Subgroups — C₇₉×#18848 #34130537

Order 20224.

858 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3507	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3228	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1653	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1648	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×#1557	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₉	C₂²	1	2	yes	—
13	#557×C₇₉	C₂²	1	2	yes	—
14	#556×C₇₉	—	2	1	no	—
15	#556×C₇₉	—	2	2	no	—
16	#554×C₇₉	—	2	1	no	—
17	#552×C₇₉	—	2	2	no	—
18	#539×C₇₉	—	2	2	no	—
19	#536×C₇₉	—	2	1	no	—
20	#533×C₇₉	C₂²	1	1	yes	characteristic
21	#533×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	C₂²	1	1	yes	characteristic
23	#529×C₇₉	—	2	2	no	—
24	#520×C₇₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	#500×C₇₉	C₂²	1	1	yes	characteristic
27	#498×C₇₉	C₂²	1	1	yes	characteristic
28	#486×C₇₉	C₂²	1	1	yes	characteristic
29	#486×C₇₉	C₂²	1	1	yes	characteristic
30	#483×C₇₉	—	2	1	no	—
31	#482×C₇₉	—	2	2	no	—
32	#478×C₇₉	—	2	2	no	—
33	#475×C₇₉	—	2	1	no	—
34	#475×C₇₉	C₂²	1	2	yes	—
35	#475×C₇₉	C₂²	1	2	yes	—
36	#470×C₇₉	—	2	2	no	—
37	#462×C₇₉	—	2	1	no	—
38	#462×C₇₉	C₂²	1	2	yes	—
39	#462×C₇₉	C₂²	1	2	yes	—
40	#451×C₇₉	—	2	1	no	—
41	#441×C₇₉	—	2	2	no	—
42	#432×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#423×C₇₉	C₂²	1	1	yes	characteristic
45	#332×C₇₉	C₂²	1	2	yes	—
46	#331×C₇₉	C₂²	1	2	yes	—
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
51	C₂×#41×C₇₉	—	2	1	no	—
52	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
53	C₂×Q₁₆×C₇₉	—	2	2	no	—
54	C₂×Q₁₆×C₇₉	—	2	2	no	—
55	C₂×M₁₆×C₇₉	—	2	1	no	—
56	C₄⋊Q₈×C₇₉	—	2	2	no	—
57	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
62	#127×C₇₉	C₂³	1	1	yes	characteristic
63	#126×C₇₉	—	2	4	no	—
64	#126×C₇₉	—	2	4	no	—
65	#125×C₇₉	—	2	2	no	—
66	#125×C₇₉	—	2	4	no	—
67	#125×C₇₉	—	2	1	no	—
68	#125×C₇₉	—	2	1	no	—
69	#124×C₇₉	—	2	2	no	—
70	#124×C₇₉	—	2	2	no	—
71	#124×C₇₉	—	2	1	no	—
72	#123×C₇₉	—	2	4	no	—
73	#123×C₇₉	—	2	4	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	1	no	—
78	C₂²⋊Q₈×C₇₉	—	2	1	no	—
79	C₂²⋊Q₈×C₇₉	—	2	1	no	—
80	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
81	#121×C₇₉	—	2	1	no	—
82	#121×C₇₉	D₄	1	2	yes	—
83	C₄×Q₈×C₇₉	—	2	2	no	—
84	C₄×Q₈×C₇₉	—	2	2	no	—
85	C₄×Q₈×C₇₉	—	2	1	no	—
86	C₄×Q₈×C₇₉	—	2	1	no	—
87	C₄×Q₈×C₇₉	—	2	1	no	—
88	C₄×Q₈×C₇₉	—	2	1	no	—
89	C₄×Q₈×C₇₉	—	2	1	no	—
90	C₄×Q₈×C₇₉	D₄	1	2	yes	—
91	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
92	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
93	C₄×D₄×C₇₉	—	2	4	no	—
94	C₄×D₄×C₇₉	—	2	2	no	—
95	C₄×D₄×C₇₉	—	2	2	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	D₄	1	2	yes	—
98	#117×C₇₉	—	2	2	no	—
99	#117×C₇₉	—	2	4	no	—
100	#117×C₇₉	—	2	1	no	—
101	#117×C₇₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	—	2	1	no	—
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	#107×C₇₉	—	2	2	no	—
108	#106×C₇₉	—	2	2	no	—
109	#106×C₇₉	—	2	2	no	—
110	#106×C₇₉	—	2	2	no	—
111	C₄⋊C₈×C₇₉	—	2	1	no	—
112	C₄⋊C₈×C₇₉	—	2	1	no	—
113	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
114	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	#103×C₇₉	—	2	2	no	—
118	#103×C₇₉	—	2	2	no	—
119	#102×C₇₉	—	2	2	no	—
120	#102×C₇₉	—	2	2	no	—
121	C₂²⋊C₈×C₇₉	—	2	1	no	—
122	C₂²⋊C₈×C₇₉	—	2	1	no	—
123	#97×C₇₉	—	2	1	no	—
124	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	#41×C₇₉	—	4	4	no	—
127	C₂×Q₈×C₇₉	—	2	1	no	—
128	C₂×Q₈×C₇₉	—	2	1	no	—
129	C₂×Q₈×C₇₉	—	2	1	no	—
130	C₂×Q₈×C₇₉	—	2	1	no	—
131	C₂×Q₈×C₇₉	—	2	1	no	—
132	C₂×Q₈×C₇₉	—	4	2	no	—
133	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₇₉	—	2	2	no	—
136	C₂×D₄×C₇₉	—	2	1	no	—
137	C₂×D₄×C₇₉	—	2	1	no	—
138	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇₉	—	2	1	no	—
140	C₂²×C₄×C₇₉	—	2	4	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₇₉	—	4	4	no	—
147	Q₁₆×C₇₉	—	8	2	no	—
148	M₁₆×C₇₉	—	8	1	no	—
149	C₂×C₈×C₇₉	—	2	1	no	—
150	C₂×C₈×C₇₉	—	2	1	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	—	2	4	no	—
154	C₄⋊C₄×C₇₉	—	2	4	no	—
155	C₄⋊C₄×C₇₉	—	2	4	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	1	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	2	no	—
163	C₄⋊C₄×C₇₉	—	2	1	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	1	no	—
166	C₄⋊C₄×C₇₉	—	2	1	no	—
167	C₄⋊C₄×C₇₉	—	2	1	no	—
168	C₄⋊C₄×C₇₉	—	2	1	no	—
169	C₄⋊C₄×C₇₉	—	4	1	no	—
170	C₄⋊C₄×C₇₉	—	4	1	no	—
171	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
174	C₂²⋊C₄×C₇₉	—	2	4	no	—
175	C₂²⋊C₄×C₇₉	—	2	4	no	—
176	C₂²⋊C₄×C₇₉	—	2	4	no	—
177	C₂²⋊C₄×C₇₉	—	2	2	no	—
178	C₂²⋊C₄×C₇₉	—	2	2	no	—
179	C₂²⋊C₄×C₇₉	—	2	2	no	—
180	C₂²⋊C₄×C₇₉	—	4	1	no	—
181	C₄²×C₇₉	—	2	4	no	—
182	C₄²×C₇₉	—	2	2	no	—
183	C₄²×C₇₉	—	2	2	no	—
184	C₄²×C₇₉	—	2	2	no	—
185	C₄²×C₇₉	—	4	1	no	—
186	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
190	C₂³×C₇₉	—	2	2	no	—
191	C₂³×C₇₉	#120	1	1	yes	characteristic
192	Q₈×C₇₉	—	2	2	no	—
193	Q₈×C₇₉	—	2	2	no	—
194	Q₈×C₇₉	—	2	2	no	—
195	Q₈×C₇₉	—	2	2	no	—
196	Q₈×C₇₉	—	4	2	no	—
197	Q₈×C₇₉	—	4	2	no	—
198	Q₈×C₇₉	—	4	2	no	—
199	Q₈×C₇₉	—	4	1	no	—
200	Q₈×C₇₉	—	4	1	no	—
201	Q₈×C₇₉	—	8	1	no	—
202	D₄×C₇₉	—	4	2	no	—
203	D₄×C₇₉	—	4	4	no	—
204	D₄×C₇₉	—	4	2	no	—
205	D₄×C₇₉	—	4	1	no	—
206	D₄×C₇₉	—	4	1	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	1	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	2	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	4	1	no	—
216	C₂×C₄×C₇₉	—	4	4	no	—
217	C₂×C₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	—	4	1	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	8	1	no	—
221	C₂×C₄×C₇₉	—	8	4	no	—
222	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₇₉	—	4	1	no	—
229	C₈×C₇₉	—	4	1	no	—
230	C₈×C₇₉	—	4	2	no	—
231	C₈×C₇₉	—	4	2	no	—
232	C₂²×C₇₉	—	2	1	no	—
233	C₂²×C₇₉	—	2	1	no	—
234	C₂²×C₇₉	—	2	1	no	—
235	C₂²×C₇₉	—	4	2	no	—
236	C₂²×C₇₉	—	4	2	no	—
237	C₂²×C₇₉	—	4	2	no	—
238	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
239	C₄×C₇₉	—	2	1	no	—
240	C₄×C₇₉	—	2	1	no	—
241	C₄×C₇₉	—	2	1	no	—
242	C₄×C₇₉	—	2	1	no	—
243	C₄×C₇₉	—	4	2	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	1	no	—
249	C₄×C₇₉	—	8	1	no	—
250	C₄×C₇₉	#575	1	2	yes	—
251	C₄×C₇₉	#577	1	1	yes	characteristic
252	C₄×C₇₉	#578	1	1	yes	characteristic
253	#18848	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₉	—	4	1	no	—
255	C₂×C₇₉	—	8	2	no	—
256	C₂×C₇₉	#3005	1	1	yes	characteristic
257	C₂×C₇₉	#3013	1	1	yes	characteristic
258	C₂×C₇₉	#3022	1	1	yes	characteristic
259	#3507	C₂×C₇₉	1	1	yes	characteristic
260	#3255	C₂×C₇₉	1	1	yes	characteristic, complemented
261	#3228	C₂×C₇₉	1	1	yes	characteristic
262	#3113	C₂×C₇₉	1	1	yes	characteristic, complemented
263	#1653	C₂×C₇₉	1	2	yes	complemented
264	#1648	C₂×C₇₉	1	2	yes	complemented
265	#1640	C₂×C₇₉	1	2	yes	complemented
266	#1640	C₂×C₇₉	1	2	yes	complemented
267	#1557	C₂×C₇₉	1	1	yes	characteristic
268	#1497	C₂×C₇₉	1	1	yes	characteristic, complemented
269	#1487	C₂×C₇₉	1	1	yes	characteristic, complemented
270	C₇₉	#18848	1	1	yes	characteristic, direct product factor, Sylow
271	#559	C₂²×C₇₉	1	2	yes	—
272	#557	C₂²×C₇₉	1	2	yes	—
273	#556	—	2	1	no	—
274	#556	—	2	2	no	—
275	#554	—	2	1	no	—
276	#552	—	2	2	no	—
277	#539	—	2	2	no	—
278	#536	—	2	1	no	—
279	#533	C₂²×C₇₉	1	1	yes	characteristic
280	#533	C₂²×C₇₉	1	1	yes	characteristic
281	#532	C₂²×C₇₉	1	1	yes	characteristic
282	#529	—	2	2	no	—
283	#520	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
285	#500	C₂²×C₇₉	1	1	yes	characteristic
286	#498	C₂²×C₇₉	1	1	yes	characteristic
287	#486	C₂²×C₇₉	1	1	yes	characteristic
288	#486	C₂²×C₇₉	1	1	yes	characteristic
289	#483	—	2	1	no	—
290	#482	—	2	2	no	—
291	#478	—	2	2	no	—
292	#475	—	2	1	no	—
293	#475	C₂²×C₇₉	1	2	yes	—
294	#475	C₂²×C₇₉	1	2	yes	—
295	#470	—	2	2	no	—
296	#462	—	2	1	no	—
297	#462	C₂²×C₇₉	1	2	yes	—
298	#462	C₂²×C₇₉	1	2	yes	—
299	#451	—	2	1	no	—
300	#441	—	2	2	no	—
301	#432	C₂²×C₇₉	1	1	yes	characteristic
302	#431	C₂²×C₇₉	1	1	yes	characteristic
303	#423	C₂²×C₇₉	1	1	yes	characteristic
304	#332	C₂²×C₇₉	1	2	yes	—
305	#331	C₂²×C₇₉	1	2	yes	—
306	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
307	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
308	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
309	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
310	C₂×#41	—	2	1	no	—
311	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
317	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
321	#127	C₂³×C₇₉	1	1	yes	characteristic
322	#126	—	2	4	no	—
323	#126	—	2	4	no	—
324	#125	—	2	2	no	—
325	#125	—	2	4	no	—
326	#125	—	2	1	no	—
327	#125	—	2	1	no	—
328	#124	—	2	2	no	—
329	#124	—	2	2	no	—
330	#124	—	2	1	no	—
331	#123	—	2	4	no	—
332	#123	—	2	4	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
340	#121	—	2	1	no	—
341	#121	D₄×C₇₉	1	2	yes	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	D₄×C₇₉	1	2	yes	—
350	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
351	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	D₄×C₇₉	1	2	yes	—
357	#117	—	2	2	no	—
358	#117	—	2	4	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
366	#107	—	2	2	no	—
367	#106	—	2	2	no	—
368	#106	—	2	2	no	—
369	#106	—	2	2	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
373	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#102	—	2	2	no	—
379	#102	—	2	2	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	#97	—	2	1	no	—
383	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
384	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
385	#41	—	4	4	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
393	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
405	Q₁₆	—	4	4	no	—
406	Q₁₆	—	8	2	no	—
407	M₁₆	—	8	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	1	no	—
445	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
448	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
449	C₂³	—	2	2	no	—
450	C₂³	#120×C₇₉	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	8	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
482	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
483	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
487	C₈	—	4	1	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	1	no	—
508	C₄	—	8	1	no	—
509	C₄	#575×C₇₉	1	2	yes	—
510	C₄	#577×C₇₉	1	1	yes	characteristic
511	C₄	#578×C₇₉	1	1	yes	characteristic
512	C₂	—	4	1	no	—
513	C₂	—	8	2	no	—
514	C₂	C₇₉×#3005	1	1	yes	characteristic
515	C₂	C₇₉×#3013	1	1	yes	characteristic
516	C₂	C₇₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	#532×C₇₉	C₂²
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
4. C₇₉×#3113	C₂	semidirect
5. C₇₉×#1653	C₂	semidirect
6. C₇₉×#1648	C₂	semidirect
7. C₇₉×#1640	C₂	semidirect
8. C₇₉×#1640	C₂	semidirect
10. C₇₉×#1497	C₂	semidirect
11. C₇₉×#1487	C₂	semidirect
253. #18848	C₇₉	direct (N × H)
260. #3255	C₂×C₇₉	semidirect
262. #3113	C₂×C₇₉	semidirect
263. #1653	C₂×C₇₉	semidirect
264. #1648	C₂×C₇₉	semidirect
265. #1640	C₂×C₇₉	semidirect
266. #1640	C₂×C₇₉	semidirect
268. #1497	C₂×C₇₉	semidirect
269. #1487	C₂×C₇₉	semidirect
270. C₇₉	#18848	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×#3507	2
C₇₉×#3255	2
C₇₉×#3228	2
C₇₉×#3113	2
C₇₉×#1653	2
C₇₉×#1648	2
C₇₉×#1640	2
C₇₉×#1557	2
C₇₉×#1497	2
C₇₉×#1487	2
#18848	79

Subgroups — C79×#18848 #34130537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18848 #34130537