Subgroups — C₇₉×#25695 #34137384

Order 20224.

974 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3507	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3141	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2038	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1980	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1859	C₂	1	4	yes	maximal, complemented
9	C₄×#101×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#559×C₇₉	—	2	1	no	—
11	#557×C₇₉	—	2	1	no	—
12	#556×C₇₉	—	2	1	no	—
13	#556×C₇₉	—	2	2	no	—
14	#554×C₇₉	—	2	1	no	—
15	#552×C₇₉	—	2	2	no	—
16	#539×C₇₉	—	2	2	no	—
17	#536×C₇₉	C₂²	1	2	yes	—
18	#533×C₇₉	C₂²	1	1	yes	characteristic
19	#532×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	#529×C₇₉	—	2	2	no	—
22	#520×C₇₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	#501×C₇₉	—	2	2	no	—
25	#500×C₇₉	—	2	1	no	—
26	#498×C₇₉	—	2	1	no	—
27	#489×C₇₉	—	2	2	no	—
28	#487×C₇₉	—	2	1	no	—
29	#486×C₇₉	—	2	1	no	—
30	#428×C₇₉	C₂²	1	4	yes	—
31	C₂×#104×C₇₉	C₂²	1	4	yes	—
32	#417×C₇₉	C₂²	1	4	yes	—
33	C₂×#101×C₇₉	C₂²	1	2	yes	—
34	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
36	#395×C₇₉	—	2	2	no	—
37	#391×C₇₉	C₂²	1	2	yes	—
38	#389×C₇₉	—	2	2	no	—
39	#384×C₇₉	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	#343×C₇₉	C₂²	1	2	yes	—
42	#339×C₇₉	C₂²	1	4	yes	—
43	C₂×#41×C₇₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₇₉	—	2	1	no	—
45	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
47	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₇₉	—	2	2	no	—
49	C₄⋊Q₈×C₇₉	—	2	1	no	—
50	C₄⋊Q₈×C₇₉	—	2	1	no	—
51	C₄⋊Q₈×C₇₉	—	2	1	no	—
52	C₄⋊Q₈×C₇₉	—	2	1	no	—
53	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
56	#127×C₇₉	D₄	1	1	yes	characteristic
57	#126×C₇₉	—	2	4	no	—
58	#126×C₇₉	—	2	4	no	—
59	#125×C₇₉	—	2	2	no	—
60	#125×C₇₉	—	2	4	no	—
61	#125×C₇₉	D₄	1	2	yes	—
62	#124×C₇₉	—	2	2	no	—
63	#124×C₇₉	—	2	2	no	—
64	#124×C₇₉	D₄	1	2	yes	—
65	#123×C₇₉	—	2	4	no	—
66	#123×C₇₉	—	2	4	no	—
67	C₂²⋊Q₈×C₇₉	—	2	4	no	—
68	C₂²⋊Q₈×C₇₉	—	2	1	no	—
69	C₂²⋊Q₈×C₇₉	—	2	1	no	—
70	C₂²⋊Q₈×C₇₉	—	2	2	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	#121×C₇₉	—	2	1	no	—
73	#121×C₇₉	—	2	1	no	—
74	C₄×Q₈×C₇₉	—	2	2	no	—
75	C₄×Q₈×C₇₉	—	2	2	no	—
76	C₄×Q₈×C₇₉	—	2	1	no	—
77	C₄×Q₈×C₇₉	—	2	1	no	—
78	C₄×Q₈×C₇₉	—	2	1	no	—
79	C₄×Q₈×C₇₉	—	2	1	no	—
80	C₄×Q₈×C₇₉	—	2	1	no	—
81	C₄×Q₈×C₇₉	—	2	1	no	—
82	C₄×D₄×C₇₉	—	2	2	no	—
83	C₄×D₄×C₇₉	—	2	2	no	—
84	C₄×D₄×C₇₉	—	2	4	no	—
85	C₄×D₄×C₇₉	—	2	1	no	—
86	C₄×D₄×C₇₉	—	2	1	no	—
87	#117×C₇₉	—	2	4	no	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
94	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	D₄	1	2	yes	—
98	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	#107×C₇₉	—	2	4	no	—
101	#106×C₇₉	—	2	4	no	—
102	#104×C₇₉	—	2	8	no	—
103	#103×C₇₉	—	2	4	no	—
104	#102×C₇₉	—	2	4	no	—
105	#101×C₇₉	—	2	4	no	—
106	#97×C₇₉	—	2	1	no	—
107	#97×C₇₉	—	2	1	no	—
108	C₄×C₈×C₇₉	—	2	1	no	—
109	C₄×C₈×C₇₉	—	2	1	no	—
110	#95×C₇₉	—	2	1	no	—
111	#95×C₇₉	—	2	4	no	—
112	#41×C₇₉	—	2	4	no	—
113	#41×C₇₉	—	2	4	no	—
114	C₂×Q₈×C₇₉	—	2	1	no	—
115	C₂×Q₈×C₇₉	—	2	1	no	—
116	C₂×Q₈×C₇₉	—	2	1	no	—
117	C₂×Q₈×C₇₉	—	2	1	no	—
118	C₂×Q₈×C₇₉	—	2	2	no	—
119	C₂×Q₈×C₇₉	—	2	2	no	—
120	C₂×Q₈×C₇₉	—	4	1	no	—
121	C₂×Q₈×C₇₉	—	4	1	no	—
122	C₂×Q₈×C₇₉	—	8	2	no	—
123	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	1	no	—
126	C₂×D₄×C₇₉	—	2	1	no	—
127	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	4	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₇₉	—	2	2	no	—
138	M₁₆×C₇₉	—	2	2	no	—
139	M₁₆×C₇₉	—	2	2	no	—
140	M₁₆×C₇₉	#41	1	4	yes	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	—	2	4	no	—
144	C₄⋊C₄×C₇₉	—	2	4	no	—
145	C₄⋊C₄×C₇₉	—	2	4	no	—
146	C₄⋊C₄×C₇₉	—	2	4	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	2	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	1	no	—
155	C₄⋊C₄×C₇₉	—	2	1	no	—
156	C₄⋊C₄×C₇₉	—	2	1	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	4	1	no	—
160	C₄⋊C₄×C₇₉	—	4	1	no	—
161	C₄⋊C₄×C₇₉	—	8	4	no	—
162	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₇₉	—	2	4	no	—
165	C₂²⋊C₄×C₇₉	—	2	4	no	—
166	C₂²⋊C₄×C₇₉	—	2	4	no	—
167	C₂²⋊C₄×C₇₉	—	2	2	no	—
168	C₂²⋊C₄×C₇₉	—	2	2	no	—
169	C₂²⋊C₄×C₇₉	—	2	2	no	—
170	C₄²×C₇₉	—	2	4	no	—
171	C₄²×C₇₉	—	2	2	no	—
172	C₄²×C₇₉	—	2	2	no	—
173	C₄²×C₇₉	—	2	2	no	—
174	C₄²×C₇₉	—	2	4	no	—
175	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂³×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₇₉	—	2	4	no	—
182	Q₈×C₇₉	—	4	2	no	—
183	Q₈×C₇₉	—	4	2	no	—
184	Q₈×C₇₉	—	4	2	no	—
185	Q₈×C₇₉	—	8	1	no	—
186	Q₈×C₇₉	—	8	2	no	—
187	Q₈×C₇₉	—	8	2	no	—
188	D₄×C₇₉	—	2	4	no	—
189	D₄×C₇₉	—	4	2	no	—
190	D₄×C₇₉	—	4	2	no	—
191	D₄×C₇₉	—	4	2	no	—
192	D₄×C₇₉	—	8	1	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	4	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	2	no	—
202	C₂×C₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	4	2	no	—
204	C₂×C₄×C₇₉	—	4	2	no	—
205	C₂×C₄×C₇₉	—	4	4	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	4	4	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	8	4	no	—
210	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
217	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
218	C₈×C₇₉	—	2	4	no	—
219	C₈×C₇₉	—	4	2	no	—
220	C₂²×C₇₉	—	2	1	no	—
221	C₂²×C₇₉	—	2	1	no	—
222	C₂²×C₇₉	—	4	2	no	—
223	C₂²×C₇₉	—	4	2	no	—
224	C₂²×C₇₉	—	4	2	no	—
225	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
226	C₂²×C₇₉	#532	1	1	yes	characteristic
227	C₂²×C₇₉	#536	1	1	yes	characteristic
228	C₄×C₇₉	—	2	1	no	—
229	C₄×C₇₉	—	2	1	no	—
230	C₄×C₇₉	—	2	1	no	—
231	C₄×C₇₉	—	4	4	no	—
232	C₄×C₇₉	—	4	2	no	—
233	C₄×C₇₉	—	4	2	no	—
234	C₄×C₇₉	—	4	2	no	—
235	C₄×C₇₉	—	4	2	no	—
236	C₄×C₇₉	—	4	2	no	—
237	C₄×C₇₉	—	8	2	no	—
238	C₄×C₇₉	#456	1	2	yes	—
239	C₄×C₇₉	#547	1	2	yes	—
240	C₄×C₇₉	#548	1	2	yes	—
241	#25695	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₇₉	—	2	1	no	—
243	C₂×C₇₉	—	2	1	no	—
244	C₂×C₇₉	—	8	2	no	—
245	C₂×C₇₉	#2432	1	1	yes	characteristic
246	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
247	C₂×C₇₉	#3021	1	1	yes	characteristic
248	#3507	C₂×C₇₉	1	1	yes	characteristic
249	#3165	C₂×C₇₉	1	1	yes	characteristic, complemented
250	#3141	C₂×C₇₉	1	1	yes	characteristic
251	#2567	C₂×C₇₉	1	1	yes	characteristic, complemented
252	#2038	C₂×C₇₉	1	4	yes	complemented
253	#1986	C₂×C₇₉	1	1	yes	characteristic, complemented
254	#1980	C₂×C₇₉	1	1	yes	characteristic
255	#1859	C₂×C₇₉	1	4	yes	complemented
256	C₄×#101	C₂×C₇₉	1	1	yes	characteristic, complemented
257	C₇₉	#25695	1	1	yes	characteristic, direct product factor, Sylow
258	#559	—	2	1	no	—
259	#557	—	2	1	no	—
260	#556	—	2	1	no	—
261	#556	—	2	2	no	—
262	#554	—	2	1	no	—
263	#552	—	2	2	no	—
264	#539	—	2	2	no	—
265	#536	C₂²×C₇₉	1	2	yes	—
266	#533	C₂²×C₇₉	1	1	yes	characteristic
267	#532	C₂²×C₇₉	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
269	#529	—	2	2	no	—
270	#520	C₂²×C₇₉	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
272	#501	—	2	2	no	—
273	#500	—	2	1	no	—
274	#498	—	2	1	no	—
275	#489	—	2	2	no	—
276	#487	—	2	1	no	—
277	#486	—	2	1	no	—
278	#428	C₂²×C₇₉	1	4	yes	—
279	C₂×#104	C₂²×C₇₉	1	4	yes	—
280	#417	C₂²×C₇₉	1	4	yes	—
281	C₂×#101	C₂²×C₇₉	1	2	yes	—
282	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
283	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
284	#395	—	2	2	no	—
285	#391	C₂²×C₇₉	1	2	yes	—
286	#389	—	2	2	no	—
287	#384	C₂²×C₇₉	1	2	yes	—
288	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
289	#343	C₂²×C₇₉	1	2	yes	—
290	#339	C₂²×C₇₉	1	4	yes	—
291	C₂×#41	C₂³×C₇₉	1	2	yes	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
294	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
295	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
302	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
303	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
304	#127	D₄×C₇₉	1	1	yes	characteristic
305	#126	—	2	4	no	—
306	#126	—	2	4	no	—
307	#125	—	2	2	no	—
308	#125	—	2	4	no	—
309	#125	D₄×C₇₉	1	2	yes	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#124	D₄×C₇₉	1	2	yes	—
313	#123	—	2	4	no	—
314	#123	—	2	4	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	#117	—	2	4	no	—
336	#117	—	2	2	no	—
337	#117	C₂³×C₇₉	1	2	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	4	no	—
342	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₇₉	1	2	yes	—
346	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
347	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
348	#107	—	2	4	no	—
349	#106	—	2	4	no	—
350	#104	—	2	8	no	—
351	#103	—	2	4	no	—
352	#102	—	2	4	no	—
353	#101	—	2	4	no	—
354	#97	—	2	1	no	—
355	#97	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	1	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	—	8	2	no	—
371	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	#41×C₇₉	1	4	yes	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	8	4	no	—
410	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	4	no	—
423	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
427	C₂³	—	2	2	no	—
428	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	8	1	no	—
434	Q₈	—	8	2	no	—
435	Q₈	—	8	2	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	8	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	4	no	—
458	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
459	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
460	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
461	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
465	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
474	C₂²	#532×C₇₉	1	1	yes	characteristic
475	C₂²	#536×C₇₉	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	4	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	2	no	—
486	C₄	#456×C₇₉	1	2	yes	—
487	C₄	#547×C₇₉	1	2	yes	—
488	C₄	#548×C₇₉	1	2	yes	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	8	2	no	—
492	C₂	C₇₉×#2432	1	1	yes	characteristic
493	C₂	C₂×#456×C₇₉	1	1	yes	characteristic
494	C₂	C₇₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	#532×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3165	C₂	semidirect
4. C₇₉×#2567	C₂	semidirect
5. C₇₉×#2038	C₂	semidirect
6. C₇₉×#1986	C₂	semidirect
8. C₇₉×#1859	C₂	semidirect
9. C₄×#101×C₇₉	C₂	semidirect
241. #25695	C₇₉	direct (N × H)
249. #3165	C₂×C₇₉	semidirect
251. #2567	C₂×C₇₉	semidirect
252. #2038	C₂×C₇₉	semidirect
253. #1986	C₂×C₇₉	semidirect
255. #1859	C₂×C₇₉	semidirect
256. C₄×#101	C₂×C₇₉	semidirect
257. C₇₉	#25695	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×#3507	2
C₇₉×#3165	2
C₇₉×#3141	2
C₇₉×#2567	2
C₇₉×#2038	2
C₇₉×#1986	2
C₇₉×#1980	2
C₇₉×#1859	2
C₄×#101×C₇₉	2
#25695	79

Subgroups — C79×#25695 #34137384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25695 #34137384