Subgroups — #35196989

Order 20224.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777972	C₂	1	8	yes	maximal, complemented
2	#23777919	C₂	1	8	yes	maximal, complemented
3	#23777757	C₂	1	8	yes	maximal, complemented
4	#23777355	C₂	1	16	yes	maximal, complemented
5	#23777294	C₂	1	4	yes	maximal, complemented
6	#23777190	C₂	1	4	yes	maximal, complemented
7	#23777089	C₂	1	8	yes	maximal, complemented
8	#23777051	C₂	1	2	yes	maximal, complemented
9	#23777035	C₂	1	2	yes	maximal, complemented
10	#23776696	C₂	1	2	yes	maximal, complemented
11	C₂²×#124×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579209	C₂²	1	2	yes	complemented
13	C₂×#14579206	C₂²	1	2	yes	complemented
14	#19099313	C₂²	1	8	yes	complemented
15	#19099307	C₂²	1	16	yes	complemented
16	#19099305	C₂²	1	8	yes	complemented
17	#19099295	C₂²	1	16	yes	complemented
18	#19099282	C₂²	1	16	yes	complemented
19	#19099275	C₂²	1	16	yes	complemented
20	#19099243	C₂²	1	16	yes	complemented
21	#19099239	C₂²	1	32	yes	complemented
22	#19099239	C₂²	1	32	yes	complemented
23	Q₈×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
24	#19099224	C₂²	1	16	yes	complemented
25	#19099221	C₂²	1	16	yes	complemented
26	#19099207	C₂²	1	16	yes	complemented
27	#19099206	C₂²	1	16	yes	complemented
28	#19099203	C₂²	1	32	yes	complemented
29	#19099203	C₂²	1	32	yes	complemented
30	D₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
31	#19099189	C₂²	1	8	yes	complemented
32	#19099182	C₂²	1	16	yes	complemented
33	#19099177	C₂²	1	32	yes	complemented
34	#19099151	C₂²	1	16	yes	complemented
35	#19099151	C₂²	1	16	yes	complemented
36	#19099147	C₂²	1	32	yes	complemented
37	#19099137	C₂²	1	4	yes	complemented
38	#19099137	C₂²	1	8	yes	complemented
39	#19099133	C₂²	1	8	yes	complemented
40	#19099131	C₂²	1	8	yes	complemented
41	#19099130	C₂²	1	4	yes	—
42	#19099125	C₂²	1	8	yes	complemented
43	#19099122	C₂²	1	8	yes	complemented
44	#19099120	C₂²	1	2	yes	complemented
45	#19099120	C₂²	1	4	yes	complemented
46	#19099113	C₂²	1	4	yes	complemented
47	#19099113	C₂²	1	2	yes	complemented
48	#19099112	C₂²	1	8	yes	complemented
49	#19099097	C₂²	1	8	yes	complemented
50	#19099097	C₂²	1	8	yes	complemented
51	#19099097	C₂²	1	8	yes	complemented
52	#19099092	C₂²	1	16	yes	complemented
53	#124×D₇₉	C₂²	1	8	yes	complemented
54	#19099074	C₂²	1	4	yes	complemented
55	#19099074	C₂²	1	8	yes	complemented
56	#19099074	C₂²	1	8	yes	complemented
57	C₂×#14579130	C₂²	1	8	yes	complemented
58	#19099041	C₂²	1	2	yes	complemented
59	#19099038	C₂²	1	2	yes	complemented
60	#19099036	C₂²	1	16	yes	complemented
61	C₄×#11929624	C₂²	1	4	yes	complemented
62	C₄×#11929624	C₂²	1	8	yes	complemented
63	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
65	C₂×#124×C₇₉	C₂²	1	4	yes	complemented
66	C₂×#124×C₇₉	C₂²	1	8	yes	complemented
67	C₂×#124×C₇₉	C₂²	1	8	yes	complemented
68	C₂×#124×C₇₉	C₂²	1	4	yes	complemented
69	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	complemented
70	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
71	#14579209	—	4	8	no	—
72	#14579206	—	4	8	no	—
73	C₂×#11929625	C₂³	1	8	yes	complemented
74	C₂×#11929624	C₂³	1	4	yes	—
75	C₂×#11929624	C₂³	1	8	yes	—
76	C₂×#11929624	C₂³	1	8	yes	—
77	C₂×#11929623	C₂³	1	8	yes	—
78	C₂×Q₈×D₇₉	C₂³	1	8	yes	complemented
79	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
80	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
81	C₂×D₄×D₇₉	C₂³	1	8	yes	—
82	#14579161	C₂³	1	4	yes	complemented
83	#14579161	C₂³	1	2	yes	complemented
84	#14579159	C₂³	1	16	yes	complemented
85	#14579159	C₂³	1	8	yes	complemented
86	#14579158	C₂³	1	2	yes	complemented
87	#14579157	C₂³	1	8	yes	—
88	#14579155	C₂³	1	16	yes	complemented
89	#14579154	C₂³	1	32	yes	complemented
90	#14579154	C₂³	1	32	yes	complemented
91	#14579153	C₂³	1	8	yes	complemented
92	#14579153	C₂³	1	4	yes	complemented
93	#14579150	C₂³	1	16	yes	complemented
94	#14579150	C₂³	1	8	yes	complemented
95	#14579149	C₂³	1	8	yes	complemented
96	#14579149	C₂³	1	4	yes	complemented
97	#14579148	C₂³	1	8	yes	—
98	#14579147	C₂³	1	32	yes	complemented
99	#14579147	C₂³	1	32	yes	complemented
100	#14579145	C₂³	1	32	yes	complemented
101	#14579144	C₂³	1	16	yes	—
102	#14579144	C₂³	1	8	yes	—
103	#14579144	C₂³	1	16	yes	—
104	#14579143	C₂³	1	32	yes	complemented
105	#14579143	C₂³	1	32	yes	complemented
106	#14579142	C₂³	1	16	yes	—
107	#14579140	C₂³	1	8	yes	—
108	#14579140	C₂³	1	16	yes	—
109	#14579140	C₂³	1	8	yes	—
110	#14579140	C₂³	1	8	yes	—
111	#14579138	C₂³	1	32	yes	complemented
112	#14579138	C₂³	1	32	yes	complemented
113	#14579137	C₂³	1	32	yes	complemented
114	#14579137	C₂³	1	16	yes	complemented
115	#14579135	C₂³	1	8	yes	—
116	#14579135	C₂³	1	16	yes	—
117	#14579135	C₂³	1	8	yes	—
118	#14579135	C₂³	1	8	yes	—
119	#14579134	C₂³	1	32	yes	complemented
120	#14579134	C₂³	1	32	yes	complemented
121	#14579133	C₂³	1	32	yes	—
122	#14579132	C₂³	1	16	yes	—
123	#14579131	C₂³	1	32	yes	complemented
124	#14579130	C₂³	1	32	yes	—
125	#14579130	C₂³	1	16	yes	—
126	#14579130	C₂³	1	8	yes	—
127	#14579129	C₂³	1	16	yes	—
128	Q₈×Dic₇₉	C₂³	1	16	yes	complemented
129	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
130	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
131	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
132	C₄×D₃₁₆	C₂³	1	8	yes	complemented
133	C₄×D₃₁₆	C₂³	1	8	yes	complemented
134	C₄×D₃₁₆	C₂³	1	8	yes	complemented
135	D₄×Dic₇₉	C₂³	1	16	yes	—
136	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
137	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	—
138	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
139	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
140	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
141	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
142	#14579120	C₂³	1	8	yes	—
143	#14579120	C₂³	1	4	yes	—
144	#14579120	C₂³	1	8	yes	—
145	#14579118	C₂³	1	8	yes	complemented
146	#14579118	C₂³	1	16	yes	complemented
147	#14579117	C₂³	1	32	yes	complemented
148	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	—
149	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
150	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
151	C₄²×D₇₉	C₂³	1	8	yes	complemented
152	C₂⁵×C₇₉	C₂³	1	2	yes	—
153	C₂²×Q₈×C₇₉	—	4	4	no	—
154	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
155	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
156	C₂²×Q₈×C₇₉	C₂³	1	8	yes	—
157	C₂²×D₄×C₇₉	—	4	4	no	—
158	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
159	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
160	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
161	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
163	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
164	#124×C₇₉	C₂³	1	16	yes	—
165	#124×C₇₉	C₂³	1	8	yes	—
166	#124×C₇₉	C₂³	1	16	yes	—
167	#124×C₇₉	C₂³	1	8	yes	—
168	#124×C₇₉	C₂³	1	8	yes	—
169	#124×C₇₉	C₂³	1	8	yes	—
170	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
171	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
172	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
173	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
174	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
175	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
178	C₂³×D₇₉	C₂⁴	1	8	yes	—
179	#11929625	—	4	16	no	—
180	#11929624	—	2	16	no	—
181	#11929624	—	4	16	no	—
182	#11929624	—	4	16	no	—
183	#11929623	—	4	16	no	—
184	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
185	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
186	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
187	Q₈×D₇₉	—	4	16	no	—
188	C₂×D₃₁₆	C₂⁴	1	4	yes	—
189	C₂×D₃₁₆	C₂⁴	1	8	yes	—
190	C₂×D₃₁₆	C₂⁴	1	8	yes	—
191	C₂×C₂²⋊D₇₉	—	4	16	no	—
192	C₂×C₂²⋊D₇₉	—	4	32	no	—
193	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
194	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
195	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
196	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
197	D₄×D₇₉	—	4	16	no	—
198	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
199	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
200	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
201	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
202	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
203	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
204	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
205	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
206	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
207	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
208	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
209	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
210	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
211	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
212	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
213	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
214	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
215	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
216	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
217	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
218	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
219	C₄×Dic₇₉	C₂⁴	1	16	yes	—
220	C₄×Dic₇₉	C₂⁴	1	8	yes	—
221	C₄×Dic₇₉	C₂⁴	1	16	yes	—
222	C₂⁴×C₇₉	—	4	4	no	—
223	C₂⁴×C₇₉	—	4	8	no	—
224	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
226	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
227	C₂×Q₈×C₇₉	—	2	8	no	—
228	C₂×Q₈×C₇₉	—	4	4	no	—
229	C₂×Q₈×C₇₉	—	4	16	no	—
230	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
231	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
232	C₂×D₄×C₇₉	—	2	8	no	—
233	C₂×D₄×C₇₉	—	4	16	no	—
234	C₂×D₄×C₇₉	—	4	4	no	—
235	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
236	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
237	C₂²×C₄×C₇₉	—	2	4	no	—
238	C₂²×C₄×C₇₉	—	4	4	no	—
239	C₂²×C₄×C₇₉	—	4	4	no	—
240	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
249	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
250	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
251	C₄²×C₇₉	C₂⁴	1	2	yes	—
252	C₄²×C₇₉	C₂⁴	1	2	yes	—
253	C₄²×C₇₉	C₂⁴	1	2	yes	—
254	C₄²×C₇₉	C₂⁴	1	4	yes	—
255	C₄²×C₇₉	C₂⁴	1	4	yes	—
256	C₄²×C₇₉	C₂⁴	1	2	yes	—
257	C₂³×C₇₉	—	2	2	no	—
258	C₂³×C₇₉	—	2	4	no	—
259	C₂³×C₇₉	—	2	8	no	—
260	C₂³×C₇₉	—	2	16	no	—
261	C₂³×C₇₉	—	4	8	no	—
262	C₂³×C₇₉	—	4	8	no	—
263	C₂³×C₇₉	—	4	8	no	—
264	C₂³×C₇₉	—	8	16	no	—
265	C₂³×C₇₉	C₂⁵	1	8	yes	—
266	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
267	C₂³×C₇₉	C₂⁵	1	2	yes	—
268	C₂²×D₇₉	—	4	8	no	—
269	C₂²×D₇₉	—	4	16	no	—
270	C₂²×D₇₉	C₂⁵	1	8	yes	—
271	Q₈×C₇₉	—	2	16	no	—
272	Q₈×C₇₉	—	4	8	no	—
273	D₄×C₇₉	—	2	16	no	—
274	D₄×C₇₉	—	4	8	no	—
275	C₂×C₄×C₇₉	—	2	8	no	—
276	C₂×C₄×C₇₉	—	2	2	no	—
277	C₂×C₄×C₇₉	—	2	8	no	—
278	C₂×C₄×C₇₉	—	2	8	no	—
279	C₂×C₄×C₇₉	—	4	2	no	—
280	C₂×C₄×C₇₉	—	4	4	no	—
281	C₂×C₄×C₇₉	—	4	2	no	—
282	C₂×C₄×C₇₉	—	4	8	no	—
283	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
284	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
285	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
286	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
287	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
288	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
289	C₂²⋊D₇₉	—	2	16	no	—
290	C₂²⋊D₇₉	—	2	32	no	—
291	C₂²⋊D₇₉	—	4	16	no	—
292	C₂²⋊D₇₉	—	4	32	no	—
293	C₂×Dic₇₉	—	4	16	no	—
294	C₂×Dic₇₉	—	4	8	no	—
295	C₂×Dic₇₉	C₂⁵	1	16	yes	—
296	C₂×Dic₇₉	C₂⁵	1	8	yes	—
297	D₃₁₆	—	2	8	no	—
298	D₃₁₆	—	4	8	no	—
299	D₃₁₆	—	4	8	no	—
300	C₄×D₇₉	—	2	16	no	—
301	C₄×D₇₉	—	4	16	no	—
302	C₄×D₇₉	—	4	16	no	—
303	Dic₁₅₈	—	2	8	no	—
304	Dic₁₅₈	—	4	8	no	—
305	Dic₁₅₈	—	4	8	no	—
306	C₂²×C₇₉	—	2	8	no	—
307	C₂²×C₇₉	—	2	2	no	—
308	C₂²×C₇₉	—	2	2	no	—
309	C₂²×C₇₉	—	2	2	no	—
310	C₂²×C₇₉	—	2	8	no	—
311	C₂²×C₇₉	—	2	16	no	—
312	C₂²×C₇₉	—	8	8	no	—
313	C₂²×C₇₉	—	8	16	no	—
314	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
315	C₂²×C₇₉	#585	1	4	yes	—
316	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
317	C₂×D₇₉	—	2	8	no	—
318	C₂×D₇₉	—	2	16	no	—
319	C₂×D₇₉	—	16	8	no	—
320	C₄×C₇₉	—	2	2	no	—
321	C₄×C₇₉	—	2	8	no	—
322	C₄×C₇₉	—	2	4	no	—
323	C₄×C₇₉	—	2	4	no	—
324	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
325	Dic₇₉	—	2	8	no	—
326	Dic₇₉	—	2	16	no	—
327	#62824	—	79	1	no	maximal, Sylow
328	C₂×C₇₉	—	2	2	no	—
329	C₂×C₇₉	—	2	4	no	—
330	C₂×C₇₉	—	4	8	no	—
331	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₇₉	C₂×#585	1	2	yes	—
333	D₇₉	—	4	8	no	—
334	#3561	—	79	8	no	—
335	#3558	—	79	8	no	—
336	#3545	—	79	8	no	—
337	#3514	—	79	16	no	—
338	#3510	—	79	4	no	—
339	#3500	—	79	4	no	—
340	#3490	—	79	8	no	—
341	#3486	—	79	2	no	—
342	#3484	—	79	2	no	—
343	#3444	—	79	2	no	—
344	C₂²×#124	D₇₉	1	1	yes	characteristic, complemented
345	C₇₉	#62824	1	1	yes	characteristic, complemented, Sylow
346	C₂×2₋¹⁺⁴	—	79	2	no	—
347	C₂×H(5,𝔽₂)	—	79	2	no	—
348	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
349	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
350	#563	—	79	8	no	—
351	#562	—	79	16	no	—
352	H(3,𝔽₄)	—	79	8	no	—
353	#559	—	79	16	no	—
354	#556	—	79	16	no	—
355	#555	—	79	16	no	—
356	#551	—	79	16	no	—
357	#551	—	79	32	no	—
358	#551	—	79	32	no	—
359	D₄×Q₈	—	79	16	no	—
360	#548	—	79	16	no	—
361	#548	—	79	16	no	—
362	#546	—	79	16	no	—
363	#546	—	79	16	no	—
364	#546	—	79	32	no	—
365	#546	—	79	32	no	—
366	D₄²	—	79	16	no	—
367	#543	—	79	8	no	—
368	#542	—	79	32	no	—
369	#542	—	79	16	no	—
370	#538	—	79	32	no	—
371	#538	—	79	16	no	—
372	#538	—	79	16	no	—
373	#536	—	79	4	no	—
374	#536	—	79	8	no	—
375	#536	—	79	8	no	—
376	#535	—	79	4	no	—
377	#535	—	79	8	no	—
378	#534	—	79	8	no	—
379	#534	—	79	8	no	—
380	#533	—	79	2	no	—
381	#533	—	79	4	no	—
382	#532	—	79	8	no	—
383	#532	—	79	2	no	—
384	#532	—	79	4	no	—
385	#529	—	79	16	no	—
386	#529	—	79	8	no	—
387	#529	—	79	8	no	—
388	#529	—	79	8	no	—
389	C₂×#124	—	79	8	no	—
390	C₂×#124	C₂×D₇₉	1	4	yes	complemented
391	C₂×#124	C₂×D₇₉	1	8	yes	complemented
392	C₂×#124	C₂×D₇₉	1	4	yes	complemented
393	C₂×#124	C₂×D₇₉	1	8	yes	complemented
394	#525	—	79	4	no	—
395	#525	—	79	8	no	—
396	#525	—	79	8	no	—
397	C₂×#120	—	79	8	no	—
398	#519	—	79	2	no	—
399	#518	—	79	2	no	—
400	#518	—	79	16	no	—
401	C₄×#41	—	79	4	no	—
402	C₄×#41	—	79	8	no	—
403	C₂²×C₂²⋊C₄	C₂×D₇₉	1	4	yes	complemented
404	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
405	C₂⁵	C₂²×D₇₉	1	2	yes	—
406	2₋¹⁺⁴	—	316	8	no	—
407	H(5,𝔽₂)	—	316	8	no	—
408	C₂×#41	—	79	8	no	—
409	C₂×#41	—	79	8	no	—
410	C₂×#41	—	79	8	no	—
411	C₂×#41	—	79	8	no	—
412	C₂×#41	—	79	4	no	—
413	C₂²×Q₈	—	4	4	no	—
414	C₂²×Q₈	—	79	8	no	—
415	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
416	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
417	C₂²×Q₈	C₂²×D₇₉	1	8	yes	—
418	C₂²×D₄	—	4	4	no	—
419	C₂²×D₄	—	79	16	no	—
420	C₂²×D₄	—	79	8	no	—
421	C₂²×D₄	—	79	8	no	—
422	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
423	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
424	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
425	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
426	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
427	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
428	C₄⋊Q₈	—	79	8	no	—
429	C₄⋊Q₈	—	79	16	no	—
430	C₄⋊Q₈	—	79	2	no	—
431	C₄⋊Q₈	—	79	4	no	—
432	#127	—	79	8	no	—
433	#127	—	79	2	no	—
434	#126	—	79	32	no	—
435	#126	—	79	32	no	—
436	#126	—	79	16	no	—
437	#125	—	79	4	no	—
438	#125	—	79	8	no	—
439	#124	—	79	8	no	—
440	#124	—	79	16	no	—
441	#124	—	79	8	no	—
442	#124	—	79	32	no	—
443	#124	—	79	32	no	—
444	#124	—	79	4	no	—
445	#124	—	79	8	no	—
446	#124	C₂²×D₇₉	1	8	yes	—
447	#124	C₂²×D₇₉	1	8	yes	—
448	#124	C₂²×D₇₉	1	16	yes	—
449	#124	C₂²×D₇₉	1	16	yes	—
450	#124	C₂²×D₇₉	1	8	yes	—
451	#124	C₂²×D₇₉	1	8	yes	—
452	#123	—	79	16	no	—
453	#123	—	79	8	no	—
454	#123	—	79	16	no	—
455	#123	—	79	16	no	—
456	#123	—	79	32	no	—
457	#123	—	79	32	no	—
458	#123	—	79	32	no	—
459	C₂²⋊Q₈	—	79	16	no	—
460	C₂²⋊Q₈	—	79	32	no	—
461	C₂²⋊Q₈	—	79	8	no	—
462	C₂²⋊Q₈	—	79	8	no	—
463	C₂²⋊Q₈	—	79	8	no	—
464	C₂²⋊Q₈	—	79	16	no	—
465	C₂²⋊Q₈	—	79	32	no	—
466	C₂²⋊Q₈	—	79	32	no	—
467	#121	—	79	16	no	—
468	#121	—	79	32	no	—
469	#121	—	79	8	no	—
470	#121	—	79	8	no	—
471	#121	—	79	8	no	—
472	#121	—	79	16	no	—
473	#121	—	79	32	no	—
474	#121	—	79	32	no	—
475	#120	—	79	8	no	—
476	#120	—	79	16	no	—
477	#120	—	79	32	no	—
478	#120	—	79	16	no	—
479	#120	—	79	32	no	—
480	C₄×Q₈	—	79	16	no	—
481	C₄×Q₈	—	79	8	no	—
482	C₄×Q₈	—	79	8	no	—
483	C₄×Q₈	—	79	8	no	—
484	C₄×D₄	—	79	16	no	—
485	C₄×D₄	—	79	16	no	—
486	C₄×D₄	—	79	16	no	—
487	C₄×D₄	—	79	16	no	—
488	C₄×D₄	—	79	32	no	—
489	C₄×D₄	—	79	32	no	—
490	C₄×D₄	—	79	32	no	—
491	C₄×D₄	—	79	8	no	—
492	C₄×D₄	—	79	8	no	—
493	C₄×D₄	—	79	8	no	—
494	#117	—	79	4	no	—
495	#117	—	79	8	no	—
496	#117	—	79	8	no	—
497	#117	—	79	32	no	—
498	#117	—	79	8	no	—
499	#117	—	79	16	no	—
500	C₂×C₂²⋊C₄	—	79	8	no	—
501	C₂×C₂²⋊C₄	—	79	16	no	—
502	C₂×C₂²⋊C₄	—	79	32	no	—
503	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
505	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	—
506	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	—
507	C₂×C₄²	—	79	8	no	—
508	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
509	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
510	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
511	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	4	8	no	—
514	C₂⁴	—	79	8	no	—
515	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
516	C₂⁴	C₂³×D₇₉	1	4	yes	—
517	C₂⁴	C₂³×D₇₉	1	8	yes	—
518	#41	—	316	16	no	—
519	#41	—	316	16	no	—
520	#41	—	316	16	no	—
521	#41	—	316	16	no	—
522	#41	—	158	16	no	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	16	no	—
526	C₂×Q₈	—	316	16	no	—
527	C₂×Q₈	—	79	8	no	—
528	C₂×Q₈	—	79	8	no	—
529	C₂×Q₈	—	79	4	no	—
530	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
531	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	4	no	—
535	C₂×D₄	—	316	32	no	—
536	C₂×D₄	—	316	16	no	—
537	C₂×D₄	—	316	16	no	—
538	C₂×D₄	—	79	32	no	—
539	C₂×D₄	—	79	16	no	—
540	C₂×D₄	—	79	16	no	—
541	C₂×D₄	—	79	8	no	—
542	C₂×D₄	—	79	8	no	—
543	C₂×D₄	—	79	8	no	—
544	C₂×D₄	—	79	4	no	—
545	C₂×D₄	C₂³×D₇₉	1	8	yes	—
546	C₂×D₄	C₂³×D₇₉	1	8	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	79	16	no	—
551	C₂²×C₄	—	79	8	no	—
552	C₂²×C₄	—	79	16	no	—
553	C₂²×C₄	—	79	16	no	—
554	C₂²×C₄	—	79	8	no	—
555	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
556	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
557	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
558	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
559	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
560	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
561	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
562	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
563	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
564	C₄⋊C₄	—	79	16	no	—
565	C₄⋊C₄	—	79	32	no	—
566	C₄⋊C₄	—	79	16	no	—
567	C₄⋊C₄	—	79	16	no	—
568	C₄⋊C₄	—	79	8	no	—
569	C₄⋊C₄	—	79	8	no	—
570	C₄⋊C₄	—	79	8	no	—
571	C₄⋊C₄	—	79	16	no	—
572	C₂²⋊C₄	—	79	8	no	—
573	C₂²⋊C₄	—	79	16	no	—
574	C₂²⋊C₄	—	79	32	no	—
575	C₂²⋊C₄	—	79	16	no	—
576	C₂²⋊C₄	—	79	16	no	—
577	C₂²⋊C₄	—	79	32	no	—
578	C₂²⋊C₄	—	79	16	no	—
579	C₂²⋊C₄	—	79	16	no	—
580	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
581	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
582	C₄²	—	79	16	no	—
583	C₄²	—	79	8	no	—
584	C₄²	—	79	16	no	—
585	C₄²	C₂³×D₇₉	1	2	yes	—
586	C₄²	C₂³×D₇₉	1	2	yes	—
587	C₄²	C₂³×D₇₉	1	2	yes	—
588	C₄²	C₂³×D₇₉	1	4	yes	—
589	C₄²	C₂³×D₇₉	1	4	yes	—
590	C₄²	C₂³×D₇₉	1	2	yes	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	8	no	—
594	C₂³	—	2	16	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	8	no	—
598	C₂³	—	8	16	no	—
599	C₂³	—	316	8	no	—
600	C₂³	—	316	16	no	—
601	C₂³	—	79	8	no	—
602	C₂³	C₂⁴×D₇₉	1	8	yes	—
603	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
604	C₂³	C₂⁴×D₇₉	1	2	yes	—
605	Q₈	—	2	16	no	—
606	Q₈	—	4	8	no	—
607	Q₈	—	316	8	no	—
608	Q₈	—	316	8	no	—
609	Q₈	—	158	8	no	—
610	D₄	—	2	16	no	—
611	D₄	—	4	8	no	—
612	D₄	—	316	8	no	—
613	D₄	—	316	8	no	—
614	D₄	—	316	16	no	—
615	D₄	—	316	32	no	—
616	D₄	—	158	16	no	—
617	D₄	—	158	32	no	—
618	D₄	—	158	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	316	16	no	—
628	C₂×C₄	—	316	16	no	—
629	C₂×C₄	—	316	8	no	—
630	C₂×C₄	—	316	16	no	—
631	C₂×C₄	—	79	16	no	—
632	C₂×C₄	—	79	8	no	—
633	C₂×C₄	—	158	16	no	—
634	C₂×C₄	#14579206	1	4	yes	—
635	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
636	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
637	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
638	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
639	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	16	no	—
646	C₂²	—	8	8	no	—
647	C₂²	—	8	16	no	—
648	C₂²	—	158	8	no	—
649	C₂²	—	158	16	no	—
650	C₂²	—	1264	8	no	—
651	C₂²	C₂×#14579206	1	2	yes	—
652	C₂²	#19099399	1	4	yes	—
653	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	158	8	no	—
659	C₄	—	158	16	no	—
660	C₄	C₂×#14579206	1	4	yes	—
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	316	8	no	—
665	C₂	C₂²×#14579206	1	1	yes	characteristic
666	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₂²×#124×C₇₉	C₂
hypercenter	C₂²×#124	D₇₉
hypocenter	C₇₉	#62824
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. #23777972	C₂	semidirect
2. #23777919	C₂	semidirect
3. #23777757	C₂	semidirect
4. #23777355	C₂	semidirect
5. #23777294	C₂	semidirect
6. #23777190	C₂	semidirect
7. #23777089	C₂	semidirect
8. #23777051	C₂	semidirect
9. #23777035	C₂	semidirect
10. #23776696	C₂	semidirect
11. C₂²×#124×C₇₉	C₂	semidirect
12. C₂×#14579209	C₂²	semidirect
13. C₂×#14579206	C₂²	semidirect
14. #19099313	C₂²	semidirect
15. #19099307	C₂²	semidirect
16. #19099305	C₂²	semidirect
17. #19099295	C₂²	semidirect
18. #19099282	C₂²	semidirect
19. #19099275	C₂²	semidirect
20. #19099243	C₂²	semidirect
21. #19099239	C₂²	semidirect
22. #19099239	C₂²	semidirect
23. Q₈×C₂²⋊D₇₉	C₂²	semidirect
24. #19099224	C₂²	semidirect
25. #19099221	C₂²	semidirect
26. #19099207	C₂²	semidirect
27. #19099206	C₂²	semidirect
28. #19099203	C₂²	semidirect
29. #19099203	C₂²	semidirect
30. D₄×C₂²⋊D₇₉	C₂²	semidirect
31. #19099189	C₂²	semidirect
32. #19099182	C₂²	semidirect
33. #19099177	C₂²	semidirect
34. #19099151	C₂²	semidirect
35. #19099151	C₂²	semidirect
36. #19099147	C₂²	semidirect
37. #19099137	C₂²	semidirect
38. #19099137	C₂²	semidirect
39. #19099133	C₂²	semidirect
40. #19099131	C₂²	semidirect
42. #19099125	C₂²	semidirect
43. #19099122	C₂²	semidirect
44. #19099120	C₂²	semidirect
45. #19099120	C₂²	semidirect
46. #19099113	C₂²	semidirect
47. #19099113	C₂²	semidirect
48. #19099112	C₂²	semidirect
49. #19099097	C₂²	semidirect
50. #19099097	C₂²	semidirect
51. #19099097	C₂²	semidirect
52. #19099092	C₂²	semidirect
53. #124×D₇₉	C₂²	semidirect
54. #19099074	C₂²	semidirect
55. #19099074	C₂²	semidirect
56. #19099074	C₂²	semidirect
57. C₂×#14579130	C₂²	semidirect
58. #19099041	C₂²	semidirect
59. #19099038	C₂²	semidirect
60. #19099036	C₂²	semidirect
61. C₄×#11929624	C₂²	semidirect
62. C₄×#11929624	C₂²	semidirect
63. C₂³×Q₈×C₇₉	C₂²	semidirect
65. C₂×#124×C₇₉	C₂²	semidirect
66. C₂×#124×C₇₉	C₂²	semidirect
67. C₂×#124×C₇₉	C₂²	semidirect
68. C₂×#124×C₇₉	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
70. C₂²×C₄²×C₇₉	C₂²	semidirect
73. C₂×#11929625	C₂³	semidirect
78. C₂×Q₈×D₇₉	C₂³	semidirect
82. #14579161	C₂³	semidirect
83. #14579161	C₂³	semidirect
84. #14579159	C₂³	semidirect
85. #14579159	C₂³	semidirect
86. #14579158	C₂³	semidirect
88. #14579155	C₂³	semidirect
89. #14579154	C₂³	semidirect
90. #14579154	C₂³	semidirect
91. #14579153	C₂³	semidirect
92. #14579153	C₂³	semidirect
93. #14579150	C₂³	semidirect
94. #14579150	C₂³	semidirect
95. #14579149	C₂³	semidirect
96. #14579149	C₂³	semidirect
98. #14579147	C₂³	semidirect
99. #14579147	C₂³	semidirect
100. #14579145	C₂³	semidirect
104. #14579143	C₂³	semidirect
105. #14579143	C₂³	semidirect
111. #14579138	C₂³	semidirect
112. #14579138	C₂³	semidirect
113. #14579137	C₂³	semidirect
114. #14579137	C₂³	semidirect
119. #14579134	C₂³	semidirect
120. #14579134	C₂³	semidirect
123. #14579131	C₂³	semidirect
128. Q₈×Dic₇₉	C₂³	semidirect
129. C₄×Dic₁₅₈	C₂³	semidirect
130. C₄×Dic₁₅₈	C₂³	semidirect
131. C₄×Dic₁₅₈	C₂³	semidirect
132. C₄×D₃₁₆	C₂³	semidirect
133. C₄×D₃₁₆	C₂³	semidirect
134. C₄×D₃₁₆	C₂³	semidirect
140. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
141. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
145. #14579118	C₂³	semidirect
146. #14579118	C₂³	semidirect
147. #14579117	C₂³	semidirect
150. C₂²⋊C₄×D₇₉	C₂³	semidirect
151. C₄²×D₇₉	C₂³	semidirect
344. C₂²×#124	D₇₉	semidirect
345. C₇₉	#62824	semidirect
348. C₂³×Q₈	C₂×D₇₉	semidirect
390. C₂×#124	C₂×D₇₉	semidirect
391. C₂×#124	C₂×D₇₉	semidirect
392. C₂×#124	C₂×D₇₉	semidirect
393. C₂×#124	C₂×D₇₉	semidirect
403. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
404. C₂²×C₄²	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777972	2
#23777919	2
#23777757	2
#23777355	2
#23777294	2
#23777190	2
#23777089	2
#23777051	2
#23777035	2
#23776696	2
C₂²×#124×C₇₉	2
#62824	79