Subgroups — C₇₉×#18937 #34130626

Order 20224.

914 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3548	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1643	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1642	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1632	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1631	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
12	#562×C₇₉	—	2	2	no	—
13	#554×C₇₉	—	2	1	no	—
14	#554×C₇₉	C₂²	1	2	yes	—
15	#550×C₇₉	—	2	1	no	—
16	#550×C₇₉	C₂²	1	2	yes	—
17	#547×C₇₉	—	2	1	no	—
18	#547×C₇₉	—	2	1	no	—
19	#540×C₇₉	—	2	2	no	—
20	#537×C₇₉	—	2	2	no	—
21	#537×C₇₉	—	2	2	no	—
22	#533×C₇₉	C₂²	1	1	yes	characteristic
23	#533×C₇₉	C₂²	1	1	yes	characteristic
24	#532×C₇₉	C₂²	1	1	yes	characteristic
25	#532×C₇₉	C₂²	1	1	yes	characteristic
26	#501×C₇₉	—	2	1	no	—
27	#494×C₇₉	C₂²	1	1	yes	characteristic
28	#492×C₇₉	C₂²	1	1	yes	characteristic
29	#491×C₇₉	—	2	1	no	—
30	#487×C₇₉	C₂²	1	1	yes	characteristic
31	#486×C₇₉	C₂²	1	1	yes	characteristic
32	#485×C₇₉	—	2	2	no	—
33	#477×C₇₉	C₂²	1	2	yes	—
34	#476×C₇₉	C₂²	1	2	yes	—
35	#475×C₇₉	—	2	1	no	—
36	#475×C₇₉	C₂²	1	2	yes	—
37	#465×C₇₉	—	2	2	no	—
38	#464×C₇₉	—	2	2	no	—
39	#461×C₇₉	C₂²	1	2	yes	—
40	#460×C₇₉	—	2	1	no	—
41	#452×C₇₉	—	2	2	no	—
42	#432×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	#333×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	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
50	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
51	C₂×#41×C₇₉	—	2	2	no	—
52	C₂×#41×C₇₉	—	2	2	no	—
53	C₂×#41×C₇₉	—	2	1	no	—
54	C₂×#41×C₇₉	D₄	1	2	yes	—
55	C₂×Q₁₆×C₇₉	—	2	2	no	—
56	C₂×SD₁₆×C₇₉	—	2	2	no	—
57	C₂×SD₁₆×C₇₉	—	2	2	no	—
58	C₂²×C₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
65	#127×C₇₉	—	2	2	no	—
66	#127×C₇₉	D₄	1	1	yes	characteristic
67	#127×C₇₉	C₂³	1	1	yes	characteristic
68	#125×C₇₉	—	2	2	no	—
69	#125×C₇₉	—	2	1	no	—
70	#125×C₇₉	—	2	1	no	—
71	#124×C₇₉	—	2	1	no	—
72	#124×C₇₉	D₄	1	2	yes	—
73	#123×C₇₉	—	2	4	no	—
74	#123×C₇₉	—	2	4	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	C₂²⋊Q₈×C₇₉	—	2	4	no	—
79	C₂²⋊Q₈×C₇₉	—	2	1	no	—
80	C₂²⋊Q₈×C₇₉	—	2	1	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
83	#121×C₇₉	—	2	4	no	—
84	#121×C₇₉	—	2	4	no	—
85	#121×C₇₉	—	2	2	no	—
86	#121×C₇₉	—	2	4	no	—
87	#121×C₇₉	—	2	4	no	—
88	#121×C₇₉	—	2	1	no	—
89	#121×C₇₉	—	2	1	no	—
90	#121×C₇₉	—	2	1	no	—
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	D₄	1	2	yes	—
93	C₄×Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
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	1	no	—
100	C₄×D₄×C₇₉	—	2	1	no	—
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	C₂³	1	2	yes	—
103	#117×C₇₉	—	2	1	no	—
104	#117×C₇₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
107	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
108	#107×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	—	8	2	no	—
127	#41×C₇₉	—	8	2	no	—
128	#41×C₇₉	—	8	4	no	—
129	#41×C₇₉	—	8	4	no	—
130	C₂×Q₈×C₇₉	—	2	1	no	—
131	C₂×Q₈×C₇₉	—	2	1	no	—
132	C₂×Q₈×C₇₉	—	2	1	no	—
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₇₉	—	2	4	no	—
137	C₂×D₄×C₇₉	—	2	4	no	—
138	C₂×D₄×C₇₉	—	2	2	no	—
139	C₂×D₄×C₇₉	—	2	2	no	—
140	C₂×D₄×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	—	2	1	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	—	2	1	no	—
144	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇₉	—	2	4	no	—
147	C₂²×C₄×C₇₉	—	2	4	no	—
148	C₂²×C₄×C₇₉	—	2	2	no	—
149	C₂²×C₄×C₇₉	—	2	2	no	—
150	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	Q₁₆×C₇₉	—	8	2	no	—
154	SD₁₆×C₇₉	—	8	2	no	—
155	SD₁₆×C₇₉	—	8	2	no	—
156	C₂×C₈×C₇₉	—	2	1	no	—
157	C₂×C₈×C₇₉	—	2	1	no	—
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	—	8	1	no	—
161	C₄⋊C₄×C₇₉	—	2	4	no	—
162	C₄⋊C₄×C₇₉	—	2	4	no	—
163	C₄⋊C₄×C₇₉	—	2	1	no	—
164	C₄⋊C₄×C₇₉	—	2	1	no	—
165	C₄⋊C₄×C₇₉	—	2	1	no	—
166	C₄⋊C₄×C₇₉	—	2	1	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	—	2	1	no	—
169	C₄⋊C₄×C₇₉	—	2	1	no	—
170	C₄⋊C₄×C₇₉	—	2	2	no	—
171	C₄⋊C₄×C₇₉	—	2	1	no	—
172	C₄⋊C₄×C₇₉	—	2	1	no	—
173	C₄⋊C₄×C₇₉	—	2	1	no	—
174	C₄⋊C₄×C₇₉	—	2	1	no	—
175	C₄⋊C₄×C₇₉	—	4	1	no	—
176	C₄⋊C₄×C₇₉	—	4	1	no	—
177	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
178	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
179	C₂²⋊C₄×C₇₉	—	2	4	no	—
180	C₂²⋊C₄×C₇₉	—	2	4	no	—
181	C₂²⋊C₄×C₇₉	—	2	2	no	—
182	C₂²⋊C₄×C₇₉	—	2	2	no	—
183	C₂²⋊C₄×C₇₉	—	2	2	no	—
184	C₂²⋊C₄×C₇₉	—	2	2	no	—
185	C₂²⋊C₄×C₇₉	—	2	2	no	—
186	C₂²⋊C₄×C₇₉	—	4	1	no	—
187	C₄²×C₇₉	—	2	2	no	—
188	C₄²×C₇₉	—	4	1	no	—
189	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
193	C₂³×C₇₉	—	2	2	no	—
194	C₂³×C₇₉	—	2	2	no	—
195	C₂³×C₇₉	#120	1	1	yes	characteristic
196	Q₈×C₇₉	—	2	4	no	—
197	Q₈×C₇₉	—	4	2	no	—
198	Q₈×C₇₉	—	4	2	no	—
199	Q₈×C₇₉	—	4	2	no	—
200	Q₈×C₇₉	—	4	1	no	—
201	Q₈×C₇₉	—	4	1	no	—
202	Q₈×C₇₉	—	8	1	no	—
203	D₄×C₇₉	—	2	2	no	—
204	D₄×C₇₉	—	2	2	no	—
205	D₄×C₇₉	—	4	2	no	—
206	D₄×C₇₉	—	4	2	no	—
207	D₄×C₇₉	—	4	1	no	—
208	D₄×C₇₉	—	4	2	no	—
209	D₄×C₇₉	—	4	1	no	—
210	D₄×C₇₉	—	8	1	no	—
211	D₄×C₇₉	—	8	2	no	—
212	D₄×C₇₉	—	8	2	no	—
213	D₄×C₇₉	—	8	4	no	—
214	D₄×C₇₉	—	8	4	no	—
215	C₂×C₄×C₇₉	—	2	1	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	2	no	—
219	C₂×C₄×C₇₉	—	2	2	no	—
220	C₂×C₄×C₇₉	—	2	2	no	—
221	C₂×C₄×C₇₉	—	2	2	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	4	no	—
224	C₂×C₄×C₇₉	—	4	4	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	1	no	—
227	C₂×C₄×C₇₉	—	8	4	no	—
228	C₂×C₄×C₇₉	—	8	4	no	—
229	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
235	C₈×C₇₉	—	4	1	no	—
236	C₈×C₇₉	—	4	1	no	—
237	C₈×C₇₉	—	4	2	no	—
238	C₈×C₇₉	—	4	2	no	—
239	C₂²×C₇₉	—	2	1	no	—
240	C₂²×C₇₉	—	2	1	no	—
241	C₂²×C₇₉	—	2	1	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	2	no	—
244	C₂²×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
249	C₄×C₇₉	—	2	1	no	—
250	C₄×C₇₉	—	2	1	no	—
251	C₄×C₇₉	—	2	1	no	—
252	C₄×C₇₉	—	2	1	no	—
253	C₄×C₇₉	—	4	2	no	—
254	C₄×C₇₉	—	4	2	no	—
255	C₄×C₇₉	—	4	2	no	—
256	C₄×C₇₉	—	4	2	no	—
257	C₄×C₇₉	—	8	1	no	—
258	C₄×C₇₉	—	8	1	no	—
259	C₄×C₇₉	#577	1	2	yes	—
260	C₄×C₇₉	#577	1	1	yes	characteristic
261	C₄×C₇₉	#578	1	1	yes	characteristic
262	#18937	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂×C₇₉	—	4	1	no	—
264	C₂×C₇₉	—	8	2	no	—
265	C₂×C₇₉	—	8	2	no	—
266	C₂×C₇₉	#3009	1	1	yes	characteristic
267	C₂×C₇₉	#3013	1	1	yes	characteristic
268	C₂×C₇₉	#3019	1	1	yes	characteristic
269	#3548	C₂×C₇₉	1	1	yes	characteristic
270	#3246	C₂×C₇₉	1	1	yes	characteristic, complemented
271	#3237	C₂×C₇₉	1	1	yes	characteristic, complemented
272	#3210	C₂×C₇₉	1	1	yes	characteristic, complemented
273	#1643	C₂×C₇₉	1	2	yes	complemented
274	#1642	C₂×C₇₉	1	2	yes	complemented
275	#1632	C₂×C₇₉	1	2	yes	complemented
276	#1631	C₂×C₇₉	1	2	yes	complemented
277	#1551	C₂×C₇₉	1	1	yes	characteristic, complemented
278	#1496	C₂×C₇₉	1	1	yes	characteristic, complemented
279	#1481	C₂×C₇₉	1	1	yes	characteristic, complemented
280	C₇₉	#18937	1	1	yes	characteristic, direct product factor, Sylow
281	#562	—	2	2	no	—
282	#554	—	2	1	no	—
283	#554	C₂²×C₇₉	1	2	yes	—
284	#550	—	2	1	no	—
285	#550	C₂²×C₇₉	1	2	yes	—
286	#547	—	2	1	no	—
287	#547	—	2	1	no	—
288	#540	—	2	2	no	—
289	#537	—	2	2	no	—
290	#537	—	2	2	no	—
291	#533	C₂²×C₇₉	1	1	yes	characteristic
292	#533	C₂²×C₇₉	1	1	yes	characteristic
293	#532	C₂²×C₇₉	1	1	yes	characteristic
294	#532	C₂²×C₇₉	1	1	yes	characteristic
295	#501	—	2	1	no	—
296	#494	C₂²×C₇₉	1	1	yes	characteristic
297	#492	C₂²×C₇₉	1	1	yes	characteristic
298	#491	—	2	1	no	—
299	#487	C₂²×C₇₉	1	1	yes	characteristic
300	#486	C₂²×C₇₉	1	1	yes	characteristic
301	#485	—	2	2	no	—
302	#477	C₂²×C₇₉	1	2	yes	—
303	#476	C₂²×C₇₉	1	2	yes	—
304	#475	—	2	1	no	—
305	#475	C₂²×C₇₉	1	2	yes	—
306	#465	—	2	2	no	—
307	#464	—	2	2	no	—
308	#461	C₂²×C₇₉	1	2	yes	—
309	#460	—	2	1	no	—
310	#452	—	2	2	no	—
311	#432	C₂²×C₇₉	1	1	yes	characteristic
312	#431	C₂²×C₇₉	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
314	#333	C₂²×C₇₉	1	2	yes	—
315	#331	C₂²×C₇₉	1	2	yes	—
316	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
317	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
318	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
319	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	1	no	—
323	C₂×#41	D₄×C₇₉	1	2	yes	—
324	C₂×Q₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
329	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
330	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
334	#127	—	2	2	no	—
335	#127	D₄×C₇₉	1	1	yes	characteristic
336	#127	C₂³×C₇₉	1	1	yes	characteristic
337	#125	—	2	2	no	—
338	#125	—	2	1	no	—
339	#125	—	2	1	no	—
340	#124	—	2	1	no	—
341	#124	D₄×C₇₉	1	2	yes	—
342	#123	—	2	4	no	—
343	#123	—	2	4	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	2	no	—
355	#121	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	2	no	—
361	#121	D₄×C₇₉	1	2	yes	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	C₂³×C₇₉	1	2	yes	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
377	#107	—	2	2	no	—
378	#106	—	2	2	no	—
379	#106	—	2	2	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
383	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
395	#41	—	8	2	no	—
396	#41	—	8	2	no	—
397	#41	—	8	4	no	—
398	#41	—	8	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
404	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
414	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
422	Q₁₆	—	8	2	no	—
423	SD₁₆	—	8	2	no	—
424	SD₁₆	—	8	2	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	8	1	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
447	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	4	1	no	—
458	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
461	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	#120×C₇₉	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	1	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	8	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	8	1	no	—
480	D₄	—	8	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	4	no	—
483	D₄	—	8	4	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	8	4	no	—
497	C₂×C₄	—	8	4	no	—
498	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
499	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
500	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
504	C₈	—	4	1	no	—
505	C₈	—	4	1	no	—
506	C₈	—	4	2	no	—
507	C₈	—	4	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	1	no	—
528	C₄	#577×C₇₉	1	2	yes	—
529	C₄	#577×C₇₉	1	1	yes	characteristic
530	C₄	#578×C₇₉	1	1	yes	characteristic
531	C₂	—	4	1	no	—
532	C₂	—	8	2	no	—
533	C₂	—	8	2	no	—
534	C₂	C₇₉×#3009	1	1	yes	characteristic
535	C₂	C₇₉×#3013	1	1	yes	characteristic
536	C₂	C₇₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3548	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×#3237	C₂	semidirect
4. C₇₉×#3210	C₂	semidirect
5. C₇₉×#1643	C₂	semidirect
6. C₇₉×#1642	C₂	semidirect
7. C₇₉×#1632	C₂	semidirect
8. C₇₉×#1631	C₂	semidirect
9. C₇₉×#1551	C₂	semidirect
10. C₇₉×#1496	C₂	semidirect
11. C₇₉×#1481	C₂	semidirect
262. #18937	C₇₉	direct (N × H)
270. #3246	C₂×C₇₉	semidirect
271. #3237	C₂×C₇₉	semidirect
272. #3210	C₂×C₇₉	semidirect
273. #1643	C₂×C₇₉	semidirect
274. #1642	C₂×C₇₉	semidirect
275. #1632	C₂×C₇₉	semidirect
276. #1631	C₂×C₇₉	semidirect
277. #1551	C₂×C₇₉	semidirect
278. #1496	C₂×C₇₉	semidirect
279. #1481	C₂×C₇₉	semidirect
280. C₇₉	#18937	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×#3548	2
C₇₉×#3246	2
C₇₉×#3237	2
C₇₉×#3210	2
C₇₉×#1643	2
C₇₉×#1642	2
C₇₉×#1632	2
C₇₉×#1631	2
C₇₉×#1551	2
C₇₉×#1496	2
C₇₉×#1481	2
#18937	79

Subgroups — C79×#18937 #34130626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18937 #34130626