Subgroups — C₇₉×#25598 #34137287

Order 20224.

1298 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2856	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2000	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1880	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₇₉	C₂²	1	4	yes	—
11	#533×C₇₉	—	2	4	no	—
12	#533×C₇₉	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₇₉	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
19	C₂×#121×C₇₉	—	2	1	no	—
20	C₂×#121×C₇₉	—	2	1	no	—
21	C₂×#121×C₇₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
24	C₂×#117×C₇₉	—	2	1	no	—
25	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
26	#492×C₇₉	—	2	4	no	—
27	#486×C₇₉	—	2	4	no	—
28	C₂×#103×C₇₉	C₂²	1	4	yes	—
29	C₂×#102×C₇₉	C₂²	1	4	yes	—
30	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
33	#390×C₇₉	—	2	1	no	—
34	#390×C₇₉	—	2	1	no	—
35	#390×C₇₉	C₂²	1	2	yes	—
36	#384×C₇₉	C₂²	1	1	yes	characteristic
37	#340×C₇₉	C₂²	1	4	yes	—
38	#336×C₇₉	C₂²	1	2	yes	—
39	C₂²×Q₈×C₇₉	—	2	1	no	—
40	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₇₉	—	2	2	no	—
42	C₂²×D₄×C₇₉	—	2	1	no	—
43	C₂²×D₄×C₇₉	—	2	1	no	—
44	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₇₉	—	2	8	no	—
49	C₂×SD₁₆×C₇₉	—	2	8	no	—
50	C₂×SD₁₆×C₇₉	—	4	4	no	—
51	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₇₉	—	2	2	no	—
54	C₄⋊Q₈×C₇₉	—	2	2	no	—
55	C₄⋊Q₈×C₇₉	D₄	1	4	yes	complemented
56	C₄⋊Q₈×C₇₉	D₄	1	4	yes	complemented
57	#127×C₇₉	—	2	2	no	—
58	#127×C₇₉	—	2	2	no	—
59	#125×C₇₉	—	2	8	no	—
60	C₂²⋊Q₈×C₇₉	—	2	8	no	—
61	C₂²⋊Q₈×C₇₉	—	2	4	no	—
62	C₂²⋊Q₈×C₇₉	—	2	4	no	—
63	#121×C₇₉	—	4	4	no	—
64	#121×C₇₉	—	4	4	no	—
65	#121×C₇₉	—	4	4	no	—
66	C₄×Q₈×C₇₉	—	2	8	no	—
67	C₄×Q₈×C₇₉	—	2	4	no	—
68	C₄×Q₈×C₇₉	—	2	4	no	—
69	#117×C₇₉	—	2	8	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₄²×C₇₉	—	2	2	no	—
84	C₂×C₄²×C₇₉	—	2	2	no	—
85	C₂×C₄²×C₇₉	—	2	2	no	—
86	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
90	#103×C₇₉	—	4	4	no	—
91	#102×C₇₉	—	2	8	no	—
92	C₂²⋊C₈×C₇₉	—	2	4	no	—
93	C₄×C₈×C₇₉	—	2	2	no	—
94	C₄×C₈×C₇₉	—	2	2	no	—
95	C₂⁴×C₇₉	—	2	2	no	—
96	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₇₉	—	2	4	no	—
98	C₂×Q₈×C₇₉	—	2	2	no	—
99	C₂×Q₈×C₇₉	—	2	4	no	—
100	C₂×Q₈×C₇₉	—	2	4	no	—
101	C₂×Q₈×C₇₉	—	4	2	no	—
102	C₂×Q₈×C₇₉	—	4	2	no	—
103	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₇₉	—	2	2	no	—
105	C₂×D₄×C₇₉	—	2	2	no	—
106	C₂×D₄×C₇₉	—	2	4	no	—
107	C₂×D₄×C₇₉	—	2	4	no	—
108	C₂×D₄×C₇₉	—	4	4	no	—
109	C₂×D₄×C₇₉	—	4	4	no	—
110	C₂×D₄×C₇₉	—	4	4	no	—
111	C₂×D₄×C₇₉	—	4	2	no	—
112	C₂×D₄×C₇₉	—	4	2	no	—
113	C₂×D₄×C₇₉	—	4	2	no	—
114	C₂×D₄×C₇₉	—	4	2	no	—
115	C₂×D₄×C₇₉	—	4	2	no	—
116	C₂×D₄×C₇₉	—	4	2	no	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	2	1	no	—
125	C₂²×C₄×C₇₉	—	2	1	no	—
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	complemented
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₇₉	—	4	16	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	2	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	#41	1	4	yes	—
143	C₄⋊C₄×C₇₉	—	2	8	no	—
144	C₄⋊C₄×C₇₉	—	2	8	no	—
145	C₄⋊C₄×C₇₉	—	2	4	no	—
146	C₄⋊C₄×C₇₉	—	2	4	no	—
147	C₄⋊C₄×C₇₉	—	2	4	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	4	no	—
150	C₄⋊C₄×C₇₉	—	4	2	no	—
151	C₄⋊C₄×C₇₉	—	4	2	no	—
152	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₇₉	—	2	8	no	—
154	C₂²⋊C₄×C₇₉	—	4	4	no	—
155	C₂²⋊C₄×C₇₉	—	4	4	no	—
156	C₂²⋊C₄×C₇₉	—	4	4	no	—
157	C₄²×C₇₉	—	2	8	no	—
158	C₄²×C₇₉	—	2	2	no	—
159	C₄²×C₇₉	—	2	2	no	—
160	C₄²×C₇₉	—	2	1	no	—
161	C₄²×C₇₉	—	2	1	no	—
162	C₄²×C₇₉	C₂×D₄	1	2	yes	—
163	C₄²×C₇₉	C₂×D₄	1	2	yes	—
164	C₂³×C₇₉	—	2	1	no	—
165	C₂³×C₇₉	—	2	1	no	—
166	C₂³×C₇₉	—	2	1	no	—
167	C₂³×C₇₉	—	2	1	no	—
168	C₂³×C₇₉	—	2	1	no	—
169	C₂³×C₇₉	—	2	1	no	—
170	C₂³×C₇₉	—	4	2	no	—
171	C₂³×C₇₉	—	4	2	no	—
172	C₂³×C₇₉	—	4	2	no	—
173	C₂³×C₇₉	—	4	2	no	—
174	C₂³×C₇₉	—	4	2	no	—
175	C₂³×C₇₉	—	4	2	no	—
176	C₂³×C₇₉	—	4	2	no	—
177	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
178	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₇₉	—	2	8	no	—
180	Q₈×C₇₉	—	4	4	no	—
181	Q₈×C₇₉	—	4	8	no	—
182	D₄×C₇₉	—	4	4	no	—
183	D₄×C₇₉	—	4	4	no	—
184	D₄×C₇₉	—	8	8	no	—
185	D₄×C₇₉	—	8	4	no	—
186	D₄×C₇₉	—	8	4	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	1	no	—
189	C₂×C₄×C₇₉	—	2	8	no	—
190	C₂×C₄×C₇₉	—	2	1	no	—
191	C₂×C₄×C₇₉	—	2	1	no	—
192	C₂×C₄×C₇₉	—	2	4	no	—
193	C₂×C₄×C₇₉	—	2	4	no	—
194	C₂×C₄×C₇₉	—	2	1	no	—
195	C₂×C₄×C₇₉	—	2	1	no	—
196	C₂×C₄×C₇₉	—	2	1	no	—
197	C₂×C₄×C₇₉	—	2	1	no	—
198	C₂×C₄×C₇₉	—	4	2	no	—
199	C₂×C₄×C₇₉	—	4	2	no	—
200	C₂×C₄×C₇₉	—	4	2	no	—
201	C₂×C₄×C₇₉	—	4	2	no	—
202	C₂×C₄×C₇₉	—	4	2	no	—
203	C₂×C₄×C₇₉	—	4	2	no	—
204	C₂×C₄×C₇₉	—	4	4	no	—
205	C₂×C₄×C₇₉	—	4	2	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	#120	1	2	yes	—
209	C₂×C₄×C₇₉	#120	1	2	yes	—
210	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₇₉	#135	1	2	yes	—
213	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₇₉	#137	1	2	yes	—
215	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
218	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₇₉	—	2	4	no	—
220	C₈×C₇₉	—	4	2	no	—
221	C₂²×C₇₉	—	2	2	no	—
222	C₂²×C₇₉	—	2	2	no	—
223	C₂²×C₇₉	—	2	2	no	—
224	C₂²×C₇₉	—	4	1	no	—
225	C₂²×C₇₉	—	4	1	no	—
226	C₂²×C₇₉	—	4	1	no	—
227	C₂²×C₇₉	—	4	1	no	—
228	C₂²×C₇₉	—	8	2	no	—
229	C₂²×C₇₉	—	8	2	no	—
230	C₂²×C₇₉	—	8	2	no	—
231	C₂²×C₇₉	—	8	2	no	—
232	C₂²×C₇₉	—	8	2	no	—
233	C₂²×C₇₉	—	8	2	no	—
234	C₂²×C₇₉	—	8	2	no	—
235	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
236	C₂²×C₇₉	#532	1	1	yes	characteristic
237	C₂²×C₇₉	#535	1	1	yes	characteristic
238	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
239	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
240	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
242	C₄×C₇₉	—	2	2	no	—
243	C₄×C₇₉	—	4	1	no	—
244	C₄×C₇₉	—	4	4	no	—
245	C₄×C₇₉	—	4	1	no	—
246	C₄×C₇₉	—	4	4	no	—
247	C₄×C₇₉	—	8	2	no	—
248	C₄×C₇₉	#448	1	4	yes	—
249	C₄×C₇₉	#449	1	4	yes	—
250	C₄×C₇₉	#546	1	2	yes	—
251	C₄×C₇₉	#550	1	2	yes	—
252	#25598	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂×C₇₉	—	4	2	no	—
254	C₂×C₇₉	—	16	2	no	—
255	C₂×C₇₉	#2431	1	1	yes	characteristic
256	C₂×C₇₉	C₂×#448	1	1	yes	characteristic
257	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
258	C₂×C₇₉	#3167	1	1	yes	characteristic
259	C₂×C₇₉	#3182	1	1	yes	characteristic
260	C₂×C₇₉	#3208	1	1	yes	characteristic
261	C₂×C₇₉	#3210	1	1	yes	characteristic
262	C₂×#533	C₂×C₇₉	1	1	yes	characteristic, complemented
263	C₂×#492	C₂×C₇₉	1	1	yes	characteristic, complemented
264	C₂×#486	C₂×C₇₉	1	1	yes	characteristic, complemented
265	#2856	C₂×C₇₉	1	1	yes	characteristic
266	#2000	C₂×C₇₉	1	4	yes	complemented
267	#1990	C₂×C₇₉	1	1	yes	characteristic, complemented
268	#1956	C₂×C₇₉	1	1	yes	characteristic, complemented
269	#1880	C₂×C₇₉	1	4	yes	complemented
270	C₄×C₂²⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
271	C₇₉	#25598	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×SD₁₆	C₂²×C₇₉	1	4	yes	—
273	#533	—	2	4	no	—
274	#533	—	2	4	no	—
275	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
277	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
278	C₂×#125	—	2	1	no	—
279	C₂×C₂²⋊Q₈	—	2	1	no	—
280	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
281	C₂×#121	—	2	1	no	—
282	C₂×#121	—	2	1	no	—
283	C₂×#121	C₂²×C₇₉	1	2	yes	—
284	C₂×C₄×Q₈	—	2	1	no	—
285	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
286	C₂×#117	—	2	1	no	—
287	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
288	#492	—	2	4	no	—
289	#486	—	2	4	no	—
290	C₂×#103	C₂²×C₇₉	1	4	yes	—
291	C₂×#102	C₂²×C₇₉	1	4	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
293	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
295	#390	—	2	1	no	—
296	#390	—	2	1	no	—
297	#390	C₂²×C₇₉	1	2	yes	—
298	#384	C₂²×C₇₉	1	1	yes	characteristic
299	#340	C₂²×C₇₉	1	4	yes	—
300	#336	C₂²×C₇₉	1	2	yes	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
307	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
310	C₂×SD₁₆	—	2	8	no	—
311	C₂×SD₁₆	—	2	8	no	—
312	C₂×SD₁₆	—	4	4	no	—
313	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
314	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₇₉	1	4	yes	complemented
318	C₄⋊Q₈	D₄×C₇₉	1	4	yes	complemented
319	#127	—	2	2	no	—
320	#127	—	2	2	no	—
321	#125	—	2	8	no	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	#121	—	4	4	no	—
326	#121	—	4	4	no	—
327	#121	—	4	4	no	—
328	C₄×Q₈	—	2	8	no	—
329	C₄×Q₈	—	2	4	no	—
330	C₄×Q₈	—	2	4	no	—
331	#117	—	2	8	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
349	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
352	#103	—	4	4	no	—
353	#102	—	2	8	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	complemented
392	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
398	SD₁₆	—	4	16	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	#41×C₇₉	1	4	yes	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₄²	—	2	8	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	C₂×D₄×C₇₉	1	2	yes	—
425	C₄²	C₂×D₄×C₇₉	1	2	yes	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
440	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
441	Q₈	—	2	8	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	4	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	8	no	—
447	D₄	—	8	4	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	#120×C₇₉	1	2	yes	—
471	C₂×C₄	#120×C₇₉	1	2	yes	—
472	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
473	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
474	C₂×C₄	#135×C₇₉	1	2	yes	—
475	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
476	C₂×C₄	#137×C₇₉	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
480	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
481	C₈	—	2	4	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
498	C₂²	#532×C₇₉	1	1	yes	characteristic
499	C₂²	#535×C₇₉	1	1	yes	characteristic
500	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
501	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
502	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
503	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	4	no	—
509	C₄	—	8	2	no	—
510	C₄	#448×C₇₉	1	4	yes	—
511	C₄	#449×C₇₉	1	4	yes	—
512	C₄	#546×C₇₉	1	2	yes	—
513	C₄	#550×C₇₉	1	2	yes	—
514	C₂	—	4	2	no	—
515	C₂	—	16	2	no	—
516	C₂	C₇₉×#2431	1	1	yes	characteristic
517	C₂	C₂×#448×C₇₉	1	1	yes	characteristic
518	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
519	C₂	C₇₉×#3167	1	1	yes	characteristic
520	C₂	C₇₉×#3182	1	1	yes	characteristic
521	C₂	C₇₉×#3208	1	1	yes	characteristic
522	C₂	C₇₉×#3210	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₇₉	C₂	semidirect
2. C₂×#492×C₇₉	C₂	semidirect
3. C₂×#486×C₇₉	C₂	semidirect
5. C₇₉×#2000	C₂	semidirect
6. C₇₉×#1990	C₂	semidirect
7. C₇₉×#1956	C₂	semidirect
8. C₇₉×#1880	C₂	semidirect
9. C₄×C₂²⋊C₈×C₇₉	C₂	semidirect
55. C₄⋊Q₈×C₇₉	D₄	semidirect
56. C₄⋊Q₈×C₇₉	D₄	semidirect
129. C₂²×C₄×C₇₉	SD₁₆	semidirect
252. #25598	C₇₉	direct (N × H)
262. C₂×#533	C₂×C₇₉	semidirect
263. C₂×#492	C₂×C₇₉	semidirect
264. C₂×#486	C₂×C₇₉	semidirect
266. #2000	C₂×C₇₉	semidirect
267. #1990	C₂×C₇₉	semidirect
268. #1956	C₂×C₇₉	semidirect
269. #1880	C₂×C₇₉	semidirect
270. C₄×C₂²⋊C₈	C₂×C₇₉	semidirect
271. C₇₉	#25598	direct (N × H)
317. C₄⋊Q₈	D₄×C₇₉	semidirect
318. C₄⋊Q₈	D₄×C₇₉	semidirect
391. C₂²×C₄	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₇₉	2
C₂×#492×C₇₉	2
C₂×#486×C₇₉	2
C₇₉×#2856	2
C₇₉×#2000	2
C₇₉×#1990	2
C₇₉×#1956	2
C₇₉×#1880	2
C₄×C₂²⋊C₈×C₇₉	2
#25598	79

Subgroups — C79×#25598 #34137287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25598 #34137287