Subgroups — C₇₉×#18418 #34130107

Order 20224.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3192	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3188	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2656	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1618	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1613	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1600	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1595	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#327×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1471	C₂	1	1	yes	maximal, characteristic, complemented
12	#560×C₇₉	—	2	2	no	—
13	#553×C₇₉	—	2	1	no	—
14	#553×C₇₉	—	2	1	no	—
15	D₄²×C₇₉	—	2	2	no	—
16	D₄²×C₇₉	—	2	1	no	—
17	D₄²×C₇₉	—	2	1	no	—
18	#540×C₇₉	—	2	1	no	—
19	#538×C₇₉	—	2	1	no	—
20	#538×C₇₉	C₂²	1	2	yes	—
21	#535×C₇₉	—	2	1	no	—
22	#534×C₇₉	—	2	1	no	—
23	#534×C₇₉	C₂²	1	2	yes	—
24	#525×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₇₉	—	2	2	no	—
26	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#484×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	#482×C₇₉	—	2	1	no	—
31	#481×C₇₉	—	2	1	no	—
32	#481×C₇₉	C₂²	1	1	yes	characteristic, complemented
33	#481×C₇₉	C₂²	1	2	yes	complemented
34	#469×C₇₉	—	2	2	no	—
35	#466×C₇₉	—	2	1	no	—
36	#465×C₇₉	—	2	1	no	—
37	#450×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	#449×C₇₉	—	2	1	no	—
39	#447×C₇₉	—	2	1	no	—
40	#447×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#447×C₇₉	C₂²	1	2	yes	complemented
42	#407×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#399×C₇₉	—	2	1	no	—
45	#399×C₇₉	C₂²	1	2	yes	complemented
46	#392×C₇₉	—	2	1	no	—
47	#392×C₇₉	C₂²	1	2	yes	complemented
48	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic, complemented
49	#328×C₇₉	C₂²	1	2	yes	complemented
50	#327×C₇₉	C₂²	1	2	yes	complemented
51	#327×C₇₉	C₂²	1	2	yes	complemented
52	#327×C₇₉	C₂²	1	2	yes	complemented
53	#323×C₇₉	C₂²	1	2	yes	complemented
54	#323×C₇₉	C₂²	1	2	yes	complemented
55	C₂×#41×C₇₉	D₄	1	1	yes	characteristic, complemented
56	C₂²×D₄×C₇₉	—	2	2	no	—
57	C₂²×D₄×C₇₉	—	2	1	no	—
58	C₂²×D₄×C₇₉	—	2	1	no	—
59	C₂²×D₄×C₇₉	—	2	2	no	—
60	C₂²×D₄×C₇₉	—	2	1	no	—
61	C₂²×D₄×C₇₉	—	2	2	no	—
62	C₂²×D₄×C₇₉	D₄	1	2	yes	—
63	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic, complemented
65	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇₉	—	2	1	no	—
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×SD₁₆×C₇₉	—	2	1	no	—
69	C₂×D₈×C₇₉	—	2	2	no	—
70	C₂×D₈×C₇₉	—	2	1	no	—
71	C₂×M₁₆×C₇₉	—	2	1	no	—
72	C₂²×C₈×C₇₉	—	2	1	no	—
73	#127×C₇₉	—	2	2	no	—
74	#127×C₇₉	—	2	1	no	—
75	#126×C₇₉	—	2	2	no	—
76	#126×C₇₉	—	2	2	no	—
77	#125×C₇₉	—	2	1	no	—
78	#124×C₇₉	—	2	2	no	—
79	#123×C₇₉	—	2	2	no	—
80	#123×C₇₉	—	2	1	no	—
81	#123×C₇₉	—	2	2	no	—
82	#123×C₇₉	—	2	2	no	—
83	#123×C₇₉	—	2	2	no	—
84	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic, complemented
85	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
86	#121×C₇₉	—	2	2	no	—
87	#121×C₇₉	—	2	1	no	—
88	#121×C₇₉	—	2	1	no	—
89	#121×C₇₉	—	2	2	no	—
90	#121×C₇₉	—	2	2	no	—
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	—	2	2	no	—
93	#121×C₇₉	—	2	1	no	—
94	#121×C₇₉	—	2	1	no	—
95	#121×C₇₉	—	2	1	no	—
96	#121×C₇₉	—	2	1	no	—
97	#121×C₇₉	—	2	1	no	—
98	#121×C₇₉	—	2	1	no	—
99	#121×C₇₉	—	2	2	no	—
100	#121×C₇₉	—	2	1	no	—
101	#121×C₇₉	—	2	1	no	—
102	#121×C₇₉	—	2	1	no	—
103	#121×C₇₉	—	2	1	no	—
104	#121×C₇₉	—	4	8	no	—
105	#121×C₇₉	D₄	1	1	yes	characteristic, complemented
106	#121×C₇₉	D₄	1	2	yes	complemented
107	#121×C₇₉	C₂³	1	2	yes	—
108	#121×C₇₉	C₂³	1	1	yes	characteristic
109	#120×C₇₉	—	2	2	no	—
110	#120×C₇₉	—	2	2	no	—
111	#120×C₇₉	—	2	2	no	—
112	#120×C₇₉	—	2	1	no	—
113	#120×C₇₉	—	2	2	no	—
114	#120×C₇₉	—	2	2	no	—
115	#120×C₇₉	—	2	2	no	—
116	C₄×D₄×C₇₉	—	2	2	no	—
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	—	2	1	no	—
119	C₄×D₄×C₇₉	—	2	1	no	—
120	C₄×D₄×C₇₉	—	2	1	no	—
121	C₄×D₄×C₇₉	—	2	2	no	—
122	#117×C₇₉	—	2	1	no	—
123	#117×C₇₉	D₄	1	1	yes	characteristic, complemented
124	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
125	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
133	#107×C₇₉	—	2	1	no	—
134	#106×C₇₉	—	2	1	no	—
135	#106×C₇₉	—	2	2	no	—
136	#103×C₇₉	—	2	1	no	—
137	#102×C₇₉	—	2	2	no	—
138	#102×C₇₉	—	2	1	no	—
139	#102×C₇₉	—	2	1	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	1	no	—
142	C₂²⋊C₈×C₇₉	—	2	1	no	—
143	C₂²⋊C₈×C₇₉	—	2	1	no	—
144	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
145	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
146	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
147	#95×C₇₉	—	2	1	no	—
148	#95×C₇₉	C₂³	1	2	yes	—
149	C₂⁴×C₇₉	—	2	2	no	—
150	C₂⁴×C₇₉	—	2	1	no	—
151	C₂⁴×C₇₉	—	2	1	no	—
152	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
154	#41×C₇₉	—	8	1	no	—
155	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₇₉	—	2	2	no	—
157	C₂×D₄×C₇₉	—	2	1	no	—
158	C₂×D₄×C₇₉	—	2	1	no	—
159	C₂×D₄×C₇₉	—	2	2	no	—
160	C₂×D₄×C₇₉	—	2	2	no	—
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	2	2	no	—
167	C₂×D₄×C₇₉	—	2	2	no	—
168	C₂×D₄×C₇₉	—	2	1	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	2	1	no	—
171	C₂×D₄×C₇₉	—	2	1	no	—
172	C₂×D₄×C₇₉	—	2	1	no	—
173	C₂×D₄×C₇₉	—	4	4	no	—
174	C₂×D₄×C₇₉	—	4	4	no	—
175	C₂×D₄×C₇₉	—	4	4	no	—
176	C₂×D₄×C₇₉	—	4	1	no	—
177	C₂×D₄×C₇₉	—	4	1	no	—
178	C₂×D₄×C₇₉	—	8	1	no	—
179	C₂×D₄×C₇₉	—	8	1	no	—
180	C₂×D₄×C₇₉	—	8	2	no	—
181	C₂×D₄×C₇₉	—	8	1	no	—
182	C₂×D₄×C₇₉	—	8	2	no	—
183	C₂×D₄×C₇₉	—	8	2	no	—
184	C₂×D₄×C₇₉	—	8	1	no	—
185	C₂×D₄×C₇₉	—	8	1	no	—
186	C₂×D₄×C₇₉	—	8	2	no	—
187	C₂×D₄×C₇₉	—	8	2	no	—
188	C₂×D₄×C₇₉	—	8	4	no	—
189	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₇₉	—	2	2	no	—
192	C₂²×C₄×C₇₉	—	2	2	no	—
193	C₂²×C₄×C₇₉	—	2	2	no	—
194	C₂²×C₄×C₇₉	—	2	4	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	1	no	—
198	C₂²×C₄×C₇₉	—	8	1	no	—
199	C₂²×C₄×C₇₉	—	8	1	no	—
200	C₂²×C₄×C₇₉	—	8	1	no	—
201	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
208	SD₁₆×C₇₉	—	8	1	no	—
209	D₈×C₇₉	—	8	2	no	—
210	D₈×C₇₉	—	8	1	no	—
211	M₁₆×C₇₉	—	8	1	no	—
212	C₂×C₈×C₇₉	—	2	1	no	—
213	C₂×C₈×C₇₉	—	2	2	no	—
214	C₂×C₈×C₇₉	—	2	1	no	—
215	C₂×C₈×C₇₉	—	8	1	no	—
216	C₄⋊C₄×C₇₉	—	2	2	no	—
217	C₄⋊C₄×C₇₉	—	2	2	no	—
218	C₄⋊C₄×C₇₉	—	2	1	no	—
219	C₄⋊C₄×C₇₉	—	2	1	no	—
220	C₄⋊C₄×C₇₉	—	2	1	no	—
221	C₄⋊C₄×C₇₉	—	2	1	no	—
222	C₄⋊C₄×C₇₉	—	2	1	no	—
223	C₄⋊C₄×C₇₉	—	2	1	no	—
224	C₄⋊C₄×C₇₉	—	2	1	no	—
225	C₄⋊C₄×C₇₉	—	4	4	no	—
226	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
227	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
228	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₇₉	—	2	2	no	—
230	C₂²⋊C₄×C₇₉	—	2	2	no	—
231	C₂²⋊C₄×C₇₉	—	2	2	no	—
232	C₂²⋊C₄×C₇₉	—	2	2	no	—
233	C₂²⋊C₄×C₇₉	—	2	2	no	—
234	C₂²⋊C₄×C₇₉	—	2	1	no	—
235	C₂²⋊C₄×C₇₉	—	2	1	no	—
236	C₂²⋊C₄×C₇₉	—	2	1	no	—
237	C₂²⋊C₄×C₇₉	—	2	2	no	—
238	C₂²⋊C₄×C₇₉	—	2	1	no	—
239	C₂²⋊C₄×C₇₉	—	2	2	no	—
240	C₂²⋊C₄×C₇₉	—	2	2	no	—
241	C₂²⋊C₄×C₇₉	—	2	2	no	—
242	C₂²⋊C₄×C₇₉	—	2	1	no	—
243	C₂²⋊C₄×C₇₉	—	4	4	no	—
244	C₂²⋊C₄×C₇₉	—	4	4	no	—
245	C₂²⋊C₄×C₇₉	—	4	1	no	—
246	C₂²⋊C₄×C₇₉	—	4	1	no	—
247	C₄²×C₇₉	—	2	2	no	—
248	C₄²×C₇₉	—	2	1	no	—
249	C₂³×C₇₉	—	2	1	no	—
250	C₂³×C₇₉	—	2	1	no	—
251	C₂³×C₇₉	—	2	2	no	—
252	C₂³×C₇₉	—	2	2	no	—
253	C₂³×C₇₉	—	2	2	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	2	2	no	—
256	C₂³×C₇₉	—	2	2	no	—
257	C₂³×C₇₉	—	4	1	no	—
258	C₂³×C₇₉	—	4	2	no	—
259	C₂³×C₇₉	—	4	2	no	—
260	C₂³×C₇₉	—	4	2	no	—
261	C₂³×C₇₉	—	4	2	no	—
262	C₂³×C₇₉	—	4	2	no	—
263	C₂³×C₇₉	—	4	1	no	—
264	C₂³×C₇₉	—	4	1	no	—
265	C₂³×C₇₉	—	4	1	no	—
266	C₂³×C₇₉	—	8	1	no	—
267	C₂³×C₇₉	—	8	1	no	—
268	C₂³×C₇₉	—	8	2	no	—
269	C₂³×C₇₉	—	8	2	no	—
270	C₂³×C₇₉	—	8	2	no	—
271	C₂³×C₇₉	#120	1	1	yes	characteristic
272	C₂³×C₇₉	#120	1	1	yes	characteristic
273	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₇₉	—	4	1	no	—
275	D₄×C₇₉	—	4	2	no	—
276	D₄×C₇₉	—	4	1	no	—
277	D₄×C₇₉	—	4	2	no	—
278	D₄×C₇₉	—	4	2	no	—
279	D₄×C₇₉	—	4	2	no	—
280	D₄×C₇₉	—	4	1	no	—
281	D₄×C₇₉	—	4	1	no	—
282	D₄×C₇₉	—	4	2	no	—
283	D₄×C₇₉	—	4	1	no	—
284	D₄×C₇₉	—	4	2	no	—
285	D₄×C₇₉	—	4	1	no	—
286	D₄×C₇₉	—	4	4	no	—
287	D₄×C₇₉	—	4	2	no	—
288	D₄×C₇₉	—	8	1	no	—
289	D₄×C₇₉	—	8	2	no	—
290	D₄×C₇₉	—	8	2	no	—
291	D₄×C₇₉	—	8	1	no	—
292	D₄×C₇₉	—	8	2	no	—
293	D₄×C₇₉	—	8	2	no	—
294	D₄×C₇₉	—	8	2	no	—
295	D₄×C₇₉	—	8	2	no	—
296	D₄×C₇₉	—	8	2	no	—
297	D₄×C₇₉	—	8	8	no	—
298	D₄×C₇₉	—	8	2	no	—
299	D₄×C₇₉	—	8	2	no	—
300	C₂×C₄×C₇₉	—	2	4	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	2	2	no	—
303	C₂×C₄×C₇₉	—	2	2	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	2	1	no	—
306	C₂×C₄×C₇₉	—	4	1	no	—
307	C₂×C₄×C₇₉	—	4	1	no	—
308	C₂×C₄×C₇₉	—	4	1	no	—
309	C₂×C₄×C₇₉	—	4	1	no	—
310	C₂×C₄×C₇₉	—	4	1	no	—
311	C₂×C₄×C₇₉	—	4	1	no	—
312	C₂×C₄×C₇₉	—	4	2	no	—
313	C₂×C₄×C₇₉	—	4	2	no	—
314	C₂×C₄×C₇₉	—	4	2	no	—
315	C₂×C₄×C₇₉	—	4	2	no	—
316	C₂×C₄×C₇₉	—	4	2	no	—
317	C₂×C₄×C₇₉	—	4	1	no	—
318	C₂×C₄×C₇₉	—	8	1	no	—
319	C₂×C₄×C₇₉	—	8	4	no	—
320	C₂×C₄×C₇₉	—	8	2	no	—
321	C₂×C₄×C₇₉	—	8	2	no	—
322	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
323	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
324	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
326	C₈×C₇₉	—	4	1	no	—
327	C₈×C₇₉	—	4	1	no	—
328	C₈×C₇₉	—	4	2	no	—
329	C₂²×C₇₉	—	2	1	no	—
330	C₂²×C₇₉	—	2	1	no	—
331	C₂²×C₇₉	—	2	1	no	—
332	C₂²×C₇₉	—	2	1	no	—
333	C₂²×C₇₉	—	2	1	no	—
334	C₂²×C₇₉	—	2	1	no	—
335	C₂²×C₇₉	—	2	1	no	—
336	C₂²×C₇₉	—	4	2	no	—
337	C₂²×C₇₉	—	4	2	no	—
338	C₂²×C₇₉	—	4	2	no	—
339	C₂²×C₇₉	—	4	2	no	—
340	C₂²×C₇₉	—	4	1	no	—
341	C₂²×C₇₉	—	4	2	no	—
342	C₂²×C₇₉	—	4	2	no	—
343	C₂²×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	4	1	no	—
345	C₂²×C₇₉	—	4	2	no	—
346	C₂²×C₇₉	—	4	2	no	—
347	C₂²×C₇₉	—	8	2	no	—
348	C₂²×C₇₉	—	8	2	no	—
349	C₂²×C₇₉	—	8	2	no	—
350	C₂²×C₇₉	—	8	2	no	—
351	C₂²×C₇₉	—	8	1	no	—
352	C₂²×C₇₉	—	8	1	no	—
353	C₂²×C₇₉	—	8	1	no	—
354	C₂²×C₇₉	—	16	2	no	—
355	C₂²×C₇₉	—	16	4	no	—
356	C₂²×C₇₉	#453	1	2	yes	—
357	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
358	C₂²×C₇₉	#576	1	1	yes	characteristic
359	C₂²×C₇₉	#577	1	1	yes	characteristic
360	C₄×C₇₉	—	2	1	no	—
361	C₄×C₇₉	—	2	1	no	—
362	C₄×C₇₉	—	2	1	no	—
363	C₄×C₇₉	—	2	1	no	—
364	C₄×C₇₉	—	4	4	no	—
365	C₄×C₇₉	—	4	2	no	—
366	C₄×C₇₉	—	4	1	no	—
367	C₄×C₇₉	—	4	2	no	—
368	C₄×C₇₉	—	4	1	no	—
369	C₄×C₇₉	—	4	1	no	—
370	C₄×C₇₉	—	8	1	no	—
371	#18418	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₇₉	—	2	1	no	—
373	C₂×C₇₉	—	2	1	no	—
374	C₂×C₇₉	—	2	2	no	—
375	C₂×C₇₉	—	4	1	no	—
376	C₂×C₇₉	—	8	2	no	—
377	C₂×C₇₉	—	8	2	no	—
378	C₂×C₇₉	—	8	1	no	—
379	C₂×C₇₉	—	16	1	no	—
380	C₂×C₇₉	#3012	1	1	yes	characteristic
381	C₂×C₇₉	C₂×#453	1	1	yes	characteristic
382	C₂×C₇₉	#3026	1	1	yes	characteristic
383	#3537	C₂×C₇₉	1	1	yes	characteristic, complemented
384	#3192	C₂×C₇₉	1	1	yes	characteristic, complemented
385	#3188	C₂×C₇₉	1	1	yes	characteristic, complemented
386	#2656	C₂×C₇₉	1	1	yes	characteristic, complemented
387	#1618	C₂×C₇₉	1	2	yes	complemented
388	#1613	C₂×C₇₉	1	2	yes	complemented
389	#1600	C₂×C₇₉	1	2	yes	complemented
390	#1595	C₂×C₇₉	1	2	yes	complemented
391	#1504	C₂×C₇₉	1	1	yes	characteristic, complemented
392	C₂×#327	C₂×C₇₉	1	1	yes	characteristic, complemented
393	#1471	C₂×C₇₉	1	1	yes	characteristic, complemented
394	C₇₉	#18418	1	1	yes	characteristic, direct product factor, Sylow
395	#560	—	2	2	no	—
396	#553	—	2	1	no	—
397	#553	—	2	1	no	—
398	D₄²	—	2	2	no	—
399	D₄²	—	2	1	no	—
400	D₄²	—	2	1	no	—
401	#540	—	2	1	no	—
402	#538	—	2	1	no	—
403	#538	C₂²×C₇₉	1	2	yes	—
404	#535	—	2	1	no	—
405	#534	—	2	1	no	—
406	#534	C₂²×C₇₉	1	2	yes	—
407	#525	C₂²×C₇₉	1	1	yes	characteristic
408	C₂×#121	—	2	2	no	—
409	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
410	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
411	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic, complemented
412	#484	C₂²×C₇₉	1	1	yes	characteristic, complemented
413	#482	—	2	1	no	—
414	#481	—	2	1	no	—
415	#481	C₂²×C₇₉	1	1	yes	characteristic, complemented
416	#481	C₂²×C₇₉	1	2	yes	complemented
417	#469	—	2	2	no	—
418	#466	—	2	1	no	—
419	#465	—	2	1	no	—
420	#450	C₂²×C₇₉	1	1	yes	characteristic, complemented
421	#449	—	2	1	no	—
422	#447	—	2	1	no	—
423	#447	C₂²×C₇₉	1	1	yes	characteristic, complemented
424	#447	C₂²×C₇₉	1	2	yes	complemented
425	#407	C₂²×C₇₉	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
427	#399	—	2	1	no	—
428	#399	C₂²×C₇₉	1	2	yes	complemented
429	#392	—	2	1	no	—
430	#392	C₂²×C₇₉	1	2	yes	complemented
431	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic, complemented
432	#328	C₂²×C₇₉	1	2	yes	complemented
433	#327	C₂²×C₇₉	1	2	yes	complemented
434	#327	C₂²×C₇₉	1	2	yes	complemented
435	#327	C₂²×C₇₉	1	2	yes	complemented
436	#323	C₂²×C₇₉	1	2	yes	complemented
437	#323	C₂²×C₇₉	1	2	yes	complemented
438	C₂×#41	D₄×C₇₉	1	1	yes	characteristic, complemented
439	C₂²×D₄	—	2	2	no	—
440	C₂²×D₄	—	2	1	no	—
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	D₄×C₇₉	1	2	yes	—
446	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
447	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic, complemented
448	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
451	C₂×SD₁₆	—	2	1	no	—
452	C₂×D₈	—	2	2	no	—
453	C₂×D₈	—	2	1	no	—
454	C₂×M₁₆	—	2	1	no	—
455	C₂²×C₈	—	2	1	no	—
456	#127	—	2	2	no	—
457	#127	—	2	1	no	—
458	#126	—	2	2	no	—
459	#126	—	2	2	no	—
460	#125	—	2	1	no	—
461	#124	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	1	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	#123	—	2	2	no	—
467	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic, complemented
468	C₂²⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
469	#121	—	2	2	no	—
470	#121	—	2	1	no	—
471	#121	—	2	1	no	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	2	no	—
483	#121	—	2	1	no	—
484	#121	—	2	1	no	—
485	#121	—	2	1	no	—
486	#121	—	2	1	no	—
487	#121	—	4	8	no	—
488	#121	D₄×C₇₉	1	2	yes	complemented
489	#121	D₄×C₇₉	1	1	yes	characteristic, complemented
490	#121	C₂³×C₇₉	1	2	yes	—
491	#121	C₂³×C₇₉	1	1	yes	characteristic
492	#120	—	2	2	no	—
493	#120	—	2	2	no	—
494	#120	—	2	2	no	—
495	#120	—	2	1	no	—
496	#120	—	2	2	no	—
497	#120	—	2	2	no	—
498	#120	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	2	no	—
505	#117	—	2	1	no	—
506	#117	D₄×C₇₉	1	1	yes	characteristic, complemented
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic, complemented
510	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
516	#107	—	2	1	no	—
517	#106	—	2	1	no	—
518	#106	—	2	2	no	—
519	#103	—	2	1	no	—
520	#102	—	2	2	no	—
521	#102	—	2	1	no	—
522	#102	—	2	1	no	—
523	#102	—	2	2	no	—
524	#102	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
528	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
529	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
530	#95	—	2	1	no	—
531	#95	C₂³×C₇₉	1	2	yes	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	1	no	—
534	C₂⁴	—	2	1	no	—
535	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
536	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
537	#41	—	8	1	no	—
538	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	—	8	1	no	—
562	C₂×D₄	—	8	1	no	—
563	C₂×D₄	—	8	2	no	—
564	C₂×D₄	—	8	1	no	—
565	C₂×D₄	—	8	2	no	—
566	C₂×D₄	—	8	2	no	—
567	C₂×D₄	—	8	1	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂×D₄	—	8	2	no	—
570	C₂×D₄	—	8	2	no	—
571	C₂×D₄	—	8	4	no	—
572	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
573	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	8	1	no	—
582	C₂²×C₄	—	8	1	no	—
583	C₂²×C₄	—	8	1	no	—
584	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
585	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
591	SD₁₆	—	8	1	no	—
592	D₈	—	8	1	no	—
593	D₈	—	8	2	no	—
594	M₁₆	—	8	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	8	1	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
610	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	1	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	2	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	—	8	1	no	—
651	C₂³	—	8	2	no	—
652	C₂³	—	8	2	no	—
653	C₂³	—	8	2	no	—
654	C₂³	#120×C₇₉	1	1	yes	characteristic
655	C₂³	#120×C₇₉	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
657	Q₈	—	4	1	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	1	no	—
671	D₄	—	8	1	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	1	no	—
675	D₄	—	8	2	no	—
676	D₄	—	8	2	no	—
677	D₄	—	8	2	no	—
678	D₄	—	8	2	no	—
679	D₄	—	8	2	no	—
680	D₄	—	8	8	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	8	1	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
706	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₈	—	4	2	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	8	2	no	—
731	C₂²	—	8	2	no	—
732	C₂²	—	8	2	no	—
733	C₂²	—	8	2	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	16	2	no	—
738	C₂²	—	16	4	no	—
739	C₂²	#453×C₇₉	1	2	yes	—
740	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
741	C₂²	#576×C₇₉	1	1	yes	characteristic
742	C₂²	#577×C₇₉	1	1	yes	characteristic
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	4	4	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	8	1	no	—
754	C₂	—	2	1	no	—
755	C₂	—	2	1	no	—
756	C₂	—	2	2	no	—
757	C₂	—	4	1	no	—
758	C₂	—	8	2	no	—
759	C₂	—	8	1	no	—
760	C₂	—	8	2	no	—
761	C₂	—	16	1	no	—
762	C₂	C₇₉×#3012	1	1	yes	characteristic
763	C₂	C₂×#453×C₇₉	1	1	yes	characteristic
764	C₂	C₇₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3537	C₂	semidirect
2. C₇₉×#3192	C₂	semidirect
3. C₇₉×#3188	C₂	semidirect
4. C₇₉×#2656	C₂	semidirect
5. C₇₉×#1618	C₂	semidirect
6. C₇₉×#1613	C₂	semidirect
7. C₇₉×#1600	C₂	semidirect
8. C₇₉×#1595	C₂	semidirect
9. C₇₉×#1504	C₂	semidirect
10. C₂×#327×C₇₉	C₂	semidirect
11. C₇₉×#1471	C₂	semidirect
28. C₂×#121×C₇₉	C₂²	semidirect
29. #484×C₇₉	C₂²	semidirect
32. #481×C₇₉	C₂²	semidirect
33. #481×C₇₉	C₂²	semidirect
37. #450×C₇₉	C₂²	semidirect
40. #447×C₇₉	C₂²	semidirect
41. #447×C₇₉	C₂²	semidirect
42. #407×C₇₉	C₂²	semidirect
43. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
45. #399×C₇₉	C₂²	semidirect
47. #392×C₇₉	C₂²	semidirect
48. C₂×#95×C₇₉	C₂²	semidirect
49. #328×C₇₉	C₂²	semidirect
50. #327×C₇₉	C₂²	semidirect
51. #327×C₇₉	C₂²	semidirect
52. #327×C₇₉	C₂²	semidirect
53. #323×C₇₉	C₂²	semidirect
54. #323×C₇₉	C₂²	semidirect
55. C₂×#41×C₇₉	D₄	semidirect
64. C₂²×D₄×C₇₉	D₄	semidirect
84. C₂²⋊Q₈×C₇₉	D₄	semidirect
105. #121×C₇₉	D₄	semidirect
106. #121×C₇₉	D₄	semidirect
123. #117×C₇₉	D₄	semidirect
126. C₂×C₄⋊C₄×C₇₉	D₄	semidirect
371. #18418	C₇₉	direct (N × H)
383. #3537	C₂×C₇₉	semidirect
384. #3192	C₂×C₇₉	semidirect
385. #3188	C₂×C₇₉	semidirect
386. #2656	C₂×C₇₉	semidirect
387. #1618	C₂×C₇₉	semidirect
388. #1613	C₂×C₇₉	semidirect
389. #1600	C₂×C₇₉	semidirect
390. #1595	C₂×C₇₉	semidirect
391. #1504	C₂×C₇₉	semidirect
392. C₂×#327	C₂×C₇₉	semidirect
393. #1471	C₂×C₇₉	semidirect
394. C₇₉	#18418	direct (N × H)
411. C₂×#121	C₂²×C₇₉	semidirect
412. #484	C₂²×C₇₉	semidirect
415. #481	C₂²×C₇₉	semidirect
416. #481	C₂²×C₇₉	semidirect
420. #450	C₂²×C₇₉	semidirect
423. #447	C₂²×C₇₉	semidirect
424. #447	C₂²×C₇₉	semidirect
425. #407	C₂²×C₇₉	semidirect
426. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
428. #399	C₂²×C₇₉	semidirect
430. #392	C₂²×C₇₉	semidirect
431. C₂×#95	C₂²×C₇₉	semidirect
432. #328	C₂²×C₇₉	semidirect
433. #327	C₂²×C₇₉	semidirect
434. #327	C₂²×C₇₉	semidirect
435. #327	C₂²×C₇₉	semidirect
436. #323	C₂²×C₇₉	semidirect
437. #323	C₂²×C₇₉	semidirect
438. C₂×#41	D₄×C₇₉	semidirect
447. C₂²×D₄	D₄×C₇₉	semidirect
467. C₂²⋊Q₈	D₄×C₇₉	semidirect
488. #121	D₄×C₇₉	semidirect
489. #121	D₄×C₇₉	semidirect
506. #117	D₄×C₇₉	semidirect
509. C₂×C₄⋊C₄	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3537	2
C₇₉×#3192	2
C₇₉×#3188	2
C₇₉×#2656	2
C₇₉×#1618	2
C₇₉×#1613	2
C₇₉×#1600	2
C₇₉×#1595	2
C₇₉×#1504	2
C₂×#327×C₇₉	2
C₇₉×#1471	2
#18418	79

Subgroups — C79×#18418 #34130107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18418 #34130107