Subgroups — C₇₉×#18576 #34130265

Order 20224.

980 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1642	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1641	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1640	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1640	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₉	—	2	1	no	—
13	#559×C₇₉	C₂²	1	2	yes	—
14	#550×C₇₉	—	2	1	no	—
15	#550×C₇₉	C₂²	1	2	yes	—
16	#546×C₇₉	—	2	2	no	—
17	#546×C₇₉	—	2	2	no	—
18	#540×C₇₉	—	2	2	no	—
19	#535×C₇₉	—	2	1	no	—
20	#533×C₇₉	C₂²	1	1	yes	characteristic
21	#533×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	—	2	1	no	—
23	#532×C₇₉	—	2	1	no	—
24	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
25	#518×C₇₉	—	2	1	no	—
26	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
27	#490×C₇₉	—	2	2	no	—
28	#486×C₇₉	C₂²	1	2	yes	—
29	#486×C₇₉	C₂²	1	2	yes	—
30	#485×C₇₉	—	2	1	no	—
31	#475×C₇₉	—	2	1	no	—
32	#475×C₇₉	C₂²	1	1	yes	characteristic, complemented
33	#475×C₇₉	C₂²	1	2	yes	complemented
34	#474×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	#470×C₇₉	—	2	2	no	—
36	#462×C₇₉	—	2	1	no	—
37	#462×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	#462×C₇₉	C₂²	1	2	yes	complemented
39	#461×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#452×C₇₉	—	2	1	no	—
41	C₄×Q₁₆×C₇₉	—	2	1	no	—
42	C₄×SD₁₆×C₇₉	—	2	1	no	—
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#423×C₇₉	C₂²	1	1	yes	characteristic
45	#418×C₇₉	—	2	2	no	—
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	#331×C₇₉	C₂²	1	2	yes	—
48	#331×C₇₉	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
50	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
51	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
52	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
53	C₂×#41×C₇₉	—	2	2	no	—
54	C₂×#41×C₇₉	—	2	2	no	—
55	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₇₉	—	2	1	no	—
57	C₂²×D₄×C₇₉	—	2	1	no	—
58	C₂²×D₄×C₇₉	D₄	1	2	yes	—
59	C₂×Q₁₆×C₇₉	—	2	1	no	—
60	C₂×Q₁₆×C₇₉	—	2	2	no	—
61	C₂×SD₁₆×C₇₉	—	2	1	no	—
62	C₂×M₁₆×C₇₉	—	2	1	no	—
63	C₂×M₁₆×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	#127×C₇₉	—	2	2	no	—
69	#127×C₇₉	—	2	1	no	—
70	#127×C₇₉	—	2	1	no	—
71	#127×C₇₉	D₄	1	2	yes	—
72	#127×C₇₉	C₂³	1	2	yes	—
73	#125×C₇₉	—	2	1	no	—
74	#125×C₇₉	—	2	1	no	—
75	#124×C₇₉	—	2	2	no	—
76	#124×C₇₉	—	2	2	no	—
77	#124×C₇₉	—	2	2	no	—
78	#123×C₇₉	—	2	4	no	—
79	#123×C₇₉	—	2	4	no	—
80	C₂²⋊Q₈×C₇₉	—	2	1	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	—	2	1	no	—
83	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
84	#121×C₇₉	—	2	2	no	—
85	#121×C₇₉	—	2	2	no	—
86	#121×C₇₉	—	2	2	no	—
87	#121×C₇₉	—	2	4	no	—
88	#121×C₇₉	—	2	4	no	—
89	#121×C₇₉	—	2	2	no	—
90	#120×C₇₉	—	2	4	no	—
91	C₄×Q₈×C₇₉	—	2	1	no	—
92	C₄×Q₈×C₇₉	—	2	1	no	—
93	C₄×Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
97	C₄×D₄×C₇₉	—	2	2	no	—
98	C₄×D₄×C₇₉	—	2	2	no	—
99	C₄×D₄×C₇₉	—	2	2	no	—
100	C₄×D₄×C₇₉	—	2	1	no	—
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	—	2	2	no	—
103	C₄×D₄×C₇₉	—	2	2	no	—
104	C₄×D₄×C₇₉	—	2	2	no	—
105	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
107	#117×C₇₉	—	2	1	no	—
108	#117×C₇₉	—	2	1	no	—
109	#117×C₇₉	—	2	1	no	—
110	#117×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
112	C₂×C₄²×C₇₉	—	2	1	no	—
113	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
114	#107×C₇₉	—	2	1	no	—
115	#106×C₇₉	—	2	1	no	—
116	#106×C₇₉	—	2	2	no	—
117	C₄⋊C₈×C₇₉	—	2	1	no	—
118	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
119	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
121	#103×C₇₉	—	2	1	no	—
122	#103×C₇₉	—	2	2	no	—
123	#103×C₇₉	—	2	1	no	—
124	#103×C₇₉	—	2	1	no	—
125	#103×C₇₉	—	2	2	no	—
126	#102×C₇₉	—	2	4	no	—
127	#102×C₇₉	—	2	4	no	—
128	#102×C₇₉	—	2	1	no	—
129	C₂²⋊C₈×C₇₉	—	2	1	no	—
130	#97×C₇₉	—	2	1	no	—
131	C₄×C₈×C₇₉	—	2	1	no	—
132	C₄×C₈×C₇₉	C₂³	1	2	yes	—
133	C₂⁴×C₇₉	—	2	2	no	—
134	#41×C₇₉	—	4	1	no	—
135	#41×C₇₉	—	4	1	no	—
136	#41×C₇₉	—	8	2	no	—
137	#41×C₇₉	—	8	2	no	—
138	#41×C₇₉	—	8	4	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	2	1	no	—
142	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₇₉	—	2	1	no	—
145	C₂×D₄×C₇₉	—	2	4	no	—
146	C₂×D₄×C₇₉	—	2	4	no	—
147	C₂×D₄×C₇₉	—	2	2	no	—
148	C₂×D₄×C₇₉	—	2	2	no	—
149	C₂×D₄×C₇₉	—	2	2	no	—
150	C₂×D₄×C₇₉	—	2	2	no	—
151	C₂×D₄×C₇₉	—	2	2	no	—
152	C₂×D₄×C₇₉	—	4	2	no	—
153	C₂×D₄×C₇₉	—	4	2	no	—
154	C₂×D₄×C₇₉	—	4	4	no	—
155	C₂×D₄×C₇₉	—	8	1	no	—
156	C₂×D₄×C₇₉	—	8	1	no	—
157	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₇₉	—	2	4	no	—
160	C₂²×C₄×C₇₉	—	2	4	no	—
161	C₂²×C₄×C₇₉	—	2	1	no	—
162	C₂²×C₄×C₇₉	—	2	1	no	—
163	C₂²×C₄×C₇₉	—	2	1	no	—
164	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
167	Q₁₆×C₇₉	—	4	2	no	—
168	Q₁₆×C₇₉	—	8	2	no	—
169	SD₁₆×C₇₉	—	4	2	no	—
170	M₁₆×C₇₉	—	4	2	no	—
171	M₁₆×C₇₉	—	8	1	no	—
172	C₂×C₈×C₇₉	—	2	1	no	—
173	C₂×C₈×C₇₉	—	2	1	no	—
174	C₂×C₈×C₇₉	—	2	2	no	—
175	C₂×C₈×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	1	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	—	2	1	no	—
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	2	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	2	2	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	—	4	1	no	—
188	C₄⋊C₄×C₇₉	—	4	1	no	—
189	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₇₉	—	2	4	no	—
193	C₂²⋊C₄×C₇₉	—	2	4	no	—
194	C₂²⋊C₄×C₇₉	—	2	4	no	—
195	C₂²⋊C₄×C₇₉	—	2	4	no	—
196	C₂²⋊C₄×C₇₉	—	2	1	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	2	1	no	—
199	C₂²⋊C₄×C₇₉	—	2	1	no	—
200	C₂²⋊C₄×C₇₉	—	4	1	no	—
201	C₄²×C₇₉	—	2	1	no	—
202	C₄²×C₇₉	—	2	1	no	—
203	C₄²×C₇₉	—	2	1	no	—
204	C₄²×C₇₉	—	2	2	no	—
205	C₄²×C₇₉	—	4	1	no	—
206	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₇₉	—	2	4	no	—
211	C₂³×C₇₉	—	2	1	no	—
212	C₂³×C₇₉	—	4	4	no	—
213	C₂³×C₇₉	—	8	2	no	—
214	C₂³×C₇₉	—	8	2	no	—
215	C₂³×C₇₉	#120	1	1	yes	characteristic
216	Q₈×C₇₉	—	2	1	no	—
217	Q₈×C₇₉	—	2	1	no	—
218	Q₈×C₇₉	—	2	2	no	—
219	Q₈×C₇₉	—	2	2	no	—
220	Q₈×C₇₉	—	4	2	no	—
221	Q₈×C₇₉	—	4	1	no	—
222	Q₈×C₇₉	—	4	1	no	—
223	Q₈×C₇₉	—	4	1	no	—
224	Q₈×C₇₉	—	4	1	no	—
225	D₄×C₇₉	—	2	1	no	—
226	D₄×C₇₉	—	2	1	no	—
227	D₄×C₇₉	—	4	4	no	—
228	D₄×C₇₉	—	4	4	no	—
229	D₄×C₇₉	—	4	2	no	—
230	D₄×C₇₉	—	4	2	no	—
231	D₄×C₇₉	—	4	2	no	—
232	D₄×C₇₉	—	4	2	no	—
233	D₄×C₇₉	—	4	2	no	—
234	D₄×C₇₉	—	4	4	no	—
235	D₄×C₇₉	—	8	2	no	—
236	D₄×C₇₉	—	8	4	no	—
237	D₄×C₇₉	—	8	4	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	1	no	—
244	C₂×C₄×C₇₉	—	2	1	no	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	2	2	no	—
248	C₂×C₄×C₇₉	—	4	2	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	2	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	8	4	no	—
255	C₂×C₄×C₇₉	—	8	4	no	—
256	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
262	C₈×C₇₉	—	4	2	no	—
263	C₈×C₇₉	—	4	1	no	—
264	C₈×C₇₉	—	4	1	no	—
265	C₈×C₇₉	—	4	2	no	—
266	C₂²×C₇₉	—	2	1	no	—
267	C₂²×C₇₉	—	2	1	no	—
268	C₂²×C₇₉	—	2	1	no	—
269	C₂²×C₇₉	—	4	1	no	—
270	C₂²×C₇₉	—	4	4	no	—
271	C₂²×C₇₉	—	4	1	no	—
272	C₂²×C₇₉	—	4	4	no	—
273	C₂²×C₇₉	—	4	1	no	—
274	C₂²×C₇₉	—	4	4	no	—
275	C₂²×C₇₉	—	16	4	no	—
276	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
277	C₄×C₇₉	—	2	1	no	—
278	C₄×C₇₉	—	2	1	no	—
279	C₄×C₇₉	—	2	1	no	—
280	C₄×C₇₉	—	4	1	no	—
281	C₄×C₇₉	—	4	1	no	—
282	C₄×C₇₉	—	4	2	no	—
283	C₄×C₇₉	—	4	1	no	—
284	C₄×C₇₉	—	4	2	no	—
285	C₄×C₇₉	—	8	1	no	—
286	C₄×C₇₉	—	8	1	no	—
287	C₄×C₇₉	#455	1	2	yes	—
288	C₄×C₇₉	#575	1	1	yes	characteristic
289	C₄×C₇₉	#575	1	1	yes	characteristic
290	C₄×C₇₉	#576	1	1	yes	characteristic
291	C₄×C₇₉	#577	1	1	yes	characteristic
292	#18576	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂×C₇₉	—	4	1	no	—
294	C₂×C₇₉	—	8	1	no	—
295	C₂×C₇₉	—	8	4	no	—
296	C₂×C₇₉	#3005	1	1	yes	characteristic
297	C₂×C₇₉	#3012	1	1	yes	characteristic
298	C₂×C₇₉	C₂×#455	1	1	yes	characteristic
299	#3508	C₂×C₇₉	1	1	yes	characteristic
300	#3255	C₂×C₇₉	1	1	yes	characteristic, complemented
301	#3138	C₂×C₇₉	1	1	yes	characteristic, complemented
302	#3107	C₂×C₇₉	1	1	yes	characteristic, complemented
303	#1642	C₂×C₇₉	1	2	yes	complemented
304	#1641	C₂×C₇₉	1	2	yes	complemented
305	#1640	C₂×C₇₉	1	2	yes	complemented
306	#1640	C₂×C₇₉	1	2	yes	complemented
307	#1545	C₂×C₇₉	1	1	yes	characteristic, complemented
308	#1489	C₂×C₇₉	1	1	yes	characteristic, complemented
309	#1485	C₂×C₇₉	1	1	yes	characteristic, complemented
310	C₇₉	#18576	1	1	yes	characteristic, direct product factor, Sylow
311	#559	—	2	1	no	—
312	#559	C₂²×C₇₉	1	2	yes	—
313	#550	—	2	1	no	—
314	#550	C₂²×C₇₉	1	2	yes	—
315	#546	—	2	2	no	—
316	#546	—	2	2	no	—
317	#540	—	2	2	no	—
318	#535	—	2	1	no	—
319	#533	C₂²×C₇₉	1	1	yes	characteristic
320	#533	C₂²×C₇₉	1	1	yes	characteristic
321	#532	—	2	1	no	—
322	#532	—	2	1	no	—
323	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
324	#518	—	2	1	no	—
325	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
326	#490	—	2	2	no	—
327	#486	C₂²×C₇₉	1	2	yes	—
328	#486	C₂²×C₇₉	1	2	yes	—
329	#485	—	2	1	no	—
330	#475	—	2	1	no	—
331	#475	C₂²×C₇₉	1	1	yes	characteristic, complemented
332	#475	C₂²×C₇₉	1	2	yes	complemented
333	#474	C₂²×C₇₉	1	1	yes	characteristic, complemented
334	#470	—	2	2	no	—
335	#462	—	2	1	no	—
336	#462	C₂²×C₇₉	1	1	yes	characteristic, complemented
337	#462	C₂²×C₇₉	1	2	yes	complemented
338	#461	C₂²×C₇₉	1	1	yes	characteristic, complemented
339	#452	—	2	1	no	—
340	C₄×Q₁₆	—	2	1	no	—
341	C₄×SD₁₆	—	2	1	no	—
342	#431	C₂²×C₇₉	1	1	yes	characteristic
343	#423	C₂²×C₇₉	1	1	yes	characteristic
344	#418	—	2	2	no	—
345	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
346	#331	C₂²×C₇₉	1	2	yes	—
347	#331	C₂²×C₇₉	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
349	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
350	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
351	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	D₄×C₇₉	1	2	yes	—
358	C₂×Q₁₆	—	2	1	no	—
359	C₂×Q₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
364	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
367	#127	—	2	2	no	—
368	#127	—	2	1	no	—
369	#127	—	2	1	no	—
370	#127	D₄×C₇₉	1	2	yes	—
371	#127	C₂³×C₇₉	1	2	yes	—
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#124	—	2	2	no	—
377	#123	—	2	4	no	—
378	#123	—	2	4	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	4	no	—
387	#121	—	2	4	no	—
388	#121	—	2	2	no	—
389	#120	—	2	4	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
395	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
405	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	D₄×C₇₉	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
413	#107	—	2	1	no	—
414	#106	—	2	1	no	—
415	#106	—	2	2	no	—
416	C₄⋊C₈	—	2	1	no	—
417	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
418	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
420	#103	—	2	1	no	—
421	#103	—	2	2	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	2	no	—
425	#102	—	2	4	no	—
426	#102	—	2	4	no	—
427	#102	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	#97	—	2	1	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	C₂³×C₇₉	1	2	yes	—
432	C₂⁴	—	2	2	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	8	2	no	—
436	#41	—	8	2	no	—
437	#41	—	8	4	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	8	1	no	—
455	C₂×D₄	—	8	1	no	—
456	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
457	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
466	Q₁₆	—	4	2	no	—
467	Q₁₆	—	8	2	no	—
468	SD₁₆	—	4	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	8	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	4	1	no	—
505	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
508	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
509	C₂³	—	2	4	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	8	2	no	—
513	C₂³	—	8	2	no	—
514	C₂³	#120×C₇₉	1	1	yes	characteristic
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	4	no	—
536	D₄	—	8	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
556	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
557	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
561	C₈	—	4	2	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	16	4	no	—
575	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	#455×C₇₉	1	2	yes	—
587	C₄	#575×C₇₉	1	1	yes	characteristic
588	C₄	#575×C₇₉	1	1	yes	characteristic
589	C₄	#576×C₇₉	1	1	yes	characteristic
590	C₄	#577×C₇₉	1	1	yes	characteristic
591	C₂	—	4	1	no	—
592	C₂	—	8	4	no	—
593	C₂	—	8	1	no	—
594	C₂	C₇₉×#3005	1	1	yes	characteristic
595	C₂	C₇₉×#3012	1	1	yes	characteristic
596	C₂	C₂×#455×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3508	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×#3255	C₂	semidirect
3. C₇₉×#3138	C₂	semidirect
4. C₇₉×#3107	C₂	semidirect
5. C₇₉×#1642	C₂	semidirect
6. C₇₉×#1641	C₂	semidirect
7. C₇₉×#1640	C₂	semidirect
8. C₇₉×#1640	C₂	semidirect
9. C₇₉×#1545	C₂	semidirect
10. C₇₉×#1489	C₂	semidirect
11. C₇₉×#1485	C₂	semidirect
32. #475×C₇₉	C₂²	semidirect
33. #475×C₇₉	C₂²	semidirect
34. #474×C₇₉	C₂²	semidirect
37. #462×C₇₉	C₂²	semidirect
38. #462×C₇₉	C₂²	semidirect
39. #461×C₇₉	C₂²	semidirect
49. Q₈⋊C₈×C₇₉	C₂²	semidirect
50. Q₈⋊C₈×C₇₉	C₂²	semidirect
51. Q₈⋊C₈×C₇₉	C₂²	semidirect
52. D₄⋊C₈×C₇₉	C₂²	semidirect
292. #18576	C₇₉	direct (N × H)
300. #3255	C₂×C₇₉	semidirect
301. #3138	C₂×C₇₉	semidirect
302. #3107	C₂×C₇₉	semidirect
303. #1642	C₂×C₇₉	semidirect
304. #1641	C₂×C₇₉	semidirect
305. #1640	C₂×C₇₉	semidirect
306. #1640	C₂×C₇₉	semidirect
307. #1545	C₂×C₇₉	semidirect
308. #1489	C₂×C₇₉	semidirect
309. #1485	C₂×C₇₉	semidirect
310. C₇₉	#18576	direct (N × H)
331. #475	C₂²×C₇₉	semidirect
332. #475	C₂²×C₇₉	semidirect
333. #474	C₂²×C₇₉	semidirect
336. #462	C₂²×C₇₉	semidirect
337. #462	C₂²×C₇₉	semidirect
338. #461	C₂²×C₇₉	semidirect
348. Q₈⋊C₈	C₂²×C₇₉	semidirect
349. Q₈⋊C₈	C₂²×C₇₉	semidirect
350. Q₈⋊C₈	C₂²×C₇₉	semidirect
351. D₄⋊C₈	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3508	2
C₇₉×#3255	2
C₇₉×#3138	2
C₇₉×#3107	2
C₇₉×#1642	2
C₇₉×#1641	2
C₇₉×#1640	2
C₇₉×#1545	2
C₇₉×#1489	2
C₇₉×#1485	2
#18576	79

Subgroups — C79×#18576 #34130265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18576 #34130265