Subgroups — #13029126

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617116	C₂	1	2	yes	maximal
2	#10610280	C₂	1	1	yes	maximal, characteristic
3	#10604737	C₂	1	1	yes	maximal, characteristic, complemented
4	#10604736	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604688	C₂	1	2	yes	maximal, complemented
6	#10603864	C₂	1	1	yes	maximal, characteristic, complemented
7	#10603863	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603862	C₂	1	2	yes	maximal, complemented
9	#10603810	C₂	1	2	yes	maximal, complemented
10	#10603809	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603807	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#4053	C₄	1	1	yes	characteristic
13	C₂×#4047	C₄	1	1	yes	characteristic
14	#65856	C₂²	1	1	yes	characteristic
15	#65754	C₂²	1	2	yes	—
16	C₄×#704	C₂²	1	2	yes	—
17	#65707	C₄	1	4	yes	—
18	#65704	C₄	1	4	yes	—
19	#65695	C₄	1	4	yes	—
20	#65694	C₄	1	4	yes	—
21	#65680	C₂²	1	2	yes	—
22	#65678	C₂²	1	2	yes	—
23	C₄×#700	C₂²	1	2	yes	—
24	C₄×D₅⋊C₈	C₂²	1	2	yes	—
25	C₅×#405	C₄	1	1	yes	characteristic
26	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
28	#65286	C₄	1	1	yes	characteristic
29	#64997	C₄	1	1	yes	characteristic
30	#64997	C₄	1	1	yes	characteristic
31	#64996	C₂²	1	1	yes	characteristic
32	#64996	C₂²	1	1	yes	characteristic
33	#64978	C₄	1	1	yes	characteristic
34	#64978	C₄	1	1	yes	characteristic
35	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
37	#170⋊C₈	C₂²	1	2	yes	—
38	#170⋊C₈	C₂²	1	2	yes	—
39	#170⋊C₈	C₂²	1	2	yes	—
40	#170⋊C₈	C₂²	1	2	yes	—
41	#64879	C₂²	1	2	yes	—
42	#64879	C₂²	1	1	yes	characteristic
43	#64879	C₂²	1	1	yes	characteristic
44	#64879	C₂²	1	2	yes	—
45	C₈×#170	C₂²	1	1	yes	characteristic
46	C₈×#170	C₂²	1	1	yes	characteristic
47	#17336	—	5	1	no	maximal, Sylow
48	C₂×#709	C₂×C₄	1	1	yes	characteristic
49	C₂×#704	C₂×C₄	1	4	yes	—
50	C₂×#700	C₂×C₄	1	4	yes	—
51	C₂×D₅⋊C₈	C₂×C₄	1	4	yes	—
52	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₅×#117	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
56	C₂×#681	C₂×C₄	1	1	yes	characteristic
57	C₂²×#168	C₂×C₄	1	1	yes	characteristic
58	#4053	—	2	4	no	—
59	#4047	—	2	4	no	—
60	C₂×#676	C₂×C₄	1	1	yes	characteristic
61	C₂×#676	C₂×C₄	1	1	yes	characteristic
62	C₂×#676	C₂×C₄	1	1	yes	characteristic
63	C₂×#676	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
68	#4039	C₂×C₄	1	2	yes	—
69	#4033	C₂×C₄	1	2	yes	—
70	#4027	C₂×C₄	1	2	yes	—
71	#4027	C₂×C₄	1	2	yes	—
72	#4018	C₂×C₄	1	1	yes	characteristic
73	#4018	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₅	C₂³	1	1	yes	characteristic
75	C₄²×D₅	C₂³	1	1	yes	characteristic
76	C₂²⋊#170	C₂×C₄	1	4	yes	—
77	#4004	C₂×C₄	1	4	yes	—
78	#4004	C₂×C₄	1	4	yes	—
79	#4003	C₂×C₄	1	4	yes	—
80	#4003	C₂×C₄	1	4	yes	—
81	#4002	C₂×C₄	1	4	yes	—
82	#4002	C₂×C₄	1	4	yes	—
83	C₄⋊#170	C₂×C₄	1	4	yes	—
84	C₄×#170	C₂×C₄	1	4	yes	—
85	C₄×#170	C₂³	1	2	yes	—
86	C₄×#170	C₂³	1	2	yes	—
87	C₄×#170	C₂³	1	2	yes	—
88	C₄×#170	C₂³	1	2	yes	—
89	C₅×#97	C₂×C₄	1	1	yes	characteristic
90	C₅×#97	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
93	#3947	C₂×C₄	1	1	yes	characteristic
94	#3947	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂³	1	1	yes	characteristic
98	C₈×Dic₅	C₂³	1	1	yes	characteristic
99	C₈×Dic₅	C₂³	1	1	yes	characteristic
100	C₈×Dic₅	C₂³	1	1	yes	characteristic
101	#3935	C₂×C₄	1	1	yes	characteristic
102	#3935	C₂×C₄	1	1	yes	characteristic
103	C₄×#168	C₂×C₄	1	1	yes	characteristic
104	C₄×#168	C₂×C₄	1	1	yes	characteristic
105	#2965	—	5	2	no	—
106	C₄×#131	—	5	1	no	—
107	#1455	—	5	1	no	—
108	#1455	—	5	1	no	—
109	#1453	—	5	1	no	—
110	#1453	—	5	1	no	—
111	#1451	—	5	2	no	—
112	#1451	—	5	2	no	—
113	#1451	—	5	2	no	—
114	#1450	—	5	1	no	—
115	C₂×#322	—	5	1	no	—
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
118	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
119	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
120	#709	—	2	2	no	—
121	#709	—	2	2	no	—
122	C₂×D₂₀	C₄²	1	1	yes	characteristic
123	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
125	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
126	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
128	#704	—	4	4	no	—
129	C₂×#170	C₂²×C₄	1	4	yes	—
130	C₂×#170	C₂²×C₄	1	4	yes	—
131	C₂×#170	C₂²×C₄	1	4	yes	—
132	C₂×#170	C₂²×C₄	1	4	yes	—
133	#700	—	4	4	no	—
134	D₅⋊C₈	—	4	4	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₅×C₄⋊C₄	C₄²	1	2	yes	—
142	C₅×C₂²⋊C₄	C₄²	1	2	yes	—
143	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
145	#685	C₄²	1	2	yes	—
146	#685	C₄²	1	2	yes	—
147	#683	C₄²	1	2	yes	—
148	#683	C₄²	1	2	yes	—
149	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂²×C₄	1	2	yes	—
151	C₄×Dic₅	C₂²×C₄	1	2	yes	—
152	C₄×Dic₅	C₂²×C₄	1	2	yes	—
153	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
154	#681	—	2	2	no	—
155	C₂×#168	—	2	2	no	—
156	C₂×#168	C₂²×C₄	1	1	yes	characteristic
157	C₂×#168	C₂²×C₄	1	1	yes	characteristic
158	C₂×#168	C₂²×C₄	1	1	yes	characteristic
159	C₂×#168	C₂²×C₄	1	1	yes	characteristic
160	#676	—	2	2	no	—
161	#676	—	2	2	no	—
162	#676	—	2	2	no	—
163	#676	—	2	2	no	—
164	C₈×D₅	—	2	2	no	—
165	C₈×D₅	—	2	2	no	—
166	C₈×D₅	M₁₆	1	4	yes	complemented
167	C₈×D₅	M₁₆	1	4	yes	complemented
168	C₂×#131	—	5	1	no	—
169	C₂×#131	—	5	1	no	—
170	C₄×#41	—	5	1	no	—
171	#446	—	5	4	no	—
172	#436	—	5	4	no	—
173	#435	—	5	4	no	—
174	#435	—	5	4	no	—
175	#431	—	5	2	no	—
176	#431	—	5	2	no	—
177	#431	—	5	2	no	—
178	#405	—	5	1	no	—
179	#405	—	5	1	no	—
180	#405	—	5	1	no	—
181	#405	—	5	1	no	—
182	#405	—	5	1	no	—
183	#405	AGL(1,𝔽₅)	1	1	yes	characteristic
184	C₄×M₁₆	—	5	2	no	—
185	C₄×M₁₆	—	5	2	no	—
186	C₄×M₁₆	—	5	1	no	—
187	C₄×M₁₆	—	5	1	no	—
188	C₄×M₁₆	—	5	1	no	—
189	C₂×C₄×C₈	—	5	2	no	—
190	C₂×C₄×C₈	—	5	1	no	—
191	C₂×C₄×C₈	—	5	1	no	—
192	C₂×C₄×C₈	—	5	1	no	—
193	#322	—	5	2	no	—
194	#322	—	5	1	no	—
195	#322	—	5	1	no	—
196	#322	—	5	2	no	—
197	#322	—	5	2	no	—
198	#322	—	5	2	no	—
199	#322	—	5	2	no	—
200	#322	—	5	2	no	—
201	C₈²	—	5	1	no	—
202	C₈²	—	5	1	no	—
203	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
205	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
211	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂²⋊D₅	—	2	2	no	—
213	C₂²⋊D₅	—	2	2	no	—
214	C₂×Dic₅	—	2	4	no	—
215	C₂×Dic₅	C₂×C₄²	1	2	yes	—
216	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
217	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
218	C₂×Dic₅	C₂³×C₄	1	2	yes	—
219	D₂₀	—	2	2	no	—
220	C₄×D₅	—	2	1	no	—
221	C₄×D₅	—	2	1	no	—
222	C₄×D₅	—	2	4	no	—
223	C₄×D₅	—	2	4	no	—
224	C₄×D₅	C₂×M₁₆	1	2	yes	—
225	C₄×D₅	C₂×M₁₆	1	2	yes	—
226	Dic₁₀	—	2	2	no	—
227	#170	—	2	4	no	—
228	#170	—	2	4	no	—
229	#170	—	2	4	no	—
230	#170	—	2	4	no	—
231	C₅×C₈	—	2	1	no	—
232	C₅×C₈	—	2	1	no	—
233	C₅×C₈	C₂×M₁₆	1	2	yes	—
234	C₅×C₈	C₂×M₁₆	1	2	yes	—
235	#168	—	2	1	no	—
236	#168	—	2	1	no	—
237	#168	C₂×M₁₆	1	2	yes	—
238	#168	C₂×M₁₆	1	2	yes	—
239	C₂×#41	—	5	1	no	—
240	#131	—	10	4	no	—
241	#131	—	10	4	no	—
242	C₂×M₁₆	—	5	1	no	—
243	C₂×M₁₆	—	5	4	no	—
244	C₂×M₁₆	—	5	4	no	—
245	C₂×M₁₆	—	5	1	no	—
246	C₂×M₁₆	—	5	1	no	—
247	C₂×M₁₆	—	5	1	no	—
248	C₂×M₁₆	—	5	1	no	—
249	C₂×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	5	1	no	—
252	C₂²×C₈	—	5	1	no	—
253	C₂²×C₈	—	5	4	no	—
254	C₂²×C₈	—	5	1	no	—
255	C₂²×C₈	—	5	1	no	—
256	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
257	C₄×Q₈	—	5	2	no	—
258	C₄×D₄	—	5	2	no	—
259	C₄×D₄	—	5	2	no	—
260	C₄×D₄	—	5	2	no	—
261	#117	—	5	1	no	—
262	#117	—	5	1	no	—
263	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	C₂×C₄²	—	5	1	no	—
267	C₄⋊C₈	—	5	4	no	—
268	C₄⋊C₈	—	5	4	no	—
269	C₄⋊C₈	—	5	4	no	—
270	C₂²⋊C₈	—	5	4	no	—
271	C₂²⋊C₈	—	5	4	no	—
272	C₂²⋊C₈	—	5	4	no	—
273	#97	—	5	4	no	—
274	#97	—	5	4	no	—
275	#97	—	5	1	no	—
276	#97	—	5	1	no	—
277	#97	—	5	1	no	—
278	#97	—	5	1	no	—
279	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
280	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
281	C₄×C₈	—	5	2	no	—
282	C₄×C₈	—	5	2	no	—
283	C₄×C₈	—	5	2	no	—
284	C₄×C₈	—	5	2	no	—
285	C₄×C₈	—	5	4	no	—
286	C₄×C₈	—	5	1	no	—
287	C₄×C₈	—	5	1	no	—
288	C₄×C₈	—	5	1	no	—
289	C₄×C₈	—	5	1	no	—
290	C₄×C₈	—	5	1	no	—
291	C₄×C₈	—	5	1	no	—
292	C₄×C₈	—	5	1	no	—
293	C₄×C₈	—	5	1	no	—
294	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
299	C₂×D₅	—	2	2	no	—
300	C₂×D₅	—	2	1	no	—
301	C₂×D₅	—	2	2	no	—
302	C₂×D₅	C₄×M₁₆	1	2	yes	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
307	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
308	Dic₅	—	2	1	no	—
309	Dic₅	—	2	2	no	—
310	Dic₅	C₄×M₁₆	1	2	yes	—
311	Dic₅	#568	1	4	yes	—
312	#41	—	10	2	no	—
313	#41	—	10	2	no	—
314	C₂×Q₈	—	5	1	no	—
315	C₂×D₄	—	5	1	no	—
316	C₂×D₄	—	5	1	no	—
317	C₂×D₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	2	no	—
320	C₂²×C₄	—	5	2	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	10	2	no	—
326	M₁₆	—	10	2	no	—
327	M₁₆	—	10	2	no	—
328	M₁₆	—	10	2	no	—
329	M₁₆	—	10	2	no	—
330	M₁₆	—	20	4	no	—
331	M₁₆	—	20	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	5	1	no	—
334	C₂×C₈	—	5	1	no	—
335	C₂×C₈	—	5	4	no	—
336	C₂×C₈	—	5	4	no	—
337	C₂×C₈	—	5	4	no	—
338	C₂×C₈	—	5	4	no	—
339	C₂×C₈	—	5	4	no	—
340	C₂×C₈	—	5	4	no	—
341	C₂×C₈	—	5	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	10	2	no	—
344	C₂×C₈	—	10	2	no	—
345	C₂×C₈	—	10	2	no	—
346	C₂×C₈	—	20	4	no	—
347	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
349	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₄⋊C₄	—	5	2	no	—
352	C₄⋊C₄	—	5	2	no	—
353	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
354	C₂²⋊C₄	—	5	2	no	—
355	C₂²⋊C₄	—	5	2	no	—
356	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
357	C₄²	—	5	2	no	—
358	C₄²	—	5	2	no	—
359	C₄²	—	5	2	no	—
360	C₄²	—	5	1	no	—
361	C₄²	—	5	1	no	—
362	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×C₅	—	4	1	no	—
365	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
366	C₂×C₅	#2875	1	2	yes	—
367	D₅	—	2	2	no	—
368	D₅	—	4	1	no	—
369	C₂³	—	5	1	no	—
370	C₂³	—	5	1	no	—
371	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
372	Q₈	—	10	2	no	—
373	D₄	—	10	2	no	—
374	D₄	—	10	2	no	—
375	D₄	—	10	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	5	2	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	10	4	no	—
385	C₂×C₄	—	10	4	no	—
386	C₂×C₄	—	10	4	no	—
387	C₂×C₄	—	10	1	no	—
388	C₂×C₄	—	10	1	no	—
389	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
391	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
392	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	5	2	no	—
396	C₈	—	5	2	no	—
397	C₈	—	10	4	no	—
398	C₈	—	10	4	no	—
399	C₈	—	10	4	no	—
400	C₈	—	10	4	no	—
401	C₈	—	10	1	no	—
402	C₈	—	10	1	no	—
403	C₈	D₅⋊M₁₆	1	2	yes	—
404	C₈	D₅⋊M₁₆	1	2	yes	—
405	C₅	#17336	1	1	yes	characteristic, complemented, Sylow
406	C₂²	—	2	2	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	5	2	no	—
409	C₂²	—	10	2	no	—
410	C₂²	—	10	2	no	—
411	C₂²	—	10	1	no	—
412	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	5	4	no	—
417	C₄	—	5	2	no	—
418	C₄	—	10	2	no	—
419	C₄	—	10	1	no	—
420	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
421	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	10	2	no	—
424	C₂	—	20	1	no	—
425	C₂	C₄×D₅⋊M₁₆	1	1	yes	characteristic
426	C₂	#10617415	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#405	C₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#405	AGL(1,𝔽₅)
hypocenter	C₅	#17336
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #10604737	C₂	semidirect
4. #10604736	C₂	semidirect
5. #10604688	C₂	semidirect
6. #10603864	C₂	semidirect
7. #10603863	C₂	semidirect
8. #10603862	C₂	semidirect
9. #10603810	C₂	semidirect
10. #10603809	C₂	semidirect
11. #10603807	C₂	semidirect
166. C₈×D₅	M₁₆	semidirect
167. C₈×D₅	M₁₆	semidirect
405. C₅	#17336	semidirect

Maximal subgroups

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

subgroup	index
#10617116	2
#10610280	2
#10604737	2
#10604736	2
#10604688	2
#10603864	2
#10603863	2
#10603862	2
#10603810	2
#10603809	2
#10603807	2
#17336	5