Subgroups — C₂×C₇₉×#2059 #34135239

Order 20224.

1238 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#106×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#389×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2059	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂×#340×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×#125×C₇₉	—	2	4	no	—
12	C₂×#125×C₇₉	—	2	4	no	—
13	C₂×#125×C₇₉	—	2	2	no	—
14	C₂×#125×C₇₉	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#107×C₇₉	—	2	4	no	—
24	C₂×#107×C₇₉	C₂²	1	4	yes	—
25	C₂×#106×C₇₉	—	2	4	no	—
26	C₂×#106×C₇₉	C₂²	1	4	yes	—
27	#389×C₇₉	—	2	2	no	—
28	#389×C₇₉	C₂²	1	4	yes	—
29	C₂×#95×C₇₉	—	2	1	no	—
30	#340×C₇₉	C₂²	1	4	yes	—
31	#340×C₇₉	C₂²	1	4	yes	—
32	#336×C₇₉	C₂²	1	4	yes	—
33	C₂³×C₄×C₇₉	—	2	1	no	—
34	C₂³×C₄×C₇₉	—	2	1	no	—
35	C₂³×C₄×C₇₉	—	2	1	no	—
36	C₂³×C₄×C₇₉	—	2	1	no	—
37	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	—	2	2	no	—
41	C₂²×C₈×C₇₉	—	2	2	no	—
42	C₂²×C₈×C₇₉	—	2	2	no	—
43	C₂²×C₈×C₇₉	—	2	2	no	—
44	C₂²×C₈×C₇₉	Q₈	1	4	yes	—
45	C₂²×C₈×C₇₉	Q₈	1	4	yes	—
46	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
48	#125×C₇₉	—	2	16	no	—
49	#125×C₇₉	—	2	8	no	—
50	#125×C₇₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
53	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	4	4	no	—
66	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₇₉	Q₈	1	4	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₇₉	—	2	2	no	—
74	C₂×C₄²×C₇₉	—	2	2	no	—
75	C₂×C₄²×C₇₉	D₄	1	2	yes	—
76	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
77	#107×C₇₉	—	2	8	no	—
78	#106×C₇₉	—	2	8	no	—
79	#95×C₇₉	—	2	4	no	—
80	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₉	—	2	2	no	—
82	C₂²×C₄×C₇₉	—	2	2	no	—
83	C₂²×C₄×C₇₉	—	2	4	no	—
84	C₂²×C₄×C₇₉	—	2	4	no	—
85	C₂²×C₄×C₇₉	—	2	4	no	—
86	C₂²×C₄×C₇₉	—	2	2	no	—
87	C₂²×C₄×C₇₉	—	2	2	no	—
88	C₂²×C₄×C₇₉	—	2	2	no	—
89	C₂²×C₄×C₇₉	—	2	2	no	—
90	C₂²×C₄×C₇₉	—	2	2	no	—
91	C₂²×C₄×C₇₉	—	2	2	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	4	2	no	—
95	C₂²×C₄×C₇₉	—	4	2	no	—
96	C₂²×C₄×C₇₉	—	4	2	no	—
97	C₂²×C₄×C₇₉	—	4	2	no	—
98	C₂²×C₄×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	—	4	2	no	—
100	C₂²×C₄×C₇₉	—	4	2	no	—
101	C₂²×C₄×C₇₉	—	4	2	no	—
102	C₂²×C₄×C₇₉	—	4	2	no	—
103	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₇₉	#41	1	2	yes	—
112	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₇₉	—	2	8	no	—
114	C₂×C₈×C₇₉	—	2	8	no	—
115	C₂×C₈×C₇₉	—	2	2	no	—
116	C₂×C₈×C₇₉	—	2	2	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	2	2	no	—
119	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	—
120	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	—
121	C₄⋊C₄×C₇₉	—	2	16	no	—
122	C₄⋊C₄×C₇₉	—	2	16	no	—
123	C₄⋊C₄×C₇₉	—	2	4	no	—
124	C₄⋊C₄×C₇₉	—	2	4	no	—
125	C₄⋊C₄×C₇₉	—	2	4	no	—
126	C₄⋊C₄×C₇₉	—	2	2	no	—
127	C₄⋊C₄×C₇₉	—	2	2	no	—
128	C₄⋊C₄×C₇₉	—	2	2	no	—
129	C₄⋊C₄×C₇₉	—	2	2	no	—
130	C₄⋊C₄×C₇₉	—	2	2	no	—
131	C₄⋊C₄×C₇₉	—	4	8	no	—
132	C₄⋊C₄×C₇₉	—	4	2	no	—
133	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
135	C₄⋊C₄×C₇₉	C₂×Q₈	1	4	yes	—
136	C₄²×C₇₉	—	2	4	no	—
137	C₄²×C₇₉	—	2	2	no	—
138	C₄²×C₇₉	—	2	2	no	—
139	C₂³×C₇₉	#120	1	2	yes	—
140	C₂³×C₇₉	C₂²⋊Q₈	1	2	yes	—
141	C₂³×C₇₉	C₄⋊Q₈	1	2	yes	—
142	C₂³×C₇₉	#135	1	2	yes	—
143	C₂³×C₇₉	#135	1	2	yes	—
144	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
145	C₂³×C₇₉	#137	1	2	yes	—
146	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	4	no	—
150	C₂×C₄×C₇₉	—	2	4	no	—
151	C₂×C₄×C₇₉	—	2	4	no	—
152	C₂×C₄×C₇₉	—	2	2	no	—
153	C₂×C₄×C₇₉	—	2	2	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	4	2	no	—
157	C₂×C₄×C₇₉	—	4	2	no	—
158	C₂×C₄×C₇₉	—	4	2	no	—
159	C₂×C₄×C₇₉	—	4	2	no	—
160	C₂×C₄×C₇₉	—	4	2	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	—	4	4	no	—
163	C₂×C₄×C₇₉	—	4	8	no	—
164	C₂×C₄×C₇₉	—	4	4	no	—
165	C₂×C₄×C₇₉	—	4	8	no	—
166	C₂×C₄×C₇₉	—	4	8	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	8	4	no	—
171	C₂×C₄×C₇₉	#120	1	2	yes	—
172	C₂×C₄×C₇₉	C₂²⋊Q₈	1	4	yes	—
173	C₂×C₄×C₇₉	C₂²⋊Q₈	1	4	yes	—
174	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₇₉	C₄⋊Q₈	1	4	yes	—
176	C₂×C₄×C₇₉	C₄⋊Q₈	1	4	yes	—
177	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
178	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
184	C₈×C₇₉	—	2	4	no	—
185	C₈×C₇₉	—	2	4	no	—
186	C₂²×C₇₉	#395	1	4	yes	—
187	C₂²×C₇₉	#449	1	4	yes	—
188	C₂²×C₇₉	#452	1	4	yes	—
189	C₂²×C₇₉	#478	1	4	yes	—
190	C₂²×C₇₉	#479	1	4	yes	—
191	C₂²×C₇₉	#499	1	4	yes	—
192	C₂²×C₇₉	#501	1	4	yes	—
193	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
194	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
196	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
197	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
198	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
200	C₄×C₇₉	—	4	4	no	—
201	C₄×C₇₉	—	4	2	no	—
202	C₄×C₇₉	—	4	4	no	—
203	C₄×C₇₉	—	4	2	no	—
204	C₄×C₇₉	—	4	4	no	—
205	C₄×C₇₉	—	8	2	no	—
206	C₄×C₇₉	#395	1	4	yes	—
207	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
208	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
210	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
211	C₂×#2059	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂×C₇₉	#2059	1	8	yes	direct product factor
213	C₂×C₇₉	C₂×#395	1	1	yes	characteristic
214	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#452	1	1	yes	characteristic
216	C₂×C₇₉	C₂×#478	1	1	yes	characteristic
217	C₂×C₇₉	C₂×#479	1	1	yes	characteristic
218	C₂×C₇₉	C₂×#499	1	1	yes	characteristic
219	C₂×C₇₉	C₂×#501	1	1	yes	characteristic
220	C₂²×#125	C₂×C₇₉	1	1	yes	characteristic
221	C₂²×#107	C₂×C₇₉	1	1	yes	characteristic
222	C₂²×#106	C₂×C₇₉	1	1	yes	characteristic
223	C₂×#389	C₂×C₇₉	1	1	yes	characteristic
224	#2059	C₂×C₇₉	1	8	yes	direct product factor
225	C₂×#340	C₂×C₇₉	1	1	yes	characteristic
226	C₂×#340	C₂×C₇₉	1	1	yes	characteristic
227	C₂×#336	C₂×C₇₉	1	1	yes	characteristic
228	C₇₉	C₂×#2059	1	1	yes	characteristic, direct product factor, Sylow
229	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
230	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
231	C₂×#125	—	2	4	no	—
232	C₂×#125	—	2	4	no	—
233	C₂×#125	—	2	2	no	—
234	C₂×#125	C₂²×C₇₉	1	4	yes	—
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	C₂²×C₄⋊C₄	—	2	1	no	—
237	C₂²×C₄⋊C₄	—	2	1	no	—
238	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
243	C₂×#107	—	2	4	no	—
244	C₂×#107	C₂²×C₇₉	1	4	yes	—
245	C₂×#106	—	2	4	no	—
246	C₂×#106	C₂²×C₇₉	1	4	yes	—
247	#389	—	2	2	no	—
248	#389	C₂²×C₇₉	1	4	yes	—
249	C₂×#95	—	2	1	no	—
250	#340	C₂²×C₇₉	1	4	yes	—
251	#340	C₂²×C₇₉	1	4	yes	—
252	#336	C₂²×C₇₉	1	4	yes	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	Q₈×C₇₉	1	4	yes	—
265	C₂²×C₈	Q₈×C₇₉	1	4	yes	—
266	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
267	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
268	#125	—	2	16	no	—
269	#125	—	2	8	no	—
270	#125	—	2	8	no	—
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	—	2	8	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	4	4	no	—
286	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
287	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
288	C₂×C₄⋊C₄	Q₈×C₇₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	D₄×C₇₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
297	#107	—	2	8	no	—
298	#106	—	2	8	no	—
299	#95	—	2	4	no	—
300	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
328	C₂²×C₄	C₂×Q₈×C₇₉	1	2	yes	—
329	C₂²×C₄	C₂×Q₈×C₇₉	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₇₉	1	2	yes	—
331	C₂²×C₄	#41×C₇₉	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×Q₈×C₇₉	1	4	yes	—
340	C₂×C₈	C₂×Q₈×C₇₉	1	4	yes	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	8	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
354	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
355	C₄⋊C₄	C₂×Q₈×C₇₉	1	4	yes	—
356	C₄²	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₂³	#120×C₇₉	1	2	yes	—
360	C₂³	C₂²⋊Q₈×C₇₉	1	2	yes	—
361	C₂³	C₄⋊Q₈×C₇₉	1	2	yes	—
362	C₂³	#135×C₇₉	1	2	yes	—
363	C₂³	#135×C₇₉	1	2	yes	—
364	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
365	C₂³	#137×C₇₉	1	2	yes	—
366	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	#120×C₇₉	1	2	yes	—
392	C₂×C₄	C₂²⋊Q₈×C₇₉	1	4	yes	—
393	C₂×C₄	C₂²⋊Q₈×C₇₉	1	4	yes	—
394	C₂×C₄	C₂²⋊Q₈×C₇₉	1	2	yes	—
395	C₂×C₄	C₄⋊Q₈×C₇₉	1	4	yes	—
396	C₂×C₄	C₄⋊Q₈×C₇₉	1	4	yes	—
397	C₂×C₄	C₄⋊Q₈×C₇₉	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	2	4	no	—
406	C₂²	#395×C₇₉	1	4	yes	—
407	C₂²	#449×C₇₉	1	4	yes	—
408	C₂²	#452×C₇₉	1	4	yes	—
409	C₂²	#478×C₇₉	1	4	yes	—
410	C₂²	#479×C₇₉	1	4	yes	—
411	C₂²	#499×C₇₉	1	4	yes	—
412	C₂²	#501×C₇₉	1	4	yes	—
413	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
414	C₂²	C₂×C₂²⋊Q₈×C₇₉	1	1	yes	characteristic
415	C₂²	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
416	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
417	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
418	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
419	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
420	C₄	—	4	4	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	8	2	no	—
426	C₄	#395×C₇₉	1	4	yes	—
427	C₄	C₂×C₂²⋊Q₈×C₇₉	1	1	yes	characteristic
428	C₄	C₂×C₂²⋊Q₈×C₇₉	1	1	yes	characteristic
429	C₄	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
430	C₄	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
431	C₂	C₇₉×#2059	1	8	yes	direct product factor
432	C₂	C₂×#395×C₇₉	1	1	yes	characteristic
433	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
434	C₂	C₂×#452×C₇₉	1	1	yes	characteristic
435	C₂	C₂×#478×C₇₉	1	1	yes	characteristic
436	C₂	C₂×#479×C₇₉	1	1	yes	characteristic
437	C₂	C₂×#499×C₇₉	1	1	yes	characteristic
438	C₂	C₂×#501×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇₉×#2059	C₂	direct (N × H)
211. C₂×#2059	C₇₉	direct (N × H)
212. C₂×C₇₉	#2059	direct (N × H)
224. #2059	C₂×C₇₉	direct (N × H)
228. C₇₉	C₂×#2059	direct (N × H)
431. C₂	C₇₉×#2059	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×#125×C₇₉	2
C₂²×#107×C₇₉	2
C₂²×#106×C₇₉	2
C₂×#389×C₇₉	2
C₇₉×#2059	2
C₂×#340×C₇₉	2
C₂×#336×C₇₉	2
C₂×#2059	79

Subgroups — C2×C79×#2059 #34135239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#2059 #34135239