Subgroups — C₇₉×#25693 #34137382

Order 20224.

1038 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3506	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, complemented
4	C₇₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2037	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, complemented
8	C₇₉×#1860	C₂	1	4	yes	maximal, complemented
9	C₄×#100×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#559×C₇₉	—	2	2	no	—
11	#556×C₇₉	—	2	1	no	—
12	#555×C₇₉	—	2	1	no	—
13	#553×C₇₉	—	2	2	no	—
14	#550×C₇₉	—	2	1	no	—
15	#547×C₇₉	—	2	1	no	—
16	#538×C₇₉	—	2	2	no	—
17	#535×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	#525×C₇₉	—	2	2	no	—
22	#520×C₇₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×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×#100×C₇₉	C₂²	1	2	yes	—
34	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
36	#393×C₇₉	—	2	2	no	—
37	#390×C₇₉	C₂²	1	2	yes	—
38	#382×C₇₉	C₂²	1	2	yes	—
39	#380×C₇₉	—	2	2	no	—
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	—	2	2	no	—
44	C₂×#41×C₇₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇₉	D₄	1	2	yes	—
48	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
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	—	2	1	no	—
54	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
57	#127×C₇₉	—	2	2	no	—
58	#127×C₇₉	D₄	1	1	yes	characteristic
59	#126×C₇₉	—	2	4	no	—
60	#125×C₇₉	D₄	1	2	yes	—
61	#124×C₇₉	—	2	4	no	—
62	#124×C₇₉	—	2	2	no	—
63	#124×C₇₉	D₄	1	2	yes	—
64	#123×C₇₉	—	2	4	no	—
65	#123×C₇₉	—	2	4	no	—
66	C₂²⋊Q₈×C₇₉	—	2	2	no	—
67	C₂²⋊Q₈×C₇₉	—	2	1	no	—
68	C₂²⋊Q₈×C₇₉	—	2	1	no	—
69	#121×C₇₉	—	2	2	no	—
70	#121×C₇₉	—	2	4	no	—
71	#121×C₇₉	—	2	1	no	—
72	#121×C₇₉	—	2	1	no	—
73	#121×C₇₉	—	2	2	no	—
74	#121×C₇₉	—	2	2	no	—
75	#120×C₇₉	—	2	4	no	—
76	C₄×Q₈×C₇₉	—	2	2	no	—
77	C₄×Q₈×C₇₉	—	2	1	no	—
78	C₄×Q₈×C₇₉	—	2	1	no	—
79	C₄×D₄×C₇₉	—	2	4	no	—
80	C₄×D₄×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	—	2	4	no	—
82	C₄×D₄×C₇₉	—	2	1	no	—
83	C₄×D₄×C₇₉	—	2	1	no	—
84	C₄×D₄×C₇₉	—	2	1	no	—
85	C₄×D₄×C₇₉	—	2	1	no	—
86	C₄×D₄×C₇₉	—	2	1	no	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	—	2	2	no	—
90	#117×C₇₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
97	C₂×C₂²⋊C₄×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	#100×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	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
113	#41×C₇₉	—	2	4	no	—
114	#41×C₇₉	—	2	4	no	—
115	#41×C₇₉	—	8	4	no	—
116	C₂×Q₈×C₇₉	—	2	1	no	—
117	C₂×Q₈×C₇₉	—	2	1	no	—
118	C₂×Q₈×C₇₉	—	4	1	no	—
119	C₂×Q₈×C₇₉	—	4	1	no	—
120	C₂×Q₈×C₇₉	—	8	2	no	—
121	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	—	2	4	no	—
124	C₂×D₄×C₇₉	—	2	4	no	—
125	C₂×D₄×C₇₉	—	2	1	no	—
126	C₂×D₄×C₇₉	—	2	1	no	—
127	C₂×D₄×C₇₉	—	2	1	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₉	—	2	4	no	—
133	C₂²×C₄×C₇₉	—	2	2	no	—
134	C₂²×C₄×C₇₉	—	2	2	no	—
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	—	4	4	no	—
139	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
143	M₁₆×C₇₉	—	2	2	no	—
144	M₁₆×C₇₉	—	2	2	no	—
145	M₁₆×C₇₉	—	2	2	no	—
146	M₁₆×C₇₉	#41	1	4	yes	complemented
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	4	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	1	no	—
156	C₄⋊C₄×C₇₉	—	2	1	no	—
157	C₄⋊C₄×C₇₉	—	2	1	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	4	2	no	—
161	C₄⋊C₄×C₇₉	—	4	1	no	—
162	C₄⋊C₄×C₇₉	—	4	1	no	—
163	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₇₉	—	2	4	no	—
166	C₂²⋊C₄×C₇₉	—	2	4	no	—
167	C₂²⋊C₄×C₇₉	—	2	4	no	—
168	C₂²⋊C₄×C₇₉	—	2	2	no	—
169	C₂²⋊C₄×C₇₉	—	2	2	no	—
170	C₂²⋊C₄×C₇₉	—	2	2	no	—
171	C₂²⋊C₄×C₇₉	—	2	2	no	—
172	C₂²⋊C₄×C₇₉	—	2	2	no	—
173	C₂²⋊C₄×C₇₉	—	8	4	no	—
174	C₄²×C₇₉	—	2	4	no	—
175	C₄²×C₇₉	—	2	2	no	—
176	C₄²×C₇₉	—	2	4	no	—
177	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₇₉	—	2	2	no	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	2	2	no	—
184	C₂³×C₇₉	—	2	2	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	4	2	no	—
187	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₇₉	—	2	4	no	—
189	Q₈×C₇₉	—	4	2	no	—
190	Q₈×C₇₉	—	8	1	no	—
191	Q₈×C₇₉	—	8	2	no	—
192	Q₈×C₇₉	—	8	2	no	—
193	D₄×C₇₉	—	2	4	no	—
194	D₄×C₇₉	—	4	2	no	—
195	D₄×C₇₉	—	4	2	no	—
196	D₄×C₇₉	—	4	2	no	—
197	D₄×C₇₉	—	4	2	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	8	1	no	—
200	D₄×C₇₉	—	8	4	no	—
201	D₄×C₇₉	—	8	4	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	2	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	4	no	—
209	C₂×C₄×C₇₉	—	4	4	no	—
210	C₂×C₄×C₇₉	—	4	2	no	—
211	C₂×C₄×C₇₉	—	4	2	no	—
212	C₂×C₄×C₇₉	—	4	4	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	—	4	2	no	—
215	C₂×C₄×C₇₉	—	4	2	no	—
216	C₂×C₄×C₇₉	—	8	2	no	—
217	C₂×C₄×C₇₉	—	8	4	no	—
218	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
219	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
226	C₈×C₇₉	—	2	4	no	—
227	C₈×C₇₉	—	4	2	no	—
228	C₂²×C₇₉	—	2	1	no	—
229	C₂²×C₇₉	—	2	1	no	—
230	C₂²×C₇₉	—	4	4	no	—
231	C₂²×C₇₉	—	4	2	no	—
232	C₂²×C₇₉	—	4	2	no	—
233	C₂²×C₇₉	—	4	2	no	—
234	C₂²×C₇₉	—	4	2	no	—
235	C₂²×C₇₉	—	4	2	no	—
236	C₂²×C₇₉	—	4	2	no	—
237	C₂²×C₇₉	—	8	2	no	—
238	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
239	C₂²×C₇₉	#532	1	1	yes	characteristic
240	C₂²×C₇₉	#536	1	1	yes	characteristic
241	C₄×C₇₉	—	2	1	no	—
242	C₄×C₇₉	—	2	1	no	—
243	C₄×C₇₉	—	2	1	no	—
244	C₄×C₇₉	—	4	2	no	—
245	C₄×C₇₉	—	4	2	no	—
246	C₄×C₇₉	—	4	2	no	—
247	C₄×C₇₉	—	4	2	no	—
248	C₄×C₇₉	—	8	2	no	—
249	C₄×C₇₉	—	8	2	no	—
250	C₄×C₇₉	#455	1	2	yes	—
251	C₄×C₇₉	#547	1	2	yes	—
252	C₄×C₇₉	#548	1	2	yes	—
253	#25693	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₉	—	2	1	no	—
255	C₂×C₇₉	—	2	1	no	—
256	C₂×C₇₉	—	8	2	no	—
257	C₂×C₇₉	—	8	2	no	—
258	C₂×C₇₉	#2432	1	1	yes	characteristic
259	C₂×C₇₉	C₂×#455	1	1	yes	characteristic
260	C₂×C₇₉	#3021	1	1	yes	characteristic
261	#3506	C₂×C₇₉	1	1	yes	characteristic
262	#3165	C₂×C₇₉	1	1	yes	characteristic, complemented
263	#3141	C₂×C₇₉	1	1	yes	characteristic, complemented
264	#2563	C₂×C₇₉	1	1	yes	characteristic, complemented
265	#2037	C₂×C₇₉	1	4	yes	complemented
266	#1986	C₂×C₇₉	1	1	yes	characteristic, complemented
267	#1980	C₂×C₇₉	1	1	yes	characteristic, complemented
268	#1860	C₂×C₇₉	1	4	yes	complemented
269	C₄×#100	C₂×C₇₉	1	1	yes	characteristic, complemented
270	C₇₉	#25693	1	1	yes	characteristic, direct product factor, Sylow
271	#559	—	2	2	no	—
272	#556	—	2	1	no	—
273	#555	—	2	1	no	—
274	#553	—	2	2	no	—
275	#550	—	2	1	no	—
276	#547	—	2	1	no	—
277	#538	—	2	2	no	—
278	#535	C₂²×C₇₉	1	2	yes	—
279	#533	C₂²×C₇₉	1	1	yes	characteristic
280	#532	C₂²×C₇₉	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
282	#525	—	2	2	no	—
283	#520	C₂²×C₇₉	1	2	yes	—
284	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
285	#501	—	2	2	no	—
286	#500	—	2	1	no	—
287	#498	—	2	1	no	—
288	#489	—	2	2	no	—
289	#487	—	2	1	no	—
290	#486	—	2	1	no	—
291	#428	C₂²×C₇₉	1	4	yes	—
292	C₂×#104	C₂²×C₇₉	1	4	yes	—
293	#417	C₂²×C₇₉	1	4	yes	—
294	C₂×#100	C₂²×C₇₉	1	2	yes	—
295	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
296	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
297	#393	—	2	2	no	—
298	#390	C₂²×C₇₉	1	2	yes	—
299	#382	C₂²×C₇₉	1	2	yes	—
300	#380	—	2	2	no	—
301	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
302	#343	C₂²×C₇₉	1	2	yes	—
303	#339	C₂²×C₇₉	1	4	yes	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	C₂³×C₇₉	1	2	yes	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₇₉	1	2	yes	—
309	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
310	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
316	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
317	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
318	#127	—	2	2	no	—
319	#127	D₄×C₇₉	1	1	yes	characteristic
320	#126	—	2	4	no	—
321	#125	D₄×C₇₉	1	2	yes	—
322	#124	—	2	4	no	—
323	#124	—	2	2	no	—
324	#124	D₄×C₇₉	1	2	yes	—
325	#123	—	2	4	no	—
326	#123	—	2	4	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	#121	—	2	2	no	—
331	#121	—	2	4	no	—
332	#121	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	#120	—	2	4	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	C₂³×C₇₉	1	2	yes	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
359	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
360	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
361	#107	—	2	4	no	—
362	#106	—	2	4	no	—
363	#104	—	2	8	no	—
364	#103	—	2	4	no	—
365	#102	—	2	4	no	—
366	#100	—	2	4	no	—
367	#97	—	2	1	no	—
368	#97	—	2	1	no	—
369	C₄×C₈	—	2	1	no	—
370	C₄×C₈	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	4	no	—
373	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	#41	—	8	4	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂×Q₈	—	8	2	no	—
382	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	#41×C₇₉	1	4	yes	complemented
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
425	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	8	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	4	no	—
438	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
449	Q₈	—	2	4	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	8	1	no	—
452	Q₈	—	8	2	no	—
453	Q₈	—	8	2	no	—
454	D₄	—	2	4	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	8	1	no	—
461	D₄	—	8	4	no	—
462	D₄	—	8	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
480	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
481	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
482	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
486	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
487	C₈	—	2	4	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
500	C₂²	#532×C₇₉	1	1	yes	characteristic
501	C₂²	#536×C₇₉	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	2	no	—
511	C₄	#455×C₇₉	1	2	yes	—
512	C₄	#547×C₇₉	1	2	yes	—
513	C₄	#548×C₇₉	1	2	yes	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	8	2	no	—
517	C₂	—	8	2	no	—
518	C₂	C₇₉×#2432	1	1	yes	characteristic
519	C₂	C₂×#455×C₇₉	1	1	yes	characteristic
520	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	C₇₉×#3506	C₂
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
3. C₇₉×#3141	C₂	semidirect
4. C₇₉×#2563	C₂	semidirect
5. C₇₉×#2037	C₂	semidirect
6. C₇₉×#1986	C₂	semidirect
7. C₇₉×#1980	C₂	semidirect
8. C₇₉×#1860	C₂	semidirect
9. C₄×#100×C₇₉	C₂	semidirect
146. M₁₆×C₇₉	#41	semidirect
253. #25693	C₇₉	direct (N × H)
262. #3165	C₂×C₇₉	semidirect
263. #3141	C₂×C₇₉	semidirect
264. #2563	C₂×C₇₉	semidirect
265. #2037	C₂×C₇₉	semidirect
266. #1986	C₂×C₇₉	semidirect
267. #1980	C₂×C₇₉	semidirect
268. #1860	C₂×C₇₉	semidirect
269. C₄×#100	C₂×C₇₉	semidirect
270. C₇₉	#25693	direct (N × H)
407. M₁₆	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3506	2
C₇₉×#3165	2
C₇₉×#3141	2
C₇₉×#2563	2
C₇₉×#2037	2
C₇₉×#1986	2
C₇₉×#1980	2
C₇₉×#1860	2
C₄×#100×C₇₉	2
#25693	79

Subgroups — C79×#25693 #34137382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25693 #34137382