Subgroups — #34271778

Order 20224.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23774712	C₂	1	1	yes	maximal, characteristic
2	#23774327	C₂	1	1	yes	maximal, characteristic
3	#23773947	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772143	C₂	1	1	yes	maximal, characteristic
5	#23762912	C₂	1	2	yes	maximal, complemented
6	#23762902	C₂	1	2	yes	maximal, complemented
7	#23762788	C₂	1	2	yes	maximal, complemented
8	#23762778	C₂	1	2	yes	maximal, complemented
9	#23762153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098308	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	—	2	1	no	—
13	#19099113	C₂²	1	1	yes	characteristic
14	C₂×#14579161	C₂²	1	1	yes	characteristic
15	#19098973	—	2	2	no	—
16	#19098966	C₂²	1	2	yes	—
17	#19098959	C₂²	1	2	yes	—
18	#19098936	—	2	1	no	—
19	#19098914	—	2	1	no	—
20	#19098850	C₂²	1	2	yes	—
21	#19098848	—	2	1	no	—
22	#19098794	—	2	2	no	—
23	#19098769	C₂²	1	2	yes	—
24	#19098769	C₂²	1	2	yes	—
25	#19098765	C₂²	1	2	yes	—
26	#19098763	—	2	1	no	—
27	#19098704	—	2	2	no	—
28	#19098640	C₂²	1	2	yes	—
29	#19098633	—	2	2	no	—
30	#19098628	C₂²	1	2	yes	—
31	#19098606	—	2	1	no	—
32	#19098606	—	2	1	no	—
33	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	#19098529	—	2	1	no	—
35	C₄×#11929608	C₂²	1	1	yes	characteristic
36	#19098315	C₂²	1	2	yes	—
37	#19098313	C₂²	1	2	yes	—
38	#19098308	C₂²	1	2	yes	—
39	#19098308	C₂²	1	2	yes	—
40	#533×C₇₉	C₂²	1	1	yes	characteristic
41	#431×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
43	#333×C₇₉	C₂²	1	1	yes	characteristic
44	#333×C₇₉	C₂²	1	1	yes	characteristic
45	#332×C₇₉	C₂²	1	1	yes	characteristic
46	#332×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	—	2	1	no	—
48	C₂²×Dic₁₅₈	—	2	1	no	—
49	C₂×#11929613	—	2	2	no	—
50	C₂×#11929613	—	2	2	no	—
51	C₂×#11929611	—	2	2	no	—
52	#14579167	—	4	4	no	—
53	C₂×#11929608	D₄	1	1	yes	characteristic
54	C₂×#11929608	D₄	1	1	yes	characteristic
55	C₂×#11929607	—	2	2	no	—
56	C₂²×C₇₉⋊C₈	—	2	1	no	—
57	C₂×C₈×D₇₉	—	2	2	no	—
58	#14579161	—	2	1	no	—
59	#14579161	—	2	1	no	—
60	#14579161	—	2	1	no	—
61	#14579161	D₄	1	1	yes	characteristic
62	#14579161	C₂³	1	2	yes	—
63	#14579158	D₄	1	1	yes	characteristic
64	#14579149	—	2	1	no	—
65	#14579135	—	2	1	no	—
66	#14579135	D₄	1	2	yes	—
67	C₄×D₃₁₆	—	2	1	no	—
68	C₄×D₃₁₆	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₇₉	—	2	1	no	—
70	C₂×C₄⋊Dic₇₉	—	2	1	no	—
71	#14579094	—	2	2	no	—
72	#14579094	—	2	2	no	—
73	#14579092	—	2	2	no	—
74	#14579092	—	2	2	no	—
75	#14579092	—	2	2	no	—
76	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
78	#14579086	—	2	2	no	—
79	#14579086	—	2	2	no	—
80	#14579085	—	2	2	no	—
81	#14579081	—	2	2	no	—
82	(C₂×D₇₉)⋊C₈	—	2	2	no	—
83	(C₂×D₇₉)⋊C₈	—	2	2	no	—
84	#14579072	D₄	1	2	yes	—
85	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
86	C₂²×C₈×C₇₉	—	2	1	no	—
87	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
89	#125×C₇₉	—	2	1	no	—
90	C₂²⋊Q₈×C₇₉	—	2	1	no	—
91	C₂²⋊Q₈×C₇₉	—	2	1	no	—
92	C₄×Q₈×C₇₉	—	2	1	no	—
93	C₄×Q₈×C₇₉	—	2	1	no	—
94	#117×C₇₉	—	2	1	no	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	—	2	1	no	—
97	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₂²⋊C₈×C₇₉	—	2	1	no	—
102	C₄×C₈×C₇₉	—	2	1	no	—
103	#11929624	—	4	2	no	—
104	#11929624	—	4	2	no	—
105	C₂×Dic₁₅₈	—	2	1	no	—
106	C₂×Dic₁₅₈	—	2	2	no	—
107	C₂×Dic₁₅₈	—	4	1	no	—
108	C₂×Dic₁₅₈	—	8	1	no	—
109	C₂×Dic₁₅₈	—	8	1	no	—
110	C₂×D₃₁₆	—	2	1	no	—
111	C₂×D₃₁₆	—	2	1	no	—
112	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
113	C₂×C₂²⋊D₇₉	—	2	2	no	—
114	C₂²×Dic₇₉	—	4	1	no	—
115	C₂×C₄×D₇₉	—	2	2	no	—
116	#11929613	—	8	2	no	—
117	#11929613	—	8	2	no	—
118	#11929611	—	8	2	no	—
119	#11929608	—	2	2	no	—
120	#11929608	SD₁₆	1	4	yes	complemented
121	#11929607	—	4	4	no	—
122	C₂×C₇₉⋊C₈	—	2	2	no	—
123	C₂×C₇₉⋊C₈	—	8	1	no	—
124	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
125	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
126	C₈×D₇₉	—	4	4	no	—
127	C₄⋊Dic₇₉	—	2	1	no	—
128	C₄⋊Dic₇₉	—	2	2	no	—
129	C₄⋊Dic₇₉	—	2	2	no	—
130	C₄⋊Dic₇₉	—	4	1	no	—
131	C₄⋊Dic₇₉	—	4	1	no	—
132	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
133	(C₂×D₇₉)⋊C₄	—	2	2	no	—
134	(C₂×D₇₉)⋊C₄	—	2	2	no	—
135	C₂×Q₈×C₇₉	—	2	1	no	—
136	C₂×Q₈×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₇₉	—	2	1	no	—
141	C₂×C₈×C₇₉	—	2	1	no	—
142	C₂×C₈×C₇₉	—	2	1	no	—
143	C₂×C₈×C₇₉	—	2	1	no	—
144	C₂×C₈×C₇₉	—	4	2	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	—	4	1	no	—
150	C₄⋊C₄×C₇₉	—	4	1	no	—
151	C₂²⋊C₄×C₇₉	—	4	1	no	—
152	C₄²×C₇₉	—	4	1	no	—
153	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₉	#41	1	1	yes	characteristic
156	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₉	#121	1	1	yes	characteristic
158	C₂²×D₇₉	—	2	2	no	—
159	Q₈×C₇₉	—	4	1	no	—
160	Q₈×C₇₉	—	4	1	no	—
161	Q₈×C₇₉	—	8	1	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₇₉	#137	1	2	yes	—
172	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₇₉	—	4	4	no	—
176	C₂×Dic₇₉	—	2	2	no	—
177	C₂×Dic₇₉	—	4	2	no	—
178	C₂×Dic₇₉	—	8	2	no	—
179	D₃₁₆	—	2	2	no	—
180	D₃₁₆	—	2	2	no	—
181	D₃₁₆	—	4	2	no	—
182	D₃₁₆	—	8	1	no	—
183	C₄×D₇₉	—	4	2	no	—
184	C₄×D₇₉	—	4	2	no	—
185	Dic₁₅₈	—	4	2	no	—
186	Dic₁₅₈	—	4	2	no	—
187	Dic₁₅₈	—	4	2	no	—
188	Dic₁₅₈	—	8	2	no	—
189	C₈×C₇₉	—	4	1	no	—
190	C₈×C₇₉	—	4	1	no	—
191	C₈×C₇₉	—	4	1	no	—
192	C₈×C₇₉	—	4	1	no	—
193	C₇₉⋊C₈	—	2	2	no	—
194	C₇₉⋊C₈	—	4	2	no	—
195	C₇₉⋊C₈	C₂×SD₁₆	1	4	yes	—
196	C₂²×C₇₉	—	2	1	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	#461	1	2	yes	—
199	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
200	C₂×D₇₉	—	4	2	no	—
201	C₂×D₇₉	—	4	2	no	—
202	C₂×D₇₉	—	4	2	no	—
203	C₄×C₇₉	—	2	1	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	8	1	no	—
207	C₄×C₇₉	—	8	1	no	—
208	C₄×C₇₉	#461	1	2	yes	—
209	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
210	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
211	C₄×C₇₉	#576	1	1	yes	characteristic
212	C₄×C₇₉	#577	1	1	yes	characteristic
213	Dic₇₉	—	4	2	no	—
214	Dic₇₉	—	8	2	no	—
215	#19232	—	79	1	no	maximal, Sylow
216	C₂×C₇₉	—	2	2	no	—
217	C₂×C₇₉	C₂×#461	1	1	yes	characteristic
218	C₂×C₇₉	#3062	1	1	yes	characteristic
219	C₂×C₇₉	#3069	1	1	yes	characteristic
220	D₇₉	—	8	2	no	—
221	#3246	—	79	1	no	—
222	#3206	—	79	1	no	—
223	#3165	—	79	1	no	—
224	#2935	—	79	1	no	—
225	#1693	—	79	2	no	—
226	#1691	—	79	2	no	—
227	#1673	—	79	2	no	—
228	#1671	—	79	2	no	—
229	#1565	—	79	1	no	—
230	#1542	D₇₉	1	1	yes	characteristic, complemented
231	C₂×#332	—	79	1	no	—
232	C₇₉	#19232	1	1	yes	characteristic, complemented, Sylow
233	C₂×#131	—	158	1	no	—
234	#533	C₂×D₇₉	1	1	yes	characteristic
235	#532	—	79	1	no	—
236	C₂×C₄⋊Q₈	—	79	1	no	—
237	#501	—	158	2	no	—
238	#500	—	79	2	no	—
239	#498	—	79	2	no	—
240	#492	—	158	1	no	—
241	#487	—	158	1	no	—
242	#476	—	79	2	no	—
243	#475	—	158	1	no	—
244	#465	—	158	2	no	—
245	#461	—	79	2	no	—
246	#461	—	79	2	no	—
247	#461	—	79	2	no	—
248	#460	—	158	1	no	—
249	#448	—	158	2	no	—
250	#436	—	79	2	no	—
251	#435	—	158	2	no	—
252	C₈×D₄	—	79	2	no	—
253	#431	C₂×D₇₉	1	1	yes	characteristic
254	#428	—	158	1	no	—
255	#428	—	158	1	no	—
256	C₂×C₄⋊C₈	—	79	1	no	—
257	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
258	#408	—	158	1	no	—
259	C₄×M₁₆	—	79	1	no	—
260	#335	—	79	2	no	—
261	#334	—	79	2	no	—
262	#333	C₂×D₇₉	1	1	yes	characteristic
263	#333	C₂×D₇₉	1	1	yes	characteristic
264	#332	—	79	2	no	—
265	#332	—	79	2	no	—
266	#332	C₂×D₇₉	1	1	yes	characteristic
267	#332	C₂×D₇₉	1	1	yes	characteristic
268	C₂×#41	—	158	1	no	—
269	C₂²×Q₈	—	158	1	no	—
270	C₂×SD₁₆	—	158	2	no	—
271	C₂×SD₁₆	—	158	2	no	—
272	C₂×SD₁₆	—	158	2	no	—
273	#131	—	316	4	no	—
274	C₂×M₁₆	—	79	1	no	—
275	C₂×M₁₆	—	79	1	no	—
276	C₂×M₁₆	—	158	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	158	2	no	—
279	C₂²×C₈	—	158	1	no	—
280	C₄⋊Q₈	—	79	1	no	—
281	C₄⋊Q₈	—	79	2	no	—
282	C₄⋊Q₈	—	158	1	no	—
283	C₄⋊Q₈	—	158	1	no	—
284	C₄⋊Q₈	—	158	1	no	—
285	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
287	#127	—	79	1	no	—
288	#125	—	2	1	no	—
289	#124	—	158	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	79	2	no	—
293	#121	—	158	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	79	2	no	—
297	C₄×D₄	—	158	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	158	1	no	—
300	C₂×C₄⋊C₄	—	158	1	no	—
301	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
302	#107	—	158	2	no	—
303	#107	—	158	2	no	—
304	#106	—	158	2	no	—
305	#106	—	158	2	no	—
306	#106	—	158	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	79	2	no	—
309	C₄⋊C₈	—	158	1	no	—
310	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
314	#103	—	158	2	no	—
315	#103	—	158	2	no	—
316	#103	—	158	2	no	—
317	#102	—	158	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	158	2	no	—
320	C₂²⋊C₈	—	158	2	no	—
321	#97	—	79	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	79	2	no	—
324	#41	—	316	2	no	—
325	#41	—	316	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	316	1	no	—
329	C₂×Q₈	—	632	1	no	—
330	C₂×Q₈	—	632	1	no	—
331	C₂×Q₈	—	158	2	no	—
332	C₂×Q₈	—	158	1	no	—
333	C₂×D₄	—	79	2	no	—
334	C₂×D₄	—	158	2	no	—
335	C₂×D₄	—	158	1	no	—
336	C₂×D₄	—	158	1	no	—
337	C₂²×C₄	—	316	1	no	—
338	C₂²×C₄	—	158	2	no	—
339	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
341	C₂²×C₄	#11929624	1	1	yes	characteristic
342	SD₁₆	—	632	2	no	—
343	SD₁₆	—	632	2	no	—
344	SD₁₆	—	632	2	no	—
345	M₁₆	—	316	4	no	—
346	M₁₆	—	79	4	no	—
347	M₁₆	—	158	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	316	4	no	—
354	C₂×C₈	—	79	2	no	—
355	C₂×C₈	—	79	2	no	—
356	C₂×C₈	—	632	1	no	—
357	C₂×C₈	—	158	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	316	1	no	—
365	C₄⋊C₄	—	316	1	no	—
366	C₄⋊C₄	—	79	2	no	—
367	C₄⋊C₄	—	158	2	no	—
368	C₄⋊C₄	—	158	2	no	—
369	C₄⋊C₄	—	158	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	158	2	no	—
372	C₂²⋊C₄	—	158	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	D₄×D₇₉	1	1	yes	characteristic
375	C₄²	D₄×D₇₉	1	1	yes	characteristic
376	C₄²	#11929624	1	1	yes	characteristic
377	C₄²	C₂³×D₇₉	1	1	yes	characteristic
378	C₂³	—	158	2	no	—
379	C₂³	#14579134	1	1	yes	characteristic
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	8	1	no	—
383	Q₈	—	316	2	no	—
384	Q₈	—	316	2	no	—
385	Q₈	—	316	2	no	—
386	Q₈	—	632	2	no	—
387	D₄	—	316	4	no	—
388	D₄	—	316	2	no	—
389	D₄	—	632	1	no	—
390	D₄	—	158	2	no	—
391	D₄	—	158	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	316	2	no	—
398	C₂×C₄	—	316	2	no	—
399	C₂×C₄	—	316	2	no	—
400	C₂×C₄	—	632	2	no	—
401	C₂×C₄	—	158	2	no	—
402	C₂×C₄	#14579134	1	1	yes	characteristic
403	C₂×C₄	#14579134	1	1	yes	characteristic
404	C₂×C₄	#14579134	1	1	yes	characteristic
405	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
406	C₂×C₄	#14579193	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	316	2	no	—
415	C₈	—	79	4	no	—
416	C₈	—	158	2	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	316	2	no	—
420	C₂²	—	316	2	no	—
421	C₂²	—	316	2	no	—
422	C₂²	#19098767	1	2	yes	—
423	C₂²	C₂×#14579134	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	—	316	2	no	—
430	C₄	—	632	2	no	—
431	C₄	#19098767	1	2	yes	—
432	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
433	C₄	C₂×#14579193	1	1	yes	characteristic
434	C₄	#19099365	1	1	yes	characteristic
435	C₄	#19099370	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	632	2	no	—
438	C₂	C₂×#19098767	1	1	yes	characteristic
439	C₂	#23773083	1	1	yes	characteristic
440	C₂	#23773140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579134
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1542	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	#19099113	C₂²
hypercenter	#1542	D₇₉
hypocenter	C₇₉	#19232
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1542

Complements

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

N	H ≅ G/N	type
3. #23773947	C₂	semidirect
5. #23762912	C₂	semidirect
6. #23762902	C₂	semidirect
7. #23762788	C₂	semidirect
8. #23762778	C₂	semidirect
9. #23762153	C₂	semidirect
10. C₂×#19098308	C₂	semidirect
11. C₇₉×#1542	C₂	semidirect
120. #11929608	SD₁₆	semidirect
230. #1542	D₇₉	semidirect
232. C₇₉	#19232	semidirect

Maximal subgroups

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

subgroup	index
#23774712	2
#23774327	2
#23773947	2
#23772143	2
#23762912	2
#23762902	2
#23762788	2
#23762778	2
#23762153	2
C₂×#19098308	2
C₇₉×#1542	2
#19232	79