Subgroups — C₇₉×#23543 #34135232

Order 20224.

1458 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₇₉	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2311	C₂	1	2	yes	maximal, complemented
5	C₇₉×#2056	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2055	C₂	1	4	yes	maximal, complemented
7	C₇₉×#2054	C₂	1	2	yes	maximal, complemented
8	C₂×#340×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₇₉	C₂²	1	2	yes	—
10	C₂×#135×C₇₉	—	2	8	no	—
11	C₂×#135×C₇₉	—	2	4	no	—
12	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	#424×C₇₉	—	2	4	no	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
22	#417×C₇₉	—	2	8	no	—
23	C₂×#103×C₇₉	C₂²	1	4	yes	—
24	C₂×#102×C₇₉	C₂²	1	4	yes	—
25	#391×C₇₉	C₂²	1	4	yes	—
26	#390×C₇₉	C₂²	1	4	yes	—
27	#386×C₇₉	—	2	4	no	—
28	#380×C₇₉	—	2	2	no	—
29	#380×C₇₉	—	2	2	no	—
30	#340×C₇₉	C₂²	1	2	yes	—
31	#340×C₇₉	C₂²	1	2	yes	—
32	C₂×#41×C₇₉	—	2	4	no	—
33	C₂×#41×C₇₉	—	2	4	no	—
34	C₂×#41×C₇₉	—	2	4	no	—
35	C₂×#41×C₇₉	—	2	4	no	—
36	C₂×#41×C₇₉	—	2	4	no	—
37	C₂×#41×C₇₉	D₄	1	8	yes	—
38	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
39	C₂²×D₄×C₇₉	—	2	2	no	—
40	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₇₉	—	2	2	no	—
42	C₂³×C₄×C₇₉	—	2	2	no	—
43	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
44	#135×C₇₉	—	2	32	no	—
45	C₂×Q₁₆×C₇₉	—	2	4	no	—
46	C₂×Q₁₆×C₇₉	—	2	2	no	—
47	C₂×SD₁₆×C₇₉	—	2	4	no	—
48	C₂×SD₁₆×C₇₉	—	2	4	no	—
49	C₂×SD₁₆×C₇₉	—	2	4	no	—
50	C₂×D₈×C₇₉	—	2	4	no	—
51	C₂×D₈×C₇₉	—	2	2	no	—
52	C₂×M₁₆×C₇₉	—	2	4	no	—
53	C₂×M₁₆×C₇₉	—	2	2	no	—
54	C₂²×C₈×C₇₉	—	2	4	no	—
55	C₂²×C₈×C₇₉	D₄	1	4	yes	—
56	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
59	#117×C₇₉	—	2	2	no	—
60	#117×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
70	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
71	C₄⋊C₈×C₇₉	—	2	4	no	—
72	C₄⋊C₈×C₇₉	—	2	4	no	—
73	#103×C₇₉	—	2	8	no	—
74	#102×C₇₉	—	2	8	no	—
75	#95×C₇₉	—	2	4	no	—
76	#95×C₇₉	—	2	4	no	—
77	C₂⁴×C₇₉	—	2	2	no	—
78	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₇₉	—	2	16	no	—
80	#41×C₇₉	—	2	16	no	—
81	#41×C₇₉	—	4	8	no	—
82	#41×C₇₉	—	4	8	no	—
83	C₂×Q₈×C₇₉	—	2	2	no	—
84	C₂×Q₈×C₇₉	—	2	2	no	—
85	C₂×Q₈×C₇₉	—	2	2	no	—
86	C₂×Q₈×C₇₉	—	2	2	no	—
87	C₂×Q₈×C₇₉	—	2	2	no	—
88	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
89	C₂×D₄×C₇₉	—	2	8	no	—
90	C₂×D₄×C₇₉	—	2	2	no	—
91	C₂×D₄×C₇₉	—	2	2	no	—
92	C₂×D₄×C₇₉	—	2	2	no	—
93	C₂×D₄×C₇₉	—	2	2	no	—
94	C₂×D₄×C₇₉	—	2	2	no	—
95	C₂×D₄×C₇₉	—	4	4	no	—
96	C₂×D₄×C₇₉	—	4	4	no	—
97	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₇₉	—	2	2	no	—
99	C₂²×C₄×C₇₉	—	2	8	no	—
100	C₂²×C₄×C₇₉	—	2	4	no	—
101	C₂²×C₄×C₇₉	—	4	4	no	—
102	C₂²×C₄×C₇₉	—	4	4	no	—
103	C₂²×C₄×C₇₉	—	4	4	no	—
104	C₂²×C₄×C₇₉	—	8	2	no	—
105	C₂²×C₄×C₇₉	—	8	2	no	—
106	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	#41	1	2	yes	—
112	C₂²×C₄×C₇₉	#41	1	4	yes	—
113	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₇₉	—	2	8	no	—
115	SD₁₆×C₇₉	—	2	16	no	—
116	D₈×C₇₉	—	2	8	no	—
117	M₁₆×C₇₉	—	4	4	no	—
118	C₂×C₈×C₇₉	—	2	8	no	—
119	C₂×C₈×C₇₉	—	2	2	no	—
120	C₂×C₈×C₇₉	—	2	2	no	—
121	C₂×C₈×C₇₉	—	2	4	no	—
122	C₂×C₈×C₇₉	—	2	2	no	—
123	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₄⋊C₄×C₇₉	—	2	2	no	—
127	C₄⋊C₄×C₇₉	—	2	4	no	—
128	C₄⋊C₄×C₇₉	—	2	4	no	—
129	C₄⋊C₄×C₇₉	—	4	4	no	—
130	C₂²⋊C₄×C₇₉	—	2	4	no	—
131	C₂²⋊C₄×C₇₉	—	8	4	no	—
132	C₂²⋊C₄×C₇₉	—	8	4	no	—
133	C₄²×C₇₉	—	2	2	no	—
134	C₄²×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	2	1	no	—
136	C₂³×C₇₉	—	2	2	no	—
137	C₂³×C₇₉	—	2	1	no	—
138	C₂³×C₇₉	—	2	4	no	—
139	C₂³×C₇₉	—	4	2	no	—
140	C₂³×C₇₉	—	4	2	no	—
141	C₂³×C₇₉	—	4	2	no	—
142	C₂³×C₇₉	—	4	2	no	—
143	C₂³×C₇₉	—	4	2	no	—
144	C₂³×C₇₉	—	4	2	no	—
145	C₂³×C₇₉	#121	1	2	yes	—
146	C₂³×C₇₉	#121	1	4	yes	—
147	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₇₉	—	2	4	no	—
149	Q₈×C₇₉	—	2	4	no	—
150	Q₈×C₇₉	—	4	2	no	—
151	Q₈×C₇₉	—	4	2	no	—
152	D₄×C₇₉	—	2	4	no	—
153	D₄×C₇₉	—	2	4	no	—
154	D₄×C₇₉	—	4	16	no	—
155	D₄×C₇₉	—	4	2	no	—
156	D₄×C₇₉	—	4	2	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	4	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	4	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	4	2	no	—
165	C₂×C₄×C₇₉	—	4	16	no	—
166	C₂×C₄×C₇₉	—	4	4	no	—
167	C₂×C₄×C₇₉	—	4	4	no	—
168	C₂×C₄×C₇₉	—	4	4	no	—
169	C₂×C₄×C₇₉	—	8	8	no	—
170	C₂×C₄×C₇₉	#120	1	4	yes	—
171	C₂×C₄×C₇₉	#121	1	2	yes	—
172	C₂×C₄×C₇₉	#121	1	4	yes	—
173	C₂×C₄×C₇₉	#123	1	8	yes	—
174	C₂×C₄×C₇₉	#124	1	4	yes	—
175	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
179	C₈×C₇₉	—	2	2	no	—
180	C₈×C₇₉	—	2	2	no	—
181	C₈×C₇₉	—	4	2	no	—
182	C₂²×C₇₉	—	2	4	no	—
183	C₂²×C₇₉	—	2	4	no	—
184	C₂²×C₇₉	—	2	2	no	—
185	C₂²×C₇₉	—	2	2	no	—
186	C₂²×C₇₉	—	4	4	no	—
187	C₂²×C₇₉	—	4	4	no	—
188	C₂²×C₇₉	—	4	4	no	—
189	C₂²×C₇₉	—	8	2	no	—
190	C₂²×C₇₉	—	8	2	no	—
191	C₂²×C₇₉	—	8	2	no	—
192	C₂²×C₇₉	—	8	2	no	—
193	C₂²×C₇₉	#394	1	4	yes	—
194	C₂²×C₇₉	C₂×#121	1	2	yes	—
195	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
196	C₂²×C₇₉	#576	1	1	yes	characteristic
197	C₂²×C₇₉	#577	1	2	yes	—
198	C₂²×C₇₉	#578	1	1	yes	characteristic
199	C₄×C₇₉	—	4	4	no	—
200	C₄×C₇₉	—	4	2	no	—
201	C₄×C₇₉	—	4	2	no	—
202	C₄×C₇₉	—	8	4	no	—
203	C₄×C₇₉	#394	1	4	yes	—
204	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
205	C₄×C₇₉	C₂×#123	1	2	yes	—
206	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
207	#23543	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₉	—	2	4	no	—
209	C₂×C₇₉	—	8	4	no	—
210	C₂×C₇₉	C₂×#394	1	1	yes	characteristic
211	C₂×C₇₉	#3045	1	2	yes	—
212	C₂×C₇₉	#3046	1	2	yes	—
213	C₂×C₇₉	#3060	1	1	yes	characteristic
214	C₂×C₇₉	#3061	1	1	yes	characteristic
215	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic
216	C₂×#424	C₂×C₇₉	1	1	yes	characteristic, complemented
217	C₂×#417	C₂×C₇₉	1	2	yes	complemented
218	#2311	C₂×C₇₉	1	2	yes	complemented
219	#2056	C₂×C₇₉	1	2	yes	complemented
220	#2055	C₂×C₇₉	1	4	yes	complemented
221	#2054	C₂×C₇₉	1	2	yes	complemented
222	C₂×#340	C₂×C₇₉	1	1	yes	characteristic, complemented
223	C₇₉	#23543	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×#41	C₂²×C₇₉	1	2	yes	—
225	C₂×#135	—	2	8	no	—
226	C₂×#135	—	2	4	no	—
227	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
228	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
229	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
230	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
232	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
234	#424	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
237	#417	—	2	8	no	—
238	C₂×#103	C₂²×C₇₉	1	4	yes	—
239	C₂×#102	C₂²×C₇₉	1	4	yes	—
240	#391	C₂²×C₇₉	1	4	yes	—
241	#390	C₂²×C₇₉	1	4	yes	—
242	#386	—	2	4	no	—
243	#380	—	2	2	no	—
244	#380	—	2	2	no	—
245	#340	C₂²×C₇₉	1	2	yes	—
246	#340	C₂²×C₇₉	1	2	yes	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	4	no	—
252	C₂×#41	D₄×C₇₉	1	8	yes	—
253	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	2	2	no	—
258	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
259	#135	—	2	32	no	—
260	C₂×Q₁₆	—	2	4	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×D₈	—	2	4	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×M₁₆	—	2	4	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	D₄×C₇₉	1	4	yes	—
271	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
272	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
285	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
286	C₄⋊C₈	—	2	4	no	—
287	C₄⋊C₈	—	2	4	no	—
288	#103	—	2	8	no	—
289	#102	—	2	8	no	—
290	#95	—	2	4	no	—
291	#95	—	2	4	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
294	#41	—	2	16	no	—
295	#41	—	2	16	no	—
296	#41	—	4	8	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	8	2	no	—
320	C₂²×C₄	—	8	2	no	—
321	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
324	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
326	C₂²×C₄	#41×C₇₉	1	2	yes	—
327	C₂²×C₄	#41×C₇₉	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
329	Q₁₆	—	2	8	no	—
330	SD₁₆	—	2	16	no	—
331	D₈	—	2	8	no	—
332	M₁₆	—	4	4	no	—
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	8	4	no	—
347	C₂²⋊C₄	—	8	4	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	#121×C₇₉	1	2	yes	—
361	C₂³	#121×C₇₉	1	4	yes	—
362	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	16	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	#120×C₇₉	1	4	yes	—
386	C₂×C₄	#121×C₇₉	1	2	yes	—
387	C₂×C₄	#121×C₇₉	1	4	yes	—
388	C₂×C₄	#123×C₇₉	1	8	yes	—
389	C₂×C₄	#124×C₇₉	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	#394×C₇₉	1	4	yes	—
409	C₂²	C₂×#121×C₇₉	1	2	yes	—
410	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
411	C₂²	#576×C₇₉	1	1	yes	characteristic
412	C₂²	#577×C₇₉	1	2	yes	—
413	C₂²	#578×C₇₉	1	1	yes	characteristic
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	8	4	no	—
418	C₄	#394×C₇₉	1	4	yes	—
419	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
420	C₄	C₂×#123×C₇₉	1	2	yes	—
421	C₄	C₂×#124×C₇₉	1	1	yes	characteristic
422	C₂	—	2	4	no	—
423	C₂	—	8	4	no	—
424	C₂	C₂×#394×C₇₉	1	1	yes	characteristic
425	C₂	C₇₉×#3045	1	2	yes	—
426	C₂	C₇₉×#3046	1	2	yes	—
427	C₂	C₇₉×#3060	1	1	yes	characteristic
428	C₂	C₇₉×#3061	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×#135×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×#117×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#424×C₇₉	C₂	semidirect
3. C₂×#417×C₇₉	C₂	semidirect
4. C₇₉×#2311	C₂	semidirect
5. C₇₉×#2056	C₂	semidirect
6. C₇₉×#2055	C₂	semidirect
7. C₇₉×#2054	C₂	semidirect
8. C₂×#340×C₇₉	C₂	semidirect
207. #23543	C₇₉	direct (N × H)
216. C₂×#424	C₂×C₇₉	semidirect
217. C₂×#417	C₂×C₇₉	semidirect
218. #2311	C₂×C₇₉	semidirect
219. #2056	C₂×C₇₉	semidirect
220. #2055	C₂×C₇₉	semidirect
221. #2054	C₂×C₇₉	semidirect
222. C₂×#340	C₂×C₇₉	semidirect
223. C₇₉	#23543	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₇₉	2
C₂×#424×C₇₉	2
C₂×#417×C₇₉	2
C₇₉×#2311	2
C₇₉×#2056	2
C₇₉×#2055	2
C₇₉×#2054	2
C₂×#340×C₇₉	2
#23543	79

Subgroups — C79×#23543 #34135232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23543 #34135232