Subgroups — C₇₉×#33645 #34145334

Order 20224.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2237	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2234	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2233	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2232	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2158	C₂	1	2	yes	maximal, complemented
10	C₇₉×#2138	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	#525×C₇₉	—	2	1	no	—
15	C₂×#117×C₇₉	—	2	1	no	—
16	C₂²×C₁₆×C₇₉	C₂²	1	2	yes	—
17	#467×C₇₉	C₂²	1	1	yes	characteristic
18	#467×C₇₉	C₂²	1	1	yes	characteristic
19	#466×C₇₉	C₂²	1	1	yes	characteristic
20	#466×C₇₉	C₂²	1	1	yes	characteristic
21	#465×C₇₉	—	2	1	no	—
22	#465×C₇₉	—	2	1	no	—
23	#427×C₇₉	—	2	1	no	—
24	#427×C₇₉	—	2	1	no	—
25	#427×C₇₉	C₂²	1	1	yes	characteristic
26	#427×C₇₉	C₂²	1	2	yes	—
27	#427×C₇₉	C₂²	1	2	yes	—
28	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#106×C₇₉	—	2	1	no	—
31	#416×C₇₉	—	2	1	no	—
32	#367×C₇₉	C₂²	1	2	yes	complemented
33	#367×C₇₉	C₂²	1	2	yes	complemented
34	#366×C₇₉	C₂²	1	2	yes	complemented
35	#366×C₇₉	C₂²	1	2	yes	complemented
36	#358×C₇₉	C₂²	1	2	yes	complemented
37	#358×C₇₉	C₂²	1	2	yes	complemented
38	#357×C₇₉	C₂²	1	2	yes	complemented
39	#357×C₇₉	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
42	C₂²⋊C₁₆×C₇₉	C₂²	1	2	yes	—
43	C₂×#41×C₇₉	—	2	1	no	—
44	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
45	#135×C₇₉	—	2	4	no	—
46	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
47	C₂×SD₁₆×C₇₉	—	2	1	no	—
48	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₇₉	—	2	4	no	—
50	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
56	#123×C₇₉	—	4	1	no	—
57	C₂²⋊Q₈×C₇₉	—	2	1	no	—
58	C₂²⋊Q₈×C₇₉	—	2	1	no	—
59	#121×C₇₉	—	2	1	no	—
60	#121×C₇₉	—	2	1	no	—
61	#120×C₇₉	—	4	1	no	—
62	C₄×D₄×C₇₉	—	4	1	no	—
63	C₄×D₄×C₇₉	—	4	1	no	—
64	#117×C₇₉	—	2	2	no	—
65	#117×C₇₉	—	2	2	no	—
66	#117×C₇₉	—	2	1	no	—
67	#117×C₇₉	—	4	1	no	—
68	#117×C₇₉	—	4	1	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
72	C₂×C₄²×C₇₉	—	4	1	no	—
73	C₂×C₁₆×C₇₉	—	2	4	no	—
74	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
75	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
76	#107×C₇₉	—	2	1	no	—
77	#107×C₇₉	—	2	1	no	—
78	#107×C₇₉	C₂³	1	2	yes	—
79	#107×C₇₉	C₂³	1	2	yes	—
80	#107×C₇₉	C₂³	1	1	yes	characteristic
81	#107×C₇₉	C₂³	1	1	yes	characteristic
82	#106×C₇₉	—	2	2	no	—
83	#106×C₇₉	—	2	2	no	—
84	#106×C₇₉	—	2	1	no	—
85	#103×C₇₉	—	2	1	no	—
86	#103×C₇₉	—	2	1	no	—
87	#102×C₇₉	—	2	1	no	—
88	#102×C₇₉	—	2	1	no	—
89	C₂⁴×C₇₉	D₈	1	1	yes	characteristic
90	#41×C₇₉	—	4	2	no	—
91	#41×C₇₉	—	4	2	no	—
92	C₂×Q₈×C₇₉	—	2	1	no	—
93	C₂×D₄×C₇₉	—	2	1	no	—
94	C₂×D₄×C₇₉	—	4	1	no	—
95	C₂×D₄×C₇₉	—	4	1	no	—
96	C₂×D₄×C₇₉	—	4	1	no	—
97	C₂²×C₄×C₇₉	—	2	2	no	—
98	C₂²×C₄×C₇₉	—	2	2	no	—
99	C₂²×C₄×C₇₉	—	4	1	no	—
100	C₂²×C₄×C₇₉	—	4	1	no	—
101	C₂²×C₄×C₇₉	—	4	1	no	—
102	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₇₉	—	2	2	no	—
109	SD₁₆×C₇₉	—	4	2	no	—
110	D₈×C₇₉	—	2	2	no	—
111	C₂×C₈×C₇₉	—	2	2	no	—
112	C₂×C₈×C₇₉	—	2	2	no	—
113	C₂×C₈×C₇₉	—	2	2	no	—
114	C₂×C₈×C₇₉	—	2	2	no	—
115	C₂×C₈×C₇₉	—	2	2	no	—
116	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₇₉	#41	1	4	yes	—
120	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
121	C₄⋊C₄×C₇₉	—	2	1	no	—
122	C₄⋊C₄×C₇₉	—	2	1	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	—	2	2	no	—
125	C₄⋊C₄×C₇₉	—	4	1	no	—
126	C₄⋊C₄×C₇₉	—	4	1	no	—
127	C₄⋊C₄×C₇₉	—	4	1	no	—
128	C₄⋊C₄×C₇₉	—	4	1	no	—
129	C₂²⋊C₄×C₇₉	—	4	2	no	—
130	C₂²⋊C₄×C₇₉	—	4	2	no	—
131	C₂²⋊C₄×C₇₉	—	4	1	no	—
132	C₂²⋊C₄×C₇₉	—	4	1	no	—
133	C₂²⋊C₄×C₇₉	—	4	1	no	—
134	C₂²⋊C₄×C₇₉	—	4	1	no	—
135	C₂²⋊C₄×C₇₉	—	4	1	no	—
136	C₄²×C₇₉	—	4	2	no	—
137	C₄²×C₇₉	—	4	2	no	—
138	C₄²×C₇₉	—	4	1	no	—
139	C₁₆×C₇₉	—	2	2	no	—
140	C₁₆×C₇₉	—	2	2	no	—
141	C₂³×C₇₉	—	2	2	no	—
142	C₂³×C₇₉	—	2	2	no	—
143	C₂³×C₇₉	—	4	1	no	—
144	C₂³×C₇₉	—	4	1	no	—
145	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
146	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
147	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
148	Q₈×C₇₉	—	4	1	no	—
149	Q₈×C₇₉	—	4	1	no	—
150	D₄×C₇₉	—	4	1	no	—
151	D₄×C₇₉	—	4	1	no	—
152	D₄×C₇₉	—	8	2	no	—
153	D₄×C₇₉	—	8	2	no	—
154	D₄×C₇₉	—	8	2	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	4	2	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	—	8	2	no	—
168	C₂×C₄×C₇₉	—	8	2	no	—
169	C₂×C₄×C₇₉	—	8	2	no	—
170	C₂×C₄×C₇₉	#123	1	2	yes	—
171	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₉	#137	1	2	yes	—
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₇₉	—	2	1	no	—
177	C₈×C₇₉	—	2	1	no	—
178	C₈×C₇₉	#123	1	2	yes	—
179	C₈×C₇₉	C₂×#41	1	2	yes	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	1	no	—
182	C₂²×C₇₉	—	2	1	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	—	2	1	no	—
185	C₂²×C₇₉	—	2	1	no	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	4	4	no	—
188	C₂²×C₇₉	—	8	1	no	—
189	C₂²×C₇₉	—	8	1	no	—
190	C₂²×C₇₉	—	8	1	no	—
191	C₂²×C₇₉	#480	1	2	yes	—
192	C₂²×C₇₉	#508	1	2	yes	—
193	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	8	1	no	—
197	C₄×C₇₉	—	8	2	no	—
198	C₄×C₇₉	—	8	1	no	—
199	C₄×C₇₉	—	8	2	no	—
200	C₄×C₇₉	—	8	1	no	—
201	C₄×C₇₉	#480	1	2	yes	—
202	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
203	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
204	#33645	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₇₉	—	2	2	no	—
206	C₂×C₇₉	—	2	2	no	—
207	C₂×C₇₉	—	4	1	no	—
208	C₂×C₇₉	—	16	1	no	—
209	C₂×C₇₉	C₂×#480	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#508	1	1	yes	characteristic
211	C₂×C₇₉	#3414	1	1	yes	characteristic
212	#3050	C₂×C₇₉	1	1	yes	characteristic
213	C₂×#427	C₂×C₇₉	1	1	yes	characteristic, complemented
214	#2237	C₂×C₇₉	1	2	yes	complemented
215	#2236	C₂×C₇₉	1	1	yes	characteristic, complemented
216	#2235	C₂×C₇₉	1	1	yes	characteristic, complemented
217	#2234	C₂×C₇₉	1	2	yes	complemented
218	#2233	C₂×C₇₉	1	1	yes	characteristic, complemented
219	#2232	C₂×C₇₉	1	1	yes	characteristic, complemented
220	#2158	C₂×C₇₉	1	2	yes	complemented
221	#2138	C₂×C₇₉	1	2	yes	complemented
222	C₂×C₂²⋊C₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
223	C₇₉	#33645	1	1	yes	characteristic, direct product factor, Sylow
224	C₂×#135	C₂²×C₇₉	1	1	yes	characteristic
225	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
226	#525	—	2	1	no	—
227	C₂×#117	—	2	1	no	—
228	C₂²×C₁₆	C₂²×C₇₉	1	2	yes	—
229	#467	C₂²×C₇₉	1	1	yes	characteristic
230	#467	C₂²×C₇₉	1	1	yes	characteristic
231	#466	C₂²×C₇₉	1	1	yes	characteristic
232	#466	C₂²×C₇₉	1	1	yes	characteristic
233	#465	—	2	1	no	—
234	#465	—	2	1	no	—
235	#427	—	2	1	no	—
236	#427	—	2	1	no	—
237	#427	C₂²×C₇₉	1	2	yes	—
238	#427	C₂²×C₇₉	1	2	yes	—
239	#427	C₂²×C₇₉	1	1	yes	characteristic
240	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
241	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
242	C₂×#106	—	2	1	no	—
243	#416	—	2	1	no	—
244	#367	C₂²×C₇₉	1	2	yes	complemented
245	#367	C₂²×C₇₉	1	2	yes	complemented
246	#366	C₂²×C₇₉	1	2	yes	complemented
247	#366	C₂²×C₇₉	1	2	yes	complemented
248	#358	C₂²×C₇₉	1	2	yes	complemented
249	#358	C₂²×C₇₉	1	2	yes	complemented
250	#357	C₂²×C₇₉	1	2	yes	complemented
251	#357	C₂²×C₇₉	1	2	yes	complemented
252	C₂²⋊C₁₆	C₂²×C₇₉	1	1	yes	characteristic
253	C₂²⋊C₁₆	C₂²×C₇₉	1	1	yes	characteristic
254	C₂²⋊C₁₆	C₂²×C₇₉	1	2	yes	—
255	C₂×#41	—	2	1	no	—
256	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
257	#135	—	2	4	no	—
258	C₂×Q₁₆	C₂³×C₇₉	1	1	yes	characteristic
259	C₂×SD₁₆	—	2	1	no	—
260	C₂×D₈	C₂³×C₇₉	1	1	yes	characteristic
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
264	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
268	#123	—	4	1	no	—
269	C₂²⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	#121	—	2	1	no	—
272	#121	—	2	1	no	—
273	#120	—	4	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	4	1	no	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	#117	—	2	1	no	—
279	#117	—	4	1	no	—
280	#117	—	4	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	4	1	no	—
284	C₂×C₄²	—	4	1	no	—
285	C₂×C₁₆	—	2	4	no	—
286	C₂×C₁₆	C₂³×C₇₉	1	2	yes	—
287	C₂×C₁₆	C₂³×C₇₉	1	2	yes	—
288	#107	—	2	1	no	—
289	#107	—	2	1	no	—
290	#107	C₂³×C₇₉	1	2	yes	—
291	#107	C₂³×C₇₉	1	2	yes	—
292	#107	C₂³×C₇₉	1	1	yes	characteristic
293	#107	C₂³×C₇₉	1	1	yes	characteristic
294	#106	—	2	2	no	—
295	#106	—	2	2	no	—
296	#106	—	2	1	no	—
297	#103	—	2	1	no	—
298	#103	—	2	1	no	—
299	#102	—	2	1	no	—
300	#102	—	2	1	no	—
301	C₂⁴	D₈×C₇₉	1	1	yes	characteristic
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
315	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
316	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
320	Q₁₆	—	2	2	no	—
321	SD₁₆	—	4	2	no	—
322	D₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
331	C₂×C₈	#41×C₇₉	1	4	yes	—
332	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₄²	—	4	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	1	no	—
351	C₁₆	—	2	2	no	—
352	C₁₆	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
358	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
359	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	#123×C₇₉	1	2	yes	—
383	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
385	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
386	C₂×C₄	#137×C₇₉	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	#123×C₇₉	1	2	yes	—
391	C₈	C₂×#41×C₇₉	1	2	yes	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	#480×C₇₉	1	2	yes	—
404	C₂²	#508×C₇₉	1	2	yes	—
405	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	1	no	—
413	C₄	#480×C₇₉	1	2	yes	—
414	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
415	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	1	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×#480×C₇₉	1	1	yes	characteristic
421	C₂	C₂×#508×C₇₉	1	1	yes	characteristic
422	C₂	C₇₉×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂²×D₈
prime radical	C₇₉×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ C₂³×C₈×C₇₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#427×C₇₉	C₂	semidirect
3. C₇₉×#2237	C₂	semidirect
4. C₇₉×#2236	C₂	semidirect
5. C₇₉×#2235	C₂	semidirect
6. C₇₉×#2234	C₂	semidirect
7. C₇₉×#2233	C₂	semidirect
8. C₇₉×#2232	C₂	semidirect
9. C₇₉×#2158	C₂	semidirect
10. C₇₉×#2138	C₂	semidirect
11. C₂×C₂²⋊C₁₆×C₇₉	C₂	semidirect
32. #367×C₇₉	C₂²	semidirect
33. #367×C₇₉	C₂²	semidirect
34. #366×C₇₉	C₂²	semidirect
35. #366×C₇₉	C₂²	semidirect
36. #358×C₇₉	C₂²	semidirect
37. #358×C₇₉	C₂²	semidirect
38. #357×C₇₉	C₂²	semidirect
39. #357×C₇₉	C₂²	semidirect
204. #33645	C₇₉	direct (N × H)
213. C₂×#427	C₂×C₇₉	semidirect
214. #2237	C₂×C₇₉	semidirect
215. #2236	C₂×C₇₉	semidirect
216. #2235	C₂×C₇₉	semidirect
217. #2234	C₂×C₇₉	semidirect
218. #2233	C₂×C₇₉	semidirect
219. #2232	C₂×C₇₉	semidirect
220. #2158	C₂×C₇₉	semidirect
221. #2138	C₂×C₇₉	semidirect
222. C₂×C₂²⋊C₁₆	C₂×C₇₉	semidirect
223. C₇₉	#33645	direct (N × H)
244. #367	C₂²×C₇₉	semidirect
245. #367	C₂²×C₇₉	semidirect
246. #366	C₂²×C₇₉	semidirect
247. #366	C₂²×C₇₉	semidirect
248. #358	C₂²×C₇₉	semidirect
249. #358	C₂²×C₇₉	semidirect
250. #357	C₂²×C₇₉	semidirect
251. #357	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×#3050	2
C₂×#427×C₇₉	2
C₇₉×#2237	2
C₇₉×#2236	2
C₇₉×#2235	2
C₇₉×#2234	2
C₇₉×#2233	2
C₇₉×#2232	2
C₇₉×#2158	2
C₇₉×#2138	2
C₂×C₂²⋊C₁₆×C₇₉	2
#33645	79

Subgroups — C79×#33645 #34145334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#33645 #34145334