Subgroups — C₄×#450×C₇₉ #34133136

Order 20224.

1880 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#450×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₇₉	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1877	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1864	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1786	C₂	1	1	yes	maximal, characteristic
10	C₄×#102×C₇₉	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₇₉	—	2	1	no	—
14	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄×D₄×C₇₉	—	2	8	no	—
18	C₂×C₄×D₄×C₇₉	—	2	1	no	—
19	C₂×C₄×D₄×C₇₉	—	2	1	no	—
20	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
24	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
25	#450×C₇₉	C₄	1	8	yes	direct product factor
26	C₄×SD₁₆×C₇₉	—	2	8	no	—
27	C₂×#106×C₇₉	C₂²	1	2	yes	complemented
28	C₂×#103×C₇₉	C₂²	1	2	yes	complemented
29	C₂×#102×C₇₉	C₂²	1	2	yes	—
30	C₂×#102×C₇₉	C₂²	1	2	yes	—
31	C₂×#102×C₇₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	complemented
35	#391×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	#389×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	#387×C₇₉	—	2	1	no	—
38	#385×C₇₉	—	2	1	no	—
39	#380×C₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
43	#340×C₇₉	C₂²	1	2	yes	complemented
44	#340×C₇₉	C₂²	1	2	yes	complemented
45	#336×C₇₉	C₂²	1	2	yes	complemented
46	C₂⁵×C₇₉	—	2	1	no	—
47	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₉	—	2	4	no	—
49	C₂²×D₄×C₇₉	—	2	4	no	—
50	C₂²×D₄×C₇₉	—	2	1	no	—
51	C₂²×D₄×C₇₉	—	2	2	no	—
52	C₂²×D₄×C₇₉	C₂×C₄	1	4	yes	—
53	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₉	—	2	8	no	—
55	C₂³×C₄×C₇₉	—	2	1	no	—
56	C₂³×C₄×C₇₉	—	2	2	no	—
57	C₂³×C₄×C₇₉	—	2	2	no	—
58	C₂³×C₄×C₇₉	—	4	4	no	—
59	C₂³×C₄×C₇₉	—	4	4	no	—
60	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₇₉	—	2	4	no	—
64	C₂×SD₁₆×C₇₉	—	2	4	no	—
65	C₂×SD₁₆×C₇₉	C₂×C₄	1	8	yes	complemented
66	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
67	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
68	C₂²⋊Q₈×C₇₉	—	2	2	no	—
69	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	complemented
70	C₄×Q₈×C₇₉	—	2	4	no	—
71	C₄×D₄×C₇₉	—	2	8	no	—
72	C₄×D₄×C₇₉	—	2	8	no	—
73	C₄×D₄×C₇₉	—	2	4	no	—
74	C₄×D₄×C₇₉	—	2	4	no	—
75	C₄×D₄×C₇₉	—	2	4	no	—
76	C₄×D₄×C₇₉	D₄	1	8	yes	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₄²×C₇₉	—	2	4	no	—
92	C₂×C₄²×C₇₉	—	2	1	no	—
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	#106×C₇₉	—	2	4	no	—
99	#103×C₇₉	—	2	4	no	—
100	#102×C₇₉	—	2	4	no	—
101	#102×C₇₉	—	2	4	no	—
102	#102×C₇₉	C₂×C₄	1	8	yes	complemented
103	C₂²⋊C₈×C₇₉	—	2	2	no	—
104	C₂²⋊C₈×C₇₉	C₂×C₄	1	4	yes	complemented
105	C₄×C₈×C₇₉	—	2	4	no	—
106	#95×C₇₉	—	2	1	no	—
107	#95×C₇₉	—	2	1	no	—
108	#95×C₇₉	—	2	1	no	—
109	#95×C₇₉	—	2	1	no	—
110	#95×C₇₉	—	2	1	no	—
111	C₂⁴×C₇₉	—	2	4	no	—
112	C₂⁴×C₇₉	—	2	4	no	—
113	C₂⁴×C₇₉	—	2	4	no	—
114	C₂⁴×C₇₉	—	2	2	no	—
115	C₂⁴×C₇₉	—	4	2	no	—
116	C₂⁴×C₇₉	—	4	2	no	—
117	C₂⁴×C₇₉	—	4	2	no	—
118	C₂⁴×C₇₉	—	4	2	no	—
119	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₇₉	—	2	1	no	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂×Q₈×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	complemented
124	C₂×D₄×C₇₉	—	2	4	no	—
125	C₂×D₄×C₇₉	—	2	4	no	—
126	C₂×D₄×C₇₉	—	2	16	no	—
127	C₂×D₄×C₇₉	—	2	16	no	—
128	C₂×D₄×C₇₉	—	2	4	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
134	C₂×D₄×C₇₉	#41	1	4	yes	—
135	C₂²×C₄×C₇₉	—	2	2	no	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	4	no	—
140	C₂²×C₄×C₇₉	—	2	8	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	—	2	2	no	—
146	C₂²×C₄×C₇₉	—	2	8	no	—
147	C₂²×C₄×C₇₉	—	2	1	no	—
148	C₂²×C₄×C₇₉	—	2	1	no	—
149	C₂²×C₄×C₇₉	—	4	1	no	—
150	C₂²×C₄×C₇₉	—	4	4	no	—
151	C₂²×C₄×C₇₉	—	4	32	no	—
152	C₂²×C₄×C₇₉	—	4	2	no	—
153	C₂²×C₄×C₇₉	—	4	2	no	—
154	C₂²×C₄×C₇₉	—	4	4	no	—
155	C₂²×C₄×C₇₉	—	4	4	no	—
156	C₂²×C₄×C₇₉	—	4	4	no	—
157	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	complemented
158	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₉	#41	1	2	yes	—
165	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
166	SD₁₆×C₇₉	—	2	16	no	—
167	C₂×C₈×C₇₉	—	2	2	no	—
168	C₂×C₈×C₇₉	—	2	2	no	—
169	C₂×C₈×C₇₉	—	2	2	no	—
170	C₂×C₈×C₇₉	—	2	2	no	—
171	C₂×C₈×C₇₉	—	2	2	no	—
172	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	complemented
173	C₄⋊C₄×C₇₉	—	2	4	no	—
174	C₄⋊C₄×C₇₉	—	2	4	no	—
175	C₄⋊C₄×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	1	no	—
177	C₄⋊C₄×C₇₉	—	2	2	no	—
178	C₄⋊C₄×C₇₉	—	2	2	no	—
179	C₄⋊C₄×C₇₉	—	4	2	no	—
180	C₄⋊C₄×C₇₉	—	4	2	no	—
181	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	complemented
182	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
183	C₂²⋊C₄×C₇₉	—	2	8	no	—
184	C₂²⋊C₄×C₇₉	—	2	4	no	—
185	C₂²⋊C₄×C₇₉	—	2	8	no	—
186	C₂²⋊C₄×C₇₉	—	4	2	no	—
187	C₄²×C₇₉	—	2	2	no	—
188	C₄²×C₇₉	—	2	2	no	—
189	C₄²×C₇₉	—	2	2	no	—
190	C₄²×C₇₉	—	4	2	no	—
191	C₄²×C₇₉	—	4	2	no	—
192	C₄²×C₇₉	C₂×D₄	1	4	yes	—
193	C₂³×C₇₉	—	2	1	no	—
194	C₂³×C₇₉	—	2	1	no	—
195	C₂³×C₇₉	—	2	1	no	—
196	C₂³×C₇₉	—	2	1	no	—
197	C₂³×C₇₉	—	2	16	no	—
198	C₂³×C₇₉	—	2	4	no	—
199	C₂³×C₇₉	—	2	4	no	—
200	C₂³×C₇₉	—	2	4	no	—
201	C₂³×C₇₉	—	4	8	no	—
202	C₂³×C₇₉	—	4	8	no	—
203	C₂³×C₇₉	—	4	8	no	—
204	C₂³×C₇₉	—	4	8	no	—
205	C₂³×C₇₉	—	4	8	no	—
206	C₂³×C₇₉	—	4	2	no	—
207	C₂³×C₇₉	—	4	2	no	—
208	C₂³×C₇₉	—	4	2	no	—
209	C₂³×C₇₉	—	4	2	no	—
210	C₂³×C₇₉	—	4	8	no	—
211	C₂³×C₇₉	C₄×D₄	1	2	yes	—
212	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
213	C₂³×C₇₉	#135	1	2	yes	—
214	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₇₉	—	2	4	no	—
216	Q₈×C₇₉	—	4	2	no	—
217	D₄×C₇₉	—	2	16	no	—
218	D₄×C₇₉	—	2	4	no	—
219	D₄×C₇₉	—	2	4	no	—
220	D₄×C₇₉	—	2	4	no	—
221	D₄×C₇₉	C₄×D₄	1	8	yes	—
222	C₂×C₄×C₇₉	—	2	1	no	—
223	C₂×C₄×C₇₉	—	2	1	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	1	no	—
228	C₂×C₄×C₇₉	—	2	4	no	—
229	C₂×C₄×C₇₉	—	2	4	no	—
230	C₂×C₄×C₇₉	—	2	8	no	—
231	C₂×C₄×C₇₉	—	2	2	no	—
232	C₂×C₄×C₇₉	—	2	2	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	4	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	4	4	no	—
238	C₂×C₄×C₇₉	—	4	16	no	—
239	C₂×C₄×C₇₉	—	4	8	no	—
240	C₂×C₄×C₇₉	—	4	1	no	—
241	C₂×C₄×C₇₉	—	4	1	no	—
242	C₂×C₄×C₇₉	—	4	2	no	—
243	C₂×C₄×C₇₉	—	4	1	no	—
244	C₂×C₄×C₇₉	—	4	2	no	—
245	C₂×C₄×C₇₉	—	4	1	no	—
246	C₂×C₄×C₇₉	—	4	16	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₇₉	#120	1	2	yes	—
255	C₂×C₄×C₇₉	#120	1	2	yes	—
256	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
257	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
258	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
259	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
262	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
263	C₈×C₇₉	—	2	4	no	—
264	C₈×C₇₉	—	4	2	no	—
265	C₂²×C₇₉	—	2	2	no	—
266	C₂²×C₇₉	—	2	2	no	—
267	C₂²×C₇₉	—	2	2	no	—
268	C₂²×C₇₉	—	2	2	no	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	8	no	—
272	C₂²×C₇₉	—	4	32	no	—
273	C₂²×C₇₉	—	4	4	no	—
274	C₂²×C₇₉	—	4	4	no	—
275	C₂²×C₇₉	—	4	4	no	—
276	C₂²×C₇₉	—	4	4	no	—
277	C₂²×C₇₉	—	4	4	no	—
278	C₂²×C₇₉	—	4	4	no	—
279	C₂²×C₇₉	C₄×SD₁₆	1	4	yes	complemented
280	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
282	C₂²×C₇₉	#525	1	1	yes	characteristic
283	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
284	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
285	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₇₉	#575	1	1	yes	characteristic
287	C₄×C₇₉	—	2	2	no	—
288	C₄×C₇₉	—	2	2	no	—
289	C₄×C₇₉	—	2	2	no	—
290	C₄×C₇₉	—	4	2	no	—
291	C₄×C₇₉	—	4	4	no	—
292	C₄×C₇₉	—	4	1	no	—
293	C₄×C₇₉	—	4	2	no	—
294	C₄×C₇₉	—	8	1	no	—
295	C₄×C₇₉	—	8	1	no	—
296	C₄×C₇₉	#450	1	4	yes	direct product factor
297	C₄×C₇₉	C₂×C₄×D₄	1	2	yes	—
298	C₄×C₇₉	#525	1	2	yes	—
299	C₄×#450	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂×C₇₉	—	2	4	no	—
301	C₂×C₇₉	—	4	8	no	—
302	C₂×C₇₉	C₄×#120	1	1	yes	characteristic
303	C₂×C₇₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
304	C₂×C₇₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₂×C₇₉	C₂×#450	1	1	yes	characteristic
306	C₂×C₇₉	#3002	1	1	yes	characteristic
307	C₂×C₇₉	#3101	1	1	yes	characteristic
308	C₂×C₇₉	#3105	1	1	yes	characteristic
309	C₂²×C₄×D₄	C₂×C₇₉	1	1	yes	characteristic
310	C₂×#450	C₂×C₇₉	1	1	yes	characteristic
311	C₂×C₄×SD₁₆	C₂×C₇₉	1	2	yes	complemented
312	C₄×C₂²⋊Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
313	#1877	C₂×C₇₉	1	2	yes	complemented
314	#1872	C₂×C₇₉	1	1	yes	characteristic, complemented
315	#1864	C₂×C₇₉	1	2	yes	complemented
316	#1853	C₂×C₇₉	1	1	yes	characteristic, complemented
317	#1786	C₂×C₇₉	1	1	yes	characteristic
318	C₄×#102	C₂×C₇₉	1	2	yes	complemented
319	C₄×C₂²⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
320	C₇₉	C₄×#450	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
322	C₂⁴×C₄	—	2	1	no	—
323	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
324	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
326	C₂×C₄×D₄	—	2	8	no	—
327	C₂×C₄×D₄	—	2	1	no	—
328	C₂×C₄×D₄	—	2	1	no	—
329	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
331	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	—	2	1	no	—
333	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
334	#450	C₄×C₇₉	1	8	yes	direct product factor
335	C₄×SD₁₆	—	2	8	no	—
336	C₂×#106	C₂²×C₇₉	1	2	yes	complemented
337	C₂×#103	C₂²×C₇₉	1	2	yes	complemented
338	C₂×#102	C₂²×C₇₉	1	2	yes	—
339	C₂×#102	C₂²×C₇₉	1	2	yes	—
340	C₂×#102	C₂²×C₇₉	1	2	yes	—
341	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	complemented
344	#391	C₂²×C₇₉	1	1	yes	characteristic, complemented
345	#389	C₂²×C₇₉	1	1	yes	characteristic, complemented
346	#387	—	2	1	no	—
347	#385	—	2	1	no	—
348	#380	C₂²×C₇₉	1	1	yes	characteristic
349	C₄×C₄⋊C₄	—	2	1	no	—
350	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
351	C₄×C₂²⋊C₄	—	2	1	no	—
352	#340	C₂²×C₇₉	1	2	yes	complemented
353	#340	C₂²×C₇₉	1	2	yes	complemented
354	#336	C₂²×C₇₉	1	2	yes	complemented
355	C₂⁵	—	2	1	no	—
356	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	C₂×C₄×C₇₉	1	4	yes	—
362	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
363	C₂³×C₄	—	2	8	no	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	2	no	—
366	C₂³×C₄	—	2	2	no	—
367	C₂³×C₄	—	4	4	no	—
368	C₂³×C₄	—	4	4	no	—
369	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
370	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	4	no	—
374	C₂×SD₁₆	C₂×C₄×C₇₉	1	8	yes	complemented
375	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
376	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	C₂×C₄×C₇₉	1	4	yes	complemented
379	C₄×Q₈	—	2	4	no	—
380	C₄×D₄	—	2	8	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	4	no	—
385	C₄×D₄	D₄×C₇₉	1	8	yes	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
395	C₂×C₂²⋊C₄	—	2	8	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	—	2	4	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
407	#106	—	2	4	no	—
408	#103	—	2	4	no	—
409	#102	—	2	4	no	—
410	#102	—	2	4	no	—
411	#102	C₂×C₄×C₇₉	1	8	yes	complemented
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	C₂×C₄×C₇₉	1	4	yes	complemented
414	C₄×C₈	—	2	4	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	C₂⁴	—	2	4	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	2	no	—
426	C₂⁴	—	4	2	no	—
427	C₂⁴	—	4	2	no	—
428	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	C₂²×C₄×C₇₉	1	2	yes	complemented
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	2	16	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	C₂²×C₄×C₇₉	1	4	yes	—
442	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
443	C₂×D₄	#41×C₇₉	1	4	yes	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	32	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	complemented
467	C₂²×C₄	C₂²×C₄×C₇₉	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
473	C₂²×C₄	#41×C₇₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
475	SD₁₆	—	2	16	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	C₂²×C₄×C₇₉	1	4	yes	complemented
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	complemented
491	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	4	2	no	—
500	C₄²	—	4	2	no	—
501	C₄²	C₂×D₄×C₇₉	1	4	yes	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	16	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	8	no	—
515	C₂³	—	4	8	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	C₄×D₄×C₇₉	1	2	yes	—
521	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
522	C₂³	#135×C₇₉	1	2	yes	—
523	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
524	Q₈	—	2	4	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	2	16	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	C₄×D₄×C₇₉	1	8	yes	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	16	no	—
548	C₂×C₄	—	4	8	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	16	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	C₄×D₄×C₇₉	1	2	yes	—
563	C₂×C₄	#120×C₇₉	1	2	yes	—
564	C₂×C₄	#120×C₇₉	1	2	yes	—
565	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
566	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
567	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
568	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
570	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
571	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	4	32	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	C₄×SD₁₆×C₇₉	1	4	yes	complemented
589	C₂²	C₂×C₄×D₄×C₇₉	1	1	yes	characteristic
590	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
591	C₂²	#525×C₇₉	1	1	yes	characteristic
592	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
593	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
594	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
595	C₂²	#575×C₇₉	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	4	no	—
602	C₄	—	4	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	#450×C₇₉	1	4	yes	direct product factor
606	C₄	C₂×C₄×D₄×C₇₉	1	2	yes	—
607	C₄	#525×C₇₉	1	2	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	8	no	—
610	C₂	C₄×#120×C₇₉	1	1	yes	characteristic
611	C₂	C₂×C₄×SD₁₆×C₇₉	1	1	yes	characteristic
612	C₂	C₄×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
613	C₂	C₂×#450×C₇₉	1	1	yes	characteristic
614	C₂	C₇₉×#3002	1	1	yes	characteristic
615	C₂	C₇₉×#3101	1	1	yes	characteristic
616	C₂	C₇₉×#3105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂³×D₄×C₇₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×SD₁₆×C₇₉	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₇₉	C₂	semidirect
5. C₇₉×#1877	C₂	semidirect
6. C₇₉×#1872	C₂	semidirect
7. C₇₉×#1864	C₂	semidirect
8. C₇₉×#1853	C₂	semidirect
10. C₄×#102×C₇₉	C₂	semidirect
11. C₄×C₂²⋊C₈×C₇₉	C₂	semidirect
16. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
25. #450×C₇₉	C₄	direct (N × H)
27. C₂×#106×C₇₉	C₂²	semidirect
28. C₂×#103×C₇₉	C₂²	semidirect
34. C₂×C₄×C₈×C₇₉	C₂²	semidirect
35. #391×C₇₉	C₂²	semidirect
36. #389×C₇₉	C₂²	semidirect
41. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
43. #340×C₇₉	C₂²	semidirect
44. #340×C₇₉	C₂²	semidirect
45. #336×C₇₉	C₂²	semidirect
65. C₂×SD₁₆×C₇₉	C₂×C₄	semidirect
69. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
102. #102×C₇₉	C₂×C₄	semidirect
104. C₂²⋊C₈×C₇₉	C₂×C₄	semidirect
123. C₂×Q₈×C₇₉	C₂²×C₄	semidirect
157. C₂²×C₄×C₇₉	SD₁₆	semidirect
172. C₂×C₈×C₇₉	C₂²×C₄	semidirect
181. C₄⋊C₄×C₇₉	C₂²×C₄	semidirect
279. C₂²×C₇₉	C₄×SD₁₆	semidirect
296. C₄×C₇₉	#450	direct (N × H)
299. C₄×#450	C₇₉	direct (N × H)
311. C₂×C₄×SD₁₆	C₂×C₇₉	semidirect
312. C₄×C₂²⋊Q₈	C₂×C₇₉	semidirect
313. #1877	C₂×C₇₉	semidirect
314. #1872	C₂×C₇₉	semidirect
315. #1864	C₂×C₇₉	semidirect
316. #1853	C₂×C₇₉	semidirect
318. C₄×#102	C₂×C₇₉	semidirect
319. C₄×C₂²⋊C₈	C₂×C₇₉	semidirect
320. C₇₉	C₄×#450	direct (N × H)
325. C₂×C₄×Q₈	C₂²×C₇₉	semidirect
334. #450	C₄×C₇₉	direct (N × H)
336. C₂×#106	C₂²×C₇₉	semidirect
337. C₂×#103	C₂²×C₇₉	semidirect
343. C₂×C₄×C₈	C₂²×C₇₉	semidirect
344. #391	C₂²×C₇₉	semidirect
345. #389	C₂²×C₇₉	semidirect
350. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
352. #340	C₂²×C₇₉	semidirect
353. #340	C₂²×C₇₉	semidirect
354. #336	C₂²×C₇₉	semidirect
374. C₂×SD₁₆	C₂×C₄×C₇₉	semidirect
378. C₂²⋊Q₈	C₂×C₄×C₇₉	semidirect
411. #102	C₂×C₄×C₇₉	semidirect
413. C₂²⋊C₈	C₂×C₄×C₇₉	semidirect
432. C₂×Q₈	C₂²×C₄×C₇₉	semidirect
466. C₂²×C₄	SD₁₆×C₇₉	semidirect
481. C₂×C₈	C₂²×C₄×C₇₉	semidirect
490. C₄⋊C₄	C₂²×C₄×C₇₉	semidirect
588. C₂²	C₄×SD₁₆×C₇₉	semidirect
605. C₄	#450×C₇₉	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×C₄×D₄×C₇₉	2
C₂×#450×C₇₉	2
C₂×C₄×SD₁₆×C₇₉	2
C₄×C₂²⋊Q₈×C₇₉	2
C₇₉×#1877	2
C₇₉×#1872	2
C₇₉×#1864	2
C₇₉×#1853	2
C₇₉×#1786	2
C₄×#102×C₇₉	2
C₄×C₂²⋊C₈×C₇₉	2
C₄×#450	79

Subgroups — C4×#450×C79 #34133136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#450×C₇₉ #34133136