Subgroups — C₂×C₇₉×#2023 #34135136

Order 20224.

1734 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₇₉	C₂	1	2	yes	maximal
3	C₂×#390×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2023	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₇₉	C₂	1	2	yes	maximal, complemented
6	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₇₉	—	2	1	no	—
8	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₇₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Q₈×C₇₉	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₇₉	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₇₉	C₂²	1	4	yes	complemented
13	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
18	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#102×C₇₉	—	2	8	no	—
20	C₂×#102×C₇₉	C₂²	1	8	yes	—
21	#390×C₇₉	—	2	2	no	—
22	#390×C₇₉	C₂²	1	4	yes	—
23	#340×C₇₉	C₂²	1	8	yes	complemented
24	#336×C₇₉	C₂²	1	4	yes	complemented
25	C₂⁵×C₇₉	—	2	1	no	—
26	C₂²×Q₈×C₇₉	—	2	8	no	—
27	C₂²×Q₈×C₇₉	—	2	4	no	—
28	C₂²×Q₈×C₇₉	—	4	4	no	—
29	C₂²×Q₈×C₇₉	—	4	4	no	—
30	C₂²×D₄×C₇₉	—	2	4	no	—
31	C₂²×D₄×C₇₉	—	2	1	no	—
32	C₂²×D₄×C₇₉	—	2	4	no	—
33	C₂²×D₄×C₇₉	—	2	2	no	—
34	C₂²×D₄×C₇₉	Q₈	1	4	yes	complemented
35	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₇₉	—	2	2	no	—
37	C₂³×C₄×C₇₉	—	2	1	no	—
38	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	—	2	4	no	—
42	C₂²×C₈×C₇₉	—	2	4	no	—
43	C₂²×C₈×C₇₉	—	2	4	no	—
44	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₇₉	—	2	16	no	—
46	C₄⋊Q₈×C₇₉	—	2	16	no	—
47	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₉	D₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
59	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
60	C₂×C₄²×C₇₉	—	2	4	no	—
61	C₂×C₄²×C₇₉	D₄	1	2	yes	—
62	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
63	#102×C₇₉	—	2	16	no	—
64	C₂⁴×C₇₉	—	2	4	no	—
65	C₂⁴×C₇₉	—	2	2	no	—
66	C₂⁴×C₇₉	—	4	2	no	—
67	C₂⁴×C₇₉	—	4	2	no	—
68	C₂⁴×C₇₉	—	4	2	no	—
69	C₂⁴×C₇₉	—	4	2	no	—
70	C₂⁴×C₇₉	—	4	2	no	—
71	C₂⁴×C₇₉	—	4	2	no	—
72	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₇₉	—	2	16	no	—
74	C₂×Q₈×C₇₉	—	4	8	no	—
75	C₂×Q₈×C₇₉	—	4	32	no	—
76	C₂×Q₈×C₇₉	—	4	8	no	—
77	C₂×D₄×C₇₉	—	2	16	no	—
78	C₂×D₄×C₇₉	—	2	4	no	—
79	C₂×D₄×C₇₉	—	2	4	no	—
80	C₂×D₄×C₇₉	—	2	4	no	—
81	C₂×D₄×C₇₉	—	2	2	no	—
82	C₂×D₄×C₇₉	—	4	2	no	—
83	C₂×D₄×C₇₉	—	4	8	no	—
84	C₂×D₄×C₇₉	—	4	2	no	—
85	C₂×D₄×C₇₉	C₂×Q₈	1	4	yes	complemented
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	8	no	—
91	C₂²×C₄×C₇₉	—	2	4	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	4	4	no	—
94	C₂²×C₄×C₇₉	—	4	4	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	D₈	1	4	yes	—
99	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	—
100	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₇₉	#41	1	4	yes	—
106	C₂²×C₄×C₇₉	#41	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₇₉	—	2	4	no	—
109	C₂×C₈×C₇₉	—	2	4	no	—
110	C₂×C₈×C₇₉	—	2	4	no	—
111	C₂×C₈×C₇₉	—	4	8	no	—
112	C₄⋊C₄×C₇₉	—	2	16	no	—
113	C₄⋊C₄×C₇₉	—	2	8	no	—
114	C₄⋊C₄×C₇₉	—	2	4	no	—
115	C₄⋊C₄×C₇₉	—	2	4	no	—
116	C₄⋊C₄×C₇₉	—	4	2	no	—
117	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
118	C₂²⋊C₄×C₇₉	—	4	8	no	—
119	C₂²⋊C₄×C₇₉	—	4	8	no	—
120	C₄²×C₇₉	—	2	4	no	—
121	C₄²×C₇₉	—	2	4	no	—
122	C₂³×C₇₉	—	2	4	no	—
123	C₂³×C₇₉	—	4	2	no	—
124	C₂³×C₇₉	—	4	2	no	—
125	C₂³×C₇₉	—	4	2	no	—
126	C₂³×C₇₉	—	4	2	no	—
127	C₂³×C₇₉	—	4	2	no	—
128	C₂³×C₇₉	—	4	2	no	—
129	C₂³×C₇₉	—	4	8	no	—
130	C₂³×C₇₉	—	4	8	no	—
131	C₂³×C₇₉	—	4	8	no	—
132	C₂³×C₇₉	—	8	4	no	—
133	C₂³×C₇₉	—	8	4	no	—
134	C₂³×C₇₉	—	8	4	no	—
135	C₂³×C₇₉	—	8	4	no	—
136	C₂³×C₇₉	#120	1	2	yes	—
137	C₂³×C₇₉	C₂²⋊Q₈	1	2	yes	—
138	C₂³×C₇₉	#124	1	2	yes	—
139	C₂³×C₇₉	C₂×D₈	1	2	yes	—
140	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
141	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
142	C₂³×C₇₉	#137	1	2	yes	—
143	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₇₉	—	4	32	no	—
145	D₄×C₇₉	—	2	8	no	—
146	D₄×C₇₉	—	4	4	no	—
147	D₄×C₇₉	—	4	8	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	2	8	no	—
153	C₂×C₄×C₇₉	—	2	8	no	—
154	C₂×C₄×C₇₉	—	2	8	no	—
155	C₂×C₄×C₇₉	—	4	4	no	—
156	C₂×C₄×C₇₉	—	4	4	no	—
157	C₂×C₄×C₇₉	—	4	16	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	—	8	4	no	—
162	C₂×C₄×C₇₉	#120	1	2	yes	—
163	C₂×C₄×C₇₉	C₂²⋊Q₈	1	8	yes	—
164	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₇₉	#124	1	8	yes	—
166	C₂×C₄×C₇₉	#124	1	2	yes	—
167	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
168	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
169	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
172	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
173	C₈×C₇₉	—	4	4	no	—
174	C₂²×C₇₉	—	4	4	no	—
175	C₂²×C₇₉	—	4	4	no	—
176	C₂²×C₇₉	—	4	4	no	—
177	C₂²×C₇₉	—	8	2	no	—
178	C₂²×C₇₉	—	8	2	no	—
179	C₂²×C₇₉	—	8	2	no	—
180	C₂²×C₇₉	—	8	2	no	—
181	C₂²×C₇₉	—	8	16	no	—
182	C₂²×C₇₉	#393	1	4	yes	—
183	C₂²×C₇₉	#447	1	4	yes	—
184	C₂²×C₇₉	#448	1	4	yes	—
185	C₂²×C₇₉	#474	1	4	yes	—
186	C₂²×C₇₉	#476	1	4	yes	—
187	C₂²×C₇₉	#486	1	4	yes	—
188	C₂²×C₇₉	#489	1	4	yes	—
189	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
190	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
191	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
192	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
193	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
194	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
196	C₄×C₇₉	—	2	4	no	—
197	C₄×C₇₉	—	2	4	no	—
198	C₄×C₇₉	—	4	8	no	—
199	C₄×C₇₉	—	8	2	no	—
200	C₄×C₇₉	#393	1	4	yes	—
201	C₄×C₇₉	C₂×C₂²⋊Q₈	1	2	yes	—
202	C₄×C₇₉	C₂×#124	1	2	yes	—
203	C₂×#2023	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂×C₇₉	—	8	4	no	—
205	C₂×C₇₉	#2023	1	8	yes	direct product factor
206	C₂×C₇₉	C₂×#393	1	1	yes	characteristic
207	C₂×C₇₉	C₂×#447	1	1	yes	characteristic
208	C₂×C₇₉	C₂×#448	1	1	yes	characteristic
209	C₂×C₇₉	C₂×#474	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#476	1	1	yes	characteristic
211	C₂×C₇₉	C₂×#486	1	1	yes	characteristic
212	C₂×C₇₉	C₂×#489	1	1	yes	characteristic
213	C₂²×C₄⋊Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
214	C₂²×#102	C₂×C₇₉	1	2	yes	—
215	C₂×#390	C₂×C₇₉	1	1	yes	characteristic
216	#2023	C₂×C₇₉	1	8	yes	direct product factor
217	C₂×#340	C₂×C₇₉	1	2	yes	complemented
218	C₂×#336	C₂×C₇₉	1	1	yes	characteristic, complemented
219	C₇₉	C₂×#2023	1	1	yes	characteristic, direct product factor, Sylow
220	C₂³×Q₈	—	2	1	no	—
221	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₇₉	1	2	yes	—
223	C₂×C₄⋊Q₈	—	2	8	no	—
224	C₂×C₄⋊Q₈	—	2	2	no	—
225	C₂×C₄⋊Q₈	C₂²×C₇₉	1	4	yes	complemented
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
229	C₂²×C₂²⋊C₄	—	2	1	no	—
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
232	C₂×#102	—	2	8	no	—
233	C₂×#102	C₂²×C₇₉	1	8	yes	—
234	#390	—	2	2	no	—
235	#390	C₂²×C₇₉	1	4	yes	—
236	#340	C₂²×C₇₉	1	8	yes	complemented
237	#336	C₂²×C₇₉	1	4	yes	complemented
238	C₂⁵	—	2	1	no	—
239	C₂²×Q₈	—	2	8	no	—
240	C₂²×Q₈	—	2	4	no	—
241	C₂²×Q₈	—	4	4	no	—
242	C₂²×Q₈	—	4	4	no	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	Q₈×C₇₉	1	4	yes	complemented
248	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
252	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	—	2	4	no	—
257	C₂²×C₈	C₂³×C₇₉	1	4	yes	—
258	C₄⋊Q₈	—	2	16	no	—
259	C₄⋊Q₈	—	2	16	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	D₄×C₇₉	1	8	yes	—
267	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	—	4	4	no	—
272	C₂×C₂²⋊C₄	—	4	4	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	D₄×C₇₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
276	#102	—	2	16	no	—
277	C₂⁴	—	2	4	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	—	4	2	no	—
282	C₂⁴	—	4	2	no	—
283	C₂⁴	—	4	2	no	—
284	C₂⁴	—	4	2	no	—
285	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
286	C₂×Q₈	—	2	16	no	—
287	C₂×Q₈	—	4	32	no	—
288	C₂×Q₈	—	4	8	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×D₄	—	2	16	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	8	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	C₂×Q₈×C₇₉	1	4	yes	complemented
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	D₈×C₇₉	1	4	yes	—
312	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
317	C₂²×C₄	C₂×Q₈×C₇₉	1	2	yes	—
318	C₂²×C₄	#41×C₇₉	1	4	yes	—
319	C₂²×C₄	#41×C₇₉	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	8	no	—
325	C₄⋊C₄	—	2	16	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
331	C₂²⋊C₄	—	4	8	no	—
332	C₂²⋊C₄	—	4	8	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	4	8	no	—
337	C₂³	—	4	8	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	8	4	no	—
348	C₂³	—	8	4	no	—
349	C₂³	#120×C₇₉	1	2	yes	—
350	C₂³	C₂²⋊Q₈×C₇₉	1	2	yes	—
351	C₂³	#124×C₇₉	1	2	yes	—
352	C₂³	C₂×D₈×C₇₉	1	2	yes	—
353	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
354	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
355	C₂³	#137×C₇₉	1	2	yes	—
356	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
357	Q₈	—	4	32	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	#120×C₇₉	1	2	yes	—
376	C₂×C₄	C₂²⋊Q₈×C₇₉	1	8	yes	—
377	C₂×C₄	C₂²⋊Q₈×C₇₉	1	2	yes	—
378	C₂×C₄	#124×C₇₉	1	8	yes	—
379	C₂×C₄	#124×C₇₉	1	2	yes	—
380	C₂×C₄	C₂×D₈×C₇₉	1	4	yes	—
381	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
383	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
385	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
386	C₈	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	16	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	#393×C₇₉	1	4	yes	—
396	C₂²	#447×C₇₉	1	4	yes	—
397	C₂²	#448×C₇₉	1	4	yes	—
398	C₂²	#474×C₇₉	1	4	yes	—
399	C₂²	#476×C₇₉	1	4	yes	—
400	C₂²	#486×C₇₉	1	4	yes	—
401	C₂²	#489×C₇₉	1	4	yes	—
402	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
403	C₂²	C₂×C₂²⋊Q₈×C₇₉	1	1	yes	characteristic
404	C₂²	C₂×#124×C₇₉	1	1	yes	characteristic
405	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
406	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
407	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
408	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	8	2	no	—
413	C₄	#393×C₇₉	1	4	yes	—
414	C₄	C₂×C₂²⋊Q₈×C₇₉	1	2	yes	—
415	C₄	C₂×#124×C₇₉	1	2	yes	—
416	C₂	—	8	4	no	—
417	C₂	C₇₉×#2023	1	8	yes	direct product factor
418	C₂	C₂×#393×C₇₉	1	1	yes	characteristic
419	C₂	C₂×#447×C₇₉	1	1	yes	characteristic
420	C₂	C₂×#448×C₇₉	1	1	yes	characteristic
421	C₂	C₂×#474×C₇₉	1	1	yes	characteristic
422	C₂	C₂×#476×C₇₉	1	1	yes	characteristic
423	C₂	C₂×#486×C₇₉	1	1	yes	characteristic
424	C₂	C₂×#489×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂³×D₄×C₇₉	C₂²
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
1. C₂²×C₄⋊Q₈×C₇₉	C₂	semidirect
4. C₇₉×#2023	C₂	direct (N × H)
5. C₂×#340×C₇₉	C₂	semidirect
6. C₂×#336×C₇₉	C₂	semidirect
12. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
23. #340×C₇₉	C₂²	semidirect
24. #336×C₇₉	C₂²	semidirect
34. C₂²×D₄×C₇₉	Q₈	semidirect
85. C₂×D₄×C₇₉	C₂×Q₈	semidirect
203. C₂×#2023	C₇₉	direct (N × H)
205. C₂×C₇₉	#2023	direct (N × H)
213. C₂²×C₄⋊Q₈	C₂×C₇₉	semidirect
216. #2023	C₂×C₇₉	direct (N × H)
217. C₂×#340	C₂×C₇₉	semidirect
218. C₂×#336	C₂×C₇₉	semidirect
219. C₇₉	C₂×#2023	direct (N × H)
225. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
236. #340	C₂²×C₇₉	semidirect
237. #336	C₂²×C₇₉	semidirect
247. C₂²×D₄	Q₈×C₇₉	semidirect
298. C₂×D₄	C₂×Q₈×C₇₉	semidirect
417. C₂	C₇₉×#2023	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×C₄⋊Q₈×C₇₉	2
C₂²×#102×C₇₉	2
C₂×#390×C₇₉	2
C₇₉×#2023	2
C₂×#340×C₇₉	2
C₂×#336×C₇₉	2
C₂×#2023	79

Subgroups — C2×C79×#2023 #34135136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#2023 #34135136