Subgroups — C₇₉×#18621 #34130310

Order 20224.

1314 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3498	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#492×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1631	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1629	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₇₉	—	2	1	no	—
11	C₂²×SD₁₆×C₇₉	—	2	2	no	—
12	#550×C₇₉	—	2	1	no	—
13	#550×C₇₉	C₂²	1	2	yes	—
14	D₄²×C₇₉	—	2	2	no	—
15	D₄²×C₇₉	—	2	2	no	—
16	D₄²×C₇₉	—	2	1	no	—
17	D₄²×C₇₉	C₂²	1	2	yes	—
18	#535×C₇₉	—	2	2	no	—
19	#535×C₇₉	—	2	1	no	—
20	#532×C₇₉	—	2	1	no	—
21	#532×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₇₉	—	2	1	no	—
24	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
25	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
26	#498×C₇₉	—	2	1	no	—
27	#492×C₇₉	—	2	2	no	—
28	#492×C₇₉	C₂²	1	4	yes	complemented
29	#486×C₇₉	—	2	1	no	—
30	#481×C₇₉	—	2	2	no	—
31	#477×C₇₉	C₂²	1	2	yes	complemented
32	#476×C₇₉	C₂²	1	2	yes	complemented
33	#476×C₇₉	C₂²	1	4	yes	complemented
34	#475×C₇₉	—	2	1	no	—
35	#474×C₇₉	—	2	1	no	—
36	#431×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	#428×C₇₉	—	2	1	no	—
38	#423×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#417×C₇₉	—	2	1	no	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#331×C₇₉	C₂²	1	4	yes	complemented
42	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
43	D₄⋊C₈×C₇₉	C₂²	1	4	yes	complemented
44	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
45	H(5,𝔽₂)×C₇₉	—	4	4	no	—
46	H(5,𝔽₂)×C₇₉	—	4	4	no	—
47	C₂×#41×C₇₉	—	2	2	no	—
48	C₂×#41×C₇₉	—	2	2	no	—
49	C₂×#41×C₇₉	—	2	1	no	—
50	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₇₉	—	2	1	no	—
52	C₂²×D₄×C₇₉	—	2	2	no	—
53	C₂²×D₄×C₇₉	—	2	4	no	—
54	C₂²×D₄×C₇₉	—	2	2	no	—
55	C₂²×D₄×C₇₉	—	2	2	no	—
56	C₂²×D₄×C₇₉	—	2	2	no	—
57	C₂²×D₄×C₇₉	—	2	1	no	—
58	C₂²×D₄×C₇₉	—	2	1	no	—
59	C₂²×D₄×C₇₉	D₄	1	2	yes	—
60	C₂×SD₁₆×C₇₉	—	2	8	no	—
61	C₂×SD₁₆×C₇₉	—	4	8	no	—
62	C₂×M₁₆×C₇₉	—	2	1	no	—
63	C₂²×C₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
69	#127×C₇₉	—	2	2	no	—
70	#127×C₇₉	—	2	2	no	—
71	#127×C₇₉	—	2	2	no	—
72	#127×C₇₉	—	2	1	no	—
73	#127×C₇₉	—	2	1	no	—
74	#127×C₇₉	D₄	1	1	yes	characteristic
75	#127×C₇₉	D₄	1	2	yes	—
76	#127×C₇₉	C₂³	1	2	yes	—
77	#124×C₇₉	—	2	2	no	—
78	#124×C₇₉	—	2	1	no	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	—	2	4	no	—
81	#121×C₇₉	—	2	4	no	—
82	#121×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	2	no	—
84	#121×C₇₉	—	2	2	no	—
85	#121×C₇₉	—	2	2	no	—
86	#121×C₇₉	D₄	1	2	yes	—
87	#120×C₇₉	—	2	4	no	—
88	#120×C₇₉	—	2	4	no	—
89	#120×C₇₉	—	2	4	no	—
90	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₇₉	—	2	2	no	—
93	C₄×D₄×C₇₉	—	2	1	no	—
94	C₄×D₄×C₇₉	—	2	1	no	—
95	C₄×D₄×C₇₉	—	2	2	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
98	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₇₉	C₂³	1	2	yes	—
100	#117×C₇₉	—	2	1	no	—
101	#117×C₇₉	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
106	#107×C₇₉	—	2	2	no	—
107	#106×C₇₉	—	2	2	no	—
108	#106×C₇₉	—	2	4	no	—
109	C₄⋊C₈×C₇₉	—	2	1	no	—
110	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
111	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
112	#103×C₇₉	—	2	2	no	—
113	#102×C₇₉	—	2	2	no	—
114	#102×C₇₉	—	2	4	no	—
115	C₂²⋊C₈×C₇₉	—	2	1	no	—
116	C₄×C₈×C₇₉	—	2	1	no	—
117	C₄×C₈×C₇₉	—	2	1	no	—
118	C₄×C₈×C₇₉	C₂³	1	2	yes	—
119	C₂⁴×C₇₉	—	2	4	no	—
120	C₂⁴×C₇₉	—	2	2	no	—
121	#41×C₇₉	—	2	2	no	—
122	#41×C₇₉	—	4	8	no	—
123	#41×C₇₉	—	4	4	no	—
124	#41×C₇₉	—	4	4	no	—
125	#41×C₇₉	—	4	2	no	—
126	#41×C₇₉	—	4	2	no	—
127	#41×C₇₉	SD₁₆	1	4	yes	complemented
128	C₂×Q₈×C₇₉	—	2	1	no	—
129	C₂×Q₈×C₇₉	—	2	2	no	—
130	C₂×Q₈×C₇₉	—	4	4	no	—
131	C₂×Q₈×C₇₉	—	4	1	no	—
132	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×D₄×C₇₉	—	2	1	no	—
134	C₂×D₄×C₇₉	—	2	4	no	—
135	C₂×D₄×C₇₉	—	2	4	no	—
136	C₂×D₄×C₇₉	—	2	2	no	—
137	C₂×D₄×C₇₉	—	2	4	no	—
138	C₂×D₄×C₇₉	—	2	4	no	—
139	C₂×D₄×C₇₉	—	2	2	no	—
140	C₂×D₄×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	—	2	2	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	—	2	2	no	—
144	C₂×D₄×C₇₉	—	2	2	no	—
145	C₂×D₄×C₇₉	—	2	2	no	—
146	C₂×D₄×C₇₉	—	4	8	no	—
147	C₂×D₄×C₇₉	—	4	4	no	—
148	C₂×D₄×C₇₉	—	4	16	no	—
149	C₂×D₄×C₇₉	—	4	4	no	—
150	C₂×D₄×C₇₉	—	4	4	no	—
151	C₂×D₄×C₇₉	—	4	2	no	—
152	C₂×D₄×C₇₉	—	4	2	no	—
153	C₂×D₄×C₇₉	—	8	2	no	—
154	C₂×D₄×C₇₉	—	8	4	no	—
155	C₂×D₄×C₇₉	—	8	4	no	—
156	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₇₉	—	2	1	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	2	no	—
164	C₂²×C₄×C₇₉	—	4	1	no	—
165	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
168	SD₁₆×C₇₉	—	4	16	no	—
169	M₁₆×C₇₉	—	4	2	no	—
170	C₂×C₈×C₇₉	—	2	4	no	—
171	C₂×C₈×C₇₉	—	2	2	no	—
172	C₂×C₈×C₇₉	—	2	2	no	—
173	C₂×C₈×C₇₉	—	2	2	no	—
174	C₄⋊C₄×C₇₉	—	2	1	no	—
175	C₄⋊C₄×C₇₉	—	2	1	no	—
176	C₄⋊C₄×C₇₉	—	2	1	no	—
177	C₄⋊C₄×C₇₉	—	2	2	no	—
178	C₄⋊C₄×C₇₉	—	2	2	no	—
179	C₄⋊C₄×C₇₉	—	4	1	no	—
180	C₄⋊C₄×C₇₉	—	4	1	no	—
181	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₇₉	—	2	4	no	—
185	C₂²⋊C₄×C₇₉	—	2	4	no	—
186	C₂²⋊C₄×C₇₉	—	2	1	no	—
187	C₂²⋊C₄×C₇₉	—	2	1	no	—
188	C₂²⋊C₄×C₇₉	—	2	2	no	—
189	C₂²⋊C₄×C₇₉	—	2	1	no	—
190	C₂²⋊C₄×C₇₉	—	2	2	no	—
191	C₄²×C₇₉	—	2	1	no	—
192	C₄²×C₇₉	—	2	1	no	—
193	C₄²×C₇₉	—	2	1	no	—
194	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
198	C₂³×C₇₉	—	2	1	no	—
199	C₂³×C₇₉	—	2	2	no	—
200	C₂³×C₇₉	—	2	4	no	—
201	C₂³×C₇₉	—	4	8	no	—
202	C₂³×C₇₉	—	4	4	no	—
203	C₂³×C₇₉	—	8	2	no	—
204	C₂³×C₇₉	—	8	2	no	—
205	C₂³×C₇₉	—	8	4	no	—
206	C₂³×C₇₉	—	8	4	no	—
207	C₂³×C₇₉	#120	1	1	yes	characteristic
208	Q₈×C₇₉	—	2	1	no	—
209	Q₈×C₇₉	—	4	4	no	—
210	Q₈×C₇₉	—	4	2	no	—
211	Q₈×C₇₉	—	8	2	no	—
212	Q₈×C₇₉	C₂×SD₁₆	1	2	yes	complemented
213	D₄×C₇₉	—	2	4	no	—
214	D₄×C₇₉	—	2	1	no	—
215	D₄×C₇₉	—	2	4	no	—
216	D₄×C₇₉	—	4	4	no	—
217	D₄×C₇₉	—	4	8	no	—
218	D₄×C₇₉	—	4	8	no	—
219	D₄×C₇₉	—	4	4	no	—
220	D₄×C₇₉	—	4	2	no	—
221	D₄×C₇₉	—	4	2	no	—
222	D₄×C₇₉	—	4	4	no	—
223	D₄×C₇₉	—	4	2	no	—
224	D₄×C₇₉	—	4	4	no	—
225	D₄×C₇₉	—	4	4	no	—
226	D₄×C₇₉	—	4	2	no	—
227	D₄×C₇₉	—	8	2	no	—
228	D₄×C₇₉	—	8	4	no	—
229	D₄×C₇₉	—	8	4	no	—
230	D₄×C₇₉	C₂×SD₁₆	1	2	yes	complemented
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	2	no	—
233	C₂×C₄×C₇₉	—	2	4	no	—
234	C₂×C₄×C₇₉	—	2	2	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	2	2	no	—
238	C₂×C₄×C₇₉	—	4	8	no	—
239	C₂×C₄×C₇₉	—	4	2	no	—
240	C₂×C₄×C₇₉	—	4	2	no	—
241	C₂×C₄×C₇₉	—	4	2	no	—
242	C₂×C₄×C₇₉	—	4	2	no	—
243	C₂×C₄×C₇₉	—	4	2	no	—
244	C₂×C₄×C₇₉	—	8	2	no	—
245	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
249	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
250	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
253	C₈×C₇₉	—	2	4	no	—
254	C₈×C₇₉	—	4	2	no	—
255	C₈×C₇₉	—	4	2	no	—
256	C₂²×C₇₉	—	2	1	no	—
257	C₂²×C₇₉	—	2	1	no	—
258	C₂²×C₇₉	—	2	2	no	—
259	C₂²×C₇₉	—	4	1	no	—
260	C₂²×C₇₉	—	4	1	no	—
261	C₂²×C₇₉	—	4	4	no	—
262	C₂²×C₇₉	—	4	2	no	—
263	C₂²×C₇₉	—	4	2	no	—
264	C₂²×C₇₉	—	4	4	no	—
265	C₂²×C₇₉	—	4	4	no	—
266	C₂²×C₇₉	—	4	2	no	—
267	C₂²×C₇₉	—	16	4	no	—
268	C₂²×C₇₉	—	16	8	no	—
269	C₂²×C₇₉	#450	1	2	yes	—
270	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
271	C₄×C₇₉	—	2	2	no	—
272	C₄×C₇₉	—	2	1	no	—
273	C₄×C₇₉	—	2	1	no	—
274	C₄×C₇₉	—	4	2	no	—
275	C₄×C₇₉	—	4	1	no	—
276	C₄×C₇₉	—	4	1	no	—
277	C₄×C₇₉	—	8	2	no	—
278	C₄×C₇₉	#450	1	2	yes	—
279	C₄×C₇₉	#453	1	2	yes	—
280	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
281	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₄×C₇₉	#577	1	2	yes	—
283	#18621	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₇₉	—	2	2	no	—
285	C₂×C₇₉	—	4	2	no	—
286	C₂×C₇₉	—	8	2	no	—
287	C₂×C₇₉	—	8	4	no	—
288	C₂×C₇₉	C₂×#450	1	1	yes	characteristic
289	C₂×C₇₉	#3009	1	1	yes	characteristic
290	C₂×C₇₉	C₂×#453	1	1	yes	characteristic
291	#3498	C₂×C₇₉	1	1	yes	characteristic
292	#3227	C₂×C₇₉	1	1	yes	characteristic, complemented
293	C₂×#492	C₂×C₇₉	1	1	yes	characteristic, complemented
294	#3079	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#1631	C₂×C₇₉	1	4	yes	complemented
296	#1629	C₂×C₇₉	1	4	yes	complemented
297	#1545	C₂×C₇₉	1	1	yes	characteristic, complemented
298	#1492	C₂×C₇₉	1	1	yes	characteristic, complemented
299	#1476	C₂×C₇₉	1	1	yes	characteristic, complemented
300	C₇₉	#18621	1	1	yes	characteristic, direct product factor, Sylow
301	C₂×H(5,𝔽₂)	—	2	1	no	—
302	C₂²×SD₁₆	—	2	2	no	—
303	#550	—	2	1	no	—
304	#550	C₂²×C₇₉	1	2	yes	—
305	D₄²	—	2	2	no	—
306	D₄²	—	2	2	no	—
307	D₄²	—	2	1	no	—
308	D₄²	C₂²×C₇₉	1	2	yes	—
309	#535	—	2	2	no	—
310	#535	—	2	1	no	—
311	#532	—	2	1	no	—
312	#532	C₂²×C₇₉	1	1	yes	characteristic
313	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
314	C₂×#127	—	2	1	no	—
315	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
316	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
317	#498	—	2	1	no	—
318	#492	—	2	2	no	—
319	#492	C₂²×C₇₉	1	4	yes	complemented
320	#486	—	2	1	no	—
321	#481	—	2	2	no	—
322	#477	C₂²×C₇₉	1	2	yes	complemented
323	#476	C₂²×C₇₉	1	2	yes	complemented
324	#476	C₂²×C₇₉	1	4	yes	complemented
325	#475	—	2	1	no	—
326	#474	—	2	1	no	—
327	#431	C₂²×C₇₉	1	1	yes	characteristic, complemented
328	#428	—	2	1	no	—
329	#423	C₂²×C₇₉	1	1	yes	characteristic, complemented
330	#417	—	2	1	no	—
331	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
332	#331	C₂²×C₇₉	1	4	yes	complemented
333	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
334	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
335	D₄⋊C₈	C₂²×C₇₉	1	4	yes	complemented
336	H(5,𝔽₂)	—	4	4	no	—
337	H(5,𝔽₂)	—	4	4	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	D₄×C₇₉	1	2	yes	—
351	C₂×SD₁₆	—	2	8	no	—
352	C₂×SD₁₆	—	4	8	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
360	#127	—	2	2	no	—
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	—	2	1	no	—
364	#127	—	2	1	no	—
365	#127	D₄×C₇₉	1	1	yes	characteristic
366	#127	D₄×C₇₉	1	2	yes	—
367	#127	C₂³×C₇₉	1	2	yes	—
368	#124	—	2	2	no	—
369	#124	—	2	1	no	—
370	#121	—	2	2	no	—
371	#121	—	2	4	no	—
372	#121	—	2	4	no	—
373	#121	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	D₄×C₇₉	1	2	yes	—
378	#120	—	2	4	no	—
379	#120	—	2	4	no	—
380	#120	—	2	4	no	—
381	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
382	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
389	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
390	C₄×D₄	C₂³×C₇₉	1	2	yes	—
391	#117	—	2	1	no	—
392	#117	D₄×C₇₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
397	#107	—	2	2	no	—
398	#106	—	2	2	no	—
399	#106	—	2	4	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
402	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
403	#103	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	4	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	C₂³×C₇₉	1	2	yes	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	4	8	no	—
414	#41	—	4	4	no	—
415	#41	—	4	4	no	—
416	#41	—	4	2	no	—
417	#41	—	4	2	no	—
418	#41	SD₁₆×C₇₉	1	4	yes	complemented
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	4	4	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	16	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	8	2	no	—
445	C₂×D₄	—	8	4	no	—
446	C₂×D₄	—	8	4	no	—
447	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
448	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
449	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
459	SD₁₆	—	4	16	no	—
460	M₁₆	—	4	2	no	—
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
474	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
488	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	4	8	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	8	2	no	—
495	C₂³	—	8	2	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	#120×C₇₉	1	1	yes	characteristic
499	Q₈	—	2	1	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	8	2	no	—
503	Q₈	C₂×SD₁₆×C₇₉	1	2	yes	complemented
504	D₄	—	2	4	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	4	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	8	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	4	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	4	no	—
520	D₄	—	8	4	no	—
521	D₄	C₂×SD₁₆×C₇₉	1	2	yes	complemented
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
537	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
538	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
539	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
540	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
544	C₈	—	2	4	no	—
545	C₈	—	4	2	no	—
546	C₈	—	4	2	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	16	4	no	—
559	C₂²	—	16	8	no	—
560	C₂²	#450×C₇₉	1	2	yes	—
561	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	8	2	no	—
569	C₄	#450×C₇₉	1	2	yes	—
570	C₄	#453×C₇₉	1	2	yes	—
571	C₄	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
572	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
573	C₄	#577×C₇₉	1	2	yes	—
574	C₂	—	2	2	no	—
575	C₂	—	4	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	4	no	—
578	C₂	C₂×#450×C₇₉	1	1	yes	characteristic
579	C₂	C₇₉×#3009	1	1	yes	characteristic
580	C₂	C₂×#453×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3498	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×#3227	C₂	semidirect
3. C₂×#492×C₇₉	C₂	semidirect
4. C₇₉×#3079	C₂	semidirect
5. C₇₉×#1631	C₂	semidirect
6. C₇₉×#1629	C₂	semidirect
7. C₇₉×#1545	C₂	semidirect
8. C₇₉×#1492	C₂	semidirect
9. C₇₉×#1476	C₂	semidirect
22. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
28. #492×C₇₉	C₂²	semidirect
31. #477×C₇₉	C₂²	semidirect
32. #476×C₇₉	C₂²	semidirect
33. #476×C₇₉	C₂²	semidirect
36. #431×C₇₉	C₂²	semidirect
38. #423×C₇₉	C₂²	semidirect
40. C₂×C₄×C₈×C₇₉	C₂²	semidirect
41. #331×C₇₉	C₂²	semidirect
42. Q₈⋊C₈×C₇₉	C₂²	semidirect
43. D₄⋊C₈×C₇₉	C₂²	semidirect
44. D₄⋊C₈×C₇₉	C₂²	semidirect
127. #41×C₇₉	SD₁₆	semidirect
212. Q₈×C₇₉	C₂×SD₁₆	semidirect
230. D₄×C₇₉	C₂×SD₁₆	semidirect
283. #18621	C₇₉	direct (N × H)
292. #3227	C₂×C₇₉	semidirect
293. C₂×#492	C₂×C₇₉	semidirect
294. #3079	C₂×C₇₉	semidirect
295. #1631	C₂×C₇₉	semidirect
296. #1629	C₂×C₇₉	semidirect
297. #1545	C₂×C₇₉	semidirect
298. #1492	C₂×C₇₉	semidirect
299. #1476	C₂×C₇₉	semidirect
300. C₇₉	#18621	direct (N × H)
313. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
319. #492	C₂²×C₇₉	semidirect
322. #477	C₂²×C₇₉	semidirect
323. #476	C₂²×C₇₉	semidirect
324. #476	C₂²×C₇₉	semidirect
327. #431	C₂²×C₇₉	semidirect
329. #423	C₂²×C₇₉	semidirect
331. C₂×C₄×C₈	C₂²×C₇₉	semidirect
332. #331	C₂²×C₇₉	semidirect
333. Q₈⋊C₈	C₂²×C₇₉	semidirect
334. D₄⋊C₈	C₂²×C₇₉	semidirect
335. D₄⋊C₈	C₂²×C₇₉	semidirect
418. #41	SD₁₆×C₇₉	semidirect
503. Q₈	C₂×SD₁₆×C₇₉	semidirect
521. D₄	C₂×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×#3498	2
C₇₉×#3227	2
C₂×#492×C₇₉	2
C₇₉×#3079	2
C₇₉×#1631	2
C₇₉×#1629	2
C₇₉×#1545	2
C₇₉×#1492	2
C₇₉×#1476	2
#18621	79

Subgroups — C79×#18621 #34130310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18621 #34130310