Subgroups — #35196808

Order 20224.

11534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#23777079	C₂	1	8	yes	maximal, complemented
4	#23777068	C₂	1	8	yes	maximal, complemented
5	#23777058	C₂	1	1	yes	maximal, characteristic, complemented
6	#23777052	C₂	1	1	yes	maximal, characteristic, complemented
7	#23777048	C₂	1	1	yes	maximal, characteristic, complemented
8	#23777042	C₂	1	6	yes	maximal, complemented
9	#23777034	C₂	1	6	yes	maximal, complemented
10	#23776890	C₂	1	8	yes	maximal, complemented
11	#23776889	C₂	1	8	yes	maximal, complemented
12	#23776731	C₂	1	6	yes	maximal, complemented
13	#525×D₇₉	C₂	1	6	yes	maximal, complemented
14	#23776602	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099400	—	2	16	no	—
17	C₂×#14579209	C₂²	1	1	yes	characteristic, complemented
18	C₂×#14579209	C₂²	1	4	yes	complemented
19	C₂×#14579207	C₂²	1	6	yes	complemented
20	C₂×#14579207	C₂²	1	4	yes	complemented
21	C₂²×#11929625	C₂²	1	1	yes	characteristic
22	C₂²×#11929625	C₂²	1	4	yes	complemented
23	C₂²×#11929624	C₂²	1	3	yes	complemented
24	C₂²×#11929623	C₂²	1	3	yes	complemented
25	C₂×#41×D₇₉	—	2	16	no	—
26	C₂×#41×D₇₉	C₂²	1	8	yes	complemented
27	C₂×#41×D₇₉	C₂²	1	8	yes	complemented
28	C₂×#41×D₇₉	C₂²	1	6	yes	complemented
29	C₂×#41×D₇₉	C₂²	1	4	yes	complemented
30	C₂²×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄×D₇₉	C₂²	1	3	yes	complemented
32	C₂³×C₄×D₇₉	C₂²	1	3	yes	complemented
33	#19099232	C₂²	1	8	yes	complemented
34	Q₈×D₃₁₆	C₂²	1	8	yes	complemented
35	Q₈×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
36	#19099225	C₂²	1	8	yes	complemented
37	#19099220	C₂²	1	8	yes	complemented
38	#19099220	C₂²	1	8	yes	complemented
39	#19099218	C₂²	1	24	yes	complemented
40	#19099215	C₂²	1	24	yes	complemented
41	#19099210	C₂²	1	24	yes	complemented
42	#19099210	C₂²	1	24	yes	complemented
43	#19099209	C₂²	1	24	yes	complemented
44	#19099206	C₂²	1	24	yes	complemented
45	#19099198	C₂²	1	24	yes	complemented
46	#19099197	C₂²	1	24	yes	complemented
47	#19099142	C₂²	1	24	yes	complemented
48	#19099139	C₂²	1	6	yes	complemented
49	#19099134	C₂²	1	6	yes	complemented
50	#19099133	C₂²	1	12	yes	complemented
51	#19099130	C₂²	1	6	yes	complemented
52	#19099126	C₂²	1	12	yes	complemented
53	#19099123	C₂²	1	24	yes	complemented
54	#19099112	C₂²	1	12	yes	complemented
55	#19099111	C₂²	1	12	yes	complemented
56	#19099076	C₂²	1	12	yes	complemented
57	#19099075	C₂²	1	6	yes	complemented
58	#19099074	C₂²	1	6	yes	complemented
59	#19099073	C₂²	1	24	yes	complemented
60	#19099073	C₂²	1	12	yes	complemented
61	#19099072	C₂²	1	24	yes	complemented
62	#19099071	C₂²	1	4	yes	complemented
63	#19099070	C₂²	1	6	yes	complemented
64	#19099069	C₂²	1	12	yes	complemented
65	#123×D₇₉	C₂²	1	12	yes	complemented
66	C₂²⋊Q₈×D₇₉	C₂²	1	12	yes	complemented
67	#121×D₇₉	C₂²	1	12	yes	complemented
68	#120×D₇₉	C₂²	1	12	yes	complemented
69	#19099045	C₂²	1	8	yes	complemented
70	#19099041	C₂²	1	1	yes	characteristic, complemented
71	#19099037	C₂²	1	6	yes	complemented
72	C₄×#11929625	C₂²	1	8	yes	complemented
73	C₄×D₄×D₇₉	C₂²	1	24	yes	complemented
74	#117×D₇₉	C₂²	1	6	yes	complemented
75	C₂×2₋¹⁺⁴×C₇₉	C₂²	1	1	yes	characteristic, complemented
76	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
77	#550×C₇₉	C₂²	1	8	yes	complemented
78	#548×C₇₉	C₂²	1	8	yes	complemented
79	#535×C₇₉	C₂²	1	6	yes	complemented
80	#525×C₇₉	C₂²	1	6	yes	complemented
81	#519×C₇₉	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×D₇₉	C₂³	1	3	yes	—
83	#14579209	—	2	8	no	—
84	#14579209	—	2	32	no	—
85	#14579207	—	2	32	no	—
86	#14579207	—	2	48	no	—
87	C₂×#11929625	—	2	32	no	—
88	C₂×#11929625	D₄	1	16	yes	complemented
89	C₂×#11929625	C₂³	1	4	yes	—
90	C₂×#11929625	C₂³	1	4	yes	—
91	C₂×#11929625	C₂³	1	12	yes	complemented
92	C₂×#11929625	C₂³	1	4	yes	complemented
93	C₂×#11929625	C₂³	1	6	yes	complemented
94	C₂×#11929624	—	2	24	no	—
95	C₂×#11929624	C₂³	1	6	yes	—
96	C₂×#11929624	C₂³	1	24	yes	—
97	C₂×#11929624	C₂³	1	12	yes	complemented
98	C₂×#11929624	C₂³	1	12	yes	complemented
99	C₂×#11929623	—	2	24	no	—
100	C₂×#11929623	C₂³	1	12	yes	—
101	C₂×#11929623	C₂³	1	4	yes	—
102	C₂×#11929623	C₂³	1	12	yes	—
103	C₂×#11929623	C₂³	1	6	yes	complemented
104	#41×D₇₉	—	2	32	no	—
105	#41×D₇₉	—	2	64	no	—
106	#41×D₇₉	—	2	64	no	—
107	#41×D₇₉	—	2	48	no	—
108	C₂²×Dic₁₅₈	C₂³	1	3	yes	—
109	C₂×Q₈×D₇₉	—	2	8	no	—
110	C₂×Q₈×D₇₉	C₂³	1	8	yes	—
111	C₂×Q₈×D₇₉	C₂³	1	4	yes	complemented
112	C₂×Q₈×D₇₉	C₂³	1	6	yes	complemented
113	C₂²×D₃₁₆	C₂³	1	3	yes	—
114	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
115	C₂²×C₂²⋊D₇₉	C₂³	1	6	yes	—
116	C₂×D₄×D₇₉	—	2	24	no	—
117	C₂×D₄×D₇₉	C₂³	1	12	yes	—
118	C₂×D₄×D₇₉	C₂³	1	24	yes	—
119	C₂×D₄×D₇₉	C₂³	1	24	yes	—
120	C₂×D₄×D₇₉	C₂³	1	12	yes	complemented
121	C₂×D₄×D₇₉	C₂³	1	6	yes	complemented
122	C₂³×Dic₇₉	C₂³	1	3	yes	—
123	C₂²×C₄×D₇₉	—	2	24	no	—
124	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
125	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
126	C₂²×C₄×D₇₉	C₂³	1	3	yes	—
127	C₂²×C₄×D₇₉	C₂³	1	3	yes	—
128	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×D₇₉	C₂³	1	3	yes	—
130	C₂²×C₄×D₇₉	C₂³	1	12	yes	complemented
131	#14579161	C₂³	1	12	yes	complemented
132	#14579159	C₂³	1	12	yes	complemented
133	#14579157	C₂³	1	12	yes	complemented
134	#14579149	C₂³	1	12	yes	complemented
135	#14579148	C₂³	1	12	yes	complemented
136	#14579148	C₂³	1	12	yes	complemented
137	#14579146	C₂³	1	24	yes	complemented
138	#14579145	C₂³	1	12	yes	—
139	#14579144	C₂³	1	4	yes	—
140	#14579143	C₂³	1	48	yes	complemented
141	#14579143	C₂³	1	24	yes	complemented
142	#14579142	C₂³	1	12	yes	—
143	#14579141	C₂³	1	12	yes	—
144	#14579141	C₂³	1	24	yes	complemented
145	#14579140	C₂³	1	24	yes	complemented
146	#14579140	C₂³	1	12	yes	complemented
147	#14579139	C₂³	1	8	yes	—
148	#14579138	C₂³	1	24	yes	complemented
149	#14579137	C₂³	1	12	yes	—
150	#14579136	C₂³	1	12	yes	—
151	#14579135	C₂³	1	12	yes	complemented
152	#14579134	C₂³	1	8	yes	—
153	#14579134	C₂³	1	48	yes	complemented
154	#14579133	C₂³	1	24	yes	complemented
155	#14579132	C₂³	1	12	yes	—
156	#14579132	C₂³	1	24	yes	complemented
157	#14579132	C₂³	1	48	yes	complemented
158	#14579131	C₂³	1	24	yes	—
159	#14579131	C₂³	1	4	yes	—
160	#14579130	C₂³	1	12	yes	—
161	#14579129	C₂³	1	24	yes	—
162	#14579129	C₂³	1	4	yes	—
163	#14579129	C₂³	1	48	yes	complemented
164	Q₈×Dic₇₉	C₂³	1	8	yes	complemented
165	C₄×D₃₁₆	C₂³	1	24	yes	—
166	C₄×D₃₁₆	C₂³	1	24	yes	complemented
167	D₄×Dic₇₉	C₂³	1	24	yes	complemented
168	#14579123	C₂³	1	8	yes	—
169	#14579123	C₂³	1	24	yes	complemented
170	C₄×C₂²⋊D₇₉	C₂³	1	24	yes	—
171	C₄×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
172	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	—
173	(C₂²⋊D₇₉)⋊C₄	C₂³	1	24	yes	complemented
174	#14579120	C₂³	1	6	yes	—
175	#14579119	C₂³	1	12	yes	complemented
176	#14579118	C₂³	1	12	yes	complemented
177	#14579117	C₂³	1	4	yes	—
178	C₄⋊C₄×D₇₉	C₂³	1	12	yes	complemented
179	C₄⋊C₄×D₇₉	C₂³	1	24	yes	complemented
180	C₂²⋊C₄×D₇₉	C₂³	1	24	yes	—
181	C₂²⋊C₄×D₇₉	C₂³	1	12	yes	—
182	C₂²⋊C₄×D₇₉	C₂³	1	24	yes	complemented
183	C₄²×D₇₉	C₂³	1	12	yes	complemented
184	2₋¹⁺⁴×C₇₉	—	2	8	no	—
185	C₂×#41×C₇₉	—	2	8	no	—
186	C₂×#41×C₇₉	C₂³	1	6	yes	—
187	C₂×#41×C₇₉	C₂³	1	8	yes	—
188	C₂×#41×C₇₉	C₂³	1	4	yes	complemented
189	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₇₉	C₂³	1	4	yes	complemented
191	C₂²×D₄×C₇₉	C₂³	1	3	yes	—
192	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
193	#127×C₇₉	C₂³	1	12	yes	complemented
194	#124×C₇₉	C₂³	1	12	yes	complemented
195	#123×C₇₉	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₇₉	C₂³	1	12	yes	complemented
197	#121×C₇₉	C₂³	1	24	yes	complemented
198	#121×C₇₉	C₂³	1	12	yes	complemented
199	#120×C₇₉	C₂³	1	12	yes	—
200	C₄×Q₈×C₇₉	C₂³	1	8	yes	complemented
201	C₄×D₄×C₇₉	C₂³	1	24	yes	complemented
202	#117×C₇₉	C₂³	1	6	yes	—
203	C₂³×D₇₉	—	2	12	no	—
204	C₂³×D₇₉	—	4	12	no	—
205	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
206	C₂³×D₇₉	C₂⁴	1	12	yes	—
207	C₂³×D₇₉	C₂⁴	1	12	yes	—
208	C₂³×D₇₉	C₂⁴	1	3	yes	—
209	#11929625	—	2	48	no	—
210	#11929625	—	2	24	no	—
211	#11929625	—	2	16	no	—
212	#11929625	C₂×D₄	1	32	yes	complemented
213	#11929625	C₂×D₄	1	32	yes	complemented
214	#11929624	—	2	96	no	—
215	#11929624	—	2	48	no	—
216	#11929624	—	2	48	no	—
217	#11929624	—	2	24	no	—
218	#11929623	—	2	16	no	—
219	#11929623	—	2	24	no	—
220	#11929623	—	2	48	no	—
221	#11929623	—	2	48	no	—
222	C₂×Dic₁₅₈	—	2	12	no	—
223	C₂×Dic₁₅₈	C₂⁴	1	12	yes	—
224	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
225	C₂×Dic₁₅₈	C₂⁴	1	6	yes	—
226	Q₈×D₇₉	—	2	24	no	—
227	Q₈×D₇₉	—	2	32	no	—
228	Q₈×D₇₉	—	2	16	no	—
229	C₂×D₃₁₆	—	2	48	no	—
230	C₂×D₃₁₆	C₂×D₄	1	24	yes	complemented
231	C₂×D₃₁₆	C₂⁴	1	6	yes	—
232	C₂×D₃₁₆	C₂⁴	1	12	yes	—
233	C₂×D₃₁₆	C₂⁴	1	8	yes	—
234	C₂×D₃₁₆	C₂⁴	1	12	yes	—
235	C₂×C₂²⋊D₇₉	—	2	24	no	—
236	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
237	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
238	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
239	C₂×C₂²⋊D₇₉	C₂⁴	1	12	yes	—
240	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
241	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
242	D₄×D₇₉	—	2	96	no	—
243	D₄×D₇₉	—	2	48	no	—
244	D₄×D₇₉	—	2	24	no	—
245	D₄×D₇₉	—	2	48	no	—
246	D₄×D₇₉	—	4	48	no	—
247	C₂²×Dic₇₉	—	2	12	no	—
248	C₂²×Dic₇₉	C₂⁴	1	3	yes	—
249	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
250	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
251	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
252	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×D₇₉	—	2	4	no	—
254	C₂×C₄×D₇₉	—	2	48	no	—
255	C₂×C₄×D₇₉	—	2	48	no	—
256	C₂×C₄×D₇₉	—	2	48	no	—
257	C₂×C₄×D₇₉	—	2	12	no	—
258	C₂×C₄×D₇₉	—	2	12	no	—
259	C₂×C₄×D₇₉	C₂×D₄	1	24	yes	complemented
260	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
261	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
262	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
263	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
264	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
265	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
266	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
267	C₂×C₄×D₇₉	C₂⁴	1	24	yes	—
268	C₂×C₄×D₇₉	C₂⁴	1	6	yes	—
269	C₂×C₄×D₇₉	C₂⁴	1	6	yes	—
270	C₄⋊Dic₇₉	C₂⁴	1	12	yes	—
271	C₄⋊Dic₇₉	C₂⁴	1	24	yes	—
272	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
273	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
274	Dic₇₉⋊C₄	C₂⁴	1	24	yes	—
275	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
276	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	—
277	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	—
278	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
279	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
280	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
281	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
282	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
283	C₄×Dic₇₉	C₂⁴	1	8	yes	—
284	C₄×Dic₇₉	C₂⁴	1	12	yes	—
285	C₂⁴×C₇₉	C₂⁴	1	3	yes	—
286	#41×C₇₉	—	2	32	no	—
287	#41×C₇₉	—	2	16	no	—
288	#41×C₇₉	—	2	24	no	—
289	C₂×Q₈×C₇₉	—	2	16	no	—
290	C₂×Q₈×C₇₉	C₂×D₄	1	8	yes	complemented
291	C₂×Q₈×C₇₉	C₂⁴	1	6	yes	—
292	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
293	C₂×D₄×C₇₉	—	2	12	no	—
294	C₂×D₄×C₇₉	C₂⁴	1	12	yes	—
295	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
296	C₂×D₄×C₇₉	C₂⁴	1	6	yes	—
297	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
298	C₂²×C₄×C₇₉	—	2	12	no	—
299	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
300	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
301	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
303	C₄⋊C₄×C₇₉	C₂⁴	1	12	yes	—
304	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
305	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
306	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
307	C₂²⋊C₄×C₇₉	C₂⁴	1	24	yes	—
308	C₄²×C₇₉	C₂⁴	1	12	yes	—
309	C₂³×C₇₉	—	2	6	no	—
310	C₂³×C₇₉	—	4	6	no	—
311	C₂³×C₇₉	C₂⁵	1	4	yes	—
312	C₂³×C₇₉	C₂⁵	1	6	yes	—
313	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
314	C₂²×D₇₉	—	2	2	no	—
315	C₂²×D₇₉	—	2	4	no	—
316	C₂²×D₇₉	—	2	24	no	—
317	C₂²×D₇₉	—	2	24	no	—
318	C₂²×D₇₉	—	2	24	no	—
319	C₂²×D₇₉	—	4	12	no	—
320	C₂²×D₇₉	—	4	6	no	—
321	C₂²×D₇₉	—	4	24	no	—
322	C₂²×D₇₉	—	4	48	no	—
323	C₂²×D₇₉	C₂²×D₄	1	12	yes	—
324	C₂²×D₇₉	C₂⁵	1	4	yes	—
325	C₂²×D₇₉	C₂⁵	1	6	yes	—
326	C₂²×D₇₉	C₂⁵	1	2	yes	—
327	Q₈×C₇₉	—	2	12	no	—
328	Q₈×C₇₉	C₂²×D₄	1	16	yes	—
329	D₄×C₇₉	—	2	8	no	—
330	D₄×C₇₉	—	2	12	no	—
331	D₄×C₇₉	—	2	24	no	—
332	D₄×C₇₉	—	4	24	no	—
333	C₂×C₄×C₇₉	—	2	2	no	—
334	C₂×C₄×C₇₉	—	2	24	no	—
335	C₂×C₄×C₇₉	—	2	24	no	—
336	C₂×C₄×C₇₉	C₂²×D₄	1	12	yes	—
337	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
338	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
339	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
340	C₂×C₄×C₇₉	C₂⁵	1	6	yes	—
341	C₂²⋊D₇₉	—	2	8	no	—
342	C₂²⋊D₇₉	—	2	24	no	—
343	C₂²⋊D₇₉	—	2	48	no	—
344	C₂²⋊D₇₉	—	2	16	no	—
345	C₂²⋊D₇₉	—	2	8	no	—
346	C₂²⋊D₇₉	—	4	24	no	—
347	C₂×Dic₇₉	—	2	6	no	—
348	C₂×Dic₇₉	—	2	8	no	—
349	C₂×Dic₇₉	—	2	12	no	—
350	C₂×Dic₇₉	—	2	12	no	—
351	C₂×Dic₇₉	C₂²×D₄	1	4	yes	—
352	C₂×Dic₇₉	C₂⁵	1	8	yes	—
353	C₂×Dic₇₉	C₂⁵	1	6	yes	—
354	C₂×Dic₇₉	C₂⁵	1	4	yes	—
355	C₂×Dic₇₉	C₂⁵	1	1	yes	characteristic
356	C₂×Dic₇₉	C₂⁵	1	1	yes	characteristic
357	D₃₁₆	—	2	24	no	—
358	D₃₁₆	—	2	16	no	—
359	D₃₁₆	—	2	12	no	—
360	D₃₁₆	C₂²×D₄	1	48	yes	—
361	C₄×D₇₉	—	2	24	no	—
362	C₄×D₇₉	—	2	24	no	—
363	C₄×D₇₉	—	2	24	no	—
364	C₄×D₇₉	—	2	24	no	—
365	C₄×D₇₉	—	2	4	no	—
366	C₄×D₇₉	—	2	4	no	—
367	C₄×D₇₉	—	2	8	no	—
368	C₄×D₇₉	—	4	24	no	—
369	C₄×D₇₉	C₂²×D₄	1	24	yes	—
370	C₄×D₇₉	C₂²×D₄	1	24	yes	—
371	Dic₁₅₈	—	2	12	no	—
372	Dic₁₅₈	—	2	24	no	—
373	Dic₁₅₈	—	2	8	no	—
374	C₂²×C₇₉	—	2	2	no	—
375	C₂²×C₇₉	—	2	4	no	—
376	C₂²×C₇₉	—	2	6	no	—
377	C₂²×C₇₉	—	2	8	no	—
378	C₂²×C₇₉	—	2	12	no	—
379	C₂²×C₇₉	—	4	12	no	—
380	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
381	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
382	C₂×D₇₉	—	2	8	no	—
383	C₂×D₇₉	—	2	2	no	—
384	C₂×D₇₉	—	2	2	no	—
385	C₂×D₇₉	—	2	12	no	—
386	C₂×D₇₉	—	2	4	no	—
387	C₂×D₇₉	—	2	8	no	—
388	C₂×D₇₉	—	4	12	no	—
389	C₂×D₇₉	—	4	48	no	—
390	C₂×D₇₉	—	8	24	no	—
391	C₂×D₇₉	C₂³×D₄	1	12	yes	—
392	C₂×D₇₉	#585	1	4	yes	complemented
393	C₄×C₇₉	—	2	2	no	—
394	C₄×C₇₉	—	2	4	no	—
395	C₄×C₇₉	—	2	8	no	—
396	C₄×C₇₉	C₂³×D₄	1	12	yes	—
397	Dic₇₉	—	2	4	no	—
398	Dic₇₉	—	2	6	no	—
399	Dic₇₉	—	2	8	no	—
400	Dic₇₉	C₂³×D₄	1	2	yes	—
401	Dic₇₉	C₂³×D₄	1	2	yes	—
402	#62811	—	79	1	no	maximal, Sylow
403	C₂×C₇₉	—	2	2	no	—
404	C₂×C₇₉	—	4	6	no	—
405	C₂×C₇₉	—	4	4	no	—
406	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
407	C₂×C₇₉	C₂×#585	1	2	yes	—
408	D₇₉	—	2	4	no	—
409	D₇₉	—	2	12	no	—
410	D₇₉	—	4	4	no	—
411	C₂×#585	—	79	1	no	—
412	C₂³×#41	—	79	1	no	—
413	#3489	—	79	8	no	—
414	#3488	—	79	8	no	—
415	#3487	—	79	1	no	—
416	#3487	D₇₉	1	1	yes	characteristic, complemented
417	#3486	—	79	1	no	—
418	#3486	—	79	1	no	—
419	#3485	—	79	6	no	—
420	#3484	—	79	6	no	—
421	D₄×#41	—	79	8	no	—
422	D₄×#41	—	79	8	no	—
423	#3449	—	79	6	no	—
424	C₂×#525	—	79	6	no	—
425	#3428	—	79	1	no	—
426	C₇₉	#62811	1	1	yes	characteristic, complemented, Sylow
427	#585	—	158	16	no	—
428	C₂×2₋¹⁺⁴	—	79	1	no	—
429	C₂×2₋¹⁺⁴	—	79	4	no	—
430	C₂×2₋¹⁺⁴	C₂×D₇₉	1	1	yes	characteristic, complemented
431	C₂×H(5,𝔽₂)	—	79	6	no	—
432	C₂×H(5,𝔽₂)	—	79	4	no	—
433	C₂²×#41	—	79	8	no	—
434	C₂²×#41	—	79	8	no	—
435	C₂²×#41	—	79	6	no	—
436	C₂²×#41	—	79	4	no	—
437	C₂²×#41	—	79	1	no	—
438	C₂²×#41	—	79	4	no	—
439	C₂²×#41	—	79	3	no	—
440	C₂²×#41	—	79	3	no	—
441	C₂²×#41	—	158	16	no	—
442	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
443	C₂³×Q₈	—	79	1	no	—
444	C₂³×D₄	—	79	3	no	—
445	C₂⁴×C₄	—	79	3	no	—
446	#550	—	79	8	no	—
447	#550	C₂×D₇₉	1	8	yes	complemented
448	D₄×Q₈	—	79	8	no	—
449	D₄×Q₈	—	79	8	no	—
450	#548	—	79	8	no	—
451	#548	—	79	8	no	—
452	#548	—	79	8	no	—
453	#548	C₂×D₇₉	1	8	yes	complemented
454	#547	—	79	24	no	—
455	#547	—	79	24	no	—
456	#546	—	79	24	no	—
457	#546	—	79	24	no	—
458	#546	—	79	24	no	—
459	#546	—	79	24	no	—
460	D₄²	—	79	24	no	—
461	D₄²	—	79	24	no	—
462	#537	—	79	24	no	—
463	#536	—	79	6	no	—
464	#536	—	79	12	no	—
465	#536	—	79	6	no	—
466	#535	—	79	6	no	—
467	#535	—	79	12	no	—
468	#535	C₂×D₇₉	1	6	yes	complemented
469	#534	—	79	24	no	—
470	#532	—	79	12	no	—
471	#532	—	79	12	no	—
472	#525	—	79	6	no	—
473	#525	—	79	6	no	—
474	#525	—	79	4	no	—
475	#525	—	79	12	no	—
476	#525	—	79	12	no	—
477	#525	—	79	24	no	—
478	#525	—	79	12	no	—
479	#525	—	79	24	no	—
480	#525	—	79	6	no	—
481	#525	C₂×D₇₉	1	6	yes	complemented
482	C₂×#123	—	79	12	no	—
483	C₂×C₂²⋊Q₈	—	79	12	no	—
484	C₂×#121	—	79	12	no	—
485	C₂×#120	—	79	12	no	—
486	#520	—	79	8	no	—
487	#519	—	79	1	no	—
488	#519	C₂×D₇₉	1	1	yes	characteristic, complemented
489	#518	—	79	6	no	—
490	C₄×#41	—	79	8	no	—
491	C₂×C₄×D₄	—	79	24	no	—
492	C₂×#117	—	79	6	no	—
493	C₂⁵	—	79	3	no	—
494	2₋¹⁺⁴	—	2	8	no	—
495	2₋¹⁺⁴	—	158	32	no	—
496	2₋¹⁺⁴	—	158	8	no	—
497	H(5,𝔽₂)	—	158	48	no	—
498	H(5,𝔽₂)	—	158	32	no	—
499	C₂×#41	—	2	8	no	—
500	C₂×#41	—	79	16	no	—
501	C₂×#41	—	79	4	no	—
502	C₂×#41	—	79	4	no	—
503	C₂×#41	—	79	6	no	—
504	C₂×#41	—	79	12	no	—
505	C₂×#41	—	79	4	no	—
506	C₂×#41	—	79	4	no	—
507	C₂×#41	—	79	12	no	—
508	C₂×#41	—	79	12	no	—
509	C₂×#41	—	79	6	no	—
510	C₂×#41	—	79	6	no	—
511	C₂×#41	—	79	24	no	—
512	C₂×#41	—	79	12	no	—
513	C₂×#41	—	79	12	no	—
514	C₂×#41	—	158	24	no	—
515	C₂×#41	—	158	24	no	—
516	C₂×#41	—	158	48	no	—
517	C₂×#41	—	158	32	no	—
518	C₂×#41	—	158	64	no	—
519	C₂×#41	—	158	64	no	—
520	C₂×#41	—	158	32	no	—
521	C₂×#41	C₂²×D₇₉	1	6	yes	—
522	C₂×#41	C₂²×D₇₉	1	8	yes	—
523	C₂×#41	C₂²×D₇₉	1	4	yes	complemented
524	C₂²×Q₈	—	79	8	no	—
525	C₂²×Q₈	—	79	6	no	—
526	C₂²×Q₈	—	79	4	no	—
527	C₂²×Q₈	—	79	3	no	—
528	C₂²×Q₈	—	158	8	no	—
529	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
530	C₂²×Q₈	C₂²×D₇₉	1	4	yes	complemented
531	C₂²×D₄	—	79	24	no	—
532	C₂²×D₄	—	79	6	no	—
533	C₂²×D₄	—	79	12	no	—
534	C₂²×D₄	—	79	6	no	—
535	C₂²×D₄	—	79	24	no	—
536	C₂²×D₄	—	79	12	no	—
537	C₂²×D₄	—	79	3	no	—
538	C₂²×D₄	—	79	12	no	—
539	C₂²×D₄	—	158	24	no	—
540	C₂²×D₄	C₂²×D₇₉	1	3	yes	—
541	C₂³×C₄	—	79	3	no	—
542	C₂³×C₄	—	79	3	no	—
543	C₂³×C₄	—	79	12	no	—
544	C₂³×C₄	—	79	12	no	—
545	C₂³×C₄	—	79	12	no	—
546	C₂³×C₄	—	79	3	no	—
547	C₂³×C₄	—	79	1	no	—
548	C₂³×C₄	—	79	3	no	—
549	C₂³×C₄	—	158	24	no	—
550	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
551	C₄⋊Q₈	—	79	12	no	—
552	C₄⋊Q₈	—	79	12	no	—
553	#127	—	79	12	no	—
554	#127	C₂²×D₇₉	1	12	yes	complemented
555	#124	—	79	12	no	—
556	#124	—	79	12	no	—
557	#124	—	79	12	no	—
558	#124	C₂²×D₇₉	1	12	yes	complemented
559	#123	—	79	12	no	—
560	#123	—	79	4	no	—
561	#123	—	79	24	no	—
562	#123	—	79	12	no	—
563	#123	—	79	24	no	—
564	#123	—	79	48	no	—
565	#123	C₂²×D₇₉	1	4	yes	—
566	C₂²⋊Q₈	—	79	12	no	—
567	C₂²⋊Q₈	—	79	12	no	—
568	C₂²⋊Q₈	—	79	24	no	—
569	C₂²⋊Q₈	—	79	8	no	—
570	C₂²⋊Q₈	—	79	12	no	—
571	C₂²⋊Q₈	—	79	24	no	—
572	C₂²⋊Q₈	—	79	24	no	—
573	C₂²⋊Q₈	C₂²×D₇₉	1	12	yes	complemented
574	#121	—	79	24	no	—
575	#121	—	79	12	no	—
576	#121	—	79	24	no	—
577	#121	—	79	48	no	—
578	#121	—	79	12	no	—
579	#121	—	79	12	no	—
580	#121	—	79	8	no	—
581	#121	—	79	48	no	—
582	#121	C₂²×D₇₉	1	12	yes	complemented
583	#121	C₂²×D₇₉	1	24	yes	complemented
584	#120	—	79	12	no	—
585	#120	—	79	4	no	—
586	#120	—	79	24	no	—
587	#120	—	79	48	no	—
588	#120	—	79	4	no	—
589	#120	—	79	24	no	—
590	#120	C₂²×D₇₉	1	12	yes	—
591	C₄×Q₈	—	79	8	no	—
592	C₄×Q₈	C₂²×D₇₉	1	8	yes	complemented
593	C₄×D₄	—	79	24	no	—
594	C₄×D₄	—	79	24	no	—
595	C₄×D₄	—	79	24	no	—
596	C₄×D₄	—	79	8	no	—
597	C₄×D₄	—	79	24	no	—
598	C₄×D₄	—	79	8	no	—
599	C₄×D₄	—	79	24	no	—
600	C₄×D₄	—	79	24	no	—
601	C₄×D₄	—	79	24	no	—
602	C₄×D₄	C₂²×D₇₉	1	24	yes	complemented
603	#117	—	79	6	no	—
604	#117	—	79	12	no	—
605	#117	—	79	4	no	—
606	#117	—	79	12	no	—
607	#117	C₂²×D₇₉	1	6	yes	—
608	C₂×C₄⋊C₄	—	79	12	no	—
609	C₂×C₄⋊C₄	—	79	24	no	—
610	C₂×C₂²⋊C₄	—	79	12	no	—
611	C₂×C₂²⋊C₄	—	79	24	no	—
612	C₂×C₂²⋊C₄	—	79	24	no	—
613	C₂×C₄²	—	79	12	no	—
614	C₂⁴	—	316	12	no	—
615	C₂⁴	—	79	3	no	—
616	C₂⁴	—	79	12	no	—
617	C₂⁴	—	79	12	no	—
618	C₂⁴	—	79	1	no	—
619	C₂⁴	—	158	12	no	—
620	C₂⁴	C₂³×D₇₉	1	3	yes	—
621	#41	—	2	32	no	—
622	#41	—	2	16	no	—
623	#41	—	2	24	no	—
624	#41	—	79	32	no	—
625	#41	—	79	32	no	—
626	#41	—	158	48	no	—
627	#41	—	158	96	no	—
628	#41	—	158	48	no	—
629	#41	—	158	16	no	—
630	#41	—	158	48	no	—
631	#41	—	158	24	no	—
632	#41	—	158	48	no	—
633	#41	—	158	24	no	—
634	#41	—	158	48	no	—
635	#41	—	158	16	no	—
636	#41	—	158	24	no	—
637	C₂×Q₈	—	2	16	no	—
638	C₂×Q₈	—	79	4	no	—
639	C₂×Q₈	—	79	12	no	—
640	C₂×Q₈	—	79	6	no	—
641	C₂×Q₈	—	158	24	no	—
642	C₂×Q₈	—	158	32	no	—
643	C₂×Q₈	—	158	16	no	—
644	C₂×Q₈	—	158	12	no	—
645	C₂×Q₈	D₄×D₇₉	1	8	yes	complemented
646	C₂×Q₈	C₂³×D₇₉	1	6	yes	—
647	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
648	C₂×D₄	—	2	12	no	—
649	C₂×D₄	—	316	48	no	—
650	C₂×D₄	—	79	24	no	—
651	C₂×D₄	—	79	8	no	—
652	C₂×D₄	—	79	4	no	—
653	C₂×D₄	—	79	12	no	—
654	C₂×D₄	—	79	24	no	—
655	C₂×D₄	—	79	4	no	—
656	C₂×D₄	—	79	12	no	—
657	C₂×D₄	—	79	8	no	—
658	C₂×D₄	—	79	12	no	—
659	C₂×D₄	—	79	6	no	—
660	C₂×D₄	—	79	24	no	—
661	C₂×D₄	—	158	48	no	—
662	C₂×D₄	—	158	24	no	—
663	C₂×D₄	—	158	96	no	—
664	C₂×D₄	—	158	48	no	—
665	C₂×D₄	—	158	48	no	—
666	C₂×D₄	—	158	24	no	—
667	C₂×D₄	C₂³×D₇₉	1	4	yes	—
668	C₂×D₄	C₂³×D₇₉	1	6	yes	—
669	C₂×D₄	C₂³×D₇₉	1	12	yes	—
670	C₂×D₄	C₂³×D₇₉	1	24	yes	—
671	C₂²×C₄	—	2	12	no	—
672	C₂²×C₄	—	79	24	no	—
673	C₂²×C₄	—	79	1	no	—
674	C₂²×C₄	—	79	6	no	—
675	C₂²×C₄	—	79	6	no	—
676	C₂²×C₄	—	79	24	no	—
677	C₂²×C₄	—	79	4	no	—
678	C₂²×C₄	—	79	6	no	—
679	C₂²×C₄	—	79	6	no	—
680	C₂²×C₄	—	79	3	no	—
681	C₂²×C₄	—	79	12	no	—
682	C₂²×C₄	—	79	12	no	—
683	C₂²×C₄	—	79	2	no	—
684	C₂²×C₄	—	79	4	no	—
685	C₂²×C₄	—	79	12	no	—
686	C₂²×C₄	—	79	12	no	—
687	C₂²×C₄	—	79	2	no	—
688	C₂²×C₄	—	158	4	no	—
689	C₂²×C₄	—	158	48	no	—
690	C₂²×C₄	—	158	48	no	—
691	C₂²×C₄	—	158	48	no	—
692	C₂²×C₄	—	158	12	no	—
693	C₂²×C₄	—	158	12	no	—
694	C₂²×C₄	—	158	12	no	—
695	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
696	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
697	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
698	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
699	C₄⋊C₄	—	79	8	no	—
700	C₄⋊C₄	—	79	8	no	—
701	C₄⋊C₄	—	79	24	no	—
702	C₄⋊C₄	—	79	12	no	—
703	C₄⋊C₄	—	79	24	no	—
704	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
705	C₄⋊C₄	C₂³×D₇₉	1	12	yes	—
706	C₂²⋊C₄	—	79	4	no	—
707	C₂²⋊C₄	—	79	24	no	—
708	C₂²⋊C₄	—	79	24	no	—
709	C₂²⋊C₄	—	79	8	no	—
710	C₂²⋊C₄	—	79	8	no	—
711	C₂²⋊C₄	—	79	8	no	—
712	C₂²⋊C₄	—	79	24	no	—
713	C₂²⋊C₄	—	79	24	no	—
714	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
715	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
716	C₂²⋊C₄	C₂³×D₇₉	1	24	yes	—
717	C₄²	—	79	8	no	—
718	C₄²	—	79	12	no	—
719	C₄²	C₂³×D₇₉	1	12	yes	—
720	C₂³	—	2	6	no	—
721	C₂³	—	4	6	no	—
722	C₂³	—	316	6	no	—
723	C₂³	—	316	12	no	—
724	C₂³	—	316	24	no	—
725	C₂³	—	316	48	no	—
726	C₂³	—	79	12	no	—
727	C₂³	—	79	2	no	—
728	C₂³	—	79	6	no	—
729	C₂³	—	79	4	no	—
730	C₂³	—	158	24	no	—
731	C₂³	—	158	24	no	—
732	C₂³	—	158	24	no	—
733	C₂³	—	158	4	no	—
734	C₂³	—	158	2	no	—
735	C₂³	C₂⁴×D₇₉	1	4	yes	—
736	C₂³	C₂⁴×D₇₉	1	6	yes	—
737	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
738	Q₈	—	2	12	no	—
739	Q₈	—	158	8	no	—
740	Q₈	—	158	12	no	—
741	Q₈	—	158	24	no	—
742	Q₈	C₂×D₄×D₇₉	1	16	yes	—
743	D₄	—	2	8	no	—
744	D₄	—	2	24	no	—
745	D₄	—	2	12	no	—
746	D₄	—	4	24	no	—
747	D₄	—	316	24	no	—
748	D₄	—	79	48	no	—
749	D₄	—	158	16	no	—
750	D₄	—	158	24	no	—
751	D₄	—	158	8	no	—
752	D₄	—	158	16	no	—
753	D₄	—	158	24	no	—
754	D₄	—	158	48	no	—
755	D₄	—	158	8	no	—
756	D₄	—	158	12	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	24	no	—
759	C₂×C₄	—	2	24	no	—
760	C₂×C₄	—	316	24	no	—
761	C₂×C₄	—	79	1	no	—
762	C₂×C₄	—	79	1	no	—
763	C₂×C₄	—	79	4	no	—
764	C₂×C₄	—	79	24	no	—
765	C₂×C₄	—	79	24	no	—
766	C₂×C₄	—	79	8	no	—
767	C₂×C₄	—	79	4	no	—
768	C₂×C₄	—	79	6	no	—
769	C₂×C₄	—	158	4	no	—
770	C₂×C₄	—	158	4	no	—
771	C₂×C₄	—	158	8	no	—
772	C₂×C₄	—	158	24	no	—
773	C₂×C₄	—	158	24	no	—
774	C₂×C₄	—	158	8	no	—
775	C₂×C₄	—	158	12	no	—
776	C₂×C₄	—	158	12	no	—
777	C₂×C₄	—	158	6	no	—
778	C₂×C₄	—	158	24	no	—
779	C₂×C₄	—	158	24	no	—
780	C₂×C₄	C₂×D₄×D₇₉	1	12	yes	—
781	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
782	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
783	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
784	C₂×C₄	C₂⁴×D₇₉	1	6	yes	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	6	no	—
788	C₂²	—	2	8	no	—
789	C₂²	—	2	12	no	—
790	C₂²	—	4	12	no	—
791	C₂²	—	316	12	no	—
792	C₂²	—	316	48	no	—
793	C₂²	—	79	12	no	—
794	C₂²	—	79	4	no	—
795	C₂²	—	632	24	no	—
796	C₂²	—	158	8	no	—
797	C₂²	—	158	4	no	—
798	C₂²	—	158	8	no	—
799	C₂²	—	158	2	no	—
800	C₂²	—	158	12	no	—
801	C₂²	—	158	2	no	—
802	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
803	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	8	no	—
807	C₄	—	79	2	no	—
808	C₄	—	79	2	no	—
809	C₄	—	158	6	no	—
810	C₄	—	158	4	no	—
811	C₄	—	158	8	no	—
812	C₄	C₂²×D₄×D₇₉	1	12	yes	—
813	C₂	—	2	2	no	—
814	C₂	—	4	6	no	—
815	C₂	—	4	4	no	—
816	C₂	—	316	4	no	—
817	C₂	—	158	4	no	—
818	C₂	—	158	12	no	—
819	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
820	C₂	#585×D₇₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3487	C₂
hypercenter	#3487	D₇₉
hypocenter	C₇₉	#62811
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3487

Complements

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

N	H ≅ G/N	type
1. C₂×#19099400	C₂	semidirect
2. C₂²×#41×D₇₉	C₂	semidirect
3. #23777079	C₂	semidirect
4. #23777068	C₂	semidirect
5. #23777058	C₂	semidirect
6. #23777052	C₂	semidirect
7. #23777048	C₂	semidirect
8. #23777042	C₂	semidirect
9. #23777034	C₂	semidirect
10. #23776890	C₂	semidirect
11. #23776889	C₂	semidirect
12. #23776731	C₂	semidirect
13. #525×D₇₉	C₂	semidirect
14. #23776602	C₂	semidirect
15. C₇₉×#3487	C₂	semidirect
17. C₂×#14579209	C₂²	semidirect
18. C₂×#14579209	C₂²	semidirect
19. C₂×#14579207	C₂²	semidirect
20. C₂×#14579207	C₂²	semidirect
22. C₂²×#11929625	C₂²	semidirect
23. C₂²×#11929624	C₂²	semidirect
24. C₂²×#11929623	C₂²	semidirect
26. C₂×#41×D₇₉	C₂²	semidirect
27. C₂×#41×D₇₉	C₂²	semidirect
28. C₂×#41×D₇₉	C₂²	semidirect
29. C₂×#41×D₇₉	C₂²	semidirect
30. C₂²×Q₈×D₇₉	C₂²	semidirect
31. C₂²×D₄×D₇₉	C₂²	semidirect
32. C₂³×C₄×D₇₉	C₂²	semidirect
33. #19099232	C₂²	semidirect
34. Q₈×D₃₁₆	C₂²	semidirect
35. Q₈×C₂²⋊D₇₉	C₂²	semidirect
36. #19099225	C₂²	semidirect
37. #19099220	C₂²	semidirect
38. #19099220	C₂²	semidirect
39. #19099218	C₂²	semidirect
40. #19099215	C₂²	semidirect
41. #19099210	C₂²	semidirect
42. #19099210	C₂²	semidirect
43. #19099209	C₂²	semidirect
44. #19099206	C₂²	semidirect
45. #19099198	C₂²	semidirect
46. #19099197	C₂²	semidirect
47. #19099142	C₂²	semidirect
48. #19099139	C₂²	semidirect
49. #19099134	C₂²	semidirect
50. #19099133	C₂²	semidirect
51. #19099130	C₂²	semidirect
52. #19099126	C₂²	semidirect
53. #19099123	C₂²	semidirect
54. #19099112	C₂²	semidirect
55. #19099111	C₂²	semidirect
56. #19099076	C₂²	semidirect
57. #19099075	C₂²	semidirect
58. #19099074	C₂²	semidirect
59. #19099073	C₂²	semidirect
60. #19099073	C₂²	semidirect
61. #19099072	C₂²	semidirect
62. #19099071	C₂²	semidirect
63. #19099070	C₂²	semidirect
64. #19099069	C₂²	semidirect
65. #123×D₇₉	C₂²	semidirect
66. C₂²⋊Q₈×D₇₉	C₂²	semidirect
67. #121×D₇₉	C₂²	semidirect
68. #120×D₇₉	C₂²	semidirect
69. #19099045	C₂²	semidirect
70. #19099041	C₂²	semidirect
71. #19099037	C₂²	semidirect
72. C₄×#11929625	C₂²	semidirect
73. C₄×D₄×D₇₉	C₂²	semidirect
74. #117×D₇₉	C₂²	semidirect
75. C₂×2₋¹⁺⁴×C₇₉	C₂²	semidirect
76. C₂²×#41×C₇₉	C₂²	semidirect
77. #550×C₇₉	C₂²	semidirect
78. #548×C₇₉	C₂²	semidirect
79. #535×C₇₉	C₂²	semidirect
80. #525×C₇₉	C₂²	semidirect
81. #519×C₇₉	C₂²	semidirect
88. C₂×#11929625	D₄	semidirect
91. C₂×#11929625	C₂³	semidirect
92. C₂×#11929625	C₂³	semidirect
93. C₂×#11929625	C₂³	semidirect
97. C₂×#11929624	C₂³	semidirect
98. C₂×#11929624	C₂³	semidirect
103. C₂×#11929623	C₂³	semidirect
111. C₂×Q₈×D₇₉	C₂³	semidirect
112. C₂×Q₈×D₇₉	C₂³	semidirect
114. C₂²×D₃₁₆	C₂³	semidirect
120. C₂×D₄×D₇₉	C₂³	semidirect
121. C₂×D₄×D₇₉	C₂³	semidirect
130. C₂²×C₄×D₇₉	C₂³	semidirect
131. #14579161	C₂³	semidirect
132. #14579159	C₂³	semidirect
133. #14579157	C₂³	semidirect
134. #14579149	C₂³	semidirect
135. #14579148	C₂³	semidirect
136. #14579148	C₂³	semidirect
137. #14579146	C₂³	semidirect
140. #14579143	C₂³	semidirect
141. #14579143	C₂³	semidirect
144. #14579141	C₂³	semidirect
145. #14579140	C₂³	semidirect
146. #14579140	C₂³	semidirect
148. #14579138	C₂³	semidirect
151. #14579135	C₂³	semidirect
153. #14579134	C₂³	semidirect
154. #14579133	C₂³	semidirect
156. #14579132	C₂³	semidirect
157. #14579132	C₂³	semidirect
163. #14579129	C₂³	semidirect
164. Q₈×Dic₇₉	C₂³	semidirect
166. C₄×D₃₁₆	C₂³	semidirect
167. D₄×Dic₇₉	C₂³	semidirect
169. #14579123	C₂³	semidirect
171. C₄×C₂²⋊D₇₉	C₂³	semidirect
173. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
175. #14579119	C₂³	semidirect
176. #14579118	C₂³	semidirect
178. C₄⋊C₄×D₇₉	C₂³	semidirect
179. C₄⋊C₄×D₇₉	C₂³	semidirect
182. C₂²⋊C₄×D₇₉	C₂³	semidirect
183. C₄²×D₇₉	C₂³	semidirect
188. C₂×#41×C₇₉	C₂³	semidirect
190. C₂²×Q₈×C₇₉	C₂³	semidirect
193. #127×C₇₉	C₂³	semidirect
194. #124×C₇₉	C₂³	semidirect
196. C₂²⋊Q₈×C₇₉	C₂³	semidirect
197. #121×C₇₉	C₂³	semidirect
198. #121×C₇₉	C₂³	semidirect
200. C₄×Q₈×C₇₉	C₂³	semidirect
201. C₄×D₄×C₇₉	C₂³	semidirect
212. #11929625	C₂×D₄	semidirect
213. #11929625	C₂×D₄	semidirect
230. C₂×D₃₁₆	C₂×D₄	semidirect
259. C₂×C₄×D₇₉	C₂×D₄	semidirect
290. C₂×Q₈×C₇₉	C₂×D₄	semidirect
392. C₂×D₇₉	#585	semidirect
416. #3487	D₇₉	semidirect
426. C₇₉	#62811	semidirect
430. C₂×2₋¹⁺⁴	C₂×D₇₉	semidirect
442. C₂²×#41	C₂×D₇₉	semidirect
447. #550	C₂×D₇₉	semidirect
453. #548	C₂×D₇₉	semidirect
468. #535	C₂×D₇₉	semidirect
481. #525	C₂×D₇₉	semidirect
488. #519	C₂×D₇₉	semidirect
523. C₂×#41	C₂²×D₇₉	semidirect
530. C₂²×Q₈	C₂²×D₇₉	semidirect
554. #127	C₂²×D₇₉	semidirect
558. #124	C₂²×D₇₉	semidirect
573. C₂²⋊Q₈	C₂²×D₇₉	semidirect
582. #121	C₂²×D₇₉	semidirect
583. #121	C₂²×D₇₉	semidirect
592. C₄×Q₈	C₂²×D₇₉	semidirect
602. C₄×D₄	C₂²×D₇₉	semidirect
645. C₂×Q₈	D₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19099400	2
C₂²×#41×D₇₉	2
#23777079	2
#23777068	2
#23777058	2
#23777052	2
#23777048	2
#23777042	2
#23777034	2
#23776890	2
#23776889	2
#23776731	2
#525×D₇₉	2
#23776602	2
C₇₉×#3487	2
#62811	79