Subgroups — C₇₉×#18770 #34130459

Order 20224.

1288 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1642	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1621	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₉	—	2	1	no	—
11	C₂×AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
12	#550×C₇₉	—	2	2	no	—
13	#550×C₇₉	—	2	2	no	—
14	#550×C₇₉	—	2	2	no	—
15	#550×C₇₉	C₂²	1	4	yes	—
16	#532×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₉	—	2	1	no	—
18	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#121×C₇₉	—	2	2	no	—
20	C₂×#121×C₇₉	—	2	1	no	—
21	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₉	—	2	1	no	—
23	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
24	#493×C₇₉	C₂²	1	2	yes	complemented
25	#486×C₇₉	C₂²	1	2	yes	complemented
26	#481×C₇₉	—	2	1	no	—
27	#475×C₇₉	C₂²	1	2	yes	complemented
28	#463×C₇₉	—	2	2	no	—
29	#461×C₇₉	C₂²	1	2	yes	complemented
30	#460×C₇₉	C₂²	1	2	yes	complemented
31	#459×C₇₉	—	2	2	no	—
32	#459×C₇₉	C₂²	1	2	yes	complemented
33	#448×C₇₉	—	2	1	no	—
34	#447×C₇₉	—	2	2	no	—
35	C₄×SD₁₆×C₇₉	—	2	2	no	—
36	#431×C₇₉	C₂²	1	1	yes	characteristic
37	#431×C₇₉	C₂²	1	1	yes	characteristic
38	#423×C₇₉	C₂²	1	1	yes	characteristic
39	#417×C₇₉	—	2	1	no	—
40	#331×C₇₉	C₂²	1	4	yes	complemented
41	Q₈⋊C₈×C₇₉	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	4	yes	complemented
43	C₂×#41×C₇₉	—	2	4	no	—
44	C₂×#41×C₇₉	—	2	4	no	—
45	C₂×#41×C₇₉	—	2	1	no	—
46	C₂×#41×C₇₉	—	4	8	no	—
47	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₇₉	—	2	2	no	—
49	C₂²×D₄×C₇₉	—	2	2	no	—
50	C₂²×D₄×C₇₉	—	2	1	no	—
51	C₂²×D₄×C₇₉	—	2	1	no	—
52	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₇₉	D₄	1	2	yes	—
54	C₂³×C₄×C₇₉	—	2	2	no	—
55	C₂³×C₄×C₇₉	—	2	1	no	—
56	AGL(1,ℤ/8)×C₇₉	—	4	4	no	—
57	C₂×SD₁₆×C₇₉	—	2	2	no	—
58	C₂×SD₁₆×C₇₉	—	2	2	no	—
59	C₂×D₈×C₇₉	—	2	2	no	—
60	C₂×D₈×C₇₉	—	2	4	no	—
61	C₂×M₁₆×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	#127×C₇₉	—	2	4	no	—
64	#127×C₇₉	—	2	4	no	—
65	#127×C₇₉	—	2	1	no	—
66	#127×C₇₉	—	2	1	no	—
67	#127×C₇₉	D₄	1	2	yes	—
68	#127×C₇₉	C₂³	1	1	yes	characteristic
69	#127×C₇₉	C₂³	1	2	yes	—
70	#124×C₇₉	—	2	1	no	—
71	#121×C₇₉	—	2	4	no	—
72	#121×C₇₉	—	2	8	no	—
73	#121×C₇₉	—	2	8	no	—
74	#121×C₇₉	—	2	4	no	—
75	#121×C₇₉	—	2	1	no	—
76	#121×C₇₉	—	2	1	no	—
77	C₄×Q₈×C₇₉	—	2	1	no	—
78	C₄×Q₈×C₇₉	—	2	1	no	—
79	C₄×Q₈×C₇₉	D₄	1	2	yes	—
80	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
81	C₄×D₄×C₇₉	—	2	4	no	—
82	C₄×D₄×C₇₉	—	2	4	no	—
83	C₄×D₄×C₇₉	—	2	1	no	—
84	C₄×D₄×C₇₉	—	2	1	no	—
85	C₄×D₄×C₇₉	—	2	1	no	—
86	C₄×D₄×C₇₉	—	2	1	no	—
87	C₄×D₄×C₇₉	D₄	1	2	yes	—
88	C₄×D₄×C₇₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	—	2	1	no	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	#106×C₇₉	—	2	2	no	—
97	C₄⋊C₈×C₇₉	—	2	1	no	—
98	C₄⋊C₈×C₇₉	—	2	1	no	—
99	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
100	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
101	#103×C₇₉	—	2	2	no	—
102	#103×C₇₉	—	2	2	no	—
103	#102×C₇₉	—	2	4	no	—
104	#102×C₇₉	—	2	2	no	—
105	#102×C₇₉	—	2	2	no	—
106	C₂²⋊C₈×C₇₉	—	2	1	no	—
107	C₂²⋊C₈×C₇₉	—	2	1	no	—
108	C₄×C₈×C₇₉	—	2	1	no	—
109	C₄×C₈×C₇₉	C₂³	1	2	yes	—
110	C₂⁴×C₇₉	—	2	1	no	—
111	C₂⁴×C₇₉	—	2	2	no	—
112	#41×C₇₉	—	4	16	no	—
113	#41×C₇₉	—	4	8	no	—
114	#41×C₇₉	—	4	8	no	—
115	#41×C₇₉	—	4	2	no	—
116	#41×C₇₉	—	4	2	no	—
117	C₂×Q₈×C₇₉	—	2	4	no	—
118	C₂×Q₈×C₇₉	—	2	1	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₇₉	—	2	8	no	—
122	C₂×D₄×C₇₉	—	2	8	no	—
123	C₂×D₄×C₇₉	—	2	1	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	2	2	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	1	no	—
132	C₂×D₄×C₇₉	—	2	1	no	—
133	C₂×D₄×C₇₉	—	2	1	no	—
134	C₂×D₄×C₇₉	—	4	8	no	—
135	C₂×D₄×C₇₉	—	4	4	no	—
136	C₂×D₄×C₇₉	—	4	1	no	—
137	C₂×D₄×C₇₉	—	4	2	no	—
138	C₂×D₄×C₇₉	—	4	2	no	—
139	C₂×D₄×C₇₉	—	8	2	no	—
140	C₂×D₄×C₇₉	—	8	4	no	—
141	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	8	no	—
145	C₂²×C₄×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	—	2	1	no	—
147	C₂²×C₄×C₇₉	—	2	2	no	—
148	C₂²×C₄×C₇₉	—	2	2	no	—
149	C₂²×C₄×C₇₉	—	4	8	no	—
150	C₂²×C₄×C₇₉	—	4	4	no	—
151	C₂²×C₄×C₇₉	—	4	1	no	—
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
155	SD₁₆×C₇₉	—	4	4	no	—
156	SD₁₆×C₇₉	—	4	4	no	—
157	D₈×C₇₉	—	4	4	no	—
158	D₈×C₇₉	—	8	4	no	—
159	M₁₆×C₇₉	—	4	2	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	2	2	no	—
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	1	no	—
165	C₄⋊C₄×C₇₉	—	2	1	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	2	1	no	—
168	C₄⋊C₄×C₇₉	—	2	1	no	—
169	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₇₉	—	2	8	no	—
172	C₂²⋊C₄×C₇₉	—	2	2	no	—
173	C₂²⋊C₄×C₇₉	—	2	2	no	—
174	C₂²⋊C₄×C₇₉	—	4	1	no	—
175	C₂²⋊C₄×C₇₉	—	4	1	no	—
176	C₄²×C₇₉	—	2	2	no	—
177	C₄²×C₇₉	—	2	2	no	—
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	2	4	no	—
184	C₂³×C₇₉	—	4	4	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	4	4	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂³×C₇₉	—	4	2	no	—
189	C₂³×C₇₉	—	4	4	no	—
190	C₂³×C₇₉	—	4	1	no	—
191	C₂³×C₇₉	#120	1	1	yes	characteristic
192	Q₈×C₇₉	—	2	4	no	—
193	Q₈×C₇₉	—	2	2	no	—
194	Q₈×C₇₉	—	4	1	no	—
195	Q₈×C₇₉	—	4	1	no	—
196	Q₈×C₇₉	AGL(1,ℤ/8)	1	4	yes	complemented
197	D₄×C₇₉	—	2	2	no	—
198	D₄×C₇₉	—	2	2	no	—
199	D₄×C₇₉	—	4	4	no	—
200	D₄×C₇₉	—	4	16	no	—
201	D₄×C₇₉	—	4	4	no	—
202	D₄×C₇₉	—	4	2	no	—
203	D₄×C₇₉	—	4	2	no	—
204	D₄×C₇₉	—	4	1	no	—
205	D₄×C₇₉	—	4	2	no	—
206	D₄×C₇₉	—	4	4	no	—
207	D₄×C₇₉	—	4	1	no	—
208	D₄×C₇₉	—	4	2	no	—
209	D₄×C₇₉	—	4	2	no	—
210	D₄×C₇₉	—	4	4	no	—
211	D₄×C₇₉	—	8	2	no	—
212	D₄×C₇₉	—	8	8	no	—
213	D₄×C₇₉	—	8	2	no	—
214	C₂×C₄×C₇₉	—	2	4	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	2	no	—
218	C₂×C₄×C₇₉	—	2	2	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	16	no	—
221	C₂×C₄×C₇₉	—	4	4	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	4	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	8	2	no	—
227	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₇₉	#135	1	2	yes	—
231	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
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	2	no	—
236	C₈×C₇₉	—	4	2	no	—
237	C₈×C₇₉	—	4	2	no	—
238	C₂²×C₇₉	—	2	1	no	—
239	C₂²×C₇₉	—	2	1	no	—
240	C₂²×C₇₉	—	4	2	no	—
241	C₂²×C₇₉	—	4	4	no	—
242	C₂²×C₇₉	—	4	4	no	—
243	C₂²×C₇₉	—	4	2	no	—
244	C₂²×C₇₉	—	4	4	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	8	4	no	—
247	C₂²×C₇₉	—	8	8	no	—
248	C₂²×C₇₉	—	8	1	no	—
249	C₂²×C₇₉	—	8	1	no	—
250	C₂²×C₇₉	—	8	1	no	—
251	C₂²×C₇₉	#449	1	2	yes	—
252	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
253	C₄×C₇₉	—	2	4	no	—
254	C₄×C₇₉	—	2	1	no	—
255	C₄×C₇₉	—	2	1	no	—
256	C₄×C₇₉	—	2	1	no	—
257	C₄×C₇₉	—	4	2	no	—
258	C₄×C₇₉	—	4	2	no	—
259	C₄×C₇₉	—	8	1	no	—
260	C₄×C₇₉	#449	1	2	yes	—
261	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
262	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
264	#18770	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂×C₇₉	—	2	2	no	—
266	C₂×C₇₉	—	8	2	no	—
267	C₂×C₇₉	—	8	4	no	—
268	C₂×C₇₉	—	16	1	no	—
269	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
270	C₂×C₇₉	#3003	1	1	yes	characteristic
271	C₂×C₇₉	#3019	1	1	yes	characteristic
272	C₂×#550	C₂×C₇₉	1	1	yes	characteristic, complemented
273	#3205	C₂×C₇₉	1	1	yes	characteristic, complemented
274	#3103	C₂×C₇₉	1	1	yes	characteristic, complemented
275	#3036	C₂×C₇₉	1	1	yes	characteristic, complemented
276	#1642	C₂×C₇₉	1	4	yes	complemented
277	#1621	C₂×C₇₉	1	4	yes	complemented
278	#1545	C₂×C₇₉	1	1	yes	characteristic, complemented
279	#1487	C₂×C₇₉	1	1	yes	characteristic, complemented
280	#1478	C₂×C₇₉	1	1	yes	characteristic, complemented
281	C₇₉	#18770	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×#41	—	2	1	no	—
283	C₂×AGL(1,ℤ/8)	—	2	1	no	—
284	#550	—	2	2	no	—
285	#550	—	2	2	no	—
286	#550	—	2	2	no	—
287	#550	C₂²×C₇₉	1	4	yes	—
288	#532	C₂²×C₇₉	1	1	yes	characteristic
289	C₂×#127	—	2	1	no	—
290	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
291	C₂×#121	—	2	2	no	—
292	C₂×#121	—	2	1	no	—
293	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
294	C₂×C₄×D₄	—	2	1	no	—
295	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
296	#493	C₂²×C₇₉	1	2	yes	complemented
297	#486	C₂²×C₇₉	1	2	yes	complemented
298	#481	—	2	1	no	—
299	#475	C₂²×C₇₉	1	2	yes	complemented
300	#463	—	2	2	no	—
301	#461	C₂²×C₇₉	1	2	yes	complemented
302	#460	C₂²×C₇₉	1	2	yes	complemented
303	#459	—	2	2	no	—
304	#459	C₂²×C₇₉	1	2	yes	complemented
305	#448	—	2	1	no	—
306	#447	—	2	2	no	—
307	C₄×SD₁₆	—	2	2	no	—
308	#431	C₂²×C₇₉	1	1	yes	characteristic
309	#431	C₂²×C₇₉	1	1	yes	characteristic
310	#423	C₂²×C₇₉	1	1	yes	characteristic
311	#417	—	2	1	no	—
312	#331	C₂²×C₇₉	1	4	yes	complemented
313	Q₈⋊C₈	C₂²×C₇₉	1	4	yes	complemented
314	D₄⋊C₈	C₂²×C₇₉	1	4	yes	complemented
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	4	8	no	—
319	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
325	C₂²×D₄	D₄×C₇₉	1	2	yes	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	2	1	no	—
328	AGL(1,ℤ/8)	—	4	4	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×D₈	—	2	2	no	—
332	C₂×D₈	—	2	4	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
335	#127	—	2	4	no	—
336	#127	—	2	4	no	—
337	#127	—	2	1	no	—
338	#127	—	2	1	no	—
339	#127	D₄×C₇₉	1	2	yes	—
340	#127	C₂³×C₇₉	1	1	yes	characteristic
341	#127	C₂³×C₇₉	1	2	yes	—
342	#124	—	2	1	no	—
343	#121	—	2	4	no	—
344	#121	—	2	8	no	—
345	#121	—	2	8	no	—
346	#121	—	2	4	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	D₄×C₇₉	1	2	yes	—
352	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₇₉	1	2	yes	—
360	C₄×D₄	C₂³×C₇₉	1	2	yes	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
368	#106	—	2	2	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
372	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#102	—	2	4	no	—
376	#102	—	2	2	no	—
377	#102	—	2	2	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	C₂³×C₇₉	1	2	yes	—
382	C₂⁴	—	2	1	no	—
383	C₂⁴	—	2	2	no	—
384	#41	—	4	16	no	—
385	#41	—	4	8	no	—
386	#41	—	4	8	no	—
387	#41	—	4	2	no	—
388	#41	—	4	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	8	2	no	—
412	C₂×D₄	—	8	4	no	—
413	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
414	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	4	8	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
427	SD₁₆	—	4	4	no	—
428	SD₁₆	—	4	4	no	—
429	D₈	—	4	4	no	—
430	D₈	—	8	4	no	—
431	M₁₆	—	4	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	4	1	no	—
447	C₂²⋊C₄	—	4	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
453	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	1	no	—
463	C₂³	#120×C₇₉	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	Q₈	AGL(1,ℤ/8)×C₇₉	1	4	yes	complemented
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	16	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	8	no	—
485	D₄	—	8	2	no	—
486	C₂×C₄	—	2	4	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	16	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
500	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
501	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
502	C₂×C₄	#135×C₇₉	1	2	yes	—
503	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₈	—	4	2	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	8	4	no	—
519	C₂²	—	8	8	no	—
520	C₂²	—	8	1	no	—
521	C₂²	—	8	1	no	—
522	C₂²	—	8	1	no	—
523	C₂²	#449×C₇₉	1	2	yes	—
524	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	8	1	no	—
532	C₄	#449×C₇₉	1	2	yes	—
533	C₄	C₂×#135×C₇₉	1	1	yes	characteristic
534	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
535	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
536	C₂	—	2	2	no	—
537	C₂	—	8	4	no	—
538	C₂	—	8	2	no	—
539	C₂	—	16	1	no	—
540	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
541	C₂	C₇₉×#3003	1	1	yes	characteristic
542	C₂	C₇₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
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
1. C₂×#550×C₇₉	C₂	semidirect
2. C₇₉×#3205	C₂	semidirect
3. C₇₉×#3103	C₂	semidirect
4. C₇₉×#3036	C₂	semidirect
5. C₇₉×#1642	C₂	semidirect
6. C₇₉×#1621	C₂	semidirect
7. C₇₉×#1545	C₂	semidirect
8. C₇₉×#1487	C₂	semidirect
9. C₇₉×#1478	C₂	semidirect
24. #493×C₇₉	C₂²	semidirect
25. #486×C₇₉	C₂²	semidirect
27. #475×C₇₉	C₂²	semidirect
29. #461×C₇₉	C₂²	semidirect
30. #460×C₇₉	C₂²	semidirect
32. #459×C₇₉	C₂²	semidirect
40. #331×C₇₉	C₂²	semidirect
41. Q₈⋊C₈×C₇₉	C₂²	semidirect
42. D₄⋊C₈×C₇₉	C₂²	semidirect
196. Q₈×C₇₉	AGL(1,ℤ/8)	semidirect
264. #18770	C₇₉	direct (N × H)
272. C₂×#550	C₂×C₇₉	semidirect
273. #3205	C₂×C₇₉	semidirect
274. #3103	C₂×C₇₉	semidirect
275. #3036	C₂×C₇₉	semidirect
276. #1642	C₂×C₇₉	semidirect
277. #1621	C₂×C₇₉	semidirect
278. #1545	C₂×C₇₉	semidirect
279. #1487	C₂×C₇₉	semidirect
280. #1478	C₂×C₇₉	semidirect
281. C₇₉	#18770	direct (N × H)
296. #493	C₂²×C₇₉	semidirect
297. #486	C₂²×C₇₉	semidirect
299. #475	C₂²×C₇₉	semidirect
301. #461	C₂²×C₇₉	semidirect
302. #460	C₂²×C₇₉	semidirect
304. #459	C₂²×C₇₉	semidirect
312. #331	C₂²×C₇₉	semidirect
313. Q₈⋊C₈	C₂²×C₇₉	semidirect
314. D₄⋊C₈	C₂²×C₇₉	semidirect
468. Q₈	AGL(1,ℤ/8)×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₇₉	2
C₇₉×#3205	2
C₇₉×#3103	2
C₇₉×#3036	2
C₇₉×#1642	2
C₇₉×#1621	2
C₇₉×#1545	2
C₇₉×#1487	2
C₇₉×#1478	2
#18770	79

Subgroups — C79×#18770 #34130459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18770 #34130459