Subgroups — #34260293

Order 20224.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773960	C₂	1	1	yes	maximal, characteristic
2	#23772502	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772466	C₂	1	1	yes	maximal, characteristic
4	#23762305	C₂	1	2	yes	maximal, complemented
5	#23762240	C₂	1	2	yes	maximal, complemented
6	#23762239	C₂	1	2	yes	maximal, complemented
7	#23762215	C₂	1	2	yes	maximal, complemented
8	#23762146	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761818	C₂	1	1	yes	maximal, characteristic
10	#23761687	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099113	C₂²	1	1	yes	characteristic
13	#19098959	C₄	1	1	yes	characteristic
14	#19098937	C₄	1	1	yes	characteristic
15	#19098913	C₄	1	1	yes	characteristic
16	#19098911	C₄	1	1	yes	characteristic
17	#19098794	C₄	1	2	yes	—
18	#19098794	C₄	1	2	yes	—
19	#19098694	—	2	1	no	—
20	#19098694	C₂²	1	2	yes	—
21	Q₈×C₇₉⋊C₈	—	2	1	no	—
22	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	—
23	C₄×#11929611	C₂²	1	2	yes	—
24	C₄×#11929611	C₂²	1	2	yes	—
25	#19098642	—	2	1	no	—
26	#19098640	C₂²	1	2	yes	—
27	C₈×D₃₁₆	—	2	1	no	—
28	#19098628	C₂²	1	2	yes	—
29	#19098624	—	2	2	no	—
30	#19098616	C₂²	1	1	yes	characteristic
31	#19098616	C₂²	1	1	yes	characteristic
32	#19098528	—	2	2	no	—
33	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
34	#19098315	C₂²	1	1	yes	characteristic
35	#19098315	C₂²	1	1	yes	characteristic
36	#19098313	C₂²	1	1	yes	characteristic
37	#19098313	C₂²	1	1	yes	characteristic
38	#19098292	C₂²	1	2	yes	—
39	#19098292	C₂²	1	2	yes	—
40	#19098285	C₂²	1	2	yes	—
41	#19098285	C₂²	1	2	yes	—
42	#533×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
46	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
47	C₂×#11929624	—	2	1	no	—
48	C₂×#11929611	C₂×C₄	1	2	yes	—
49	C₂×#11929611	C₂×C₄	1	2	yes	—
50	C₂×#11929607	—	2	2	no	—
51	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₇₉	—	2	2	no	—
54	#14579161	C₂×C₄	1	1	yes	characteristic
55	#14579158	C₂×C₄	1	1	yes	characteristic
56	#14579149	—	2	1	no	—
57	#14579135	—	2	1	no	—
58	#14579135	C₂×C₄	1	2	yes	—
59	C₄×D₃₁₆	—	2	1	no	—
60	C₄×D₃₁₆	C₂³	1	2	yes	—
61	#14579092	C₂×C₄	1	2	yes	—
62	#14579092	C₂×C₄	1	2	yes	—
63	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
66	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
69	#14579085	C₂×C₄	1	2	yes	—
70	#14579085	C₂×C₄	1	2	yes	—
71	#14579081	C₂×C₄	1	2	yes	—
72	#14579081	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
75	(C₂×D₇₉)⋊C₈	—	2	2	no	—
76	(C₂×D₇₉)⋊C₈	—	2	2	no	—
77	#14579072	—	2	2	no	—
78	C₄×C₇₉⋊C₈	—	2	1	no	—
79	C₄×C₇₉⋊C₈	—	2	2	no	—
80	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
85	C₂×M₁₆×C₇₉	—	2	1	no	—
86	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
88	#125×C₇₉	—	2	1	no	—
89	C₂²⋊Q₈×C₇₉	—	2	1	no	—
90	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
91	C₄×Q₈×C₇₉	—	2	1	no	—
92	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
93	#117×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂²⋊C₈×C₇₉	—	2	1	no	—
98	#97×C₇₉	—	2	1	no	—
99	C₄×C₈×C₇₉	—	2	1	no	—
100	C₄×C₈×C₇₉	C₂³	1	2	yes	—
101	#11929624	—	8	1	no	—
102	#11929624	—	8	1	no	—
103	C₂×Dic₁₅₈	—	2	1	no	—
104	C₂×D₃₁₆	—	2	1	no	—
105	C₂×D₃₁₆	—	2	1	no	—
106	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
107	C₂×C₂²⋊D₇₉	—	2	2	no	—
108	C₂×C₄×D₇₉	—	2	2	no	—
109	#11929611	—	2	4	no	—
110	#11929611	—	4	2	no	—
111	#11929607	—	8	2	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	1	no	—
115	C₂×C₇₉⋊C₈	—	4	1	no	—
116	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
121	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
122	C₈×D₇₉	—	8	2	no	—
123	C₄⋊Dic₇₉	—	2	1	no	—
124	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
125	(C₂×D₇₉)⋊C₄	—	2	2	no	—
126	(C₂×D₇₉)⋊C₄	—	2	2	no	—
127	C₂×Q₈×C₇₉	—	2	1	no	—
128	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
132	M₁₆×C₇₉	—	4	2	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	—	2	1	no	—
139	C₄⋊C₄×C₇₉	—	2	2	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₇₉	—	2	2	no	—
143	C₄²×C₇₉	—	2	2	no	—
144	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₉	#41	1	1	yes	characteristic
147	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₇₉	—	2	2	no	—
150	Q₈×C₇₉	—	2	2	no	—
151	Q₈×C₇₉	—	2	2	no	—
152	Q₈×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₇₉	—	8	2	no	—
167	C₂×Dic₇₉	—	2	2	no	—
168	D₃₁₆	—	2	2	no	—
169	D₃₁₆	—	2	2	no	—
170	D₃₁₆	—	4	2	no	—
171	D₃₁₆	—	8	1	no	—
172	C₄×D₇₉	—	4	2	no	—
173	C₄×D₇₉	—	4	2	no	—
174	Dic₁₅₈	—	8	1	no	—
175	C₈×C₇₉	—	4	2	no	—
176	C₈×C₇₉	—	4	1	no	—
177	C₈×C₇₉	—	4	1	no	—
178	C₇₉⋊C₈	—	2	1	no	—
179	C₇₉⋊C₈	—	2	1	no	—
180	C₇₉⋊C₈	—	2	1	no	—
181	C₇₉⋊C₈	—	2	2	no	—
182	C₇₉⋊C₈	—	2	2	no	—
183	C₇₉⋊C₈	—	4	1	no	—
184	C₇₉⋊C₈	—	4	1	no	—
185	C₇₉⋊C₈	#131	1	2	yes	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	2	1	no	—
188	C₂²×C₇₉	—	2	1	no	—
189	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂×D₇₉	—	4	2	no	—
191	C₂×D₇₉	—	4	2	no	—
192	C₂×D₇₉	—	4	2	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	4	2	no	—
197	C₄×C₇₉	—	4	2	no	—
198	C₄×C₇₉	#444	1	2	yes	—
199	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
200	C₄×C₇₉	#568	1	1	yes	characteristic
201	C₄×C₇₉	#577	1	1	yes	characteristic
202	C₄×C₇₉	#577	1	1	yes	characteristic
203	Dic₇₉	—	4	2	no	—
204	#18089	—	79	1	no	maximal, Sylow
205	C₂×C₇₉	—	4	1	no	—
206	C₂×C₇₉	#2935	1	1	yes	characteristic
207	C₂×C₇₉	#2949	1	1	yes	characteristic
208	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
209	D₇₉	—	8	2	no	—
210	#3167	—	79	1	no	—
211	#2986	—	79	1	no	—
212	#2979	—	79	1	no	—
213	#1592	—	79	2	no	—
214	#1583	—	79	2	no	—
215	#1582	—	79	2	no	—
216	SD₁₆⋊C₈	—	79	2	no	—
217	#1564	—	79	1	no	—
218	#1485	D₇₉	1	1	yes	characteristic, complemented
219	#1484	—	79	1	no	—
220	#1451	—	79	1	no	—
221	C₇₉	#18089	1	1	yes	characteristic, complemented, Sylow
222	#533	C₂×D₇₉	1	1	yes	characteristic
223	#532	—	79	1	no	—
224	#498	—	79	1	no	—
225	#492	—	79	1	no	—
226	#487	—	79	1	no	—
227	#486	—	79	1	no	—
228	#465	—	79	2	no	—
229	#465	—	79	2	no	—
230	#446	—	79	2	no	—
231	#446	—	158	1	no	—
232	C₈×Q₈	—	79	2	no	—
233	C₈×Q₈	—	158	1	no	—
234	C₄×SD₁₆	—	79	2	no	—
235	C₄×SD₁₆	—	79	2	no	—
236	#436	—	79	2	no	—
237	#436	—	158	1	no	—
238	C₈×D₄	—	79	2	no	—
239	C₈×D₄	—	158	1	no	—
240	#433	—	158	2	no	—
241	#431	—	79	1	no	—
242	#431	—	79	1	no	—
243	#431	C₂×D₇₉	1	1	yes	characteristic
244	#408	—	158	2	no	—
245	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
246	C₂×C₄×C₈	—	79	1	no	—
247	#335	—	79	1	no	—
248	#335	—	79	1	no	—
249	#334	—	79	1	no	—
250	#334	—	79	1	no	—
251	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
252	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
253	D₄⋊C₈	—	79	2	no	—
254	D₄⋊C₈	—	79	2	no	—
255	#322	—	79	2	no	—
256	#322	—	79	2	no	—
257	C₂×#41	—	158	1	no	—
258	C₂×SD₁₆	—	79	2	no	—
259	C₂×SD₁₆	—	79	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	158	2	no	—
262	C₂²×C₈	—	79	1	no	—
263	C₂²×C₈	—	79	1	no	—
264	C₂²×C₈	—	158	2	no	—
265	C₄⋊Q₈	—	79	1	no	—
266	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
268	#127	—	79	1	no	—
269	#125	—	2	1	no	—
270	#124	—	158	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
273	#121	—	79	2	no	—
274	#121	—	158	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
277	C₄×D₄	—	79	2	no	—
278	C₄×D₄	—	158	1	no	—
279	#117	—	2	1	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	#106	—	79	2	no	—
282	#106	—	79	2	no	—
283	C₄⋊C₈	—	79	1	no	—
284	C₄⋊C₈	—	79	1	no	—
285	C₄⋊C₈	—	79	1	no	—
286	C₄⋊C₈	—	79	1	no	—
287	C₄⋊C₈	—	158	2	no	—
288	C₄⋊C₈	—	158	2	no	—
289	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
291	#103	—	79	2	no	—
292	#103	—	79	2	no	—
293	#102	—	79	2	no	—
294	#102	—	79	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	79	2	no	—
297	C₂²⋊C₈	—	158	2	no	—
298	C₂²⋊C₈	—	158	2	no	—
299	C₂²⋊C₈	—	158	1	no	—
300	#97	—	2	1	no	—
301	#97	—	158	2	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	79	1	no	—
304	C₄×C₈	—	79	1	no	—
305	C₄×C₈	—	79	1	no	—
306	C₄×C₈	—	79	1	no	—
307	C₄×C₈	—	79	2	no	—
308	C₄×C₈	—	158	2	no	—
309	C₄×C₈	—	158	1	no	—
310	C₄×C₈	C₂²×D₇₉	1	2	yes	—
311	#41	—	632	1	no	—
312	#41	—	632	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	158	1	no	—
315	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
316	C₂×D₄	—	79	2	no	—
317	C₂×D₄	—	158	2	no	—
318	C₂×D₄	—	158	1	no	—
319	C₂×D₄	—	158	1	no	—
320	C₂²×C₄	—	158	2	no	—
321	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
323	C₂²×C₄	#11929623	1	1	yes	characteristic
324	SD₁₆	—	316	2	no	—
325	SD₁₆	—	158	4	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	632	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	316	1	no	—
332	C₂×C₈	—	79	1	no	—
333	C₂×C₈	—	79	1	no	—
334	C₂×C₈	—	79	1	no	—
335	C₂×C₈	—	79	1	no	—
336	C₂×C₈	—	79	2	no	—
337	C₂×C₈	—	79	2	no	—
338	C₂×C₈	—	632	2	no	—
339	C₂×C₈	—	158	1	no	—
340	C₂×C₈	—	158	1	no	—
341	C₂×C₈	—	158	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	79	2	no	—
348	C₄⋊C₄	—	158	1	no	—
349	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	158	2	no	—
352	C₂²⋊C₄	—	158	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
355	C₄²	D₄×D₇₉	1	1	yes	characteristic
356	C₄²	#11929623	1	1	yes	characteristic
357	C₄²	C₂³×D₇₉	1	1	yes	characteristic
358	C₂³	—	158	2	no	—
359	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	632	1	no	—
364	D₄	—	316	2	no	—
365	D₄	—	632	1	no	—
366	D₄	—	632	2	no	—
367	D₄	—	158	2	no	—
368	D₄	—	158	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	316	2	no	—
377	C₂×C₄	—	316	2	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
385	C₈	—	4	2	no	—
386	C₈	—	4	1	no	—
387	C₈	—	4	1	no	—
388	C₈	—	316	1	no	—
389	C₈	—	316	1	no	—
390	C₈	—	79	2	no	—
391	C₈	—	158	1	no	—
392	C₈	—	158	1	no	—
393	C₈	—	158	1	no	—
394	C₈	—	158	2	no	—
395	C₈	—	158	2	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	316	2	no	—
400	C₂²	—	316	2	no	—
401	C₂²	—	316	2	no	—
402	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	316	2	no	—
409	C₄	#19098682	1	2	yes	—
410	C₄	#131×D₇₉	1	1	yes	characteristic
411	C₄	#19099328	1	1	yes	characteristic
412	C₄	#19099372	1	1	yes	characteristic
413	C₄	#19099372	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	632	2	no	—
416	C₂	#23772140	1	1	yes	characteristic
417	C₂	#23772255	1	1	yes	characteristic
418	C₂	C₂×#19098682	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1485	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#19099113	C₂²
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1485	D₇₉
hypocenter	C₇₉	#18089
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1485

Complements

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

N	H ≅ G/N	type
2. #23772502	C₂	semidirect
4. #23762305	C₂	semidirect
5. #23762240	C₂	semidirect
6. #23762239	C₂	semidirect
7. #23762215	C₂	semidirect
8. #23762146	C₂	semidirect
10. #23761687	C₂	semidirect
11. C₇₉×#1485	C₂	semidirect
218. #1485	D₇₉	semidirect
221. C₇₉	#18089	semidirect

Maximal subgroups

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

subgroup	index
#23773960	2
#23772502	2
#23772466	2
#23762305	2
#23762240	2
#23762239	2
#23762215	2
#23762146	2
#23761818	2
#23761687	2
C₇₉×#1485	2
#18089	79