Subgroups — C₇₉×#18663 #34130352

Order 20224.

1206 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3496	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1654	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1639	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1635	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1629	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₇₉	—	2	1	no	—
13	#547×C₇₉	—	2	1	no	—
14	#547×C₇₉	C₂²	1	2	yes	—
15	#546×C₇₉	—	2	2	no	—
16	#546×C₇₉	—	2	2	no	—
17	D₄²×C₇₉	—	2	1	no	—
18	D₄²×C₇₉	C₂²	1	2	yes	—
19	#537×C₇₉	—	2	1	no	—
20	#534×C₇₉	—	2	2	no	—
21	#533×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	#532×C₇₉	C₂²	1	1	yes	characteristic
23	#532×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₇₉	—	2	2	no	—
25	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
26	#498×C₇₉	C₂²	1	1	yes	characteristic, complemented
27	#492×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	#478×C₇₉	—	2	2	no	—
31	#476×C₇₉	C₂²	1	2	yes	complemented
32	#476×C₇₉	C₂²	1	2	yes	complemented
33	#475×C₇₉	—	2	1	no	—
34	#474×C₇₉	C₂²	1	2	yes	complemented
35	#465×C₇₉	—	2	2	no	—
36	#465×C₇₉	—	2	2	no	—
37	#461×C₇₉	C₂²	1	2	yes	complemented
38	#460×C₇₉	—	2	1	no	—
39	C₄×SD₁₆×C₇₉	—	2	2	no	—
40	#428×C₇₉	—	2	1	no	—
41	#423×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#418×C₇₉	—	2	1	no	—
44	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	#332×C₇₉	C₂²	1	2	yes	complemented
46	#331×C₇₉	C₂²	1	2	yes	complemented
47	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
48	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
49	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
50	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
51	H(5,𝔽₂)×C₇₉	—	4	4	no	—
52	H(5,𝔽₂)×C₇₉	—	4	4	no	—
53	C₂×#41×C₇₉	—	2	2	no	—
54	C₂×#41×C₇₉	—	2	2	no	—
55	C₂×#41×C₇₉	—	2	1	no	—
56	C₂×#41×C₇₉	—	2	1	no	—
57	C₂²×D₄×C₇₉	—	2	4	no	—
58	C₂²×D₄×C₇₉	—	2	2	no	—
59	C₂²×D₄×C₇₉	—	2	2	no	—
60	C₂²×D₄×C₇₉	—	2	2	no	—
61	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₇₉	—	2	1	no	—
63	C₂×SD₁₆×C₇₉	—	2	2	no	—
64	C₂×SD₁₆×C₇₉	—	2	2	no	—
65	C₂×M₁₆×C₇₉	—	2	1	no	—
66	C₂²×C₈×C₇₉	—	2	1	no	—
67	C₂²×C₈×C₇₉	—	2	1	no	—
68	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
72	#127×C₇₉	D₄	1	1	yes	characteristic
73	#127×C₇₉	C₂³	1	1	yes	characteristic
74	#125×C₇₉	—	2	1	no	—
75	#124×C₇₉	—	2	1	no	—
76	#124×C₇₉	—	2	1	no	—
77	#123×C₇₉	—	2	4	no	—
78	#123×C₇₉	—	2	4	no	—
79	C₂²⋊Q₈×C₇₉	—	2	2	no	—
80	C₂²⋊Q₈×C₇₉	—	2	2	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	4	no	—
84	#121×C₇₉	—	2	4	no	—
85	#121×C₇₉	—	2	2	no	—
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	D₄	1	2	yes	—
92	#121×C₇₉	D₄	1	2	yes	—
93	#120×C₇₉	—	2	4	no	—
94	#120×C₇₉	—	2	4	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×Q₈×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	—	2	1	no	—
98	C₄×D₄×C₇₉	—	2	1	no	—
99	C₄×D₄×C₇₉	—	2	1	no	—
100	C₄×D₄×C₇₉	—	2	1	no	—
101	C₄×D₄×C₇₉	D₄	1	2	yes	—
102	C₄×D₄×C₇₉	D₄	1	2	yes	—
103	C₄×D₄×C₇₉	C₂³	1	2	yes	—
104	C₄×D₄×C₇₉	C₂³	1	2	yes	—
105	#117×C₇₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
110	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	#107×C₇₉	—	2	2	no	—
112	#106×C₇₉	—	2	2	no	—
113	#106×C₇₉	—	2	2	no	—
114	#106×C₇₉	—	2	2	no	—
115	C₄⋊C₈×C₇₉	—	2	1	no	—
116	C₄⋊C₈×C₇₉	—	2	1	no	—
117	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
118	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
119	#103×C₇₉	—	2	2	no	—
120	#103×C₇₉	—	2	2	no	—
121	#102×C₇₉	—	2	2	no	—
122	#102×C₇₉	—	2	2	no	—
123	#102×C₇₉	—	2	2	no	—
124	#102×C₇₉	—	2	2	no	—
125	C₄×C₈×C₇₉	—	2	1	no	—
126	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
128	C₂⁴×C₇₉	—	2	1	no	—
129	C₂⁴×C₇₉	—	2	4	no	—
130	#41×C₇₉	—	4	4	no	—
131	#41×C₇₉	—	4	8	no	—
132	#41×C₇₉	—	4	4	no	—
133	#41×C₇₉	—	4	2	no	—
134	#41×C₇₉	—	4	2	no	—
135	#41×C₇₉	—	4	2	no	—
136	#41×C₇₉	—	4	2	no	—
137	C₂×Q₈×C₇₉	—	2	1	no	—
138	C₂×Q₈×C₇₉	—	2	1	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	—	2	4	no	—
142	C₂×D₄×C₇₉	—	2	4	no	—
143	C₂×D₄×C₇₉	—	2	2	no	—
144	C₂×D₄×C₇₉	—	2	2	no	—
145	C₂×D₄×C₇₉	—	2	4	no	—
146	C₂×D₄×C₇₉	—	2	1	no	—
147	C₂×D₄×C₇₉	—	2	1	no	—
148	C₂×D₄×C₇₉	—	2	1	no	—
149	C₂×D₄×C₇₉	—	2	2	no	—
150	C₂×D₄×C₇₉	—	2	1	no	—
151	C₂×D₄×C₇₉	—	2	1	no	—
152	C₂×D₄×C₇₉	—	4	4	no	—
153	C₂×D₄×C₇₉	—	4	8	no	—
154	C₂×D₄×C₇₉	—	4	16	no	—
155	C₂×D₄×C₇₉	—	4	4	no	—
156	C₂×D₄×C₇₉	—	8	2	no	—
157	C₂×D₄×C₇₉	—	8	2	no	—
158	C₂×D₄×C₇₉	SD₁₆	1	4	yes	complemented
159	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₇₉	—	2	4	no	—
163	C₂²×C₄×C₇₉	—	2	1	no	—
164	C₂²×C₄×C₇₉	—	2	2	no	—
165	C₂²×C₄×C₇₉	—	2	2	no	—
166	C₂²×C₄×C₇₉	—	2	2	no	—
167	C₂²×C₄×C₇₉	—	2	2	no	—
168	C₂²×C₄×C₇₉	—	8	1	no	—
169	C₂²×C₄×C₇₉	—	8	1	no	—
170	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	SD₁₆×C₇₉	—	4	4	no	—
174	SD₁₆×C₇₉	—	8	2	no	—
175	M₁₆×C₇₉	—	4	2	no	—
176	C₂×C₈×C₇₉	—	2	1	no	—
177	C₂×C₈×C₇₉	—	2	1	no	—
178	C₂×C₈×C₇₉	—	2	2	no	—
179	C₂×C₈×C₇₉	—	2	2	no	—
180	C₂×C₈×C₇₉	—	4	2	no	—
181	C₂×C₈×C₇₉	—	8	1	no	—
182	C₄⋊C₄×C₇₉	—	2	4	no	—
183	C₄⋊C₄×C₇₉	—	2	1	no	—
184	C₄⋊C₄×C₇₉	—	2	1	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	1	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	—	4	1	no	—
191	C₄⋊C₄×C₇₉	—	4	1	no	—
192	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
195	C₂²⋊C₄×C₇₉	—	2	4	no	—
196	C₂²⋊C₄×C₇₉	—	2	4	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	2	2	no	—
199	C₂²⋊C₄×C₇₉	—	2	2	no	—
200	C₂²⋊C₄×C₇₉	—	2	2	no	—
201	C₂²⋊C₄×C₇₉	—	2	2	no	—
202	C₂²⋊C₄×C₇₉	—	2	2	no	—
203	C₂²⋊C₄×C₇₉	—	4	1	no	—
204	C₄²×C₇₉	—	4	1	no	—
205	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
209	C₂³×C₇₉	—	2	2	no	—
210	C₂³×C₇₉	—	2	4	no	—
211	C₂³×C₇₉	—	2	2	no	—
212	C₂³×C₇₉	—	2	2	no	—
213	C₂³×C₇₉	—	4	8	no	—
214	C₂³×C₇₉	—	8	1	no	—
215	C₂³×C₇₉	—	8	1	no	—
216	C₂³×C₇₉	—	8	4	no	—
217	C₂³×C₇₉	—	8	4	no	—
218	C₂³×C₇₉	#120	1	1	yes	characteristic
219	Q₈×C₇₉	—	4	2	no	—
220	Q₈×C₇₉	—	4	1	no	—
221	Q₈×C₇₉	—	4	1	no	—
222	Q₈×C₇₉	—	4	2	no	—
223	Q₈×C₇₉	—	4	1	no	—
224	Q₈×C₇₉	—	4	1	no	—
225	D₄×C₇₉	—	2	2	no	—
226	D₄×C₇₉	—	2	2	no	—
227	D₄×C₇₉	—	2	2	no	—
228	D₄×C₇₉	—	2	4	no	—
229	D₄×C₇₉	—	4	2	no	—
230	D₄×C₇₉	—	4	8	no	—
231	D₄×C₇₉	—	4	8	no	—
232	D₄×C₇₉	—	4	4	no	—
233	D₄×C₇₉	—	4	4	no	—
234	D₄×C₇₉	—	4	1	no	—
235	D₄×C₇₉	—	4	1	no	—
236	D₄×C₇₉	—	4	1	no	—
237	D₄×C₇₉	—	4	1	no	—
238	D₄×C₇₉	—	4	2	no	—
239	D₄×C₇₉	—	8	1	no	—
240	D₄×C₇₉	—	8	4	no	—
241	D₄×C₇₉	C₂×SD₁₆	1	4	yes	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	2	1	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	2	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	8	no	—
249	C₂×C₄×C₇₉	—	4	2	no	—
250	C₂×C₄×C₇₉	—	4	2	no	—
251	C₂×C₄×C₇₉	—	4	2	no	—
252	C₂×C₄×C₇₉	—	4	2	no	—
253	C₂×C₄×C₇₉	—	4	4	no	—
254	C₂×C₄×C₇₉	—	4	1	no	—
255	C₂×C₄×C₇₉	—	4	1	no	—
256	C₂×C₄×C₇₉	—	8	2	no	—
257	C₂×C₄×C₇₉	—	8	1	no	—
258	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
262	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
266	C₈×C₇₉	—	2	2	no	—
267	C₈×C₇₉	—	4	1	no	—
268	C₈×C₇₉	—	4	2	no	—
269	C₈×C₇₉	—	4	2	no	—
270	C₂²×C₇₉	—	2	1	no	—
271	C₂²×C₇₉	—	2	1	no	—
272	C₂²×C₇₉	—	2	4	no	—
273	C₂²×C₇₉	—	4	2	no	—
274	C₂²×C₇₉	—	4	2	no	—
275	C₂²×C₇₉	—	4	2	no	—
276	C₂²×C₇₉	—	4	2	no	—
277	C₂²×C₇₉	—	4	2	no	—
278	C₂²×C₇₉	—	4	2	no	—
279	C₂²×C₇₉	—	4	2	no	—
280	C₂²×C₇₉	—	4	2	no	—
281	C₂²×C₇₉	—	8	4	no	—
282	C₂²×C₇₉	—	16	8	no	—
283	C₂²×C₇₉	#450	1	2	yes	—
284	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
285	C₄×C₇₉	—	2	1	no	—
286	C₄×C₇₉	—	2	1	no	—
287	C₄×C₇₉	—	2	1	no	—
288	C₄×C₇₉	—	4	2	no	—
289	C₄×C₇₉	—	4	2	no	—
290	C₄×C₇₉	—	4	2	no	—
291	C₄×C₇₉	—	8	1	no	—
292	C₄×C₇₉	—	8	1	no	—
293	C₄×C₇₉	#450	1	2	yes	—
294	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
295	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₄×C₇₉	#576	1	1	yes	characteristic
297	C₄×C₇₉	#577	1	1	yes	characteristic
298	#18663	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂×C₇₉	—	2	2	no	—
300	C₂×C₇₉	—	4	4	no	—
301	C₂×C₇₉	—	8	2	no	—
302	C₂×C₇₉	—	8	2	no	—
303	C₂×C₇₉	C₂×#450	1	1	yes	characteristic
304	C₂×C₇₉	#3012	1	1	yes	characteristic
305	C₂×C₇₉	#3018	1	1	yes	characteristic
306	#3496	C₂×C₇₉	1	1	yes	characteristic
307	#3246	C₂×C₇₉	1	1	yes	characteristic, complemented
308	#3167	C₂×C₇₉	1	1	yes	characteristic, complemented
309	#3077	C₂×C₇₉	1	1	yes	characteristic, complemented
310	#1654	C₂×C₇₉	1	2	yes	complemented
311	#1639	C₂×C₇₉	1	2	yes	complemented
312	#1635	C₂×C₇₉	1	2	yes	complemented
313	#1629	C₂×C₇₉	1	2	yes	complemented
314	#1547	C₂×C₇₉	1	1	yes	characteristic, complemented
315	#1492	C₂×C₇₉	1	1	yes	characteristic, complemented
316	C₂×D₄⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
317	C₇₉	#18663	1	1	yes	characteristic, direct product factor, Sylow
318	C₂×H(5,𝔽₂)	—	2	1	no	—
319	#547	—	2	1	no	—
320	#547	C₂²×C₇₉	1	2	yes	—
321	#546	—	2	2	no	—
322	#546	—	2	2	no	—
323	D₄²	—	2	1	no	—
324	D₄²	C₂²×C₇₉	1	2	yes	—
325	#537	—	2	1	no	—
326	#534	—	2	2	no	—
327	#533	C₂²×C₇₉	1	1	yes	characteristic, complemented
328	#532	C₂²×C₇₉	1	1	yes	characteristic
329	#532	C₂²×C₇₉	1	1	yes	characteristic
330	C₂×#121	—	2	2	no	—
331	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
332	#498	C₂²×C₇₉	1	1	yes	characteristic, complemented
333	#492	C₂²×C₇₉	1	1	yes	characteristic, complemented
334	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
335	#486	C₂²×C₇₉	1	1	yes	characteristic, complemented
336	#478	—	2	2	no	—
337	#476	C₂²×C₇₉	1	2	yes	complemented
338	#476	C₂²×C₇₉	1	2	yes	complemented
339	#475	—	2	1	no	—
340	#474	C₂²×C₇₉	1	2	yes	complemented
341	#465	—	2	2	no	—
342	#465	—	2	2	no	—
343	#461	C₂²×C₇₉	1	2	yes	complemented
344	#460	—	2	1	no	—
345	C₄×SD₁₆	—	2	2	no	—
346	#428	—	2	1	no	—
347	#423	C₂²×C₇₉	1	1	yes	characteristic, complemented
348	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
349	#418	—	2	1	no	—
350	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
351	#332	C₂²×C₇₉	1	2	yes	complemented
352	#331	C₂²×C₇₉	1	2	yes	complemented
353	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
354	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
355	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
356	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
357	H(5,𝔽₂)	—	4	4	no	—
358	H(5,𝔽₂)	—	4	4	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂²×D₄	—	2	4	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
378	#127	D₄×C₇₉	1	1	yes	characteristic
379	#127	C₂³×C₇₉	1	1	yes	characteristic
380	#125	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#123	—	2	4	no	—
384	#123	—	2	4	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	2	no	—
396	#121	—	2	2	no	—
397	#121	D₄×C₇₉	1	2	yes	—
398	#121	D₄×C₇₉	1	2	yes	—
399	#120	—	2	4	no	—
400	#120	—	2	4	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	D₄×C₇₉	1	2	yes	—
408	C₄×D₄	D₄×C₇₉	1	2	yes	—
409	C₄×D₄	C₂³×C₇₉	1	2	yes	—
410	C₄×D₄	C₂³×C₇₉	1	2	yes	—
411	#117	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	4	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
417	#107	—	2	2	no	—
418	#106	—	2	2	no	—
419	#106	—	2	2	no	—
420	#106	—	2	2	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
424	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
434	C₂⁴	—	2	1	no	—
435	C₂⁴	—	2	4	no	—
436	#41	—	4	8	no	—
437	#41	—	4	4	no	—
438	#41	—	4	4	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	16	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	8	2	no	—
463	C₂×D₄	—	8	2	no	—
464	C₂×D₄	SD₁₆×C₇₉	1	4	yes	complemented
465	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
466	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	8	1	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
479	SD₁₆	—	4	4	no	—
480	SD₁₆	—	8	2	no	—
481	M₁₆	—	4	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	2	no	—
487	C₂×C₈	—	8	1	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
499	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
500	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
514	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	8	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	4	no	—
523	C₂³	—	8	4	no	—
524	C₂³	#120×C₇₉	1	1	yes	characteristic
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	8	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	8	1	no	—
546	D₄	—	8	4	no	—
547	D₄	C₂×SD₁₆×C₇₉	1	4	yes	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
565	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
566	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
567	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
568	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	4	no	—
588	C₂²	—	16	8	no	—
589	C₂²	#450×C₇₉	1	2	yes	—
590	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	#450×C₇₉	1	2	yes	—
600	C₄	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
601	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
602	C₄	#576×C₇₉	1	1	yes	characteristic
603	C₄	#577×C₇₉	1	1	yes	characteristic
604	C₂	—	2	2	no	—
605	C₂	—	4	4	no	—
606	C₂	—	8	2	no	—
607	C₂	—	8	2	no	—
608	C₂	C₂×#450×C₇₉	1	1	yes	characteristic
609	C₂	C₇₉×#3012	1	1	yes	characteristic
610	C₂	C₇₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3496	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3246	C₂	semidirect
3. C₇₉×#3167	C₂	semidirect
4. C₇₉×#3077	C₂	semidirect
5. C₇₉×#1654	C₂	semidirect
6. C₇₉×#1639	C₂	semidirect
7. C₇₉×#1635	C₂	semidirect
8. C₇₉×#1629	C₂	semidirect
9. C₇₉×#1547	C₂	semidirect
10. C₇₉×#1492	C₂	semidirect
11. C₂×D₄⋊C₈×C₇₉	C₂	semidirect
21. #533×C₇₉	C₂²	semidirect
26. #498×C₇₉	C₂²	semidirect
27. #492×C₇₉	C₂²	semidirect
28. #487×C₇₉	C₂²	semidirect
29. #486×C₇₉	C₂²	semidirect
31. #476×C₇₉	C₂²	semidirect
32. #476×C₇₉	C₂²	semidirect
34. #474×C₇₉	C₂²	semidirect
37. #461×C₇₉	C₂²	semidirect
41. #423×C₇₉	C₂²	semidirect
42. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
44. C₂×C₄×C₈×C₇₉	C₂²	semidirect
45. #332×C₇₉	C₂²	semidirect
46. #331×C₇₉	C₂²	semidirect
47. D₄⋊C₈×C₇₉	C₂²	semidirect
48. D₄⋊C₈×C₇₉	C₂²	semidirect
49. D₄⋊C₈×C₇₉	C₂²	semidirect
50. D₄⋊C₈×C₇₉	C₂²	semidirect
158. C₂×D₄×C₇₉	SD₁₆	semidirect
298. #18663	C₇₉	direct (N × H)
307. #3246	C₂×C₇₉	semidirect
308. #3167	C₂×C₇₉	semidirect
309. #3077	C₂×C₇₉	semidirect
310. #1654	C₂×C₇₉	semidirect
311. #1639	C₂×C₇₉	semidirect
312. #1635	C₂×C₇₉	semidirect
313. #1629	C₂×C₇₉	semidirect
314. #1547	C₂×C₇₉	semidirect
315. #1492	C₂×C₇₉	semidirect
316. C₂×D₄⋊C₈	C₂×C₇₉	semidirect
317. C₇₉	#18663	direct (N × H)
327. #533	C₂²×C₇₉	semidirect
332. #498	C₂²×C₇₉	semidirect
333. #492	C₂²×C₇₉	semidirect
334. #487	C₂²×C₇₉	semidirect
335. #486	C₂²×C₇₉	semidirect
337. #476	C₂²×C₇₉	semidirect
338. #476	C₂²×C₇₉	semidirect
340. #474	C₂²×C₇₉	semidirect
343. #461	C₂²×C₇₉	semidirect
347. #423	C₂²×C₇₉	semidirect
348. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
350. C₂×C₄×C₈	C₂²×C₇₉	semidirect
351. #332	C₂²×C₇₉	semidirect
352. #331	C₂²×C₇₉	semidirect
353. D₄⋊C₈	C₂²×C₇₉	semidirect
354. D₄⋊C₈	C₂²×C₇₉	semidirect
355. D₄⋊C₈	C₂²×C₇₉	semidirect
356. D₄⋊C₈	C₂²×C₇₉	semidirect
464. C₂×D₄	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3496	2
C₇₉×#3246	2
C₇₉×#3167	2
C₇₉×#3077	2
C₇₉×#1654	2
C₇₉×#1639	2
C₇₉×#1635	2
C₇₉×#1629	2
C₇₉×#1547	2
C₇₉×#1492	2
C₂×D₄⋊C₈×C₇₉	2
#18663	79

Subgroups — C79×#18663 #34130352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18663 #34130352