Subgroups — #35197281

Order 20224.

11770 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579207	C₂	1	2	yes	maximal, complemented
2	#23777163	C₂	1	8	yes	maximal, complemented
3	#23777162	C₂	1	8	yes	maximal, complemented
4	#23777043	C₂	1	8	yes	maximal, complemented
5	#23777042	C₂	1	8	yes	maximal, complemented
6	#23777034	C₂	1	8	yes	maximal, complemented
7	#23777033	C₂	1	8	yes	maximal, complemented
8	#23776733	C₂	1	1	yes	maximal, characteristic, complemented
9	#23776729	C₂	1	2	yes	maximal, complemented
10	#534×D₇₉	C₂	1	8	yes	maximal, complemented
11	C₂×#19099037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14579207	—	2	32	no	—
14	C₂×#14579207	C₂²	1	8	yes	complemented
15	C₂×#14579207	C₂²	1	8	yes	complemented
16	C₂×#14579207	C₂²	1	8	yes	complemented
17	C₂×#14579207	C₂²	1	8	yes	complemented
18	C₂²×#11929625	C₂²	1	4	yes	complemented
19	C₂²×#11929624	C₂²	1	2	yes	complemented
20	C₂²×#11929624	C₂²	1	4	yes	complemented
21	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
22	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₇₉	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
25	#19099218	C₂²	1	16	yes	complemented
26	#19099216	C₂²	1	16	yes	complemented
27	#19099215	C₂²	1	32	yes	complemented
28	#19099210	C₂²	1	32	yes	complemented
29	#19099209	C₂²	1	32	yes	complemented
30	#19099206	C₂²	1	32	yes	complemented
31	#19099204	C₂²	1	32	yes	complemented
32	D₄×D₃₁₆	C₂²	1	16	yes	complemented
33	#19099198	C₂²	1	16	yes	complemented
34	#19099197	C₂²	1	32	yes	complemented
35	#19099144	C₂²	1	4	yes	complemented
36	#19099141	C₂²	1	8	yes	complemented
37	#19099139	C₂²	1	4	yes	complemented
38	#19099137	C₂²	1	4	yes	complemented
39	#19099134	C₂²	1	4	yes	complemented
40	#19099132	C₂²	1	4	yes	complemented
41	#19099130	C₂²	1	4	yes	complemented
42	#19099127	C₂²	1	4	yes	complemented
43	#19099125	C₂²	1	4	yes	complemented
44	#19099124	C₂²	1	32	yes	complemented
45	#19099123	C₂²	1	32	yes	complemented
46	#19099122	C₂²	1	8	yes	complemented
47	#19099121	C₂²	1	32	yes	complemented
48	#19099113	C₂²	1	4	yes	complemented
49	#19099109	C₂²	1	8	yes	complemented
50	#19099075	C₂²	1	8	yes	complemented
51	#19099074	C₂²	1	8	yes	complemented
52	#19099070	C₂²	1	8	yes	complemented
53	#123×D₇₉	C₂²	1	32	yes	complemented
54	#121×D₇₉	C₂²	1	32	yes	complemented
55	#120×D₇₉	C₂²	1	32	yes	complemented
56	#19099037	C₂²	1	8	yes	complemented
57	#19099037	C₂²	1	8	yes	complemented
58	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
59	C₂×#14579123	C₂²	1	4	yes	complemented
60	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
62	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
63	#537×C₇₉	C₂²	1	4	yes	complemented
64	#536×C₇₉	C₂²	1	4	yes	complemented
65	#535×C₇₉	C₂²	1	4	yes	complemented
66	#534×C₇₉	C₂²	1	4	yes	complemented
67	#532×C₇₉	C₂²	1	4	yes	complemented
68	#525×C₇₉	C₂²	1	8	yes	complemented
69	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₇₉	C₂³	1	2	yes	—
71	C₂⁴×D₇₉	C₂³	1	8	yes	complemented
72	#14579207	—	2	64	no	—
73	#14579207	—	2	64	no	—
74	#14579207	—	2	64	no	—
75	#14579207	—	2	64	no	—
76	C₂×#11929625	—	2	32	no	—
77	C₂×#11929625	C₂³	1	16	yes	complemented
78	C₂×#11929625	C₂³	1	16	yes	complemented
79	C₂×#11929624	—	2	16	no	—
80	C₂×#11929624	—	2	32	no	—
81	C₂×#11929624	C₂³	1	4	yes	—
82	C₂×#11929624	C₂³	1	4	yes	—
83	C₂×#11929624	C₂³	1	4	yes	complemented
84	C₂×#11929624	C₂³	1	4	yes	complemented
85	C₂×#11929624	C₂³	1	16	yes	complemented
86	C₂×#11929624	C₂³	1	16	yes	complemented
87	C₂²×Dic₁₅₈	C₂³	1	2	yes	complemented
88	C₂²×D₃₁₆	—	2	32	no	—
89	C₂²×D₃₁₆	D₄	1	16	yes	complemented
90	C₂²×D₃₁₆	C₂³	1	2	yes	—
91	C₂²×D₃₁₆	C₂³	1	2	yes	—
92	C₂²×D₃₁₆	C₂³	1	4	yes	—
93	C₂²×D₃₁₆	C₂³	1	4	yes	—
94	C₂²×D₃₁₆	C₂³	1	16	yes	complemented
95	C₂²×D₃₁₆	C₂³	1	16	yes	complemented
96	C₂²×D₃₁₆	C₂³	1	8	yes	complemented
97	C₂²×D₃₁₆	C₂³	1	2	yes	complemented
98	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
99	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	complemented
100	C₂×D₄×D₇₉	—	2	64	no	—
101	C₂×D₄×D₇₉	—	2	32	no	—
102	C₂×D₄×D₇₉	C₂³	1	32	yes	—
103	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
104	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
105	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
106	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
107	C₂²×C₄×D₇₉	C₂³	1	8	yes	complemented
108	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
109	C₂²×C₄×D₇₉	C₂³	1	8	yes	complemented
110	#14579161	C₂³	1	4	yes	complemented
111	#14579159	C₂³	1	8	yes	complemented
112	#14579158	C₂³	1	4	yes	complemented
113	#14579157	C₂³	1	8	yes	complemented
114	#14579150	C₂³	1	8	yes	complemented
115	#14579149	C₂³	1	8	yes	complemented
116	#14579148	C₂³	1	8	yes	complemented
117	#14579146	C₂³	1	64	yes	complemented
118	#14579145	C₂³	1	16	yes	complemented
119	#14579144	C₂³	1	16	yes	complemented
120	#14579143	C₂³	1	64	yes	complemented
121	#14579142	C₂³	1	16	yes	complemented
122	#14579141	C₂³	1	16	yes	complemented
123	#14579140	C₂³	1	16	yes	complemented
124	#14579137	C₂³	1	16	yes	complemented
125	#14579136	C₂³	1	16	yes	complemented
126	#14579136	C₂³	1	32	yes	complemented
127	#14579135	C₂³	1	16	yes	complemented
128	#14579135	C₂³	1	16	yes	complemented
129	#14579134	C₂³	1	64	yes	complemented
130	#14579133	C₂³	1	32	yes	complemented
131	#14579132	C₂³	1	16	yes	complemented
132	#14579132	C₂³	1	32	yes	complemented
133	#14579131	C₂³	1	64	yes	complemented
134	#14579131	C₂³	1	16	yes	complemented
135	#14579130	C₂³	1	16	yes	complemented
136	#14579129	C₂³	1	64	yes	complemented
137	#14579129	C₂³	1	16	yes	complemented
138	C₄×D₃₁₆	C₂³	1	16	yes	complemented
139	C₄×D₃₁₆	C₂³	1	16	yes	complemented
140	C₄×D₃₁₆	C₂³	1	16	yes	complemented
141	#14579123	C₂³	1	32	yes	complemented
142	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
143	#14579120	C₂³	1	4	yes	complemented
144	#14579120	C₂³	1	4	yes	complemented
145	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	complemented
146	C₄⋊C₄×D₇₉	C₂³	1	32	yes	complemented
147	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
148	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
149	C₂²⋊C₄×D₇₉	C₂³	1	64	yes	complemented
150	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
151	C₂×C₄×Dic₇₉	C₂³	1	2	yes	complemented
152	C₂×#41×C₇₉	—	2	16	no	—
153	C₂×#41×C₇₉	C₂³	1	4	yes	—
154	C₂×#41×C₇₉	C₂³	1	4	yes	—
155	C₂×#41×C₇₉	C₂³	1	4	yes	complemented
156	C₂×#41×C₇₉	C₂³	1	4	yes	complemented
157	C₂²×Q₈×C₇₉	C₂³	1	2	yes	complemented
158	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
159	C₂²×D₄×C₇₉	C₂³	1	2	yes	complemented
160	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₇₉	C₂³	1	4	yes	complemented
162	C₄⋊Q₈×C₇₉	C₂³	1	4	yes	complemented
163	#127×C₇₉	C₂³	1	4	yes	complemented
164	#124×C₇₉	C₂³	1	8	yes	complemented
165	#123×C₇₉	C₂³	1	16	yes	complemented
166	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	complemented
167	#121×C₇₉	C₂³	1	16	yes	complemented
168	#121×C₇₉	C₂³	1	16	yes	complemented
169	#120×C₇₉	C₂³	1	16	yes	complemented
170	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
171	#117×C₇₉	C₂³	1	4	yes	complemented
172	#117×C₇₉	C₂³	1	4	yes	complemented
173	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	complemented
174	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₇₉	C₂³	1	2	yes	complemented
176	C₂³×D₇₉	—	2	32	no	—
177	C₂³×D₇₉	—	8	4	no	—
178	C₂³×D₇₉	—	8	16	no	—
179	C₂³×D₇₉	C₂×D₄	1	16	yes	complemented
180	C₂³×D₇₉	C₂⁴	1	4	yes	—
181	C₂³×D₇₉	C₂⁴	1	32	yes	—
182	C₂³×D₇₉	C₂⁴	1	8	yes	—
183	C₂³×D₇₉	C₂⁴	1	4	yes	—
184	#11929625	—	2	64	no	—
185	#11929625	—	2	64	no	—
186	#11929624	—	2	64	no	—
187	#11929624	—	2	64	no	—
188	#11929624	—	2	16	no	—
189	#11929624	—	2	16	no	—
190	#11929624	—	2	16	no	—
191	#11929624	—	2	16	no	—
192	C₂×Dic₁₅₈	—	2	8	no	—
193	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
194	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
195	C₂×D₃₁₆	—	2	64	no	—
196	C₂×D₃₁₆	—	2	64	no	—
197	C₂×D₃₁₆	—	2	32	no	—
198	C₂×D₃₁₆	—	2	8	no	—
199	C₂×D₃₁₆	C₂×D₄	1	32	yes	complemented
200	C₂×D₃₁₆	C₂×D₄	1	32	yes	complemented
201	C₂×D₃₁₆	C₂×D₄	1	16	yes	complemented
202	C₂×D₃₁₆	C₂×D₄	1	16	yes	complemented
203	C₂×D₃₁₆	C₂⁴	1	4	yes	—
204	C₂×D₃₁₆	C₂⁴	1	4	yes	—
205	C₂×D₃₁₆	C₂⁴	1	32	yes	—
206	C₂×D₃₁₆	C₂⁴	1	16	yes	—
207	C₂×D₃₁₆	C₂⁴	1	4	yes	—
208	C₂×D₃₁₆	C₂⁴	1	8	yes	—
209	C₂×D₃₁₆	C₂⁴	1	4	yes	—
210	C₂×C₂²⋊D₇₉	—	2	16	no	—
211	C₂×C₂²⋊D₇₉	—	2	32	no	—
212	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
213	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
214	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
215	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
216	D₄×D₇₉	—	2	64	no	—
217	D₄×D₇₉	—	2	64	no	—
218	D₄×D₇₉	—	2	128	no	—
219	D₄×D₇₉	—	2	128	no	—
220	D₄×D₇₉	—	8	32	no	—
221	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
222	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
223	C₂×C₄×D₇₉	—	2	32	no	—
224	C₂×C₄×D₇₉	—	2	16	no	—
225	C₂×C₄×D₇₉	—	8	8	no	—
226	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
227	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
228	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
229	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
230	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
231	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
232	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
233	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
234	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
235	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
236	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
237	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
238	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
239	C₄×Dic₇₉	C₂⁴	1	8	yes	—
240	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
241	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
242	#41×C₇₉	—	2	16	no	—
243	#41×C₇₉	—	2	16	no	—
244	#41×C₇₉	—	2	16	no	—
245	#41×C₇₉	—	2	16	no	—
246	C₂×Q₈×C₇₉	—	2	8	no	—
247	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
249	C₂×D₄×C₇₉	—	2	16	no	—
250	C₂×D₄×C₇₉	—	2	8	no	—
251	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
252	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
253	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
254	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
255	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
256	C₂²×C₄×C₇₉	—	2	16	no	—
257	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	complemented
258	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
259	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
260	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
267	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
268	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
269	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
270	C₄²×C₇₉	C₂⁴	1	4	yes	—
271	C₄²×C₇₉	C₂⁴	1	4	yes	—
272	C₂³×C₇₉	—	2	8	no	—
273	C₂³×C₇₉	—	4	2	no	—
274	C₂³×C₇₉	—	4	8	no	—
275	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
276	C₂³×C₇₉	C₂⁵	1	8	yes	—
277	C₂³×C₇₉	C₂⁵	1	2	yes	—
278	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
279	C₂²×D₇₉	—	2	8	no	—
280	C₂²×D₇₉	—	2	64	no	—
281	C₂²×D₇₉	—	4	8	no	—
282	C₂²×D₇₉	—	4	16	no	—
283	C₂²×D₇₉	—	4	8	no	—
284	C₂²×D₇₉	—	4	64	no	—
285	C₂²×D₇₉	—	8	16	no	—
286	C₂²×D₇₉	—	8	64	no	—
287	C₂²×D₇₉	C₂²×D₄	1	32	yes	—
288	C₂²×D₇₉	C₂²×D₄	1	16	yes	—
289	C₂²×D₇₉	C₂⁵	1	8	yes	—
290	C₂²×D₇₉	C₂⁵	1	8	yes	—
291	Q₈×C₇₉	—	2	8	no	—
292	Q₈×C₇₉	—	2	8	no	—
293	D₄×C₇₉	—	2	16	no	—
294	D₄×C₇₉	—	2	16	no	—
295	D₄×C₇₉	—	2	8	no	—
296	D₄×C₇₉	—	2	8	no	—
297	D₄×C₇₉	—	4	16	no	—
298	C₂×C₄×C₇₉	—	2	8	no	—
299	C₂×C₄×C₇₉	—	2	16	no	—
300	C₂×C₄×C₇₉	—	2	16	no	—
301	C₂×C₄×C₇₉	—	4	4	no	—
302	C₂×C₄×C₇₉	C₂²×D₄	1	8	yes	—
303	C₂×C₄×C₇₉	C₂²×D₄	1	8	yes	—
304	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
306	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
307	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
308	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
309	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
310	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
311	C₂²⋊D₇₉	—	2	16	no	—
312	C₂²⋊D₇₉	—	2	16	no	—
313	C₂²⋊D₇₉	—	2	64	no	—
314	C₂²⋊D₇₉	—	4	32	no	—
315	C₂×Dic₇₉	—	2	8	no	—
316	C₂×Dic₇₉	—	4	4	no	—
317	C₂×Dic₇₉	C₂⁵	1	8	yes	—
318	C₂×Dic₇₉	C₂⁵	1	8	yes	—
319	D₃₁₆	—	2	64	no	—
320	D₃₁₆	—	2	8	no	—
321	D₃₁₆	—	2	8	no	—
322	D₃₁₆	—	4	16	no	—
323	D₃₁₆	C₂²×D₄	1	16	yes	—
324	D₃₁₆	C₂²×D₄	1	32	yes	—
325	D₃₁₆	C₂²×D₄	1	16	yes	—
326	C₄×D₇₉	—	2	64	no	—
327	C₄×D₇₉	—	2	16	no	—
328	C₄×D₇₉	—	2	16	no	—
329	C₄×D₇₉	—	4	32	no	—
330	Dic₁₅₈	—	2	8	no	—
331	Dic₁₅₈	—	2	8	no	—
332	C₂²×C₇₉	—	2	2	no	—
333	C₂²×C₇₉	—	2	4	no	—
334	C₂²×C₇₉	—	2	8	no	—
335	C₂²×C₇₉	—	2	16	no	—
336	C₂²×C₇₉	—	4	4	no	—
337	C₂²×C₇₉	—	4	16	no	—
338	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
339	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
340	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
341	C₂×D₇₉	—	2	16	no	—
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	C₂×D₇₉	—	4	16	no	—
347	C₂×D₇₉	—	8	64	no	—
348	C₂×D₇₉	C₂³×D₄	1	16	yes	—
349	C₄×C₇₉	—	2	8	no	—
350	C₄×C₇₉	—	2	8	no	—
351	C₄×C₇₉	C₂³×D₄	1	2	yes	—
352	C₄×C₇₉	C₂³×D₄	1	4	yes	—
353	C₄×C₇₉	C₂³×D₄	1	2	yes	—
354	Dic₇₉	—	2	8	no	—
355	Dic₇₉	—	2	8	no	—
356	#62842	—	79	1	no	maximal, Sylow
357	C₂×C₇₉	—	2	4	no	—
358	C₂×C₇₉	—	2	2	no	—
359	C₂×C₇₉	—	4	8	no	—
360	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
361	C₂×C₇₉	H(7,𝔽₂)	1	2	yes	—
362	D₇₉	—	2	16	no	—
363	D₇₉	—	4	8	no	—
364	C₂²×H(5,𝔽₂)	—	79	2	no	—
365	#3496	—	79	8	no	—
366	#3496	—	79	8	no	—
367	#3485	—	79	8	no	—
368	#3485	—	79	8	no	—
369	#3484	—	79	8	no	—
370	#3484	—	79	8	no	—
371	#3449	—	79	2	no	—
372	#3449	—	79	1	no	—
373	#3449	D₇₉	1	1	yes	characteristic, complemented
374	C₂×#534	—	79	8	no	—
375	C₂×#518	—	79	1	no	—
376	C₇₉	#62842	1	1	yes	characteristic, complemented, Sylow
377	C₂×H(5,𝔽₂)	—	79	8	no	—
378	C₂×H(5,𝔽₂)	—	79	8	no	—
379	C₂×H(5,𝔽₂)	—	79	8	no	—
380	C₂×H(5,𝔽₂)	—	79	8	no	—
381	C₂×H(5,𝔽₂)	—	158	32	no	—
382	C₂²×#41	—	79	4	no	—
383	C₂²×#41	—	79	2	no	—
384	C₂²×#41	—	79	4	no	—
385	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
386	C₂³×D₄	—	79	8	no	—
387	C₂³×D₄	—	79	4	no	—
388	C₂³×D₄	—	79	1	no	—
389	C₂³×D₄	—	79	4	no	—
390	#547	—	79	16	no	—
391	#547	—	79	32	no	—
392	#547	—	79	16	no	—
393	#546	—	79	32	no	—
394	#546	—	79	32	no	—
395	#546	—	79	32	no	—
396	#546	—	79	32	no	—
397	D₄²	—	79	16	no	—
398	D₄²	—	79	32	no	—
399	D₄²	—	79	16	no	—
400	#537	—	79	8	no	—
401	#537	—	79	4	no	—
402	#537	C₂×D₇₉	1	4	yes	complemented
403	#536	—	79	4	no	—
404	#536	—	79	4	no	—
405	#536	—	79	4	no	—
406	#536	C₂×D₇₉	1	4	yes	complemented
407	#535	—	79	4	no	—
408	#535	—	79	4	no	—
409	#535	—	79	4	no	—
410	#535	C₂×D₇₉	1	4	yes	complemented
411	#534	—	79	8	no	—
412	#534	—	79	32	no	—
413	#534	—	79	32	no	—
414	#534	—	79	32	no	—
415	#534	—	79	4	no	—
416	#534	C₂×D₇₉	1	4	yes	complemented
417	#532	—	79	8	no	—
418	#532	—	79	4	no	—
419	#532	C₂×D₇₉	1	4	yes	complemented
420	#525	—	79	8	no	—
421	#525	—	79	8	no	—
422	#525	—	79	8	no	—
423	#525	C₂×D₇₉	1	8	yes	complemented
424	C₂×#123	—	79	32	no	—
425	C₂×#121	—	79	32	no	—
426	C₂×#120	—	79	32	no	—
427	#518	—	79	8	no	—
428	#518	—	79	8	no	—
429	C₂×C₄×D₄	—	79	4	no	—
430	C₂×C₄×D₄	—	79	4	no	—
431	C₂×#117	—	79	1	no	—
432	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
433	C₂²×C₂²⋊C₄	—	79	4	no	—
434	C₂⁵	—	79	2	no	—
435	C₂⁵	—	79	8	no	—
436	H(5,𝔽₂)	—	158	64	no	—
437	H(5,𝔽₂)	—	158	64	no	—
438	H(5,𝔽₂)	—	158	64	no	—
439	H(5,𝔽₂)	—	158	64	no	—
440	C₂×#41	—	2	16	no	—
441	C₂×#41	—	79	16	no	—
442	C₂×#41	—	79	16	no	—
443	C₂×#41	—	79	4	no	—
444	C₂×#41	—	79	4	no	—
445	C₂×#41	—	79	4	no	—
446	C₂×#41	—	79	4	no	—
447	C₂×#41	—	79	16	no	—
448	C₂×#41	—	79	16	no	—
449	C₂×#41	—	158	32	no	—
450	C₂×#41	—	158	32	no	—
451	C₂×#41	—	158	16	no	—
452	C₂×#41	C₂²×D₇₉	1	4	yes	—
453	C₂×#41	C₂²×D₇₉	1	4	yes	—
454	C₂×#41	C₂²×D₇₉	1	4	yes	complemented
455	C₂×#41	C₂²×D₇₉	1	4	yes	complemented
456	C₂²×Q₈	—	79	2	no	—
457	C₂²×Q₈	C₂²×D₇₉	1	2	yes	complemented
458	C₂²×D₄	—	79	4	no	—
459	C₂²×D₄	—	79	8	no	—
460	C₂²×D₄	—	79	32	no	—
461	C₂²×D₄	—	79	32	no	—
462	C₂²×D₄	—	79	32	no	—
463	C₂²×D₄	—	79	16	no	—
464	C₂²×D₄	—	79	16	no	—
465	C₂²×D₄	—	79	16	no	—
466	C₂²×D₄	—	79	2	no	—
467	C₂²×D₄	—	79	2	no	—
468	C₂²×D₄	—	79	4	no	—
469	C₂²×D₄	—	79	4	no	—
470	C₂²×D₄	—	79	8	no	—
471	C₂²×D₄	—	79	2	no	—
472	C₂²×D₄	—	79	16	no	—
473	C₂²×D₄	—	79	16	no	—
474	C₂²×D₄	—	158	32	no	—
475	C₂²×D₄	—	158	32	no	—
476	C₂²×D₄	—	158	64	no	—
477	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
478	C₂²×D₄	C₂²×D₇₉	1	2	yes	complemented
479	C₂³×C₄	—	79	8	no	—
480	C₂³×C₄	—	79	8	no	—
481	C₂³×C₄	—	79	4	no	—
482	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
483	C₂³×C₄	C₂²×D₇₉	1	4	yes	complemented
484	C₄⋊Q₈	—	79	8	no	—
485	C₄⋊Q₈	—	79	4	no	—
486	C₄⋊Q₈	C₂²×D₇₉	1	4	yes	complemented
487	#127	—	79	8	no	—
488	#127	—	79	4	no	—
489	#127	C₂²×D₇₉	1	4	yes	complemented
490	#124	—	79	8	no	—
491	#124	—	79	8	no	—
492	#124	—	79	8	no	—
493	#124	C₂²×D₇₉	1	8	yes	complemented
494	#123	—	79	16	no	—
495	#123	—	79	16	no	—
496	#123	—	79	64	no	—
497	#123	—	79	16	no	—
498	#123	—	79	64	no	—
499	#123	C₂²×D₇₉	1	16	yes	complemented
500	C₂²⋊Q₈	—	79	16	no	—
501	C₂²⋊Q₈	—	79	16	no	—
502	C₂²⋊Q₈	—	79	16	no	—
503	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	complemented
504	#121	—	79	32	no	—
505	#121	—	79	32	no	—
506	#121	—	79	16	no	—
507	#121	—	79	16	no	—
508	#121	—	79	16	no	—
509	#121	—	79	32	no	—
510	#121	—	79	16	no	—
511	#121	—	79	64	no	—
512	#121	C₂²×D₇₉	1	16	yes	complemented
513	#121	C₂²×D₇₉	1	16	yes	complemented
514	#120	—	79	16	no	—
515	#120	—	79	16	no	—
516	#120	—	79	64	no	—
517	#120	—	79	16	no	—
518	#120	—	79	64	no	—
519	#120	C₂²×D₇₉	1	16	yes	complemented
520	C₄×D₄	—	79	32	no	—
521	C₄×D₄	—	79	32	no	—
522	C₄×D₄	—	79	16	no	—
523	C₄×D₄	—	79	16	no	—
524	C₄×D₄	—	79	16	no	—
525	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
526	#117	—	79	4	no	—
527	#117	—	79	4	no	—
528	#117	C₂²×D₇₉	1	4	yes	complemented
529	#117	C₂²×D₇₉	1	4	yes	complemented
530	C₂×C₄⋊C₄	—	79	2	no	—
531	C₂×C₄⋊C₄	—	79	32	no	—
532	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	complemented
533	C₂×C₂²⋊C₄	—	79	2	no	—
534	C₂×C₂²⋊C₄	—	79	8	no	—
535	C₂×C₂²⋊C₄	—	79	32	no	—
536	C₂×C₂²⋊C₄	—	79	64	no	—
537	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
538	C₂×C₄²	—	79	2	no	—
539	C₂×C₄²	C₂²×D₇₉	1	2	yes	complemented
540	C₂⁴	—	79	8	no	—
541	C₂⁴	—	79	4	no	—
542	C₂⁴	—	79	32	no	—
543	C₂⁴	—	79	4	no	—
544	C₂⁴	—	79	16	no	—
545	C₂⁴	—	632	4	no	—
546	C₂⁴	—	632	16	no	—
547	C₂⁴	—	158	32	no	—
548	C₂⁴	C₂³×D₇₉	1	4	yes	—
549	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
550	#41	—	2	16	no	—
551	#41	—	2	16	no	—
552	#41	—	2	16	no	—
553	#41	—	2	16	no	—
554	#41	—	158	64	no	—
555	#41	—	158	64	no	—
556	#41	—	158	64	no	—
557	#41	—	158	64	no	—
558	#41	—	158	16	no	—
559	#41	—	158	16	no	—
560	#41	—	158	16	no	—
561	#41	—	158	16	no	—
562	C₂×Q₈	—	2	8	no	—
563	C₂×Q₈	—	79	4	no	—
564	C₂×Q₈	—	79	4	no	—
565	C₂×Q₈	—	158	8	no	—
566	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
567	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
568	C₂×D₄	—	2	16	no	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	79	32	no	—
571	C₂×D₄	—	79	8	no	—
572	C₂×D₄	—	79	32	no	—
573	C₂×D₄	—	79	8	no	—
574	C₂×D₄	—	79	16	no	—
575	C₂×D₄	—	79	8	no	—
576	C₂×D₄	—	79	4	no	—
577	C₂×D₄	—	79	4	no	—
578	C₂×D₄	—	79	32	no	—
579	C₂×D₄	—	79	4	no	—
580	C₂×D₄	—	79	4	no	—
581	C₂×D₄	—	79	32	no	—
582	C₂×D₄	—	79	32	no	—
583	C₂×D₄	—	79	16	no	—
584	C₂×D₄	—	79	16	no	—
585	C₂×D₄	—	632	32	no	—
586	C₂×D₄	—	158	64	no	—
587	C₂×D₄	—	158	64	no	—
588	C₂×D₄	—	158	32	no	—
589	C₂×D₄	—	158	64	no	—
590	C₂×D₄	—	158	64	no	—
591	C₂×D₄	—	158	128	no	—
592	C₂×D₄	—	158	128	no	—
593	C₂×D₄	—	158	32	no	—
594	C₂×D₄	—	158	16	no	—
595	C₂×D₄	—	158	8	no	—
596	C₂×D₄	C₂³×D₇₉	1	8	yes	—
597	C₂×D₄	C₂³×D₇₉	1	8	yes	—
598	C₂×D₄	C₂³×D₇₉	1	4	yes	—
599	C₂×D₄	C₂³×D₇₉	1	4	yes	—
600	C₂×D₄	C₂³×D₇₉	1	16	yes	—
601	C₂²×C₄	—	2	16	no	—
602	C₂²×C₄	—	79	4	no	—
603	C₂²×C₄	—	79	32	no	—
604	C₂²×C₄	—	79	4	no	—
605	C₂²×C₄	—	79	32	no	—
606	C₂²×C₄	—	79	8	no	—
607	C₂²×C₄	—	79	8	no	—
608	C₂²×C₄	—	632	8	no	—
609	C₂²×C₄	—	158	32	no	—
610	C₂²×C₄	—	158	16	no	—
611	C₂²×C₄	D₄×D₇₉	1	8	yes	complemented
612	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
613	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
614	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
615	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
616	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
617	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
618	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
619	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
620	C₄⋊C₄	—	79	32	no	—
621	C₄⋊C₄	—	79	16	no	—
622	C₄⋊C₄	—	79	4	no	—
623	C₄⋊C₄	—	79	4	no	—
624	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
625	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
626	C₂²⋊C₄	—	79	8	no	—
627	C₂²⋊C₄	—	79	32	no	—
628	C₂²⋊C₄	—	79	32	no	—
629	C₂²⋊C₄	—	79	32	no	—
630	C₂²⋊C₄	—	79	32	no	—
631	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
632	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
633	C₄²	—	79	8	no	—
634	C₄²	C₂³×D₇₉	1	4	yes	—
635	C₄²	C₂³×D₇₉	1	4	yes	—
636	C₂³	—	2	8	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	8	no	—
639	C₂³	—	316	8	no	—
640	C₂³	—	316	8	no	—
641	C₂³	—	316	16	no	—
642	C₂³	—	316	64	no	—
643	C₂³	—	79	32	no	—
644	C₂³	—	79	16	no	—
645	C₂³	—	79	8	no	—
646	C₂³	—	79	8	no	—
647	C₂³	—	632	16	no	—
648	C₂³	—	632	64	no	—
649	C₂³	—	158	64	no	—
650	C₂³	—	158	8	no	—
651	C₂³	C₂×D₄×D₇₉	1	4	yes	—
652	C₂³	C₂⁴×D₇₉	1	8	yes	—
653	C₂³	C₂⁴×D₇₉	1	2	yes	—
654	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
655	Q₈	—	2	8	no	—
656	Q₈	—	2	8	no	—
657	Q₈	—	158	8	no	—
658	Q₈	—	158	8	no	—
659	D₄	—	2	16	no	—
660	D₄	—	2	16	no	—
661	D₄	—	2	8	no	—
662	D₄	—	2	8	no	—
663	D₄	—	4	16	no	—
664	D₄	—	316	16	no	—
665	D₄	—	316	32	no	—
666	D₄	—	79	16	no	—
667	D₄	—	79	32	no	—
668	D₄	—	79	16	no	—
669	D₄	—	158	64	no	—
670	D₄	—	158	64	no	—
671	D₄	—	158	16	no	—
672	D₄	—	158	16	no	—
673	D₄	—	158	8	no	—
674	D₄	—	158	8	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	16	no	—
677	C₂×C₄	—	2	16	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	316	32	no	—
680	C₂×C₄	—	316	4	no	—
681	C₂×C₄	—	79	8	no	—
682	C₂×C₄	—	79	8	no	—
683	C₂×C₄	—	158	64	no	—
684	C₂×C₄	—	158	8	no	—
685	C₂×C₄	—	158	16	no	—
686	C₂×C₄	—	158	16	no	—
687	C₂×C₄	C₂×D₄×D₇₉	1	8	yes	—
688	C₂×C₄	C₂×D₄×D₇₉	1	8	yes	—
689	C₂×C₄	C₂×D₄×D₇₉	1	4	yes	—
690	C₂×C₄	C₂×D₄×D₇₉	1	4	yes	—
691	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
692	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
693	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
694	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
695	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	8	no	—
699	C₂²	—	2	16	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	16	no	—
702	C₂²	—	316	16	no	—
703	C₂²	—	316	32	no	—
704	C₂²	—	316	16	no	—
705	C₂²	—	79	16	no	—
706	C₂²	—	632	64	no	—
707	C₂²	—	158	8	no	—
708	C₂²	—	158	16	no	—
709	C₂²	—	158	16	no	—
710	C₂²	C₂²×D₄×D₇₉	1	4	yes	—
711	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
712	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
713	C₄	—	2	8	no	—
714	C₄	—	2	8	no	—
715	C₄	—	158	8	no	—
716	C₄	—	158	8	no	—
717	C₄	C₂²×D₄×D₇₉	1	2	yes	—
718	C₄	C₂²×D₄×D₇₉	1	4	yes	—
719	C₄	C₂²×D₄×D₇₉	1	2	yes	—
720	C₂	—	2	4	no	—
721	C₂	—	2	2	no	—
722	C₂	—	4	8	no	—
723	C₂	—	316	8	no	—
724	C₂	—	158	16	no	—
725	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
726	C₂	#23778211	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3449	C₂
hypercenter	#3449	D₇₉
hypocenter	C₇₉	#62842
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂²×#14579207	C₂	semidirect
2. #23777163	C₂	semidirect
3. #23777162	C₂	semidirect
4. #23777043	C₂	semidirect
5. #23777042	C₂	semidirect
6. #23777034	C₂	semidirect
7. #23777033	C₂	semidirect
8. #23776733	C₂	semidirect
9. #23776729	C₂	semidirect
10. #534×D₇₉	C₂	semidirect
11. C₂×#19099037	C₂	semidirect
12. C₇₉×#3449	C₂	semidirect
14. C₂×#14579207	C₂²	semidirect
15. C₂×#14579207	C₂²	semidirect
16. C₂×#14579207	C₂²	semidirect
17. C₂×#14579207	C₂²	semidirect
18. C₂²×#11929625	C₂²	semidirect
19. C₂²×#11929624	C₂²	semidirect
20. C₂²×#11929624	C₂²	semidirect
22. C₂³×D₃₁₆	C₂²	semidirect
23. C₂²×D₄×D₇₉	C₂²	semidirect
24. C₂²×D₄×D₇₉	C₂²	semidirect
25. #19099218	C₂²	semidirect
26. #19099216	C₂²	semidirect
27. #19099215	C₂²	semidirect
28. #19099210	C₂²	semidirect
29. #19099209	C₂²	semidirect
30. #19099206	C₂²	semidirect
31. #19099204	C₂²	semidirect
32. D₄×D₃₁₆	C₂²	semidirect
33. #19099198	C₂²	semidirect
34. #19099197	C₂²	semidirect
35. #19099144	C₂²	semidirect
36. #19099141	C₂²	semidirect
37. #19099139	C₂²	semidirect
38. #19099137	C₂²	semidirect
39. #19099134	C₂²	semidirect
40. #19099132	C₂²	semidirect
41. #19099130	C₂²	semidirect
42. #19099127	C₂²	semidirect
43. #19099125	C₂²	semidirect
44. #19099124	C₂²	semidirect
45. #19099123	C₂²	semidirect
46. #19099122	C₂²	semidirect
47. #19099121	C₂²	semidirect
48. #19099113	C₂²	semidirect
49. #19099109	C₂²	semidirect
50. #19099075	C₂²	semidirect
51. #19099074	C₂²	semidirect
52. #19099070	C₂²	semidirect
53. #123×D₇₉	C₂²	semidirect
54. #121×D₇₉	C₂²	semidirect
55. #120×D₇₉	C₂²	semidirect
56. #19099037	C₂²	semidirect
57. #19099037	C₂²	semidirect
58. C₂×C₄×D₃₁₆	C₂²	semidirect
59. C₂×#14579123	C₂²	semidirect
60. C₂×#14579120	C₂²	semidirect
61. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
62. C₂²×#41×C₇₉	C₂²	semidirect
63. #537×C₇₉	C₂²	semidirect
64. #536×C₇₉	C₂²	semidirect
65. #535×C₇₉	C₂²	semidirect
66. #534×C₇₉	C₂²	semidirect
67. #532×C₇₉	C₂²	semidirect
68. #525×C₇₉	C₂²	semidirect
69. C₂×#117×C₇₉	C₂²	semidirect
71. C₂⁴×D₇₉	C₂³	semidirect
77. C₂×#11929625	C₂³	semidirect
78. C₂×#11929625	C₂³	semidirect
83. C₂×#11929624	C₂³	semidirect
84. C₂×#11929624	C₂³	semidirect
85. C₂×#11929624	C₂³	semidirect
86. C₂×#11929624	C₂³	semidirect
87. C₂²×Dic₁₅₈	C₂³	semidirect
89. C₂²×D₃₁₆	D₄	semidirect
94. C₂²×D₃₁₆	C₂³	semidirect
95. C₂²×D₃₁₆	C₂³	semidirect
96. C₂²×D₃₁₆	C₂³	semidirect
97. C₂²×D₃₁₆	C₂³	semidirect
99. C₂²×C₂²⋊D₇₉	C₂³	semidirect
103. C₂×D₄×D₇₉	C₂³	semidirect
104. C₂×D₄×D₇₉	C₂³	semidirect
105. C₂×D₄×D₇₉	C₂³	semidirect
106. C₂×D₄×D₇₉	C₂³	semidirect
107. C₂²×C₄×D₇₉	C₂³	semidirect
108. C₂²×C₄×D₇₉	C₂³	semidirect
109. C₂²×C₄×D₇₉	C₂³	semidirect
110. #14579161	C₂³	semidirect
111. #14579159	C₂³	semidirect
112. #14579158	C₂³	semidirect
113. #14579157	C₂³	semidirect
114. #14579150	C₂³	semidirect
115. #14579149	C₂³	semidirect
116. #14579148	C₂³	semidirect
117. #14579146	C₂³	semidirect
118. #14579145	C₂³	semidirect
119. #14579144	C₂³	semidirect
120. #14579143	C₂³	semidirect
121. #14579142	C₂³	semidirect
122. #14579141	C₂³	semidirect
123. #14579140	C₂³	semidirect
124. #14579137	C₂³	semidirect
125. #14579136	C₂³	semidirect
126. #14579136	C₂³	semidirect
127. #14579135	C₂³	semidirect
128. #14579135	C₂³	semidirect
129. #14579134	C₂³	semidirect
130. #14579133	C₂³	semidirect
131. #14579132	C₂³	semidirect
132. #14579132	C₂³	semidirect
133. #14579131	C₂³	semidirect
134. #14579131	C₂³	semidirect
135. #14579130	C₂³	semidirect
136. #14579129	C₂³	semidirect
137. #14579129	C₂³	semidirect
138. C₄×D₃₁₆	C₂³	semidirect
139. C₄×D₃₁₆	C₂³	semidirect
140. C₄×D₃₁₆	C₂³	semidirect
141. #14579123	C₂³	semidirect
142. C₄×C₂²⋊D₇₉	C₂³	semidirect
143. #14579120	C₂³	semidirect
144. #14579120	C₂³	semidirect
145. C₂×C₄⋊Dic₇₉	C₂³	semidirect
146. C₄⋊C₄×D₇₉	C₂³	semidirect
148. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
149. C₂²⋊C₄×D₇₉	C₂³	semidirect
150. C₂²⋊C₄×D₇₉	C₂³	semidirect
151. C₂×C₄×Dic₇₉	C₂³	semidirect
155. C₂×#41×C₇₉	C₂³	semidirect
156. C₂×#41×C₇₉	C₂³	semidirect
157. C₂²×Q₈×C₇₉	C₂³	semidirect
159. C₂²×D₄×C₇₉	C₂³	semidirect
161. C₂³×C₄×C₇₉	C₂³	semidirect
162. C₄⋊Q₈×C₇₉	C₂³	semidirect
163. #127×C₇₉	C₂³	semidirect
164. #124×C₇₉	C₂³	semidirect
165. #123×C₇₉	C₂³	semidirect
166. C₂²⋊Q₈×C₇₉	C₂³	semidirect
167. #121×C₇₉	C₂³	semidirect
168. #121×C₇₉	C₂³	semidirect
169. #120×C₇₉	C₂³	semidirect
170. C₄×D₄×C₇₉	C₂³	semidirect
171. #117×C₇₉	C₂³	semidirect
172. #117×C₇₉	C₂³	semidirect
173. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
175. C₂×C₄²×C₇₉	C₂³	semidirect
179. C₂³×D₇₉	C₂×D₄	semidirect
199. C₂×D₃₁₆	C₂×D₄	semidirect
200. C₂×D₃₁₆	C₂×D₄	semidirect
201. C₂×D₃₁₆	C₂×D₄	semidirect
202. C₂×D₃₁₆	C₂×D₄	semidirect
257. C₂²×C₄×C₇₉	C₂×D₄	semidirect
373. #3449	D₇₉	semidirect
376. C₇₉	#62842	semidirect
385. C₂²×#41	C₂×D₇₉	semidirect
402. #537	C₂×D₇₉	semidirect
406. #536	C₂×D₇₉	semidirect
410. #535	C₂×D₇₉	semidirect
416. #534	C₂×D₇₉	semidirect
419. #532	C₂×D₇₉	semidirect
423. #525	C₂×D₇₉	semidirect
432. C₂×#117	C₂×D₇₉	semidirect
454. C₂×#41	C₂²×D₇₉	semidirect
455. C₂×#41	C₂²×D₇₉	semidirect
457. C₂²×Q₈	C₂²×D₇₉	semidirect
478. C₂²×D₄	C₂²×D₇₉	semidirect
483. C₂³×C₄	C₂²×D₇₉	semidirect
486. C₄⋊Q₈	C₂²×D₇₉	semidirect
489. #127	C₂²×D₇₉	semidirect
493. #124	C₂²×D₇₉	semidirect
499. #123	C₂²×D₇₉	semidirect
503. C₂²⋊Q₈	C₂²×D₇₉	semidirect
512. #121	C₂²×D₇₉	semidirect
513. #121	C₂²×D₇₉	semidirect
519. #120	C₂²×D₇₉	semidirect
525. C₄×D₄	C₂²×D₇₉	semidirect
528. #117	C₂²×D₇₉	semidirect
529. #117	C₂²×D₇₉	semidirect
532. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
539. C₂×C₄²	C₂²×D₇₉	semidirect
611. C₂²×C₄	D₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579207	2
#23777163	2
#23777162	2
#23777043	2
#23777042	2
#23777034	2
#23777033	2
#23776733	2
#23776729	2
#534×D₇₉	2
C₂×#19099037	2
C₇₉×#3449	2
#62842	79