Subgroups — C₂²×#135×D₇₉ #35202052

Order 20224.

11422 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₉
commutator, cosocle	C₄×C₇₉	C₂⁶
Frattini	C₄	C₂⁵×D₇₉
Fitting	C₂²×#135×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
hypercenter	C₂²×#135	D₇₉
hypocenter	C₇₉	C₂³×#135
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₇₉	C₂	semidirect
2. C₂²×#14579184	C₂	semidirect
3. C₂²×#14579183	C₂	semidirect
4. C₂²×#14579182	C₂	semidirect
5. C₂²×#14579181	C₂	semidirect
6. C₂²×#14579180	C₂	semidirect
7. C₂×#135×D₇₉	C₂	direct (N × H)
8. C₂²×Q₁₆×D₇₉	C₂	semidirect
9. C₂²×SD₁₆×D₇₉	C₂	semidirect
10. C₂²×D₈×D₇₉	C₂	semidirect
11. C₂³×C₈×D₇₉	C₂	semidirect
12. C₂²×#135×C₇₉	C₂	semidirect
13. C₂²×#11929625	C₂²	semidirect
15. C₂²×#11929624	C₂²	semidirect
17. C₂²×#11929623	C₂²	semidirect
19. C₂×#41×D₇₉	C₂²	semidirect
25. C₂×#14579184	C₂²	semidirect
26. C₂×#14579183	C₂²	semidirect
27. C₂×#14579182	C₂²	semidirect
28. C₂×#14579181	C₂²	semidirect
29. C₂×#14579180	C₂²	semidirect
30. #135×D₇₉	C₂²	direct (N × H)
31. C₂²×Dic₃₁₆	C₂²	semidirect
32. C₂²×#11929614	C₂²	semidirect
33. C₂×Q₁₆×D₇₉	C₂²	semidirect
34. C₂²×#11929613	C₂²	semidirect
35. C₂²×#11929612	C₂²	semidirect
36. C₂²×#11929611	C₂²	semidirect
37. C₂×SD₁₆×D₇₉	C₂²	semidirect
38. C₂²×D₆₃₂	C₂²	semidirect
39. C₂²×#11929609	C₂²	semidirect
40. C₂×D₈×D₇₉	C₂²	semidirect
41. C₂³×C₇₉⋊C₈	C₂²	semidirect
44. C₂²×C₈×D₇₉	C₂²	semidirect
45. C₂²×C₈×D₇₉	C₂²	semidirect
46. C₂²×C₈×D₇₉	C₂²	semidirect
47. C₂²×#41×C₇₉	C₂²	semidirect
48. C₂×#135×C₇₉	C₂²	semidirect
49. C₂²×Q₁₆×C₇₉	C₂²	semidirect
50. C₂²×SD₁₆×C₇₉	C₂²	semidirect
51. C₂²×D₈×C₇₉	C₂²	semidirect
52. C₂³×C₈×C₇₉	C₂²	semidirect
56. C₂×#11929625	C₂³	semidirect
59. C₂×#11929624	C₂³	semidirect
62. C₂×#11929623	C₂³	semidirect
64. #41×D₇₉	C₂³	semidirect
89. #14579184	C₂³	semidirect
90. #14579183	C₂³	semidirect
91. #14579182	C₂³	semidirect
92. #14579181	C₂³	semidirect
93. #14579180	C₂³	semidirect
94. C₂×Dic₃₁₆	C₂³	semidirect
95. C₂×#11929614	C₂³	semidirect
96. Q₁₆×D₇₉	C₂³	semidirect
97. C₂×#11929613	C₂³	semidirect
98. C₂×#11929612	C₂³	semidirect
99. C₂×#11929611	C₂³	semidirect
100. SD₁₆×D₇₉	C₂³	semidirect
101. C₂×D₆₃₂	C₂³	semidirect
102. C₂×#11929609	C₂³	semidirect
103. D₈×D₇₉	C₂³	semidirect
106. C₂²×C₇₉⋊C₈	C₂³	semidirect
109. C₂×C₈×D₇₉	C₂³	semidirect
110. C₂×C₈×D₇₉	C₂³	semidirect
111. C₂×C₈×D₇₉	C₂³	semidirect
113. C₂×#41×C₇₉	C₂³	semidirect
119. #135×C₇₉	C₂³	semidirect
120. C₂×Q₁₆×C₇₉	C₂³	semidirect
121. C₂×SD₁₆×C₇₉	C₂³	semidirect
122. C₂×D₈×C₇₉	C₂³	semidirect
125. C₂²×C₈×C₇₉	C₂³	semidirect
134. #11929625	C₂⁴	semidirect
137. #11929624	C₂⁴	semidirect
140. #11929623	C₂⁴	semidirect
172. Dic₃₁₆	C₂⁴	semidirect
173. #11929614	C₂⁴	semidirect
174. #11929613	C₂⁴	semidirect
175. #11929612	C₂⁴	semidirect
176. #11929611	C₂⁴	semidirect
177. D₆₃₂	C₂⁴	semidirect
178. #11929609	C₂⁴	semidirect
181. C₂×C₇₉⋊C₈	C₂⁴	semidirect
184. C₈×D₇₉	C₂⁴	semidirect
185. C₈×D₇₉	C₂⁴	semidirect
189. #41×C₇₉	C₂⁴	semidirect
201. Q₁₆×C₇₉	C₂⁴	semidirect
202. SD₁₆×C₇₉	C₂⁴	semidirect
203. D₈×C₇₉	C₂⁴	semidirect
206. C₂×C₈×C₇₉	C₂⁴	semidirect
218. C₂²×D₇₉	#135	direct (N × H)
264. C₂²×C₇₉	C₂×#135	semidirect
272. C₂×D₇₉	C₂×#135	direct (N × H)
285. C₂×C₇₉	C₂²×#135	semidirect
289. D₇₉	C₂²×#135	direct (N × H)
297. C₂²×#135	D₇₉	direct (N × H)
302. C₇₉	C₂³×#135	semidirect
310. C₂²×#41	C₂×D₇₉	semidirect
322. C₂×#135	C₂×D₇₉	direct (N × H)
326. C₂²×Q₁₆	C₂×D₇₉	semidirect
331. C₂²×SD₁₆	C₂×D₇₉	semidirect
335. C₂²×D₈	C₂×D₇₉	semidirect
342. C₂³×C₈	C₂×D₇₉	semidirect
356. C₂×#41	C₂²×D₇₉	semidirect
391. #135	C₂²×D₇₉	direct (N × H)
395. C₂×Q₁₆	C₂²×D₇₉	semidirect
400. C₂×SD₁₆	C₂²×D₇₉	semidirect
404. C₂×D₈	C₂²×D₇₉	semidirect
415. C₂²×C₈	C₂²×D₇₉	semidirect
434. #41	C₂³×D₇₉	semidirect
479. Q₁₆	C₂³×D₇₉	semidirect
483. SD₁₆	C₂³×D₇₉	semidirect
486. D₈	C₂³×D₇₉	semidirect
496. C₂×C₈	C₂³×D₇₉	semidirect
562. C₂²	#135×D₇₉	direct (N × H)
577. C₂	C₂×#135×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#41×D₇₉	2
C₂²×#14579184	2
C₂²×#14579183	2
C₂²×#14579182	2
C₂²×#14579181	2
C₂²×#14579180	2
C₂×#135×D₇₉	2
C₂²×Q₁₆×D₇₉	2
C₂²×SD₁₆×D₇₉	2
C₂²×D₈×D₇₉	2
C₂³×C₈×D₇₉	2
C₂²×#135×C₇₉	2
C₂³×#135	79

Subgroups — C22×#135×D79 #35202052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#135×D₇₉ #35202052