Subgroups — C₇₉×#25689 #34137378

Order 20224.

988 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3510	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3080	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2038	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2037	C₂	1	2	yes	maximal
7	C₇₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1967	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1857	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1856	C₂	1	2	yes	maximal, complemented
11	C₄×#104×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₉	—	2	2	no	—
13	#556×C₇₉	—	2	2	no	—
14	#551×C₇₉	—	2	4	no	—
15	#542×C₇₉	—	2	2	no	—
16	#536×C₇₉	C₂²	1	1	yes	characteristic
17	#535×C₇₉	C₂²	1	1	yes	characteristic
18	#533×C₇₉	C₂²	1	1	yes	characteristic
19	#529×C₇₉	—	2	2	no	—
20	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
22	#519×C₇₉	C₂²	1	1	yes	characteristic
23	#518×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
25	#501×C₇₉	—	2	2	no	—
26	#499×C₇₉	—	2	2	no	—
27	#479×C₇₉	—	2	2	no	—
28	#478×C₇₉	—	2	2	no	—
29	#428×C₇₉	C₂²	1	2	yes	—
30	#428×C₇₉	C₂²	1	2	yes	—
31	#428×C₇₉	C₂²	1	2	yes	—
32	#423×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#104×C₇₉	C₂²	1	2	yes	—
34	#417×C₇₉	C₂²	1	2	yes	—
35	C₂×#101×C₇₉	C₂²	1	2	yes	—
36	C₂×#100×C₇₉	C₂²	1	2	yes	—
37	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
38	#391×C₇₉	C₂²	1	2	yes	—
39	#390×C₇₉	C₂²	1	2	yes	—
40	#388×C₇₉	—	2	4	no	—
41	C₄³×C₇₉	C₂²	1	1	yes	characteristic
42	#339×C₇₉	C₂²	1	2	yes	—
43	#339×C₇₉	C₂²	1	2	yes	—
44	#339×C₇₉	C₂²	1	2	yes	—
45	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
52	#127×C₇₉	—	2	1	no	—
53	#126×C₇₉	—	2	4	no	—
54	#126×C₇₉	—	2	4	no	—
55	#125×C₇₉	—	2	2	no	—
56	#125×C₇₉	—	2	1	no	—
57	#125×C₇₉	—	2	1	no	—
58	#125×C₇₉	D₄	1	2	yes	—
59	#124×C₇₉	—	2	4	no	—
60	#124×C₇₉	—	2	1	no	—
61	#124×C₇₉	—	2	1	no	—
62	#124×C₇₉	—	2	1	no	—
63	#124×C₇₉	—	2	1	no	—
64	#124×C₇₉	—	2	2	no	—
65	#123×C₇₉	—	2	4	no	—
66	#123×C₇₉	—	2	4	no	—
67	#123×C₇₉	—	2	2	no	—
68	C₂²⋊Q₈×C₇₉	—	2	4	no	—
69	C₂²⋊Q₈×C₇₉	—	2	2	no	—
70	C₂²⋊Q₈×C₇₉	—	2	2	no	—
71	#121×C₇₉	—	2	2	no	—
72	#120×C₇₉	—	2	2	no	—
73	C₄×Q₈×C₇₉	—	2	2	no	—
74	C₄×Q₈×C₇₉	—	2	2	no	—
75	C₄×Q₈×C₇₉	—	2	2	no	—
76	C₄×Q₈×C₇₉	D₄	1	2	yes	—
77	C₄×D₄×C₇₉	—	2	4	no	—
78	C₄×D₄×C₇₉	—	2	2	no	—
79	C₄×D₄×C₇₉	—	2	2	no	—
80	C₄×D₄×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	D₄	1	2	yes	—
82	#117×C₇₉	—	2	4	no	—
83	#117×C₇₉	—	2	2	no	—
84	#117×C₇₉	—	2	1	no	—
85	#117×C₇₉	C₂³	1	1	yes	characteristic
86	#117×C₇₉	C₂³	1	1	yes	characteristic
87	#117×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₇₉	D₄	1	4	yes	—
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	—	2	2	no	—
95	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
97	#107×C₇₉	—	2	2	no	—
98	#107×C₇₉	—	2	2	no	—
99	#107×C₇₉	—	2	2	no	—
100	#106×C₇₉	—	2	2	no	—
101	#106×C₇₉	—	2	2	no	—
102	#106×C₇₉	—	2	2	no	—
103	C₄⋊C₈×C₇₉	—	2	2	no	—
104	#104×C₇₉	—	2	4	no	—
105	#103×C₇₉	—	2	2	no	—
106	#102×C₇₉	—	2	2	no	—
107	#101×C₇₉	—	2	4	no	—
108	#100×C₇₉	—	2	4	no	—
109	#97×C₇₉	—	2	1	no	—
110	C₄×C₈×C₇₉	—	2	1	no	—
111	#95×C₇₉	—	2	4	no	—
112	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
113	#41×C₇₉	—	2	2	no	—
114	#41×C₇₉	—	2	2	no	—
115	C₂×Q₈×C₇₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₇₉	—	2	1	no	—
122	C₂×D₄×C₇₉	—	2	4	no	—
123	C₂×D₄×C₇₉	—	2	1	no	—
124	C₂×D₄×C₇₉	—	2	1	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	4	no	—
130	C₂²×C₄×C₇₉	—	2	1	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	2	2	no	—
133	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₇₉	—	2	2	no	—
137	M₁₆×C₇₉	—	2	2	no	—
138	M₁₆×C₇₉	—	2	2	no	—
139	M₁₆×C₇₉	#41	1	4	yes	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₄⋊C₄×C₇₉	—	2	4	no	—
143	C₄⋊C₄×C₇₉	—	2	4	no	—
144	C₄⋊C₄×C₇₉	—	2	2	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	2	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	—	4	2	no	—
151	C₄⋊C₄×C₇₉	—	4	2	no	—
152	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₇₉	—	2	4	no	—
156	C₂²⋊C₄×C₇₉	—	2	4	no	—
157	C₂²⋊C₄×C₇₉	—	2	4	no	—
158	C₂²⋊C₄×C₇₉	—	2	1	no	—
159	C₂²⋊C₄×C₇₉	—	2	1	no	—
160	C₂²⋊C₄×C₇₉	—	2	1	no	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	2	4	no	—
163	C₂²⋊C₄×C₇₉	—	2	2	no	—
164	C₂²⋊C₄×C₇₉	—	4	8	no	—
165	C₄²×C₇₉	—	2	4	no	—
166	C₄²×C₇₉	—	2	2	no	—
167	C₄²×C₇₉	—	2	1	no	—
168	C₄²×C₇₉	—	2	1	no	—
169	C₄²×C₇₉	—	2	1	no	—
170	C₄²×C₇₉	—	2	2	no	—
171	C₄²×C₇₉	—	2	2	no	—
172	C₄²×C₇₉	—	4	4	no	—
173	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₇₉	C₂×D₄	1	2	yes	—
176	C₂³×C₇₉	—	2	2	no	—
177	C₂³×C₇₉	—	2	1	no	—
178	C₂³×C₇₉	—	2	4	no	—
179	C₂³×C₇₉	—	4	4	no	—
180	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₇₉	—	2	1	no	—
182	Q₈×C₇₉	—	2	1	no	—
183	Q₈×C₇₉	—	4	1	no	—
184	Q₈×C₇₉	—	4	1	no	—
185	Q₈×C₇₉	—	4	2	no	—
186	Q₈×C₇₉	—	8	2	no	—
187	D₄×C₇₉	—	2	1	no	—
188	D₄×C₇₉	—	2	1	no	—
189	D₄×C₇₉	—	4	2	no	—
190	D₄×C₇₉	—	4	1	no	—
191	D₄×C₇₉	—	4	1	no	—
192	D₄×C₇₉	—	4	2	no	—
193	D₄×C₇₉	—	8	4	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	1	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	4	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	2	no	—
205	C₂×C₄×C₇₉	—	4	4	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	8	2	no	—
208	C₂×C₄×C₇₉	—	8	4	no	—
209	C₂×C₄×C₇₉	#120	1	2	yes	—
210	C₂×C₄×C₇₉	#120	1	2	yes	—
211	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
215	C₈×C₇₉	—	2	4	no	—
216	C₈×C₇₉	—	4	2	no	—
217	C₂²×C₇₉	—	2	2	no	—
218	C₂²×C₇₉	—	4	1	no	—
219	C₂²×C₇₉	—	4	2	no	—
220	C₂²×C₇₉	—	4	2	no	—
221	C₂²×C₇₉	—	4	4	no	—
222	C₂²×C₇₉	—	8	4	no	—
223	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
224	C₂²×C₇₉	#547	1	2	yes	—
225	C₄×C₇₉	—	2	2	no	—
226	C₄×C₇₉	—	2	2	no	—
227	C₄×C₇₉	—	4	4	no	—
228	C₄×C₇₉	—	4	2	no	—
229	C₄×C₇₉	—	4	1	no	—
230	C₄×C₇₉	—	4	2	no	—
231	C₄×C₇₉	—	4	2	no	—
232	C₄×C₇₉	—	4	2	no	—
233	C₄×C₇₉	—	8	2	no	—
234	C₄×C₇₉	#532	1	1	yes	characteristic
235	C₄×C₇₉	#536	1	1	yes	characteristic
236	C₄×C₇₉	#548	1	2	yes	—
237	#25689	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂×C₇₉	—	2	2	no	—
239	C₂×C₇₉	—	8	1	no	—
240	C₂×C₇₉	—	8	2	no	—
241	C₂×C₇₉	#2432	1	1	yes	characteristic
242	C₂×C₇₉	#3018	1	2	yes	—
243	#3510	C₂×C₇₉	1	1	yes	characteristic
244	#3166	C₂×C₇₉	1	1	yes	characteristic, complemented
245	#3080	C₂×C₇₉	1	1	yes	characteristic, complemented
246	#2861	C₂×C₇₉	1	1	yes	characteristic, complemented
247	#2038	C₂×C₇₉	1	2	yes	complemented
248	#2037	C₂×C₇₉	1	2	yes	—
249	#1994	C₂×C₇₉	1	1	yes	characteristic, complemented
250	#1967	C₂×C₇₉	1	1	yes	characteristic, complemented
251	#1857	C₂×C₇₉	1	2	yes	complemented
252	#1856	C₂×C₇₉	1	2	yes	complemented
253	C₄×#104	C₂×C₇₉	1	1	yes	characteristic, complemented
254	C₇₉	#25689	1	1	yes	characteristic, direct product factor, Sylow
255	#559	—	2	2	no	—
256	#556	—	2	2	no	—
257	#551	—	2	4	no	—
258	#542	—	2	2	no	—
259	#536	C₂²×C₇₉	1	1	yes	characteristic
260	#535	C₂²×C₇₉	1	1	yes	characteristic
261	#533	C₂²×C₇₉	1	1	yes	characteristic
262	#529	—	2	2	no	—
263	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
264	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
265	#519	C₂²×C₇₉	1	1	yes	characteristic
266	#518	C₂²×C₇₉	1	1	yes	characteristic
267	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
268	#501	—	2	2	no	—
269	#499	—	2	2	no	—
270	#479	—	2	2	no	—
271	#478	—	2	2	no	—
272	#428	C₂²×C₇₉	1	2	yes	—
273	#428	C₂²×C₇₉	1	2	yes	—
274	#428	C₂²×C₇₉	1	2	yes	—
275	#423	C₂²×C₇₉	1	1	yes	characteristic
276	C₂×#104	C₂²×C₇₉	1	2	yes	—
277	#417	C₂²×C₇₉	1	2	yes	—
278	C₂×#101	C₂²×C₇₉	1	2	yes	—
279	C₂×#100	C₂²×C₇₉	1	2	yes	—
280	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
281	#391	C₂²×C₇₉	1	2	yes	—
282	#390	C₂²×C₇₉	1	2	yes	—
283	#388	—	2	4	no	—
284	C₄³	C₂²×C₇₉	1	1	yes	characteristic
285	#339	C₂²×C₇₉	1	2	yes	—
286	#339	C₂²×C₇₉	1	2	yes	—
287	#339	C₂²×C₇₉	1	2	yes	—
288	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
292	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
295	#127	—	2	1	no	—
296	#126	—	2	4	no	—
297	#126	—	2	4	no	—
298	#125	—	2	2	no	—
299	#125	—	2	1	no	—
300	#125	—	2	1	no	—
301	#125	D₄×C₇₉	1	2	yes	—
302	#124	—	2	4	no	—
303	#124	—	2	1	no	—
304	#124	—	2	1	no	—
305	#124	—	2	1	no	—
306	#124	—	2	1	no	—
307	#124	—	2	2	no	—
308	#123	—	2	4	no	—
309	#123	—	2	4	no	—
310	#123	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	#121	—	2	2	no	—
315	#120	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	D₄×C₇₉	1	2	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₇₉	1	2	yes	—
325	#117	—	2	4	no	—
326	#117	—	2	2	no	—
327	#117	—	2	1	no	—
328	#117	C₂³×C₇₉	1	1	yes	characteristic
329	#117	C₂³×C₇₉	1	1	yes	characteristic
330	#117	C₂³×C₇₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	D₄×C₇₉	1	4	yes	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
339	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	#106	—	2	2	no	—
344	#106	—	2	2	no	—
345	#106	—	2	2	no	—
346	C₄⋊C₈	—	2	2	no	—
347	#104	—	2	4	no	—
348	#103	—	2	2	no	—
349	#102	—	2	2	no	—
350	#101	—	2	4	no	—
351	#100	—	2	4	no	—
352	#97	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	#95	—	2	4	no	—
355	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	#41×C₇₉	1	4	yes	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	4	4	no	—
416	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₇₉	1	2	yes	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
424	Q₈	—	2	1	no	—
425	Q₈	—	2	1	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	8	2	no	—
430	D₄	—	2	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	8	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	#120×C₇₉	1	2	yes	—
453	C₂×C₄	#120×C₇₉	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
457	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	8	4	no	—
466	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
467	C₂²	#547×C₇₉	1	2	yes	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	2	no	—
477	C₄	#532×C₇₉	1	1	yes	characteristic
478	C₄	#536×C₇₉	1	1	yes	characteristic
479	C₄	#548×C₇₉	1	2	yes	—
480	C₂	—	2	2	no	—
481	C₂	—	8	2	no	—
482	C₂	—	8	1	no	—
483	C₂	C₇₉×#2432	1	1	yes	characteristic
484	C₂	C₇₉×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	#535×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×#3166	C₂	semidirect
3. C₇₉×#3080	C₂	semidirect
4. C₇₉×#2861	C₂	semidirect
5. C₇₉×#2038	C₂	semidirect
7. C₇₉×#1994	C₂	semidirect
8. C₇₉×#1967	C₂	semidirect
9. C₇₉×#1857	C₂	semidirect
10. C₇₉×#1856	C₂	semidirect
11. C₄×#104×C₇₉	C₂	semidirect
237. #25689	C₇₉	direct (N × H)
244. #3166	C₂×C₇₉	semidirect
245. #3080	C₂×C₇₉	semidirect
246. #2861	C₂×C₇₉	semidirect
247. #2038	C₂×C₇₉	semidirect
249. #1994	C₂×C₇₉	semidirect
250. #1967	C₂×C₇₉	semidirect
251. #1857	C₂×C₇₉	semidirect
252. #1856	C₂×C₇₉	semidirect
253. C₄×#104	C₂×C₇₉	semidirect
254. C₇₉	#25689	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×#3510	2
C₇₉×#3166	2
C₇₉×#3080	2
C₇₉×#2861	2
C₇₉×#2038	2
C₇₉×#2037	2
C₇₉×#1994	2
C₇₉×#1967	2
C₇₉×#1857	2
C₇₉×#1856	2
C₄×#104×C₇₉	2
#25689	79

Subgroups — C79×#25689 #34137378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25689 #34137378