Subgroups — #35202126

Order 20224.

10894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778210	C₂	1	2	yes	maximal, complemented
2	#23778180	C₂	1	2	yes	maximal, complemented
3	#23778176	C₂	1	12	yes	maximal, complemented
4	#23778175	C₂	1	16	yes	maximal, complemented
5	#23778174	C₂	1	1	yes	maximal, characteristic, complemented
6	#23778169	C₂	1	6	yes	maximal, complemented
7	#23778168	C₂	1	8	yes	maximal, complemented
8	C₂×#19099364	C₂	1	6	yes	maximal, complemented
9	#576×D₇₉	C₂	1	8	yes	maximal, complemented
10	#23778111	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#576×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099399	—	2	4	no	—
13	#19099399	C₂²	1	1	yes	characteristic
14	#19099399	C₂²	1	2	yes	complemented
15	#19099399	C₂²	1	12	yes	complemented
16	#19099398	—	2	8	no	—
17	#19099398	C₂²	1	16	yes	complemented
18	C₂×#14579206	—	2	12	no	—
19	C₂×#14579206	C₂²	1	12	yes	complemented
20	H(5,𝔽₂)×D₇₉	—	2	8	no	—
21	H(5,𝔽₂)×D₇₉	C₂²	1	16	yes	complemented
22	#19099380	C₂²	1	4	yes	complemented
23	#19099377	C₂²	1	12	yes	complemented
24	#19099376	C₂²	1	4	yes	complemented
25	#19099375	C₂²	1	8	yes	complemented
26	#19099374	C₂²	1	16	yes	complemented
27	#19099373	C₂²	1	48	yes	complemented
28	#19099370	C₂²	1	24	yes	complemented
29	#19099369	C₂²	1	24	yes	complemented
30	#19099368	C₂²	1	4	yes	complemented
31	#19099367	C₂²	1	48	yes	complemented
32	#19099366	C₂²	1	16	yes	complemented
33	#19099365	C₂²	1	12	yes	complemented
34	#19099364	C₂²	1	24	yes	complemented
35	#19099364	C₂²	1	12	yes	complemented
36	#19099364	C₂²	1	24	yes	complemented
37	#19099364	C₂²	1	24	yes	complemented
38	#19099363	C₂²	1	6	yes	complemented
39	#19099361	C₂²	1	12	yes	complemented
40	#19099360	C₂²	1	24	yes	complemented
41	#19099359	C₂²	1	48	yes	complemented
42	C₂×#14579187	C₂²	1	12	yes	complemented
43	C₂×#14579185	C₂²	1	24	yes	complemented
44	AGL(1,ℤ/8)×D₇₉	C₂²	1	48	yes	complemented
45	C₂×#14579183	C₂²	1	6	yes	complemented
46	C₂×#14579180	C₂²	1	12	yes	complemented
47	#135×D₇₉	C₂²	1	24	yes	complemented
48	C₂×D₈×D₇₉	C₂²	1	12	yes	complemented
49	#19099330	C₂²	1	1	yes	characteristic, complemented
50	#19099329	C₂²	1	6	yes	complemented
51	#19099328	C₂²	1	8	yes	complemented
52	C₂×#14579167	C₂²	1	6	yes	complemented
53	#131×D₇₉	C₂²	1	8	yes	complemented
54	C₂×H(5,𝔽₂)×C₇₉	C₂²	1	2	yes	complemented
55	#576×C₇₉	C₂²	1	8	yes	complemented
56	#576×C₇₉	C₂²	1	8	yes	complemented
57	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	6	yes	complemented
58	C₂×#135×C₇₉	C₂²	1	3	yes	complemented
59	C₂²×D₈×C₇₉	C₂²	1	3	yes	complemented
60	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic, complemented
61	#14579209	—	2	2	no	—
62	#14579209	D₄	1	2	yes	—
63	#14579209	C₂³	1	8	yes	complemented
64	#14579208	—	2	12	no	—
65	#14579208	—	2	16	no	—
66	#14579208	D₄	1	4	yes	—
67	#14579208	C₂³	1	8	yes	complemented
68	#14579208	C₂³	1	24	yes	complemented
69	#14579207	—	2	16	no	—
70	#14579207	—	2	12	no	—
71	#14579207	D₄	1	4	yes	—
72	#14579207	C₂³	1	8	yes	complemented
73	#14579207	C₂³	1	24	yes	complemented
74	#14579206	—	2	6	no	—
75	#14579206	—	2	24	no	—
76	#14579206	—	2	24	no	—
77	#14579206	—	2	48	no	—
78	#14579206	—	2	24	no	—
79	#14579206	—	2	48	no	—
80	#14579206	D₄	1	6	yes	—
81	#14579206	C₂³	1	48	yes	complemented
82	#14579206	C₂³	1	24	yes	complemented
83	C₂×#11929624	—	2	24	no	—
84	C₂×#11929624	C₂³	1	6	yes	—
85	C₂×#11929624	C₂³	1	12	yes	complemented
86	C₂×#11929623	—	2	48	no	—
87	C₂×#11929623	—	2	12	no	—
88	C₂×#11929623	C₂³	1	24	yes	complemented
89	#41×D₇₉	—	2	8	no	—
90	#41×D₇₉	—	2	16	no	—
91	#41×D₇₉	—	2	24	no	—
92	#41×D₇₉	—	2	16	no	—
93	#41×D₇₉	C₂³	1	8	yes	—
94	#41×D₇₉	C₂³	1	48	yes	complemented
95	C₂²×C₂²⋊D₇₉	—	2	24	no	—
96	C₂×D₄×D₇₉	—	2	12	no	—
97	C₂×D₄×D₇₉	—	2	48	no	—
98	C₂×D₄×D₇₉	C₂³	1	24	yes	complemented
99	#14579194	C₂³	1	24	yes	complemented
100	#14579193	C₂³	1	16	yes	complemented
101	#14579192	C₂³	1	8	yes	complemented
102	#14579191	C₂³	1	24	yes	complemented
103	#14579190	C₂³	1	48	yes	complemented
104	#14579189	C₂³	1	24	yes	complemented
105	#14579188	C₂³	1	48	yes	complemented
106	#14579187	C₂³	1	48	yes	complemented
107	#14579187	C₂³	1	24	yes	complemented
108	#14579186	C₂³	1	24	yes	complemented
109	#14579185	C₂³	1	96	yes	complemented
110	#14579185	C₂³	1	48	yes	complemented
111	#14579184	C₂³	1	8	yes	complemented
112	#14579183	C₂³	1	12	yes	complemented
113	#14579183	C₂³	1	4	yes	complemented
114	#14579183	C₂³	1	12	yes	complemented
115	#14579183	C₂³	1	12	yes	complemented
116	#14579182	C₂³	1	48	yes	complemented
117	#14579181	C₂³	1	48	yes	complemented
118	#14579180	C₂³	1	24	yes	complemented
119	#14579180	C₂³	1	48	yes	complemented
120	C₂×Dic₃₁₆	C₂³	1	6	yes	complemented
121	Q₁₆×D₇₉	C₂³	1	8	yes	complemented
122	C₂×#11929613	C₂³	1	12	yes	complemented
123	C₂×#11929612	C₂³	1	24	yes	complemented
124	SD₁₆×D₇₉	C₂³	1	48	yes	complemented
125	C₂×D₆₃₂	C₂³	1	6	yes	complemented
126	C₂×#11929609	C₂³	1	24	yes	complemented
127	D₈×D₇₉	C₂³	1	24	yes	complemented
128	D₈×D₇₉	C₂³	1	48	yes	complemented
129	#14579169	C₂³	1	24	yes	complemented
130	#14579168	C₂³	1	8	yes	complemented
131	#14579167	C₂³	1	12	yes	complemented
132	#14579167	C₂³	1	4	yes	complemented
133	#14579167	C₂³	1	12	yes	complemented
134	#14579167	C₂³	1	12	yes	complemented
135	C₂×#11929608	C₂³	1	6	yes	complemented
136	C₂×#11929607	C₂³	1	12	yes	complemented
137	M₁₆×D₇₉	C₂³	1	24	yes	complemented
138	C₂×C₈×D₇₉	C₂³	1	12	yes	complemented
139	H(5,𝔽₂)×C₇₉	—	2	8	no	—
140	H(5,𝔽₂)×C₇₉	C₂³	1	16	yes	complemented
141	C₂×#41×C₇₉	—	2	2	no	—
142	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₇₉	C₂³	1	6	yes	complemented
144	C₂²×D₄×C₇₉	—	2	6	no	—
145	C₂²×D₄×C₇₉	C₂³	1	6	yes	complemented
146	AGL(1,ℤ/8)×C₇₉	C₂³	1	48	yes	complemented
147	#135×C₇₉	C₂³	1	12	yes	complemented
148	#135×C₇₉	C₂³	1	12	yes	complemented
149	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic, complemented
150	C₂×SD₁₆×C₇₉	C₂³	1	6	yes	complemented
151	C₂×D₈×C₇₉	C₂³	1	3	yes	complemented
152	C₂×D₈×C₇₉	C₂³	1	6	yes	complemented
153	C₂×D₈×C₇₉	C₂³	1	12	yes	complemented
154	C₂×D₈×C₇₉	C₂³	1	12	yes	complemented
155	#131×C₇₉	C₂³	1	4	yes	complemented
156	#131×C₇₉	C₂³	1	4	yes	complemented
157	C₂×M₁₆×C₇₉	C₂³	1	3	yes	complemented
158	C₂²×C₈×C₇₉	C₂³	1	3	yes	complemented
159	C₂³×D₇₉	—	2	24	no	—
160	#11929625	—	2	8	no	—
161	#11929625	—	2	8	no	—
162	#11929625	C₂×D₄	1	8	yes	—
163	#11929625	C₂⁴	1	16	yes	—
164	#11929624	—	2	24	no	—
165	#11929624	—	2	48	no	—
166	#11929624	—	2	24	no	—
167	#11929624	—	2	12	no	—
168	#11929624	—	2	12	no	—
169	#11929624	—	2	16	no	—
170	#11929624	C₂×D₄	1	12	yes	—
171	#11929624	C₂×D₄	1	12	yes	—
172	#11929624	C₂⁴	1	24	yes	—
173	#11929624	C₂⁴	1	8	yes	—
174	#11929624	C₂⁴	1	12	yes	—
175	#11929624	C₂⁴	1	4	yes	—
176	#11929623	—	2	48	no	—
177	#11929623	—	2	48	no	—
178	#11929623	—	2	24	no	—
179	#11929623	—	2	48	no	—
180	#11929623	—	2	24	no	—
181	#11929623	—	2	48	no	—
182	#11929623	C₂×D₄	1	24	yes	—
183	#11929623	C₂⁴	1	48	yes	—
184	C₂×Dic₁₅₈	—	2	24	no	—
185	C₂×Dic₁₅₈	C₂×D₄	1	6	yes	—
186	C₂×Dic₁₅₈	C₂⁴	1	12	yes	—
187	Q₈×D₇₉	—	2	8	no	—
188	Q₈×D₇₉	—	2	8	no	—
189	Q₈×D₇₉	C₂×D₄	1	8	yes	—
190	Q₈×D₇₉	C₂⁴	1	16	yes	—
191	C₂×D₃₁₆	—	2	24	no	—
192	C₂×D₃₁₆	C₂×D₄	1	6	yes	—
193	C₂×D₃₁₆	C₂⁴	1	12	yes	—
194	C₂×C₂²⋊D₇₉	—	2	24	no	—
195	C₂×C₂²⋊D₇₉	—	2	12	no	—
196	C₂×C₂²⋊D₇₉	—	2	24	no	—
197	C₂×C₂²⋊D₇₉	—	2	96	no	—
198	C₂×C₂²⋊D₇₉	—	2	48	no	—
199	C₂×C₂²⋊D₇₉	C₂×D₄	1	12	yes	—
200	D₄×D₇₉	—	2	24	no	—
201	D₄×D₇₉	—	2	48	no	—
202	D₄×D₇₉	—	2	48	no	—
203	D₄×D₇₉	—	2	48	no	—
204	D₄×D₇₉	—	2	24	no	—
205	D₄×D₇₉	—	2	48	no	—
206	D₄×D₇₉	C₂×D₄	1	24	yes	—
207	D₄×D₇₉	C₂⁴	1	48	yes	—
208	C₂²×Dic₇₉	—	2	24	no	—
209	C₂×C₄×D₇₉	—	2	48	no	—
210	C₂×C₄×D₇₉	—	2	12	no	—
211	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
212	Dic₃₁₆	C₂⁴	1	4	yes	—
213	Dic₃₁₆	C₂⁴	1	12	yes	—
214	#11929614	C₂⁴	1	16	yes	—
215	#11929613	C₂⁴	1	24	yes	—
216	#11929613	C₂⁴	1	8	yes	—
217	#11929612	C₂⁴	1	48	yes	—
218	#11929611	C₂⁴	1	16	yes	—
219	D₆₃₂	C₂⁴	1	4	yes	—
220	D₆₃₂	C₂⁴	1	12	yes	—
221	#11929609	C₂⁴	1	48	yes	—
222	#11929608	C₂⁴	1	12	yes	—
223	#11929608	C₂⁴	1	4	yes	—
224	#11929607	C₂⁴	1	24	yes	—
225	#11929607	C₂⁴	1	8	yes	—
226	C₂×C₇₉⋊C₈	C₂⁴	1	12	yes	—
227	C₈×D₇₉	C₂⁴	1	8	yes	—
228	C₈×D₇₉	C₂⁴	1	24	yes	—
229	C₂⁴×C₇₉	—	2	6	no	—
230	#41×C₇₉	—	2	16	no	—
231	#41×C₇₉	—	2	12	no	—
232	#41×C₇₉	C₂×D₄	1	4	yes	—
233	#41×C₇₉	C₂⁴	1	24	yes	—
234	#41×C₇₉	C₂⁴	1	4	yes	—
235	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
237	C₂×D₄×C₇₉	—	2	6	no	—
238	C₂×D₄×C₇₉	—	2	48	no	—
239	C₂×D₄×C₇₉	—	2	12	no	—
240	C₂×D₄×C₇₉	—	2	6	no	—
241	C₂×D₄×C₇₉	C₂×D₄	1	3	yes	—
242	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
243	C₂×D₄×C₇₉	C₂⁴	1	6	yes	—
244	C₂²×C₄×C₇₉	—	2	6	no	—
245	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
246	Q₁₆×C₇₉	C₂⁴	1	2	yes	—
247	Q₁₆×C₇₉	C₂⁴	1	2	yes	—
248	SD₁₆×C₇₉	C₂⁴	1	24	yes	—
249	D₈×C₇₉	C₂⁴	1	6	yes	—
250	D₈×C₇₉	C₂⁴	1	6	yes	—
251	D₈×C₇₉	C₂⁴	1	24	yes	—
252	M₁₆×C₇₉	C₂⁴	1	12	yes	—
253	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₇₉	C₂⁴	1	3	yes	—
255	C₂×C₈×C₇₉	C₂⁴	1	6	yes	—
256	C₂×C₈×C₇₉	C₂⁴	1	6	yes	—
257	C₂³×C₇₉	—	2	24	no	—
258	C₂³×C₇₉	—	2	6	no	—
259	C₂³×C₇₉	—	16	6	no	—
260	C₂³×C₇₉	C₂²×D₄	1	3	yes	—
261	C₂²×D₇₉	—	2	12	no	—
262	C₂²×D₇₉	—	2	48	no	—
263	C₂²×D₇₉	—	16	24	no	—
264	C₂²×D₇₉	C₂²×D₄	1	12	yes	—
265	Q₈×C₇₉	—	2	2	no	—
266	Q₈×C₇₉	C₂²×D₄	1	4	yes	—
267	Q₈×C₇₉	C₂⁵	1	4	yes	—
268	D₄×C₇₉	—	2	24	no	—
269	D₄×C₇₉	—	2	24	no	—
270	D₄×C₇₉	—	2	6	no	—
271	D₄×C₇₉	C₂²×D₄	1	12	yes	—
272	D₄×C₇₉	C₂⁵	1	12	yes	—
273	C₂×C₄×C₇₉	—	2	2	no	—
274	C₂×C₄×C₇₉	—	2	24	no	—
275	C₂×C₄×C₇₉	C₂²×D₄	1	6	yes	—
276	C₂×C₄×C₇₉	C₂²×D₄	1	3	yes	—
277	C₂×C₄×C₇₉	C₂⁵	1	6	yes	—
278	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
279	C₂²⋊D₇₉	—	2	24	no	—
280	C₂²⋊D₇₉	—	2	8	no	—
281	C₂²⋊D₇₉	—	2	48	no	—
282	C₂²⋊D₇₉	—	2	48	no	—
283	C₂²⋊D₇₉	C₂²×D₄	1	24	yes	—
284	C₂²⋊D₇₉	C₂²×D₄	1	8	yes	—
285	C₂×Dic₇₉	—	2	12	no	—
286	C₂×Dic₇₉	—	2	48	no	—
287	C₂×Dic₇₉	C₂²×D₄	1	12	yes	—
288	D₃₁₆	—	2	16	no	—
289	D₃₁₆	—	2	12	no	—
290	D₃₁₆	C₂²×D₄	1	4	yes	—
291	D₃₁₆	C₂²×D₄	1	12	yes	—
292	D₃₁₆	C₂⁵	1	8	yes	—
293	C₄×D₇₉	—	2	16	no	—
294	C₄×D₇₉	—	2	24	no	—
295	C₄×D₇₉	—	2	8	no	—
296	C₄×D₇₉	—	2	16	no	—
297	C₄×D₇₉	C₂²×D₄	1	24	yes	—
298	C₄×D₇₉	C₂⁵	1	8	yes	—
299	Dic₁₅₈	—	2	12	no	—
300	Dic₁₅₈	—	2	16	no	—
301	Dic₁₅₈	C₂²×D₄	1	4	yes	—
302	Dic₁₅₈	C₂²×D₄	1	12	yes	—
303	Dic₁₅₈	C₂⁵	1	8	yes	—
304	C₈×C₇₉	C₂⁵	1	1	yes	characteristic
305	C₈×C₇₉	C₂⁵	1	6	yes	—
306	C₈×C₇₉	C₂⁵	1	1	yes	characteristic
307	C₇₉⋊C₈	C₂⁵	1	8	yes	—
308	C₂²×C₇₉	—	2	12	no	—
309	C₂²×C₇₉	—	4	3	no	—
310	C₂²×C₇₉	—	8	24	no	—
311	C₂²×C₇₉	—	8	6	no	—
312	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
314	C₂×D₇₉	—	2	8	no	—
315	C₂×D₇₉	—	4	12	no	—
316	C₂×D₇₉	—	8	48	no	—
317	C₂×D₇₉	—	8	12	no	—
318	C₂×D₇₉	C₂³×D₄	1	8	yes	—
319	C₄×C₇₉	—	2	4	no	—
320	C₄×C₇₉	C₂³×D₄	1	6	yes	—
321	C₄×C₇₉	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₇₉	C₂⁶	1	1	yes	characteristic
323	Dic₇₉	—	2	8	no	—
324	Dic₇₉	C₂³×D₄	1	8	yes	—
325	#63091	—	79	1	no	maximal, Sylow
326	C₂×C₇₉	—	2	6	no	—
327	C₂×C₇₉	—	2	1	no	—
328	C₂×C₇₉	—	4	12	no	—
329	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
330	D₇₉	—	2	8	no	—
331	D₇₉	—	4	8	no	—
332	H(7,𝔽₂)	—	79	2	no	—
333	#3585	—	79	2	no	—
334	#3585	—	79	16	no	—
335	#3585	—	79	12	no	—
336	#3584	—	79	8	no	—
337	#3584	—	79	6	no	—
338	#3584	—	79	1	no	—
339	C₂×#576	—	79	8	no	—
340	C₂×#576	—	79	6	no	—
341	C₂×#576	D₇₉	1	1	yes	characteristic, complemented
342	#3573	—	79	1	no	—
343	C₇₉	#63091	1	1	yes	characteristic, complemented, Sylow
344	#585	—	79	1	no	—
345	#585	—	79	16	no	—
346	#585	—	79	2	no	—
347	#585	—	79	12	no	—
348	#585	—	158	4	no	—
349	#585	—	158	8	no	—
350	C₂×H(5,𝔽₂)	—	79	16	no	—
351	C₂×H(5,𝔽₂)	—	79	12	no	—
352	C₂×H(5,𝔽₂)	—	158	12	no	—
353	C₂×H(5,𝔽₂)	—	158	8	no	—
354	C₂×H(5,𝔽₂)	C₂×D₇₉	1	2	yes	complemented
355	#578	—	79	12	no	—
356	#578	—	79	4	no	—
357	#578	—	79	4	no	—
358	#577	—	79	16	no	—
359	#577	—	79	48	no	—
360	#577	—	79	24	no	—
361	#577	—	79	24	no	—
362	#577	—	79	8	no	—
363	#576	—	79	16	no	—
364	#576	—	79	48	no	—
365	#576	—	79	12	no	—
366	#576	—	79	24	no	—
367	#576	—	79	12	no	—
368	#576	—	79	24	no	—
369	#576	—	79	24	no	—
370	#576	—	79	4	no	—
371	#576	C₂×D₇₉	1	8	yes	complemented
372	#576	C₂×D₇₉	1	8	yes	complemented
373	#575	—	79	12	no	—
374	#575	—	79	48	no	—
375	#575	—	79	24	no	—
376	#575	—	79	6	no	—
377	C₂×AGL(1,ℤ/8)	—	79	12	no	—
378	C₂×AGL(1,ℤ/8)	—	79	48	no	—
379	C₂×AGL(1,ℤ/8)	—	79	24	no	—
380	C₂×AGL(1,ℤ/8)	C₂×D₇₉	1	6	yes	complemented
381	C₂×#135	—	79	24	no	—
382	C₂×#135	—	79	12	no	—
383	C₂×#135	—	79	6	no	—
384	C₂×#135	C₂×D₇₉	1	3	yes	complemented
385	C₂²×D₈	—	79	12	no	—
386	C₂²×D₈	C₂×D₇₉	1	3	yes	complemented
387	#568	—	79	1	no	—
388	#568	—	79	8	no	—
389	#568	—	79	6	no	—
390	C₂×#131	—	79	8	no	—
391	C₂×#131	—	79	6	no	—
392	C₂×#131	C₂×D₇₉	1	1	yes	characteristic, complemented
393	2₋¹⁺⁴	—	79	4	no	—
394	2₋¹⁺⁴	—	79	2	no	—
395	2₋¹⁺⁴	—	79	24	no	—
396	2₋¹⁺⁴	—	79	8	no	—
397	2₋¹⁺⁴	—	79	8	no	—
398	2₋¹⁺⁴	—	158	16	no	—
399	2₋¹⁺⁴	—	158	12	no	—
400	2₋¹⁺⁴	—	158	2	no	—
401	H(5,𝔽₂)	—	2	8	no	—
402	H(5,𝔽₂)	—	79	4	no	—
403	H(5,𝔽₂)	—	79	6	no	—
404	H(5,𝔽₂)	—	79	24	no	—
405	H(5,𝔽₂)	—	79	8	no	—
406	H(5,𝔽₂)	—	79	48	no	—
407	H(5,𝔽₂)	—	79	24	no	—
408	H(5,𝔽₂)	—	158	24	no	—
409	H(5,𝔽₂)	—	158	48	no	—
410	H(5,𝔽₂)	—	158	48	no	—
411	H(5,𝔽₂)	—	158	24	no	—
412	H(5,𝔽₂)	—	158	24	no	—
413	H(5,𝔽₂)	—	158	12	no	—
414	H(5,𝔽₂)	—	158	16	no	—
415	H(5,𝔽₂)	—	158	6	no	—
416	H(5,𝔽₂)	C₂²×D₇₉	1	16	yes	complemented
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	79	8	no	—
419	C₂×#41	—	79	6	no	—
420	C₂×#41	—	79	48	no	—
421	C₂×#41	—	79	24	no	—
422	C₂×#41	—	79	12	no	—
423	C₂×#41	—	158	24	no	—
424	C₂×#41	—	158	12	no	—
425	C₂×#41	—	158	48	no	—
426	C₂×#41	—	158	16	no	—
427	C₂×#41	—	158	16	no	—
428	C₂×#41	—	158	24	no	—
429	C₂×#41	—	158	8	no	—
430	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
431	C₂×#41	C₂²×D₇₉	1	6	yes	complemented
432	C₂²×D₄	—	2	6	no	—
433	C₂²×D₄	—	79	24	no	—
434	C₂²×D₄	—	158	48	no	—
435	C₂²×D₄	—	158	12	no	—
436	C₂²×D₄	—	158	24	no	—
437	C₂²×D₄	C₂²×D₇₉	1	6	yes	complemented
438	#137	—	79	24	no	—
439	#137	—	79	8	no	—
440	#137	—	79	16	no	—
441	#137	—	79	48	no	—
442	#137	—	79	24	no	—
443	AGL(1,ℤ/8)	—	79	24	no	—
444	AGL(1,ℤ/8)	—	79	48	no	—
445	AGL(1,ℤ/8)	—	79	24	no	—
446	AGL(1,ℤ/8)	—	79	48	no	—
447	AGL(1,ℤ/8)	—	79	96	no	—
448	AGL(1,ℤ/8)	—	79	48	no	—
449	AGL(1,ℤ/8)	—	79	24	no	—
450	AGL(1,ℤ/8)	C₂²×D₇₉	1	48	yes	complemented
451	#135	—	79	48	no	—
452	#135	—	79	8	no	—
453	#135	—	79	48	no	—
454	#135	—	79	24	no	—
455	#135	—	79	48	no	—
456	#135	—	79	12	no	—
457	#135	—	79	4	no	—
458	#135	—	79	12	no	—
459	#135	—	79	12	no	—
460	#135	C₂²×D₇₉	1	12	yes	complemented
461	#135	C₂²×D₇₉	1	12	yes	complemented
462	C₂×Q₁₆	—	79	8	no	—
463	C₂×Q₁₆	—	79	6	no	—
464	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic, complemented
465	C₂×SD₁₆	—	79	24	no	—
466	C₂×SD₁₆	—	79	48	no	—
467	C₂×SD₁₆	—	79	12	no	—
468	C₂×SD₁₆	C₂²×D₇₉	1	6	yes	complemented
469	C₂×D₈	—	79	24	no	—
470	C₂×D₈	—	79	24	no	—
471	C₂×D₈	—	79	48	no	—
472	C₂×D₈	—	79	6	no	—
473	C₂×D₈	C₂²×D₇₉	1	12	yes	complemented
474	C₂×D₈	C₂²×D₇₉	1	3	yes	complemented
475	C₂×D₈	C₂²×D₇₉	1	12	yes	complemented
476	C₂×D₈	C₂²×D₇₉	1	6	yes	complemented
477	#131	—	79	8	no	—
478	#131	—	79	24	no	—
479	#131	—	79	12	no	—
480	#131	—	79	4	no	—
481	#131	—	79	12	no	—
482	#131	—	79	12	no	—
483	#131	C₂²×D₇₉	1	4	yes	complemented
484	#131	C₂²×D₇₉	1	4	yes	complemented
485	C₂×M₁₆	—	79	6	no	—
486	C₂×M₁₆	—	79	24	no	—
487	C₂×M₁₆	—	79	12	no	—
488	C₂×M₁₆	C₂²×D₇₉	1	3	yes	complemented
489	C₂²×C₈	—	79	12	no	—
490	C₂²×C₈	C₂²×D₇₉	1	3	yes	complemented
491	C₂⁴	—	2	6	no	—
492	C₂⁴	—	158	24	no	—
493	#41	—	2	16	no	—
494	#41	—	2	12	no	—
495	#41	—	79	8	no	—
496	#41	—	79	24	no	—
497	#41	—	79	12	no	—
498	#41	—	79	4	no	—
499	#41	—	79	12	no	—
500	#41	—	79	12	no	—
501	#41	—	79	16	no	—
502	#41	—	79	48	no	—
503	#41	—	79	24	no	—
504	#41	—	79	8	no	—
505	#41	—	158	48	no	—
506	#41	—	158	16	no	—
507	#41	—	158	24	no	—
508	#41	—	158	24	no	—
509	#41	—	158	48	no	—
510	#41	—	158	48	no	—
511	#41	—	158	48	no	—
512	#41	—	158	24	no	—
513	#41	—	158	48	no	—
514	#41	—	158	8	no	—
515	#41	—	158	8	no	—
516	#41	—	158	24	no	—
517	#41	—	158	12	no	—
518	#41	—	158	12	no	—
519	#41	D₄×D₇₉	1	4	yes	—
520	#41	C₂³×D₇₉	1	24	yes	—
521	#41	C₂³×D₇₉	1	4	yes	—
522	C₂×Q₈	—	79	8	no	—
523	C₂×Q₈	—	79	6	no	—
524	C₂×Q₈	—	79	16	no	—
525	C₂×Q₈	—	79	12	no	—
526	C₂×Q₈	—	158	24	no	—
527	C₂×Q₈	—	158	8	no	—
528	C₂×Q₈	—	158	8	no	—
529	C₂×Q₈	D₄×D₇₉	1	1	yes	characteristic
530	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
531	C₂×D₄	—	2	6	no	—
532	C₂×D₄	—	2	48	no	—
533	C₂×D₄	—	2	6	no	—
534	C₂×D₄	—	2	12	no	—
535	C₂×D₄	—	79	12	no	—
536	C₂×D₄	—	79	24	no	—
537	C₂×D₄	—	79	48	no	—
538	C₂×D₄	—	79	12	no	—
539	C₂×D₄	—	79	6	no	—
540	C₂×D₄	—	158	24	no	—
541	C₂×D₄	—	158	48	no	—
542	C₂×D₄	—	158	24	no	—
543	C₂×D₄	—	158	48	no	—
544	C₂×D₄	—	158	48	no	—
545	C₂×D₄	—	158	24	no	—
546	C₂×D₄	—	158	48	no	—
547	C₂×D₄	—	158	48	no	—
548	C₂×D₄	—	158	96	no	—
549	C₂×D₄	—	158	24	no	—
550	C₂×D₄	—	158	12	no	—
551	C₂×D₄	—	158	24	no	—
552	C₂×D₄	D₄×D₇₉	1	3	yes	—
553	C₂×D₄	C₂³×D₇₉	1	24	yes	—
554	C₂×D₄	C₂³×D₇₉	1	6	yes	—
555	C₂²×C₄	—	2	6	no	—
556	C₂²×C₄	—	79	12	no	—
557	C₂²×C₄	—	158	48	no	—
558	C₂²×C₄	—	158	24	no	—
559	C₂²×C₄	—	158	12	no	—
560	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
561	Q₁₆	—	79	16	no	—
562	Q₁₆	—	79	4	no	—
563	Q₁₆	—	79	12	no	—
564	Q₁₆	C₂³×D₇₉	1	2	yes	—
565	Q₁₆	C₂³×D₇₉	1	2	yes	—
566	SD₁₆	—	79	16	no	—
567	SD₁₆	—	79	48	no	—
568	SD₁₆	—	79	24	no	—
569	SD₁₆	—	79	8	no	—
570	SD₁₆	C₂³×D₇₉	1	24	yes	—
571	D₈	—	79	48	no	—
572	D₈	—	79	4	no	—
573	D₈	—	79	12	no	—
574	D₈	C₂³×D₇₉	1	6	yes	—
575	D₈	C₂³×D₇₉	1	24	yes	—
576	D₈	C₂³×D₇₉	1	6	yes	—
577	M₁₆	—	79	12	no	—
578	M₁₆	—	79	4	no	—
579	M₁₆	—	79	24	no	—
580	M₁₆	—	79	8	no	—
581	M₁₆	C₂³×D₇₉	1	12	yes	—
582	C₂×C₈	—	79	12	no	—
583	C₂×C₈	—	79	8	no	—
584	C₂×C₈	—	79	24	no	—
585	C₂×C₈	C₂³×D₇₉	1	6	yes	—
586	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
587	C₂×C₈	C₂³×D₇₉	1	6	yes	—
588	C₂×C₈	C₂³×D₇₉	1	3	yes	—
589	C₂³	—	2	6	no	—
590	C₂³	—	2	24	no	—
591	C₂³	—	16	6	no	—
592	C₂³	—	79	12	no	—
593	C₂³	—	158	48	no	—
594	C₂³	—	158	12	no	—
595	C₂³	—	1264	24	no	—
596	C₂³	C₂×D₄×D₇₉	1	3	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	79	12	no	—
599	Q₈	—	79	4	no	—
600	Q₈	—	79	8	no	—
601	Q₈	—	158	16	no	—
602	Q₈	—	158	12	no	—
603	Q₈	C₂×D₄×D₇₉	1	4	yes	—
604	Q₈	C₂⁴×D₇₉	1	4	yes	—
605	D₄	—	2	24	no	—
606	D₄	—	2	24	no	—
607	D₄	—	2	6	no	—
608	D₄	—	79	8	no	—
609	D₄	—	79	24	no	—
610	D₄	—	79	8	no	—
611	D₄	—	79	12	no	—
612	D₄	—	79	4	no	—
613	D₄	—	158	16	no	—
614	D₄	—	158	48	no	—
615	D₄	—	158	48	no	—
616	D₄	—	158	8	no	—
617	D₄	—	158	24	no	—
618	D₄	—	158	12	no	—
619	D₄	C₂×D₄×D₇₉	1	12	yes	—
620	D₄	C₂⁴×D₇₉	1	12	yes	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	24	no	—
623	C₂×C₄	—	79	12	no	—
624	C₂×C₄	—	79	8	no	—
625	C₂×C₄	—	79	24	no	—
626	C₂×C₄	—	158	16	no	—
627	C₂×C₄	—	158	16	no	—
628	C₂×C₄	—	158	48	no	—
629	C₂×C₄	—	158	12	no	—
630	C₂×C₄	—	158	24	no	—
631	C₂×C₄	—	158	8	no	—
632	C₂×C₄	C₂×D₄×D₇₉	1	3	yes	—
633	C₂×C₄	C₂×D₄×D₇₉	1	6	yes	—
634	C₂×C₄	C₂⁴×D₇₉	1	6	yes	—
635	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
636	C₈	—	79	8	no	—
637	C₈	C₂⁴×D₇₉	1	1	yes	characteristic
638	C₈	C₂⁴×D₇₉	1	6	yes	—
639	C₈	C₂⁴×D₇₉	1	1	yes	characteristic
640	C₂²	—	2	12	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	8	6	no	—
643	C₂²	—	8	24	no	—
644	C₂²	—	316	12	no	—
645	C₂²	—	79	8	no	—
646	C₂²	—	632	12	no	—
647	C₂²	—	632	48	no	—
648	C₂²	—	158	8	no	—
649	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
650	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
651	C₄	—	2	4	no	—
652	C₄	—	79	8	no	—
653	C₄	—	158	8	no	—
654	C₄	C₂²×D₄×D₇₉	1	6	yes	—
655	C₄	C₂²×D₄×D₇₉	1	1	yes	characteristic
656	C₄	C₂⁵×D₇₉	1	1	yes	characteristic
657	C₂	—	2	1	no	—
658	C₂	—	2	6	no	—
659	C₂	—	4	12	no	—
660	C₂	—	316	8	no	—
661	C₂	—	158	8	no	—
662	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₇₉
commutator, cosocle	C₄×C₇₉	C₂⁶
Frattini	C₄	C₂⁵×D₇₉
Fitting	C₂×#576×C₇₉	C₂
socle	C₂×C₇₉	C₂⁴×D₄
hypercenter	C₂×#576	D₇₉
hypocenter	C₇₉	#63091
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #23778210	C₂	semidirect
2. #23778180	C₂	semidirect
3. #23778176	C₂	semidirect
4. #23778175	C₂	semidirect
5. #23778174	C₂	semidirect
6. #23778169	C₂	semidirect
7. #23778168	C₂	semidirect
8. C₂×#19099364	C₂	semidirect
9. #576×D₇₉	C₂	semidirect
10. #23778111	C₂	semidirect
11. C₂×#576×C₇₉	C₂	semidirect
14. #19099399	C₂²	semidirect
15. #19099399	C₂²	semidirect
17. #19099398	C₂²	semidirect
19. C₂×#14579206	C₂²	semidirect
21. H(5,𝔽₂)×D₇₉	C₂²	semidirect
22. #19099380	C₂²	semidirect
23. #19099377	C₂²	semidirect
24. #19099376	C₂²	semidirect
25. #19099375	C₂²	semidirect
26. #19099374	C₂²	semidirect
27. #19099373	C₂²	semidirect
28. #19099370	C₂²	semidirect
29. #19099369	C₂²	semidirect
30. #19099368	C₂²	semidirect
31. #19099367	C₂²	semidirect
32. #19099366	C₂²	semidirect
33. #19099365	C₂²	semidirect
34. #19099364	C₂²	semidirect
35. #19099364	C₂²	semidirect
36. #19099364	C₂²	semidirect
37. #19099364	C₂²	semidirect
38. #19099363	C₂²	semidirect
39. #19099361	C₂²	semidirect
40. #19099360	C₂²	semidirect
41. #19099359	C₂²	semidirect
42. C₂×#14579187	C₂²	semidirect
43. C₂×#14579185	C₂²	semidirect
44. AGL(1,ℤ/8)×D₇₉	C₂²	semidirect
45. C₂×#14579183	C₂²	semidirect
46. C₂×#14579180	C₂²	semidirect
47. #135×D₇₉	C₂²	semidirect
48. C₂×D₈×D₇₉	C₂²	semidirect
49. #19099330	C₂²	semidirect
50. #19099329	C₂²	semidirect
51. #19099328	C₂²	semidirect
52. C₂×#14579167	C₂²	semidirect
53. #131×D₇₉	C₂²	semidirect
54. C₂×H(5,𝔽₂)×C₇₉	C₂²	semidirect
55. #576×C₇₉	C₂²	semidirect
56. #576×C₇₉	C₂²	semidirect
57. C₂×AGL(1,ℤ/8)×C₇₉	C₂²	semidirect
58. C₂×#135×C₇₉	C₂²	semidirect
59. C₂²×D₈×C₇₉	C₂²	semidirect
60. C₂×#131×C₇₉	C₂²	semidirect
63. #14579209	C₂³	semidirect
67. #14579208	C₂³	semidirect
68. #14579208	C₂³	semidirect
72. #14579207	C₂³	semidirect
73. #14579207	C₂³	semidirect
81. #14579206	C₂³	semidirect
82. #14579206	C₂³	semidirect
85. C₂×#11929624	C₂³	semidirect
88. C₂×#11929623	C₂³	semidirect
94. #41×D₇₉	C₂³	semidirect
98. C₂×D₄×D₇₉	C₂³	semidirect
99. #14579194	C₂³	semidirect
100. #14579193	C₂³	semidirect
101. #14579192	C₂³	semidirect
102. #14579191	C₂³	semidirect
103. #14579190	C₂³	semidirect
104. #14579189	C₂³	semidirect
105. #14579188	C₂³	semidirect
106. #14579187	C₂³	semidirect
107. #14579187	C₂³	semidirect
108. #14579186	C₂³	semidirect
109. #14579185	C₂³	semidirect
110. #14579185	C₂³	semidirect
111. #14579184	C₂³	semidirect
112. #14579183	C₂³	semidirect
113. #14579183	C₂³	semidirect
114. #14579183	C₂³	semidirect
115. #14579183	C₂³	semidirect
116. #14579182	C₂³	semidirect
117. #14579181	C₂³	semidirect
118. #14579180	C₂³	semidirect
119. #14579180	C₂³	semidirect
120. C₂×Dic₃₁₆	C₂³	semidirect
121. Q₁₆×D₇₉	C₂³	semidirect
122. C₂×#11929613	C₂³	semidirect
123. C₂×#11929612	C₂³	semidirect
124. SD₁₆×D₇₉	C₂³	semidirect
125. C₂×D₆₃₂	C₂³	semidirect
126. C₂×#11929609	C₂³	semidirect
127. D₈×D₇₉	C₂³	semidirect
128. D₈×D₇₉	C₂³	semidirect
129. #14579169	C₂³	semidirect
130. #14579168	C₂³	semidirect
131. #14579167	C₂³	semidirect
132. #14579167	C₂³	semidirect
133. #14579167	C₂³	semidirect
134. #14579167	C₂³	semidirect
135. C₂×#11929608	C₂³	semidirect
136. C₂×#11929607	C₂³	semidirect
137. M₁₆×D₇₉	C₂³	semidirect
138. C₂×C₈×D₇₉	C₂³	semidirect
140. H(5,𝔽₂)×C₇₉	C₂³	semidirect
143. C₂×#41×C₇₉	C₂³	semidirect
145. C₂²×D₄×C₇₉	C₂³	semidirect
146. AGL(1,ℤ/8)×C₇₉	C₂³	semidirect
147. #135×C₇₉	C₂³	semidirect
148. #135×C₇₉	C₂³	semidirect
149. C₂×Q₁₆×C₇₉	C₂³	semidirect
150. C₂×SD₁₆×C₇₉	C₂³	semidirect
151. C₂×D₈×C₇₉	C₂³	semidirect
152. C₂×D₈×C₇₉	C₂³	semidirect
153. C₂×D₈×C₇₉	C₂³	semidirect
154. C₂×D₈×C₇₉	C₂³	semidirect
155. #131×C₇₉	C₂³	semidirect
156. #131×C₇₉	C₂³	semidirect
157. C₂×M₁₆×C₇₉	C₂³	semidirect
158. C₂²×C₈×C₇₉	C₂³	semidirect
341. C₂×#576	D₇₉	semidirect
343. C₇₉	#63091	semidirect
354. C₂×H(5,𝔽₂)	C₂×D₇₉	semidirect
371. #576	C₂×D₇₉	semidirect
372. #576	C₂×D₇₉	semidirect
380. C₂×AGL(1,ℤ/8)	C₂×D₇₉	semidirect
384. C₂×#135	C₂×D₇₉	semidirect
386. C₂²×D₈	C₂×D₇₉	semidirect
392. C₂×#131	C₂×D₇₉	semidirect
416. H(5,𝔽₂)	C₂²×D₇₉	semidirect
431. C₂×#41	C₂²×D₇₉	semidirect
437. C₂²×D₄	C₂²×D₇₉	semidirect
450. AGL(1,ℤ/8)	C₂²×D₇₉	semidirect
460. #135	C₂²×D₇₉	semidirect
461. #135	C₂²×D₇₉	semidirect
464. C₂×Q₁₆	C₂²×D₇₉	semidirect
468. C₂×SD₁₆	C₂²×D₇₉	semidirect
473. C₂×D₈	C₂²×D₇₉	semidirect
474. C₂×D₈	C₂²×D₇₉	semidirect
475. C₂×D₈	C₂²×D₇₉	semidirect
476. C₂×D₈	C₂²×D₇₉	semidirect
483. #131	C₂²×D₇₉	semidirect
484. #131	C₂²×D₇₉	semidirect
488. C₂×M₁₆	C₂²×D₇₉	semidirect
490. C₂²×C₈	C₂²×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23778210	2
#23778180	2
#23778176	2
#23778175	2
#23778174	2
#23778169	2
#23778168	2
C₂×#19099364	2
#576×D₇₉	2
#23778111	2
C₂×#576×C₇₉	2
#63091	79