79	1	no	—
389	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
390	C₂³×D₄	—	79	2	no	—
391	C₂³×D₄	—	79	1	no	—
392	C₂³×D₄	C₂×D₇₉	1	2	yes	—
393	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
394	C₂⁴×C₄	—	79	2	no	—
395	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
396	C₂⁴×C₄	C₂×D₇₉	1	2	yes	complemented
397	#537	—	79	64	no	—
398	#536	—	79	32	no	—
399	#536	—	79	32	no	—
400	#535	—	79	32	no	—
401	#535	—	79	32	no	—
402	#534	—	79	64	no	—
403	#532	—	79	64	no	—
404	C₂×C₄⋊Q₈	—	79	4	no	—
405	C₂×#127	—	79	4	no	—
406	C₂×#124	—	79	4	no	—
407	C₂×#124	—	79	4	no	—
408	#525	—	79	64	no	—
409	#525	—	79	64	no	—
410	C₂×#123	—	79	8	no	—
411	C₂×#123	—	79	8	no	—
412	C₂×C₂²⋊Q₈	—	79	8	no	—
413	C₂×C₂²⋊Q₈	—	79	8	no	—
414	C₂×#121	—	79	8	no	—
415	C₂×#121	—	79	16	no	—
416	C₂×#121	—	79	8	no	—
417	C₂×#120	—	79	8	no	—
418	C₂×#120	—	79	8	no	—
419	C₂×C₄×D₄	—	79	16	no	—
420	C₂×#117	—	79	2	no	—
421	C₂×#117	—	79	2	no	—
422	C₂×#117	—	79	2	no	—
423	C₂×#117	—	79	2	no	—
424	C₂×#117	—	79	16	no	—
425	C₂²×C₄⋊C₄	—	79	2	no	—
426	C₂²×C₂²⋊C₄	—	79	2	no	—
427	C₂²×C₄²	—	79	2	no	—
428	C₂⁵	—	79	2	no	—
429	C₂⁵	C₂²×D₇₉	1	2	yes	—
430	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
431	C₂×#41	—	2	16	no	—
432	C₂×#41	—	2	16	no	—
433	C₂×#41	—	2	16	no	—
434	C₂×#41	—	2	16	no	—
435	C₂×#41	—	2	128	no	—
436	C₂×#41	—	79	16	no	—
437	C₂×#41	—	79	16	no	—
438	C₂×#41	—	79	16	no	—
439	C₂×#41	—	79	16	no	—
440	C₂×#41	—	158	16	no	—
441	C₂×#41	—	158	16	no	—
442	C₂×#41	—	158	16	no	—
443	C₂×#41	—	158	16	no	—
444	C₂×#41	—	158	128	no	—
445	C₂×#41	C₂²×D₇₉	1	16	yes	—
446	C₂×#41	C₂²×D₇₉	1	16	yes	—
447	C₂×#41	C₂²×D₇₉	1	16	yes	complemented
448	C₂×#41	C₂²×D₇₉	1	16	yes	complemented
449	C₂²×Q₈	—	2	8	no	—
450	C₂²×Q₈	—	79	2	no	—
451	C₂²×Q₈	—	79	2	no	—
452	C₂²×Q₈	—	79	8	no	—
453	C₂²×Q₈	—	158	8	no	—
454	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
455	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
456	C₂²×Q₈	C₂²×D₇₉	1	8	yes	complemented
457	C₂²×D₄	—	2	16	no	—
458	C₂²×D₄	—	2	8	no	—
459	C₂²×D₄	—	79	16	no	—
460	C₂²×D₄	—	79	4	no	—
461	C₂²×D₄	—	79	4	no	—
462	C₂²×D₄	—	79	16	no	—
463	C₂²×D₄	—	79	2	no	—
464	C₂²×D₄	—	79	2	no	—
465	C₂²×D₄	—	79	8	no	—
466	C₂²×D₄	—	158	16	no	—
467	C₂²×D₄	—	158	8	no	—
468	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
469	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
470	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
471	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
472	C₂²×D₄	C₂²×D₇₉	1	16	yes	—
473	C₂²×D₄	C₂²×D₇₉	1	8	yes	complemented
474	C₂³×C₄	—	2	16	no	—
475	C₂³×C₄	—	79	4	no	—
476	C₂³×C₄	—	79	2	no	—
477	C₂³×C₄	—	79	4	no	—
478	C₂³×C₄	—	79	16	no	—
479	C₂³×C₄	—	79	4	no	—
480	C₂³×C₄	—	158	16	no	—
481	C₂³×C₄	C₂²⋊D₇₉	1	16	yes	complemented
482	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
483	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
484	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
485	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
486	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
487	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
488	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
489	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
490	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
491	C₂³×C₄	C₂²×D₇₉	1	8	yes	—
492	C₂³×C₄	C₂²×D₇₉	1	16	yes	complemented
493	C₄⋊Q₈	—	79	32	no	—
494	#127	—	79	32	no	—
495	#124	—	79	32	no	—
496	#124	—	79	32	no	—
497	#123	—	79	64	no	—
498	#123	—	79	64	no	—
499	C₂²⋊Q₈	—	79	64	no	—
500	C₂²⋊Q₈	—	79	64	no	—
501	#121	—	79	64	no	—
502	#121	—	79	128	no	—
503	#121	—	79	64	no	—
504	#120	—	79	64	no	—
505	#120	—	79	64	no	—
506	C₄×D₄	—	79	128	no	—
507	#117	—	79	16	no	—
508	#117	—	79	16	no	—
509	#117	—	79	16	no	—
510	#117	—	79	16	no	—
511	C₂×C₄⋊C₄	—	79	4	no	—
512	C₂×C₄⋊C₄	—	79	4	no	—
513	C₂×C₄⋊C₄	—	79	16	no	—
514	C₂×C₄⋊C₄	—	79	16	no	—
515	C₂×C₂²⋊C₄	—	79	4	no	—
516	C₂×C₂²⋊C₄	—	79	4	no	—
517	C₂×C₂²⋊C₄	—	79	16	no	—
518	C₂×C₂²⋊C₄	—	79	16	no	—
519	C₂×C₂²⋊C₄	—	79	16	no	—
520	C₂×C₄²	—	79	4	no	—
521	C₂×C₄²	—	79	16	no	—
522	C₂×C₄²	—	79	4	no	—
523	C₂⁴	—	2	8	no	—
524	C₂⁴	—	4	4	no	—
525	C₂⁴	—	4	8	no	—
526	C₂⁴	—	316	8	no	—
527	C₂⁴	—	79	8	no	—
528	C₂⁴	—	79	4	no	—
529	C₂⁴	—	158	8	no	—
530	C₂⁴	C₂×C₂²⋊D₇₉	1	8	yes	—
531	C₂⁴	C₂³×D₇₉	1	4	yes	—
532	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
533	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
534	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
535	C₂⁴	C₂³×D₇₉	1	8	yes	—
536	C₂⁴	C₂³×D₇₉	1	4	yes	—
537	#41	—	2	64	no	—
538	#41	—	2	64	no	—
539	#41	—	2	64	no	—
540	#41	—	2	64	no	—
541	#41	—	158	64	no	—
542	#41	—	158	64	no	—
543	#41	—	158	64	no	—
544	#41	—	158	64	no	—
545	C₂×Q₈	—	2	8	no	—
546	C₂×Q₈	—	2	8	no	—
547	C₂×Q₈	—	2	32	no	—
548	C₂×Q₈	—	79	8	no	—
549	C₂×Q₈	—	79	8	no	—
550	C₂×Q₈	—	158	8	no	—
551	C₂×Q₈	—	158	8	no	—
552	C₂×Q₈	—	158	32	no	—
553	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
554	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
555	C₂×D₄	—	2	16	no	—
556	C₂×D₄	—	2	16	no	—
557	C₂×D₄	—	2	64	no	—
558	C₂×D₄	—	2	8	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	32	no	—
561	C₂×D₄	—	316	32	no	—
562	C₂×D₄	—	79	64	no	—
563	C₂×D₄	—	79	16	no	—
564	C₂×D₄	—	79	16	no	—
565	C₂×D₄	—	79	8	no	—
566	C₂×D₄	—	79	8	no	—
567	C₂×D₄	—	158	16	no	—
568	C₂×D₄	—	158	16	no	—
569	C₂×D₄	—	158	64	no	—
570	C₂×D₄	—	158	8	no	—
571	C₂×D₄	—	158	8	no	—
572	C₂×D₄	—	158	32	no	—
573	C₂×D₄	C₂³×D₇₉	1	16	yes	—
574	C₂×D₄	C₂³×D₇₉	1	16	yes	—
575	C₂×D₄	C₂³×D₇₉	1	8	yes	—
576	C₂×D₄	C₂³×D₇₉	1	8	yes	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	16	no	—
579	C₂²×C₄	—	2	16	no	—
580	C₂²×C₄	—	2	64	no	—
581	C₂²×C₄	—	316	8	no	—
582	C₂²×C₄	—	79	16	no	—
583	C₂²×C₄	—	79	8	no	—
584	C₂²×C₄	—	79	4	no	—
585	C₂²×C₄	—	79	8	no	—
586	C₂²×C₄	—	79	16	no	—
587	C₂²×C₄	—	79	16	no	—
588	C₂²×C₄	—	158	8	no	—
589	C₂²×C₄	—	158	16	no	—
590	C₂²×C₄	—	158	16	no	—
591	C₂²×C₄	—	158	64	no	—
592	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
593	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
594	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
595	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
596	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
597	C₂²×C₄	C₂×C₂²⋊D₇₉	1	8	yes	—
598	C₂²×C₄	C₂×C₂²⋊D₇₉	1	64	yes	complemented
599	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
600	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
601	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
602	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
603	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
604	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
605	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
606	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
607	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
608	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
609	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
610	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
611	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
612	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
613	C₄⋊C₄	—	79	64	no	—
614	C₄⋊C₄	—	79	16	no	—
615	C₄⋊C₄	—	79	16	no	—
616	C₂²⋊C₄	—	79	16	no	—
617	C₂²⋊C₄	—	79	16	no	—
618	C₂²⋊C₄	—	79	64	no	—
619	C₂²⋊C₄	—	79	64	no	—
620	C₄²	—	79	16	no	—
621	C₄²	—	79	16	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	16	no	—
626	C₂³	—	2	16	no	—
627	C₂³	—	2	8	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	16	no	—
631	C₂³	—	4	32	no	—
632	C₂³	—	316	32	no	—
633	C₂³	—	316	16	no	—
634	C₂³	—	79	8	no	—
635	C₂³	—	158	16	no	—
636	C₂³	—	158	16	no	—
637	C₂³	—	158	8	no	—
638	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
639	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
640	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
641	C₂³	C₂²×C₂²⋊D₇₉	1	16	yes	—
642	C₂³	C₂⁴×D₇₉	1	8	yes	—
643	C₂³	C₂⁴×D₇₉	1	2	yes	—
644	C₂³	C₂⁴×D₇₉	1	2	yes	—
645	C₂³	C₂⁴×D₇₉	1	2	yes	—
646	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
647	Q₈	—	2	16	no	—
648	Q₈	—	2	16	no	—
649	Q₈	—	158	16	no	—
650	Q₈	—	158	16	no	—
651	D₄	—	2	32	no	—
652	D₄	—	2	32	no	—
653	D₄	—	2	16	no	—
654	D₄	—	2	16	no	—
655	D₄	—	316	64	no	—
656	D₄	—	158	32	no	—
657	D₄	—	158	32	no	—
658	D₄	—	158	16	no	—
659	D₄	—	158	16	no	—
660	C₂×C₄	—	2	16	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	2	32	no	—
663	C₂×C₄	—	2	32	no	—
664	C₂×C₄	—	316	16	no	—
665	C₂×C₄	—	79	16	no	—
666	C₂×C₄	—	79	8	no	—
667	C₂×C₄	—	158	16	no	—
668	C₂×C₄	—	158	16	no	—
669	C₂×C₄	—	158	8	no	—
670	C₂×C₄	—	158	32	no	—
671	C₂×C₄	—	158	32	no	—
672	C₂×C₄	C₂²×C₂²⋊D₇₉	1	4	yes	—
673	C₂×C₄	C₂²×C₂²⋊D₇₉	1	4	yes	—
674	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
675	C₂×C₄	C₂²×C₂²⋊D₇₉	1	4	yes	—
676	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
677	C₂×C₄	C₂²×C₂²⋊D₇₉	1	4	yes	—
678	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
679	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
680	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
681	C₂×C₄	C₂²×C₂²⋊D₇₉	1	16	yes	—
682	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
683	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
684	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
685	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
686	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	8	no	—
691	C₂²	—	2	8	no	—
692	C₂²	—	2	8	no	—
693	C₂²	—	2	8	no	—
694	C₂²	—	2	16	no	—
695	C₂²	—	4	16	no	—
696	C₂²	—	4	32	no	—
697	C₂²	—	4	16	no	—
698	C₂²	—	316	32	no	—
699	C₂²	—	316	16	no	—
700	C₂²	—	158	8	no	—
701	C₂²	—	158	16	no	—
702	C₂²	C₂³×C₂²⋊D₇₉	1	4	yes	—
703	C₂²	C₂³×C₂²⋊D₇₉	1	4	yes	—
704	C₂²	C₂³×C₂²⋊D₇₉	1	4	yes	—
705	C₂²	C₂³×C₂²⋊D₇₉	1	2	yes	—
706	C₂²	#19099399	1	4	yes	—
707	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
708	C₄	—	2	8	no	—
709	C₄	—	158	8	no	—
710	C₄	—	158	16	no	—
711	C₄	C₂³×C₂²⋊D₇₉	1	4	yes	—
712	C₄	C₂³×C₂²⋊D₇₉	1	4	yes	—
713	C₄	C₂³×C₂²⋊D₇₉	1	4	yes	—
714	C₄	C₂³×C₂²⋊D₇₉	1	4	yes	—
715	C₂	—	2	4	no	—
716	C₂	—	2	4	no	—
717	C₂	—	2	4	no	—
718	C₂	—	4	8	no	—
719	C₂	—	316	8	no	—
720	C₂	#23776729	1	4	yes	direct product factor
721	C₂	C₂⁴×C₂²⋊D₇₉	1	1	yes	characteristic
722	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂³×#41×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂³×#41	D₇₉
hypocenter	C₇₉	C₂×#3449
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929624	C₂	semidirect
2. #23776729	C₂	direct (N × H)
3. C₂×#19099141	C₂	semidirect
4. C₂×#19099137	C₂	semidirect
5. C₂×#19099134	C₂	semidirect
6. C₂×#19099130	C₂	semidirect
7. C₂×#19099127	C₂	semidirect
8. C₂×#19099122	C₂	semidirect
9. C₂×#19099109	C₂	semidirect
10. C₂×#19099074	C₂	semidirect
11. C₂×#19099070	C₂	semidirect
12. C₂²×#14579120	C₂	semidirect
13. C₂³×#41×C₇₉	C₂	semidirect
17. C₂²×#11929624	C₂²	semidirect
18. C₂²×#11929624	C₂²	semidirect
19. C₂²×#11929624	C₂²	semidirect
20. C₂³×Dic₁₅₈	C₂²	semidirect
21. C₂³×D₃₁₆	C₂²	semidirect
23. C₂³×C₄×D₇₉	C₂²	semidirect
24. #19099141	C₂²	semidirect
25. #19099137	C₂²	semidirect
26. #19099134	C₂²	semidirect
27. #19099130	C₂²	semidirect
28. #19099127	C₂²	semidirect
29. #19099122	C₂²	semidirect
30. #19099109	C₂²	semidirect
31. C₂×#14579159	C₂²	semidirect
32. C₂×#14579157	C₂²	semidirect
33. C₂×#14579150	C₂²	semidirect
34. C₂×#14579148	C₂²	semidirect
35. #19099074	C₂²	semidirect
36. #19099070	C₂²	semidirect
37. C₂×#14579144	C₂²	semidirect
38. C₂×#14579142	C₂²	semidirect
39. C₂×#14579140	C₂²	semidirect
40. C₂×#14579137	C₂²	semidirect
41. C₂×#14579135	C₂²	semidirect
42. C₂×#14579133	C₂²	semidirect
43. C₂×#14579132	C₂²	semidirect
44. C₂×#14579130	C₂²	semidirect
45. C₂×#14579129	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
47. C₂×#14579120	C₂²	semidirect
48. C₂×#14579120	C₂²	semidirect
49. C₂×#14579120	C₂²	semidirect
50. C₂×#14579120	C₂²	semidirect
51. C₂×#14579120	C₂²	semidirect
52. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
54. C₂²×C₄×Dic₇₉	C₂²	semidirect
58. C₂²×#41×C₇₉	C₂²	semidirect
59. C₂²×#41×C₇₉	C₂²	semidirect
60. C₂²×#41×C₇₉	C₂²	semidirect
61. C₂³×Q₈×C₇₉	C₂²	semidirect
63. C₂³×D₄×C₇₉	C₂²	semidirect
65. C₂⁴×C₄×C₇₉	C₂²	semidirect
74. C₂×#11929624	C₂³	semidirect
75. C₂×#11929624	C₂³	semidirect
79. C₂²×Dic₁₅₈	C₂³	semidirect
83. C₂²×D₃₁₆	C₂³	semidirect
94. C₂²×C₄×D₇₉	C₂³	semidirect
95. #14579159	C₂³	semidirect
96. #14579157	C₂³	semidirect
97. #14579150	C₂³	semidirect
98. #14579148	C₂³	semidirect
99. #14579144	C₂³	semidirect
100. #14579142	C₂³	semidirect
101. #14579140	C₂³	semidirect
102. #14579137	C₂³	semidirect
103. #14579135	C₂³	semidirect
104. #14579133	C₂³	semidirect
105. #14579132	C₂³	semidirect
106. #14579130	C₂³	semidirect
107. #14579129	C₂³	semidirect
108. C₄×C₂²⋊D₇₉	C₂³	semidirect
109. #14579120	C₂³	semidirect
110. #14579120	C₂³	semidirect
111. #14579120	C₂³	semidirect
112. #14579120	C₂³	semidirect
115. C₂×C₄⋊Dic₇₉	C₂³	semidirect
124. C₂×C₄×Dic₇₉	C₂³	semidirect
134. C₂×#41×C₇₉	C₂³	semidirect
135. C₂×#41×C₇₉	C₂³	semidirect
139. C₂²×Q₈×C₇₉	C₂³	semidirect
147. C₂²×D₄×C₇₉	C₂³	semidirect
149. C₂³×C₄×C₇₉	D₄	semidirect
160. C₂³×C₄×C₇₉	C₂³	semidirect
245. C₂²×C₄×C₇₉	C₂×D₄	semidirect
358. C₂×C₇₉	#3449	semidirect
363. C₂³×#41	D₇₉	semidirect
375. C₇₉	C₂×#3449	semidirect
385. C₂²×#41	C₂×D₇₉	semidirect
386. C₂²×#41	C₂×D₇₉	semidirect
387. C₂²×#41	C₂×D₇₉	semidirect
389. C₂³×Q₈	C₂×D₇₉	semidirect
393. C₂³×D₄	C₂×D₇₉	semidirect
396. C₂⁴×C₄	C₂×D₇₉	semidirect
447. C₂×#41	C₂²×D₇₉	semidirect
448. C₂×#41	C₂²×D₇₉	semidirect
456. C₂²×Q₈	C₂²×D₇₉	semidirect
473. C₂²×D₄	C₂²×D₇₉	semidirect
481. C₂³×C₄	C₂²⋊D₇₉	semidirect
492. C₂³×C₄	C₂²×D₇₉	semidirect
598. C₂²×C₄	C₂×C₂²⋊D₇₉	semidirect
720. C₂	#23776729	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11929624	2
#23776729	2
C₂×#19099141	2
C₂×#19099137	2
C₂×#19099134	2
C₂×#19099130	2
C₂×#19099127	2
C₂×#19099122	2
C₂×#19099109	2
C₂×#19099074	2
C₂×#19099070	2
C₂²×#14579120	2
C₂³×#41×C₇₉	2
C₂×#3449	79

Subgroups — C2×#23776729 #35195106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23776729 #35195106