Subgroups — #34271789

Order 20224.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 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	#23774530	C₂	1	1	yes	maximal, characteristic
3	#23773947	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772143	C₂	1	1	yes	maximal, characteristic
5	#23762922	C₂	1	2	yes	maximal, complemented
6	#23762898	C₂	1	2	yes	maximal, complemented
7	#23762798	C₂	1	2	yes	maximal, complemented
8	#23762774	C₂	1	2	yes	maximal, complemented
9	#23762153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098311	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	#19098961	—	2	1	no	—
18	#19098959	C₂²	1	2	yes	—
19	#19098910	—	2	1	no	—
20	#19098882	—	2	2	no	—
21	#19098854	C₂²	1	2	yes	—
22	#19098854	C₂²	1	2	yes	—
23	#19098850	C₂²	1	2	yes	—
24	#19098848	—	2	1	no	—
25	#19098794	—	2	2	no	—
26	#19098765	C₂²	1	2	yes	—
27	#19098763	—	2	1	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	#19098311	C₂²	1	2	yes	—
39	#19098311	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×#11929611	—	2	2	no	—
50	#14579167	—	4	4	no	—
51	C₂×#11929608	D₄	1	1	yes	characteristic
52	C₂×#11929608	D₄	1	1	yes	characteristic
53	C₂×#11929607	—	2	2	no	—
54	C₂²×C₇₉⋊C₈	—	2	1	no	—
55	C₂×C₈×D₇₉	—	2	2	no	—
56	#14579161	—	2	1	no	—
57	#14579161	—	2	1	no	—
58	#14579161	—	2	1	no	—
59	#14579161	D₄	1	1	yes	characteristic
60	#14579161	C₂³	1	2	yes	—
61	#14579158	D₄	1	1	yes	characteristic
62	#14579149	—	2	1	no	—
63	#14579135	—	2	1	no	—
64	#14579135	D₄	1	2	yes	—
65	C₄×D₃₁₆	—	2	1	no	—
66	C₄×D₃₁₆	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₇₉	—	2	1	no	—
68	C₂×C₄⋊Dic₇₉	—	2	1	no	—
69	#14579094	—	2	2	no	—
70	#14579094	—	2	2	no	—
71	#14579093	—	2	2	no	—
72	#14579093	—	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	#14579085	—	2	2	no	—
79	#14579083	—	2	2	no	—
80	#14579083	—	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	2	no	—
109	C₂×D₃₁₆	—	2	1	no	—
110	C₂×D₃₁₆	—	2	1	no	—
111	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
112	C₂×C₂²⋊D₇₉	—	2	2	no	—
113	C₂²×Dic₇₉	—	4	1	no	—
114	C₂×C₄×D₇₉	—	2	2	no	—
115	#11929611	—	8	2	no	—
116	#11929608	—	2	2	no	—
117	#11929608	SD₁₆	1	4	yes	complemented
118	#11929607	—	4	4	no	—
119	C₂×C₇₉⋊C₈	—	2	2	no	—
120	C₂×C₇₉⋊C₈	—	8	1	no	—
121	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
122	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
123	C₈×D₇₉	—	4	4	no	—
124	C₄⋊Dic₇₉	—	2	1	no	—
125	C₄⋊Dic₇₉	—	2	2	no	—
126	C₄⋊Dic₇₉	—	2	2	no	—
127	C₄⋊Dic₇₉	—	4	1	no	—
128	C₄⋊Dic₇₉	—	4	1	no	—
129	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
130	(C₂×D₇₉)⋊C₄	—	2	2	no	—
131	(C₂×D₇₉)⋊C₄	—	2	2	no	—
132	C₂×Q₈×C₇₉	—	2	1	no	—
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
137	C₂×C₈×C₇₉	—	2	1	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	2	1	no	—
140	C₂×C₈×C₇₉	—	2	1	no	—
141	C₂×C₈×C₇₉	—	4	2	no	—
142	C₄⋊C₄×C₇₉	—	2	1	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	4	1	no	—
147	C₄⋊C₄×C₇₉	—	4	1	no	—
148	C₂²⋊C₄×C₇₉	—	4	1	no	—
149	C₄²×C₇₉	—	4	1	no	—
150	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₉	#41	1	1	yes	characteristic
153	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₇₉	#121	1	1	yes	characteristic
155	C₂²×D₇₉	—	2	2	no	—
156	Q₈×C₇₉	—	4	1	no	—
157	Q₈×C₇₉	—	4	1	no	—
158	Q₈×C₇₉	—	8	1	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	4	1	no	—
162	C₂×C₄×C₇₉	—	4	1	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₇₉	#137	1	2	yes	—
169	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₇₉	—	4	4	no	—
173	C₂×Dic₇₉	—	2	2	no	—
174	C₂×Dic₇₉	—	4	2	no	—
175	C₂×Dic₇₉	—	8	2	no	—
176	D₃₁₆	—	2	2	no	—
177	D₃₁₆	—	2	2	no	—
178	D₃₁₆	—	4	2	no	—
179	D₃₁₆	—	8	1	no	—
180	C₄×D₇₉	—	4	2	no	—
181	C₄×D₇₉	—	4	2	no	—
182	Dic₁₅₈	—	4	2	no	—
183	Dic₁₅₈	—	8	2	no	—
184	Dic₁₅₈	—	8	2	no	—
185	C₈×C₇₉	—	4	1	no	—
186	C₈×C₇₉	—	4	1	no	—
187	C₈×C₇₉	—	4	1	no	—
188	C₈×C₇₉	—	4	1	no	—
189	C₇₉⋊C₈	—	2	2	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₇₉⋊C₈	C₂×SD₁₆	1	4	yes	—
192	C₂²×C₇₉	—	2	1	no	—
193	C₂²×C₇₉	—	2	1	no	—
194	C₂²×C₇₉	#461	1	2	yes	—
195	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
196	C₂×D₇₉	—	4	2	no	—
197	C₂×D₇₉	—	4	2	no	—
198	C₂×D₇₉	—	4	2	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	8	1	no	—
203	C₄×C₇₉	—	8	1	no	—
204	C₄×C₇₉	#461	1	2	yes	—
205	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
206	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
207	C₄×C₇₉	#577	1	1	yes	characteristic
208	C₄×C₇₉	#578	1	1	yes	characteristic
209	Dic₇₉	—	4	2	no	—
210	Dic₇₉	—	8	2	no	—
211	#19233	—	79	1	no	maximal, Sylow
212	C₂×C₇₉	—	2	2	no	—
213	C₂×C₇₉	C₂×#461	1	1	yes	characteristic
214	C₂×C₇₉	#3063	1	1	yes	characteristic
215	C₂×C₇₉	#3068	1	1	yes	characteristic
216	D₇₉	—	8	2	no	—
217	#3246	—	79	1	no	—
218	#3227	—	79	1	no	—
219	#3165	—	79	1	no	—
220	#2935	—	79	1	no	—
221	#1695	—	79	2	no	—
222	#1691	—	79	2	no	—
223	#1675	—	79	2	no	—
224	#1671	—	79	2	no	—
225	#1565	—	79	1	no	—
226	#1542	D₇₉	1	1	yes	characteristic, complemented
227	C₂×#333	—	79	1	no	—
228	C₇₉	#19233	1	1	yes	characteristic, complemented, Sylow
229	C₂×#131	—	158	1	no	—
230	#533	C₂×D₇₉	1	1	yes	characteristic
231	#532	—	79	1	no	—
232	C₂×C₄⋊Q₈	—	79	1	no	—
233	#501	—	158	2	no	—
234	#500	—	79	2	no	—
235	#498	—	79	2	no	—
236	#498	—	158	1	no	—
237	#486	—	158	1	no	—
238	#481	—	158	2	no	—
239	#476	—	79	2	no	—
240	#476	—	79	2	no	—
241	#476	—	79	2	no	—
242	#475	—	158	1	no	—
243	#465	—	158	2	no	—
244	#461	—	79	2	no	—
245	#460	—	158	1	no	—
246	#436	—	79	2	no	—
247	#435	—	158	2	no	—
248	C₈×D₄	—	79	2	no	—
249	#431	C₂×D₇₉	1	1	yes	characteristic
250	#428	—	158	1	no	—
251	#428	—	158	1	no	—
252	C₂×C₄⋊C₈	—	79	1	no	—
253	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
254	#408	—	158	1	no	—
255	C₄×M₁₆	—	79	1	no	—
256	#335	—	79	2	no	—
257	#334	—	79	2	no	—
258	#333	—	79	2	no	—
259	#333	—	79	2	no	—
260	#333	C₂×D₇₉	1	1	yes	characteristic
261	#333	C₂×D₇₉	1	1	yes	characteristic
262	#332	C₂×D₇₉	1	1	yes	characteristic
263	#332	C₂×D₇₉	1	1	yes	characteristic
264	C₂×#41	—	158	1	no	—
265	C₂²×Q₈	—	158	1	no	—
266	C₂×SD₁₆	—	158	2	no	—
267	#131	—	316	4	no	—
268	C₂×M₁₆	—	79	1	no	—
269	C₂×M₁₆	—	79	1	no	—
270	C₂×M₁₆	—	158	2	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	158	2	no	—
273	C₂²×C₈	—	158	1	no	—
274	C₄⋊Q₈	—	79	1	no	—
275	C₄⋊Q₈	—	79	2	no	—
276	C₄⋊Q₈	—	158	1	no	—
277	C₄⋊Q₈	—	158	1	no	—
278	C₄⋊Q₈	—	158	1	no	—
279	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
281	#127	—	79	1	no	—
282	#125	—	2	1	no	—
283	#124	—	158	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	#121	—	79	2	no	—
287	#121	—	158	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×D₄	—	79	2	no	—
291	C₄×D₄	—	158	1	no	—
292	#117	—	2	1	no	—
293	C₂×C₄⋊C₄	—	158	1	no	—
294	C₂×C₄⋊C₄	—	158	1	no	—
295	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
296	#107	—	158	2	no	—
297	#107	—	158	2	no	—
298	#106	—	158	2	no	—
299	#106	—	158	2	no	—
300	#106	—	158	2	no	—
301	#106	—	158	2	no	—
302	#106	—	158	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	79	2	no	—
305	C₄⋊C₈	—	158	1	no	—
306	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
310	#103	—	158	2	no	—
311	#102	—	158	2	no	—
312	#102	—	158	2	no	—
313	#102	—	158	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	158	2	no	—
316	C₂²⋊C₈	—	158	2	no	—
317	#97	—	79	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	79	2	no	—
320	#41	—	316	2	no	—
321	#41	—	316	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	316	1	no	—
325	C₂×Q₈	—	632	2	no	—
326	C₂×Q₈	—	158	2	no	—
327	C₂×Q₈	—	158	1	no	—
328	C₂×D₄	—	79	2	no	—
329	C₂×D₄	—	158	2	no	—
330	C₂×D₄	—	158	1	no	—
331	C₂×D₄	—	158	1	no	—
332	C₂²×C₄	—	316	1	no	—
333	C₂²×C₄	—	158	2	no	—
334	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
336	C₂²×C₄	#11929624	1	1	yes	characteristic
337	SD₁₆	—	632	2	no	—
338	M₁₆	—	316	4	no	—
339	M₁₆	—	79	4	no	—
340	M₁₆	—	158	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	316	4	no	—
347	C₂×C₈	—	79	2	no	—
348	C₂×C₈	—	79	2	no	—
349	C₂×C₈	—	632	1	no	—
350	C₂×C₈	—	158	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	316	1	no	—
358	C₄⋊C₄	—	316	1	no	—
359	C₄⋊C₄	—	79	2	no	—
360	C₄⋊C₄	—	158	2	no	—
361	C₄⋊C₄	—	158	2	no	—
362	C₄⋊C₄	—	158	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	158	2	no	—
365	C₂²⋊C₄	—	158	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	D₄×D₇₉	1	1	yes	characteristic
368	C₄²	D₄×D₇₉	1	1	yes	characteristic
369	C₄²	#11929624	1	1	yes	characteristic
370	C₄²	C₂³×D₇₉	1	1	yes	characteristic
371	C₂³	—	158	2	no	—
372	C₂³	#14579134	1	1	yes	characteristic
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	316	2	no	—
377	Q₈	—	632	2	no	—
378	Q₈	—	632	2	no	—
379	D₄	—	316	4	no	—
380	D₄	—	316	2	no	—
381	D₄	—	632	1	no	—
382	D₄	—	158	2	no	—
383	D₄	—	158	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	316	2	no	—
390	C₂×C₄	—	316	2	no	—
391	C₂×C₄	—	316	2	no	—
392	C₂×C₄	—	632	2	no	—
393	C₂×C₄	—	158	2	no	—
394	C₂×C₄	#14579134	1	1	yes	characteristic
395	C₂×C₄	#14579134	1	1	yes	characteristic
396	C₂×C₄	#14579134	1	1	yes	characteristic
397	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
398	C₂×C₄	#14579193	1	2	yes	—
399	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	316	2	no	—
407	C₈	—	79	4	no	—
408	C₈	—	158	2	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	316	2	no	—
412	C₂²	—	316	2	no	—
413	C₂²	—	316	2	no	—
414	C₂²	#19098767	1	2	yes	—
415	C₂²	C₂×#14579134	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	316	2	no	—
422	C₄	—	632	2	no	—
423	C₄	#19098767	1	2	yes	—
424	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
425	C₄	C₂×#14579193	1	1	yes	characteristic
426	C₄	#19099370	1	1	yes	characteristic
427	C₄	#19099377	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	632	2	no	—
430	C₂	C₂×#19098767	1	1	yes	characteristic
431	C₂	#23773094	1	1	yes	characteristic
432	C₂	#23773131	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	#19233
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. #23762922	C₂	semidirect
6. #23762898	C₂	semidirect
7. #23762798	C₂	semidirect
8. #23762774	C₂	semidirect
9. #23762153	C₂	semidirect
10. C₂×#19098311	C₂	semidirect
11. C₇₉×#1542	C₂	semidirect
117. #11929608	SD₁₆	semidirect
226. #1542	D₇₉	semidirect
228. C₇₉	#19233	semidirect

Maximal subgroups

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

subgroup	index
#23774712	2
#23774530	2
#23773947	2
#23772143	2
#23762922	2
#23762898	2
#23762798	2
#23762774	2
#23762153	2
C₂×#19098311	2
C₇₉×#1542	2
#19233	79