Subgroups — #34178227

Order 20224.

612 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772032	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098585	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23761275	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761274	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761274	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929607	C₄	1	2	yes	—
9	C₂×M₁₆×D₇₉	—	2	1	no	—
10	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
11	#19098619	—	2	1	no	—
12	#19098619	C₄	1	2	yes	—
13	#19098615	—	2	1	no	—
14	#19098615	C₄	1	2	yes	—
15	#19098587	C₂²	1	1	yes	characteristic
16	#19098587	C₂²	1	1	yes	characteristic
17	#19098586	—	2	1	no	—
18	#19098585	—	2	1	no	—
19	#19098585	—	2	1	no	—
20	#19098585	—	2	1	no	—
21	#19098585	—	2	1	no	—
22	#19098585	—	2	1	no	—
23	#19098585	C₄	1	2	yes	—
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Dic₇₉⋊C₈	C₄	1	2	yes	—
26	C₄⋊C₈×D₇₉	—	2	1	no	—
27	C₄⋊C₈×D₇₉	C₄	1	2	yes	—
28	#19098526	—	2	1	no	—
29	M₁₆×Dic₇₉	—	2	1	no	—
30	#423×C₇₉	C₂²	1	1	yes	characteristic
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
36	C₂×#11929608	—	2	1	no	—
37	C₂×#11929608	—	2	1	no	—
38	C₂×#11929607	—	2	2	no	—
39	C₂×#11929607	—	2	2	no	—
40	C₂×#11929607	—	2	2	no	—
41	C₂×#11929607	—	4	4	no	—
42	M₁₆×D₇₉	—	4	2	no	—
43	M₁₆×D₇₉	—	4	2	no	—
44	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₇₉	—	2	2	no	—
46	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
49	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₇₉	D₄	1	1	yes	characteristic
54	C₄²×D₇₉	D₄	1	1	yes	characteristic
55	C₄²×D₇₉	D₄	1	1	yes	characteristic
56	C₄²×D₇₉	D₄	1	1	yes	characteristic
57	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
62	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
63	Dic₇₉⋊C₈	—	2	2	no	—
64	Dic₇₉⋊C₈	—	2	2	no	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	—	2	2	no	—
67	(C₂×D₇₉)⋊C₈	—	2	2	no	—
68	(C₂×D₇₉)⋊C₈	—	2	2	no	—
69	#14579071	—	2	2	no	—
70	C₈×Dic₇₉	—	2	2	no	—
71	C₂×M₁₆×C₇₉	—	2	1	no	—
72	C₂×M₁₆×C₇₉	—	2	1	no	—
73	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₇₉	—	2	1	no	—
76	C₄⋊C₈×C₇₉	—	2	1	no	—
77	C₄⋊C₈×C₇₉	—	2	1	no	—
78	C₄⋊C₈×C₇₉	—	2	1	no	—
79	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
80	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
81	C₂³×D₇₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₇₉	—	2	2	no	—
86	C₂×C₄×D₇₉	—	2	2	no	—
87	C₂×C₄×D₇₉	—	2	1	no	—
88	C₂×C₄×D₇₉	—	2	1	no	—
89	C₂×C₄×D₇₉	—	2	1	no	—
90	C₂×C₄×D₇₉	—	2	1	no	—
91	C₂×C₄×D₇₉	—	4	2	no	—
92	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
104	#11929608	—	4	1	no	—
105	#11929608	—	4	1	no	—
106	#11929608	—	4	1	no	—
107	#11929608	—	4	1	no	—
108	#11929607	—	4	4	no	—
109	#11929607	—	4	4	no	—
110	#11929607	—	4	4	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	—	4	2	no	—
115	C₈×D₇₉	—	4	4	no	—
116	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
117	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
118	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
131	M₁₆×C₇₉	—	4	1	no	—
132	M₁₆×C₇₉	—	4	1	no	—
133	M₁₆×C₇₉	—	4	1	no	—
134	M₁₆×C₇₉	—	4	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	4	2	no	—
139	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₇₉	—	2	1	no	—
145	C₂²×D₇₉	—	2	1	no	—
146	C₂²×D₇₉	—	2	2	no	—
147	C₂²×D₇₉	—	4	1	no	—
148	C₂²×D₇₉	#95	1	1	yes	characteristic
149	C₂²×D₇₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	2	no	—
166	C₂×Dic₇₉	—	2	2	no	—
167	C₂×Dic₇₉	#95	1	1	yes	characteristic
168	C₂×Dic₇₉	#95	1	1	yes	characteristic
169	C₂×Dic₇₉	#95	1	1	yes	characteristic
170	C₂×Dic₇₉	#95	1	1	yes	characteristic
171	C₂×Dic₇₉	#95	1	1	yes	characteristic
172	C₂×Dic₇₉	#95	1	1	yes	characteristic
173	C₄×D₇₉	—	2	2	no	—
174	C₄×D₇₉	—	2	1	no	—
175	C₄×D₇₉	—	2	1	no	—
176	C₄×D₇₉	—	2	1	no	—
177	C₄×D₇₉	—	2	1	no	—
178	C₄×D₇₉	—	2	1	no	—
179	C₄×D₇₉	—	2	1	no	—
180	C₄×D₇₉	—	2	1	no	—
181	C₄×D₇₉	—	2	1	no	—
182	C₄×D₇₉	—	2	1	no	—
183	C₄×D₇₉	—	2	1	no	—
184	C₄×D₇₉	—	2	2	no	—
185	C₄×D₇₉	—	2	2	no	—
186	C₄×D₇₉	—	2	2	no	—
187	C₄×D₇₉	—	4	1	no	—
188	C₄×D₇₉	—	4	1	no	—
189	C₄×D₇₉	#100	1	2	yes	—
190	C₄×D₇₉	#101	1	2	yes	—
191	C₈×C₇₉	—	4	2	no	—
192	C₈×C₇₉	—	4	2	no	—
193	C₈×C₇₉	—	4	2	no	—
194	C₇₉⋊C₈	—	4	2	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₇₉⋊C₈	—	4	2	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	2	1	no	—
199	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
200	C₂²×C₇₉	#428	1	1	yes	characteristic
201	C₂²×C₇₉	#428	1	1	yes	characteristic
202	C₂×D₇₉	—	2	1	no	—
203	C₂×D₇₉	—	2	1	no	—
204	C₂×D₇₉	—	2	1	no	—
205	C₂×D₇₉	—	2	1	no	—
206	C₂×D₇₉	—	2	1	no	—
207	C₂×D₇₉	—	4	2	no	—
208	C₂×D₇₉	—	4	2	no	—
209	C₂×D₇₉	#343	1	2	yes	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	—	2	1	no	—
212	C₄×C₇₉	—	2	1	no	—
213	C₄×C₇₉	C₂×#100	1	1	yes	characteristic
214	C₄×C₇₉	C₂×#101	1	1	yes	characteristic
215	C₄×C₇₉	#417	1	1	yes	characteristic
216	C₄×C₇₉	#417	1	1	yes	characteristic
217	C₄×C₇₉	#418	1	1	yes	characteristic
218	C₄×C₇₉	#419	1	1	yes	characteristic
219	Dic₇₉	—	2	1	no	—
220	Dic₇₉	—	2	1	no	—
221	Dic₇₉	—	2	1	no	—
222	Dic₇₉	—	2	1	no	—
223	Dic₇₉	#338	1	2	yes	—
224	Dic₇₉	#343	1	2	yes	—
225	#8004	—	79	1	no	maximal, Sylow
226	C₂×C₇₉	—	2	1	no	—
227	C₂×C₇₉	—	2	1	no	—
228	C₂×C₇₉	C₂×#338	1	1	yes	characteristic
229	C₂×C₇₉	#1736	1	1	yes	characteristic
230	C₂×C₇₉	C₂×#343	1	1	yes	characteristic
231	D₇₉	—	2	2	no	—
232	D₇₉	—	4	1	no	—
233	#2920	—	79	1	no	—
234	C₂×#423	—	79	1	no	—
235	C₂×#423	—	79	1	no	—
236	#1292	—	79	1	no	—
237	#1292	—	79	1	no	—
238	#1292	—	79	1	no	—
239	#1292	D₇₉	1	1	yes	characteristic, complemented
240	C₇₉	#8004	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	79	2	no	—
242	C₂²×M₁₆	—	158	1	no	—
243	C₂²×C₄²	—	79	1	no	—
244	#432	—	79	2	no	—
245	#432	—	158	1	no	—
246	#431	—	79	2	no	—
247	#431	—	158	1	no	—
248	#423	—	79	1	no	—
249	#423	—	79	1	no	—
250	#423	—	79	2	no	—
251	#423	—	158	1	no	—
252	#423	—	158	1	no	—
253	#423	—	158	1	no	—
254	#423	—	158	1	no	—
255	#423	—	158	1	no	—
256	#423	—	158	1	no	—
257	#423	C₂×D₇₉	1	1	yes	characteristic
258	#423	C₂×D₇₉	1	1	yes	characteristic
259	C₂×C₄⋊C₈	—	79	2	no	—
260	C₂×C₄⋊C₈	—	79	2	no	—
261	C₂×C₄⋊C₈	—	79	1	no	—
262	C₂×C₄⋊C₈	—	158	1	no	—
263	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
264	#407	—	158	1	no	—
265	C₄×M₁₆	—	158	1	no	—
266	C₂³×C₄	—	79	1	no	—
267	C₂³×C₄	—	79	1	no	—
268	C₂³×C₄	—	79	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	316	4	no	—
272	C₂×M₁₆	—	316	2	no	—
273	C₂×M₁₆	—	316	2	no	—
274	C₂×M₁₆	—	158	2	no	—
275	C₂×M₁₆	—	158	2	no	—
276	C₂×M₁₆	—	158	2	no	—
277	C₂×M₁₆	—	158	1	no	—
278	C₂×M₁₆	—	158	1	no	—
279	C₂²×C₈	—	79	2	no	—
280	C₂²×C₈	—	158	2	no	—
281	C₂²×C₈	C₄×D₇₉	1	2	yes	—
282	C₂×C₄²	—	79	1	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	1	no	—
288	C₂×C₄²	—	79	1	no	—
289	C₂×C₄²	—	79	1	no	—
290	C₂×C₄²	—	79	1	no	—
291	C₂×C₄²	—	79	1	no	—
292	C₂×C₄²	—	79	1	no	—
293	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	79	2	no	—
299	C₄⋊C₈	—	79	2	no	—
300	C₄⋊C₈	—	158	2	no	—
301	C₄⋊C₈	—	158	2	no	—
302	C₄⋊C₈	—	158	2	no	—
303	C₄⋊C₈	—	158	2	no	—
304	C₄⋊C₈	—	158	1	no	—
305	C₄⋊C₈	—	158	1	no	—
306	C₄⋊C₈	—	158	1	no	—
307	C₄⋊C₈	—	158	1	no	—
308	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
309	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
310	C₂²⋊C₈	—	158	2	no	—
311	C₂²⋊C₈	—	158	2	no	—
312	#97	—	158	2	no	—
313	C₄×C₈	—	158	2	no	—
314	C₂⁴	—	79	1	no	—
315	C₂²×C₄	—	316	2	no	—
316	C₂²×C₄	—	79	1	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	79	1	no	—
320	C₂²×C₄	—	79	1	no	—
321	C₂²×C₄	—	79	1	no	—
322	C₂²×C₄	—	79	1	no	—
323	C₂²×C₄	—	79	1	no	—
324	C₂²×C₄	—	79	1	no	—
325	C₂²×C₄	—	79	1	no	—
326	C₂²×C₄	—	79	1	no	—
327	C₂²×C₄	—	79	1	no	—
328	C₂²×C₄	—	79	1	no	—
329	C₂²×C₄	—	79	1	no	—
330	C₂²×C₄	—	79	1	no	—
331	C₂²×C₄	—	158	2	no	—
332	C₂²×C₄	—	158	2	no	—
333	C₂²×C₄	—	158	1	no	—
334	C₂²×C₄	—	158	1	no	—
335	C₂²×C₄	—	158	1	no	—
336	C₂²×C₄	—	158	1	no	—
337	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
339	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	316	4	no	—
345	M₁₆	—	316	4	no	—
346	M₁₆	—	316	4	no	—
347	M₁₆	—	316	1	no	—
348	M₁₆	—	316	1	no	—
349	M₁₆	—	316	1	no	—
350	M₁₆	—	316	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	316	4	no	—
356	C₂×C₈	—	316	2	no	—
357	C₂×C₈	—	158	2	no	—
358	C₂×C₈	—	158	2	no	—
359	C₂×C₈	—	158	2	no	—
360	C₄²	—	79	1	no	—
361	C₄²	—	79	1	no	—
362	C₄²	—	79	1	no	—
363	C₄²	—	79	1	no	—
364	C₄²	—	79	1	no	—
365	C₄²	—	79	1	no	—
366	C₄²	—	79	1	no	—
367	C₄²	—	79	1	no	—
368	C₄²	—	79	1	no	—
369	C₄²	—	79	1	no	—
370	C₄²	—	79	1	no	—
371	C₄²	—	79	1	no	—
372	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
373	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
374	C₄²	D₄×D₇₉	1	1	yes	characteristic
375	C₄²	D₄×D₇₉	1	1	yes	characteristic
376	C₂³	—	316	1	no	—
377	C₂³	—	79	1	no	—
378	C₂³	—	79	1	no	—
379	C₂³	—	158	2	no	—
380	C₂³	—	158	1	no	—
381	C₂³	—	158	1	no	—
382	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	316	1	no	—
387	C₂×C₄	—	316	1	no	—
388	C₂×C₄	—	79	1	no	—
389	C₂×C₄	—	79	1	no	—
390	C₂×C₄	—	79	2	no	—
391	C₂×C₄	—	79	2	no	—
392	C₂×C₄	—	79	1	no	—
393	C₂×C₄	—	79	1	no	—
394	C₂×C₄	—	79	1	no	—
395	C₂×C₄	—	79	1	no	—
396	C₂×C₄	—	158	2	no	—
397	C₂×C₄	—	158	2	no	—
398	C₂×C₄	—	158	2	no	—
399	C₂×C₄	—	158	2	no	—
400	C₂×C₄	—	158	2	no	—
401	C₂×C₄	—	158	2	no	—
402	C₂×C₄	—	158	1	no	—
403	C₂×C₄	—	158	1	no	—
404	C₂×C₄	—	158	1	no	—
405	C₂×C₄	—	158	1	no	—
406	C₂×C₄	—	158	1	no	—
407	C₂×C₄	—	158	1	no	—
408	C₂×C₄	—	158	1	no	—
409	C₂×C₄	—	158	1	no	—
410	C₂×C₄	—	158	1	no	—
411	C₂×C₄	—	158	1	no	—
412	C₂×C₄	—	158	1	no	—
413	C₂×C₄	—	158	1	no	—
414	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
415	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
417	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
420	C₂×C₄	#14579185	1	1	yes	characteristic
421	C₂×C₄	#14579188	1	1	yes	characteristic
422	C₂×C₄	#14579190	1	1	yes	characteristic
423	C₂×C₄	#14579193	1	1	yes	characteristic
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	316	2	no	—
428	C₈	—	316	2	no	—
429	C₈	—	316	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	316	2	no	—
433	C₂²	—	316	2	no	—
434	C₂²	—	79	2	no	—
435	C₂²	—	158	1	no	—
436	C₂²	—	158	1	no	—
437	C₂²	—	158	1	no	—
438	C₂²	—	158	1	no	—
439	C₂²	—	158	1	no	—
440	C₂²	#95×D₇₉	1	1	yes	characteristic
441	C₂²	#19098602	1	1	yes	characteristic
442	C₂²	#19098604	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	79	2	no	—
447	C₄	—	79	2	no	—
448	C₄	—	158	1	no	—
449	C₄	—	158	1	no	—
450	C₄	—	158	1	no	—
451	C₄	—	158	1	no	—
452	C₄	#100×D₇₉	1	1	yes	characteristic
453	C₄	#101×D₇₉	1	1	yes	characteristic
454	C₄	#19098561	1	1	yes	characteristic
455	C₄	#19098563	1	1	yes	characteristic
456	C₄	#19098566	1	1	yes	characteristic
457	C₄	#19098570	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	316	1	no	—
461	C₂	—	158	2	no	—
462	C₂	#338×D₇₉	1	1	yes	characteristic
463	C₂	#23763118	1	1	yes	characteristic
464	C₂	#343×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#95×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1292	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1292	D₇₉
hypocenter	C₇₉	#8004
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

Complements

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

N	H ≅ G/N	type
4. #23761275	C₂	semidirect
5. #23761274	C₂	semidirect
6. #23761274	C₂	semidirect
7. C₇₉×#1292	C₂	semidirect
239. #1292	D₇₉	semidirect
240. C₇₉	#8004	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
C₂×#19098585	2
#423×D₇₉	2
#23761275	2
#23761274	2
C₇₉×#1292	2
#8004	79