Subgroups — C₇₉×#24543 #34136232

Order 20224.

980 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2503	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2341	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2073	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1878	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1805	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	#452×C₇₉	—	2	4	no	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	#417×C₇₉	—	2	4	no	—
22	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₉	C₂²	1	2	yes	—
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
25	C₂×#102×C₇₉	C₂²	1	2	yes	—
26	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	#400×C₇₉	—	2	1	no	—
29	#400×C₇₉	—	2	1	no	—
30	#391×C₇₉	C₂²	1	2	yes	—
31	#390×C₇₉	—	2	2	no	—
32	#390×C₇₉	C₂²	1	2	yes	—
33	#382×C₇₉	C₂²	1	2	yes	—
34	#381×C₇₉	—	2	2	no	—
35	#380×C₇₉	—	2	1	no	—
36	#380×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	#340×C₇₉	C₂²	1	2	yes	—
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	—	2	4	no	—
45	C₂×#41×C₇₉	—	4	2	no	—
46	C₂×#41×C₇₉	D₄	1	4	yes	—
47	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	1	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₇₉	—	2	2	no	—
55	C₂×Q₁₆×C₇₉	—	2	4	no	—
56	C₂×SD₁₆×C₇₉	—	2	2	no	—
57	C₂×SD₁₆×C₇₉	—	4	2	no	—
58	C₂×M₁₆×C₇₉	—	2	2	no	—
59	C₂×M₁₆×C₇₉	—	4	2	no	—
60	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₇₉	—	2	2	no	—
64	C₂²⋊Q₈×C₇₉	—	2	2	no	—
65	C₄×Q₈×C₇₉	—	2	4	no	—
66	C₄×Q₈×C₇₉	—	4	2	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
80	C₂×C₄²×C₇₉	—	2	2	no	—
81	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₇₉	—	4	2	no	—
83	#103×C₇₉	—	2	4	no	—
84	#103×C₇₉	—	2	2	no	—
85	#103×C₇₉	—	4	2	no	—
86	#102×C₇₉	—	2	4	no	—
87	#102×C₇₉	—	2	2	no	—
88	C₂²⋊C₈×C₇₉	—	2	2	no	—
89	#95×C₇₉	—	2	1	no	—
90	#95×C₇₉	—	2	2	no	—
91	#95×C₇₉	—	2	2	no	—
92	#95×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	2	no	—
94	#95×C₇₉	D₄	1	1	yes	characteristic
95	#95×C₇₉	D₄	1	1	yes	characteristic
96	C₂⁴×C₇₉	—	2	1	no	—
97	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
98	#41×C₇₉	—	2	8	no	—
99	#41×C₇₉	—	4	4	no	—
100	#41×C₇₉	—	4	8	no	—
101	C₂×Q₈×C₇₉	—	2	1	no	—
102	C₂×Q₈×C₇₉	—	2	2	no	—
103	C₂×Q₈×C₇₉	—	2	1	no	—
104	C₂×Q₈×C₇₉	—	2	1	no	—
105	C₂×Q₈×C₇₉	—	2	2	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₇₉	#41	1	4	yes	—
109	C₂×D₄×C₇₉	—	2	4	no	—
110	C₂×D₄×C₇₉	—	2	2	no	—
111	C₂×D₄×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	4	4	no	—
114	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₉	—	2	1	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	4	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	—	2	1	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	4	4	no	—
124	C₂²×C₄×C₇₉	—	4	4	no	—
125	C₂²×C₄×C₇₉	—	4	2	no	—
126	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₉	#41	1	2	yes	—
131	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₇₉	—	4	4	no	—
133	SD₁₆×C₇₉	—	4	4	no	—
134	M₁₆×C₇₉	—	4	4	no	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	2	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₄⋊C₄×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	2	2	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	4	4	no	—
149	C₄⋊C₄×C₇₉	—	4	2	no	—
150	C₄⋊C₄×C₇₉	—	4	2	no	—
151	C₂²⋊C₄×C₇₉	—	4	2	no	—
152	C₂²⋊C₄×C₇₉	—	4	4	no	—
153	C₂²⋊C₄×C₇₉	—	4	2	no	—
154	C₂²⋊C₄×C₇₉	—	8	2	no	—
155	C₂²⋊C₄×C₇₉	—	8	1	no	—
156	C₄²×C₇₉	—	2	2	no	—
157	C₄²×C₇₉	—	2	2	no	—
158	C₄²×C₇₉	—	4	4	no	—
159	C₂³×C₇₉	—	2	2	no	—
160	C₂³×C₇₉	—	2	2	no	—
161	C₂³×C₇₉	—	2	1	no	—
162	C₂³×C₇₉	—	2	1	no	—
163	C₂³×C₇₉	—	2	2	no	—
164	C₂³×C₇₉	—	4	2	no	—
165	C₂³×C₇₉	—	4	2	no	—
166	C₂³×C₇₉	—	4	1	no	—
167	C₂³×C₇₉	—	4	1	no	—
168	C₂³×C₇₉	#121	1	2	yes	—
169	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₇₉	—	2	2	no	—
171	Q₈×C₇₉	—	2	4	no	—
172	Q₈×C₇₉	—	4	1	no	—
173	Q₈×C₇₉	—	4	1	no	—
174	Q₈×C₇₉	—	4	2	no	—
175	Q₈×C₇₉	#123	1	4	yes	—
176	D₄×C₇₉	—	2	2	no	—
177	D₄×C₇₉	—	2	2	no	—
178	D₄×C₇₉	—	4	8	no	—
179	D₄×C₇₉	—	4	2	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	4	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	2	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	4	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	2	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	4	8	no	—
193	C₂×C₄×C₇₉	—	4	1	no	—
194	C₂×C₄×C₇₉	—	4	1	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	4	2	no	—
197	C₂×C₄×C₇₉	—	4	2	no	—
198	C₂×C₄×C₇₉	—	4	2	no	—
199	C₂×C₄×C₇₉	—	4	4	no	—
200	C₂×C₄×C₇₉	—	4	2	no	—
201	C₂×C₄×C₇₉	—	4	1	no	—
202	C₂×C₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	8	4	no	—
204	C₂×C₄×C₇₉	#121	1	2	yes	—
205	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
207	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
209	C₈×C₇₉	—	4	1	no	—
210	C₈×C₇₉	—	4	2	no	—
211	C₈×C₇₉	—	4	1	no	—
212	C₂²×C₇₉	—	2	2	no	—
213	C₂²×C₇₉	—	2	2	no	—
214	C₂²×C₇₉	—	2	2	no	—
215	C₂²×C₇₉	—	4	2	no	—
216	C₂²×C₇₉	—	4	2	no	—
217	C₂²×C₇₉	—	4	2	no	—
218	C₂²×C₇₉	—	4	2	no	—
219	C₂²×C₇₉	—	4	2	no	—
220	C₂²×C₇₉	—	8	2	no	—
221	C₂²×C₇₉	—	8	2	no	—
222	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
223	C₂²×C₇₉	#546	1	2	yes	—
224	C₂²×C₇₉	#575	1	2	yes	—
225	C₂²×C₇₉	#577	1	1	yes	characteristic
226	C₂²×C₇₉	#578	1	1	yes	characteristic
227	C₄×C₇₉	—	2	2	no	—
228	C₄×C₇₉	—	2	4	no	—
229	C₄×C₇₉	—	4	2	no	—
230	C₄×C₇₉	—	4	2	no	—
231	C₄×C₇₉	—	8	1	no	—
232	C₄×C₇₉	—	8	2	no	—
233	C₄×C₇₉	—	8	1	no	—
234	C₄×C₇₉	—	8	2	no	—
235	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
236	C₄×C₇₉	#534	1	1	yes	characteristic
237	C₄×C₇₉	#551	1	2	yes	—
238	#24543	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₇₉	—	4	2	no	—
240	C₂×C₇₉	—	8	2	no	—
241	C₂×C₇₉	#2412	1	1	yes	characteristic
242	C₂×C₇₉	#3040	1	1	yes	characteristic
243	C₂×C₇₉	#3046	1	1	yes	characteristic
244	C₂×C₇₉	#3317	1	2	yes	—
245	C₂×C₇₉	#3327	1	2	yes	—
246	C₂×#452	C₂×C₇₉	1	1	yes	characteristic
247	C₂×#417	C₂×C₇₉	1	1	yes	characteristic
248	#2503	C₂×C₇₉	1	1	yes	characteristic, complemented
249	#2341	C₂×C₇₉	1	1	yes	characteristic
250	#2073	C₂×C₇₉	1	2	yes	complemented
251	#2055	C₂×C₇₉	1	2	yes	complemented
252	#1894	C₂×C₇₉	1	1	yes	characteristic, complemented
253	#1878	C₂×C₇₉	1	2	yes	complemented
254	#1851	C₂×C₇₉	1	1	yes	characteristic, complemented
255	#1824	C₂×C₇₉	1	1	yes	characteristic, complemented
256	#1805	C₂×C₇₉	1	2	yes	complemented
257	C₇₉	#24543	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
259	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
265	#452	—	2	4	no	—
266	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
267	#417	—	2	4	no	—
268	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇₉	1	2	yes	—
270	C₂×#103	C₂²×C₇₉	1	2	yes	—
271	C₂×#102	C₂²×C₇₉	1	2	yes	—
272	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
274	#400	—	2	1	no	—
275	#400	—	2	1	no	—
276	#391	C₂²×C₇₉	1	2	yes	—
277	#390	—	2	2	no	—
278	#390	C₂²×C₇₉	1	2	yes	—
279	#382	C₂²×C₇₉	1	2	yes	—
280	#381	—	2	2	no	—
281	#380	—	2	1	no	—
282	#380	C₂²×C₇₉	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	—	2	1	no	—
284	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
285	#340	C₂²×C₇₉	1	2	yes	—
286	#340	C₂²×C₇₉	1	2	yes	—
287	#340	C₂²×C₇₉	1	2	yes	—
288	#336	C₂²×C₇₉	1	2	yes	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	4	2	no	—
292	C₂×#41	D₄×C₇₉	1	4	yes	—
293	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	4	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	4	2	no	—
306	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
307	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	—	4	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
328	C₄⋊C₈	—	4	2	no	—
329	#103	—	2	4	no	—
330	#103	—	2	2	no	—
331	#103	—	4	2	no	—
332	#102	—	2	4	no	—
333	#102	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	D₄×C₇₉	1	1	yes	characteristic
341	#95	D₄×C₇₉	1	1	yes	characteristic
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
344	#41	—	2	8	no	—
345	#41	—	4	4	no	—
346	#41	—	4	8	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
354	C₂×Q₈	#41×C₇₉	1	4	yes	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
376	C₂²×C₄	#41×C₇₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
378	Q₁₆	—	4	4	no	—
379	SD₁₆	—	4	4	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₂²⋊C₄	—	8	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	4	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	#121×C₇₉	1	2	yes	—
415	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	2	no	—
421	Q₈	#123×C₇₉	1	4	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	#121×C₇₉	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
453	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
455	C₈	—	4	1	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
469	C₂²	#546×C₇₉	1	2	yes	—
470	C₂²	#575×C₇₉	1	2	yes	—
471	C₂²	#577×C₇₉	1	1	yes	characteristic
472	C₂²	#578×C₇₉	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
482	C₄	#534×C₇₉	1	1	yes	characteristic
483	C₄	#551×C₇₉	1	2	yes	—
484	C₂	—	4	2	no	—
485	C₂	—	8	2	no	—
486	C₂	C₇₉×#2412	1	1	yes	characteristic
487	C₂	C₇₉×#3040	1	1	yes	characteristic
488	C₂	C₇₉×#3046	1	1	yes	characteristic
489	C₂	C₇₉×#3317	1	2	yes	—
490	C₂	C₇₉×#3327	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×#41×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇₉×#2503	C₂	semidirect
5. C₇₉×#2073	C₂	semidirect
6. C₇₉×#2055	C₂	semidirect
7. C₇₉×#1894	C₂	semidirect
8. C₇₉×#1878	C₂	semidirect
9. C₇₉×#1851	C₂	semidirect
10. C₇₉×#1824	C₂	semidirect
11. C₇₉×#1805	C₂	semidirect
238. #24543	C₇₉	direct (N × H)
248. #2503	C₂×C₇₉	semidirect
250. #2073	C₂×C₇₉	semidirect
251. #2055	C₂×C₇₉	semidirect
252. #1894	C₂×C₇₉	semidirect
253. #1878	C₂×C₇₉	semidirect
254. #1851	C₂×C₇₉	semidirect
255. #1824	C₂×C₇₉	semidirect
256. #1805	C₂×C₇₉	semidirect
257. C₇₉	#24543	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#452×C₇₉	2
C₂×#417×C₇₉	2
C₇₉×#2503	2
C₇₉×#2341	2
C₇₉×#2073	2
C₇₉×#2055	2
C₇₉×#1894	2
C₇₉×#1878	2
C₇₉×#1851	2
C₇₉×#1824	2
C₇₉×#1805	2
#24543	79

Subgroups — C79×#24543 #34136232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24543 #34136232