Subgroups — C₇₉×#24483 #34136172

Order 20224.

984 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#481×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2436	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2066	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2042	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1983	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1927	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1893	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×#124×C₇₉	C₂²	1	2	yes	—
15	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
17	#481×C₇₉	—	2	4	no	—
18	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₂×#103×C₇₉	—	2	4	no	—
22	C₂×#103×C₇₉	C₂²	1	2	yes	—
23	C₂×#103×C₇₉	C₂²	1	2	yes	—
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
25	C₂×#103×C₇₉	C₂²	1	2	yes	—
26	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#102×C₇₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	#393×C₇₉	—	2	2	no	—
31	#391×C₇₉	C₂²	1	2	yes	—
32	#389×C₇₉	C₂²	1	2	yes	—
33	#387×C₇₉	—	2	2	no	—
34	#386×C₇₉	—	2	1	no	—
35	#386×C₇₉	—	2	1	no	—
36	#380×C₇₉	—	2	1	no	—
37	#380×C₇₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	#340×C₇₉	C₂²	1	2	yes	—
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₉	—	2	1	no	—
44	C₂²×Q₈×C₇₉	—	2	4	no	—
45	C₂²×Q₈×C₇₉	—	2	2	no	—
46	C₂²×Q₈×C₇₉	—	2	2	no	—
47	C₂²×Q₈×C₇₉	—	4	2	no	—
48	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	1	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₉	—	2	2	no	—
55	C₂²×C₈×C₇₉	—	4	2	no	—
56	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
59	#124×C₇₉	—	2	4	no	—
60	#124×C₇₉	—	4	2	no	—
61	#121×C₇₉	—	2	2	no	—
62	#121×C₇₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₉	—	2	2	no	—
78	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
79	#106×C₇₉	—	2	2	no	—
80	#106×C₇₉	—	2	2	no	—
81	C₄⋊C₈×C₇₉	—	4	2	no	—
82	#103×C₇₉	—	2	4	no	—
83	#103×C₇₉	—	2	4	no	—
84	#103×C₇₉	—	2	4	no	—
85	#103×C₇₉	—	4	2	no	—
86	#102×C₇₉	—	2	2	no	—
87	#102×C₇₉	—	2	2	no	—
88	#102×C₇₉	—	4	2	no	—
89	C₂²⋊C₈×C₇₉	—	2	2	no	—
90	#95×C₇₉	—	2	2	no	—
91	#95×C₇₉	—	2	2	no	—
92	#95×C₇₉	—	2	1	no	—
93	#95×C₇₉	—	2	2	no	—
94	#95×C₇₉	—	2	2	no	—
95	#95×C₇₉	D₄	1	2	yes	—
96	C₂⁴×C₇₉	—	2	1	no	—
97	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₇₉	—	2	2	no	—
99	C₂×Q₈×C₇₉	—	2	8	no	—
100	C₂×Q₈×C₇₉	—	2	2	no	—
101	C₂×Q₈×C₇₉	—	2	2	no	—
102	C₂×Q₈×C₇₉	—	2	2	no	—
103	C₂×Q₈×C₇₉	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	4	4	no	—
105	C₂×Q₈×C₇₉	—	4	8	no	—
106	C₂×Q₈×C₇₉	—	4	4	no	—
107	C₂×Q₈×C₇₉	—	4	2	no	—
108	C₂×Q₈×C₇₉	#41	1	4	yes	—
109	C₂×D₄×C₇₉	—	2	1	no	—
110	C₂×D₄×C₇₉	—	2	1	no	—
111	C₂×D₄×C₇₉	—	2	2	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	4	2	no	—
114	C₂×D₄×C₇₉	—	4	2	no	—
115	C₂×D₄×C₇₉	—	4	2	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	1	no	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	1	no	—
121	C₂²×C₄×C₇₉	—	2	4	no	—
122	C₂²×C₄×C₇₉	—	2	1	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	4	4	no	—
125	C₂²×C₄×C₇₉	—	4	2	no	—
126	C₂²×C₄×C₇₉	—	8	2	no	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇₉	#41	1	2	yes	—
132	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	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	—	4	4	no	—
141	C₄⋊C₄×C₇₉	—	2	4	no	—
142	C₄⋊C₄×C₇₉	—	2	1	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	8	2	no	—
149	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₇₉	—	2	2	no	—
152	C₂²⋊C₄×C₇₉	—	2	2	no	—
153	C₂²⋊C₄×C₇₉	—	4	4	no	—
154	C₂²⋊C₄×C₇₉	—	4	4	no	—
155	C₂²⋊C₄×C₇₉	—	4	2	no	—
156	C₂²⋊C₄×C₇₉	—	4	2	no	—
157	C₄²×C₇₉	—	2	2	no	—
158	C₄²×C₇₉	—	2	2	no	—
159	C₄²×C₇₉	—	8	2	no	—
160	C₂³×C₇₉	—	2	2	no	—
161	C₂³×C₇₉	—	2	2	no	—
162	C₂³×C₇₉	—	4	1	no	—
163	C₂³×C₇₉	—	4	2	no	—
164	C₂³×C₇₉	—	4	1	no	—
165	C₂³×C₇₉	—	4	1	no	—
166	C₂³×C₇₉	—	4	2	no	—
167	C₂³×C₇₉	#121	1	2	yes	—
168	C₂³×C₇₉	#135	1	2	yes	—
169	C₂³×C₇₉	#137	1	2	yes	—
170	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₇₉	—	2	4	no	—
172	Q₈×C₇₉	—	2	4	no	—
173	Q₈×C₇₉	—	4	8	no	—
174	Q₈×C₇₉	—	4	2	no	—
175	Q₈×C₇₉	—	4	2	no	—
176	D₄×C₇₉	—	4	1	no	—
177	D₄×C₇₉	—	4	1	no	—
178	D₄×C₇₉	—	4	2	no	—
179	D₄×C₇₉	—	8	4	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	4	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	4	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	2	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	4	8	no	—
194	C₂×C₄×C₇₉	—	4	2	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	4	2	no	—
197	C₂×C₄×C₇₉	—	4	2	no	—
198	C₂×C₄×C₇₉	—	4	1	no	—
199	C₂×C₄×C₇₉	—	4	2	no	—
200	C₂×C₄×C₇₉	—	4	2	no	—
201	C₂×C₄×C₇₉	—	4	1	no	—
202	C₂×C₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	4	2	no	—
204	C₂×C₄×C₇₉	—	8	4	no	—
205	C₂×C₄×C₇₉	#121	1	2	yes	—
206	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
210	C₈×C₇₉	—	4	1	no	—
211	C₈×C₇₉	—	4	1	no	—
212	C₈×C₇₉	—	4	2	no	—
213	C₂²×C₇₉	—	2	2	no	—
214	C₂²×C₇₉	—	2	2	no	—
215	C₂²×C₇₉	—	2	4	no	—
216	C₂²×C₇₉	—	2	4	no	—
217	C₂²×C₇₉	—	8	1	no	—
218	C₂²×C₇₉	—	8	1	no	—
219	C₂²×C₇₉	—	8	1	no	—
220	C₂²×C₇₉	—	8	2	no	—
221	C₂²×C₇₉	—	8	2	no	—
222	C₂²×C₇₉	#464	1	4	yes	—
223	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
224	C₂²×C₇₉	#546	1	2	yes	—
225	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
226	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
227	C₂²×C₇₉	#577	1	2	yes	—
228	C₄×C₇₉	—	2	2	no	—
229	C₄×C₇₉	—	4	4	no	—
230	C₄×C₇₉	—	4	2	no	—
231	C₄×C₇₉	—	4	2	no	—
232	C₄×C₇₉	—	4	2	no	—
233	C₄×C₇₉	—	4	2	no	—
234	C₄×C₇₉	—	8	1	no	—
235	C₄×C₇₉	—	8	2	no	—
236	C₄×C₇₉	#525	1	1	yes	characteristic
237	C₄×C₇₉	#535	1	1	yes	characteristic
238	C₄×C₇₉	#551	1	2	yes	—
239	#24483	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₇₉	—	2	4	no	—
241	C₂×C₇₉	—	16	1	no	—
242	C₂×C₇₉	#2411	1	1	yes	characteristic
243	C₂×C₇₉	C₂×#464	1	1	yes	characteristic
244	C₂×C₇₉	#3042	1	1	yes	characteristic
245	C₂×C₇₉	#3301	1	2	yes	—
246	C₂×C₇₉	#3316	1	2	yes	—
247	C₂×#481	C₂×C₇₉	1	1	yes	characteristic
248	C₂²×#103	C₂×C₇₉	1	1	yes	characteristic, complemented
249	#2436	C₂×C₇₉	1	1	yes	characteristic
250	#2345	C₂×C₇₉	1	1	yes	characteristic, complemented
251	#2066	C₂×C₇₉	1	2	yes	complemented
252	#2042	C₂×C₇₉	1	2	yes	complemented
253	#1983	C₂×C₇₉	1	2	yes	complemented
254	#1927	C₂×C₇₉	1	2	yes	complemented
255	#1893	C₂×C₇₉	1	1	yes	characteristic
256	#1850	C₂×C₇₉	1	1	yes	characteristic, complemented
257	#1787	C₂×C₇₉	1	1	yes	characteristic, complemented
258	C₇₉	#24483	1	1	yes	characteristic, direct product factor, Sylow
259	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
260	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
261	C₂×#124	C₂²×C₇₉	1	2	yes	—
262	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
264	#481	—	2	4	no	—
265	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
266	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
268	C₂×#103	—	2	4	no	—
269	C₂×#103	C₂²×C₇₉	1	2	yes	—
270	C₂×#103	C₂²×C₇₉	1	2	yes	—
271	C₂×#103	C₂²×C₇₉	1	2	yes	—
272	C₂×#103	C₂²×C₇₉	1	2	yes	—
273	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
274	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
275	C₂×#102	C₂²×C₇₉	1	2	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
277	#393	—	2	2	no	—
278	#391	C₂²×C₇₉	1	2	yes	—
279	#389	C₂²×C₇₉	1	2	yes	—
280	#387	—	2	2	no	—
281	#386	—	2	1	no	—
282	#386	—	2	1	no	—
283	#380	—	2	1	no	—
284	#380	C₂²×C₇₉	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
286	C₄×C₂²⋊C₄	—	2	1	no	—
287	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
288	#340	C₂²×C₇₉	1	2	yes	—
289	#336	C₂²×C₇₉	1	2	yes	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	—	2	4	no	—
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	4	2	no	—
295	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	4	2	no	—
303	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
306	#124	—	2	4	no	—
307	#124	—	4	2	no	—
308	#121	—	2	2	no	—
309	#121	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
326	#106	—	2	2	no	—
327	#106	—	2	2	no	—
328	C₄⋊C₈	—	4	2	no	—
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#103	—	2	4	no	—
332	#103	—	4	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	4	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	D₄×C₇₉	1	2	yes	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	8	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	—	4	8	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	#41×C₇₉	1	4	yes	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	8	2	no	—
374	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
378	C₂²×C₄	#41×C₇₉	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	8	2	no	—
396	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	8	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	#121×C₇₉	1	2	yes	—
415	C₂³	#135×C₇₉	1	2	yes	—
416	C₂³	#137×C₇₉	1	2	yes	—
417	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	4	8	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	#121×C₇₉	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
457	C₈	—	4	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	1	no	—
469	C₂²	#464×C₇₉	1	4	yes	—
470	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
471	C₂²	#546×C₇₉	1	2	yes	—
472	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
473	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
474	C₂²	#577×C₇₉	1	2	yes	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	#525×C₇₉	1	1	yes	characteristic
484	C₄	#535×C₇₉	1	1	yes	characteristic
485	C₄	#551×C₇₉	1	2	yes	—
486	C₂	—	2	4	no	—
487	C₂	—	16	1	no	—
488	C₂	C₇₉×#2411	1	1	yes	characteristic
489	C₂	C₂×#464×C₇₉	1	1	yes	characteristic
490	C₂	C₇₉×#3042	1	1	yes	characteristic
491	C₂	C₇₉×#3301	1	2	yes	—
492	C₂	C₇₉×#3316	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#121×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#103×C₇₉	C₂	semidirect
4. C₇₉×#2345	C₂	semidirect
5. C₇₉×#2066	C₂	semidirect
6. C₇₉×#2042	C₂	semidirect
7. C₇₉×#1983	C₂	semidirect
8. C₇₉×#1927	C₂	semidirect
10. C₇₉×#1850	C₂	semidirect
11. C₇₉×#1787	C₂	semidirect
239. #24483	C₇₉	direct (N × H)
248. C₂²×#103	C₂×C₇₉	semidirect
250. #2345	C₂×C₇₉	semidirect
251. #2066	C₂×C₇₉	semidirect
252. #2042	C₂×C₇₉	semidirect
253. #1983	C₂×C₇₉	semidirect
254. #1927	C₂×C₇₉	semidirect
256. #1850	C₂×C₇₉	semidirect
257. #1787	C₂×C₇₉	semidirect
258. C₇₉	#24483	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#481×C₇₉	2
C₂²×#103×C₇₉	2
C₇₉×#2436	2
C₇₉×#2345	2
C₇₉×#2066	2
C₇₉×#2042	2
C₇₉×#1983	2
C₇₉×#1927	2
C₇₉×#1893	2
C₇₉×#1850	2
C₇₉×#1787	2
#24483	79

Subgroups — C79×#24483 #34136172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24483 #34136172