Subgroups — C₃×D₅⋊#350 #14312972

Order 1920.

448 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64932	C₂	1	2	yes	maximal, complemented
5	C₃×#64898	C₂	1	2	yes	maximal, complemented
6	D₅⋊#350	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×D₅×#41	C₄	1	1	yes	characteristic
8	C₃×C₅×#131	C₄	1	1	yes	characteristic
9	C₃×#4094	C₂²	1	1	yes	characteristic
10	C₃×#4053	—	2	1	no	—
11	C₃×#4053	C₂²	1	1	yes	characteristic
12	C₃×D₅×M₁₆	—	2	1	no	—
13	C₃×D₅×M₁₆	C₄	1	1	yes	characteristic
14	C₃×#4047	—	2	1	no	—
15	C₃×#4047	C₄	1	1	yes	characteristic
16	C₂×C₃×C₈×D₅	—	2	1	no	—
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₃×#3998	C₂²	1	2	yes	complemented
19	C₂×C₃×#674	C₂²	1	2	yes	complemented
20	C₃×#3990	—	2	1	no	—
21	C₃×D₅⋊C₁₆	—	2	1	no	—
22	C₃×D₅⋊C₁₆	—	2	1	no	—
23	C₃×D₅⋊C₁₆	—	2	1	no	—
24	C₂×C₃×#350	—	5	1	no	maximal, Hall
25	D₅×#131	C₂×C₃	1	1	yes	characteristic
26	D₅⋊M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×D₅⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
28	#64932	C₂×C₃	1	2	yes	complemented
29	#64898	C₂×C₃	1	2	yes	complemented
30	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic
31	C₃×#713	C₈	1	1	yes	characteristic
32	C₃×Q₈×D₅	C₈	1	1	yes	characteristic
33	C₃×#711	—	2	1	no	—
34	C₃×#711	C₈	1	1	yes	characteristic
35	C₃×D₄×D₅	—	2	1	no	—
36	C₃×D₄×D₅	C₈	1	1	yes	characteristic
37	C₃×#709	—	2	1	no	—
38	C₃×#709	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₃×C₅×M₁₆	—	2	1	no	—
42	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₃×#681	—	2	1	no	—
46	C₃×#681	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×#168	—	2	1	no	—
48	C₂×C₃×#168	C₂³	1	1	yes	characteristic
49	C₃×#676	—	2	1	no	—
50	C₃×#676	—	2	1	no	—
51	C₃×#676	—	2	1	no	—
52	C₃×C₈×D₅	—	2	1	no	—
53	C₃×C₈×D₅	—	2	1	no	—
54	C₃×C₈×D₅	—	2	1	no	—
55	C₃×C₈×D₅	D₄	1	1	yes	characteristic
56	C₃×C₈×D₅	D₄	1	1	yes	characteristic
57	C₃×C₈×D₅	D₄	1	1	yes	characteristic
58	C₃×C₈×D₅	D₄	1	1	yes	characteristic
59	C₃×#674	—	2	2	no	—
60	C₃×#674	—	2	2	no	—
61	C₂×C₃×#131	—	5	1	no	—
62	C₂×C₃×M₃₂	—	5	1	no	—
63	C₂²×C₃×C₁₆	—	5	1	no	—
64	C₃×#350	—	5	2	no	—
65	C₃×#350	—	5	2	no	—
66	D₅×#41	C₃×C₄	1	1	yes	characteristic
67	C₅×#131	C₃×C₄	1	1	yes	characteristic
68	#4094	C₂²×C₃	1	1	yes	characteristic
69	#4053	—	2	1	no	—
70	#4053	C₂²×C₃	1	1	yes	characteristic
71	D₅×M₁₆	—	2	1	no	—
72	D₅×M₁₆	C₃×C₄	1	1	yes	characteristic
73	#4047	—	2	1	no	—
74	#4047	C₃×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅	—	2	1	no	—
76	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
77	#3998	C₂²×C₃	1	2	yes	complemented
78	C₂×#674	C₂²×C₃	1	2	yes	complemented
79	#3990	—	2	1	no	—
80	D₅⋊C₁₆	—	2	1	no	—
81	D₅⋊C₁₆	—	2	1	no	—
82	D₅⋊C₁₆	—	2	1	no	—
83	C₂×#350	—	5	1	no	Sylow
84	C₂²×C₃×D₅	—	2	1	no	—
85	C₂²×C₃×D₅	M₁₆	1	1	yes	characteristic
86	C₃×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
87	C₃×C₅×D₄	—	2	1	no	—
88	C₃×C₅×D₄	C₂×C₈	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₃×C₂²⋊D₅	—	2	1	no	—
92	C₃×C₂²⋊D₅	—	2	1	no	—
93	C₃×C₂²⋊D₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	1	no	—
95	C₂×C₃×Dic₅	M₁₆	1	1	yes	characteristic
96	C₃×D₂₀	—	2	1	no	—
97	C₃×D₂₀	C₂×C₈	1	1	yes	characteristic
98	C₃×C₄×D₅	—	2	1	no	—
99	C₃×C₄×D₅	—	2	1	no	—
100	C₃×C₄×D₅	—	2	1	no	—
101	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
104	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
105	C₃×Dic₁₀	—	2	1	no	—
106	C₃×Dic₁₀	C₂×C₈	1	1	yes	characteristic
107	C₃×C₅×C₈	—	2	1	no	—
108	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₃×#168	—	2	1	no	—
111	C₃×#168	C₂×D₄	1	1	yes	characteristic
112	C₃×#168	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×#41	—	5	1	no	—
114	C₃×#131	—	5	1	no	—
115	C₃×#131	—	5	1	no	—
116	C₃×#131	—	5	1	no	—
117	C₃×#131	—	10	1	no	—
118	C₃×#131	—	10	1	no	—
119	C₃×#131	AGL(1,𝔽₅)	1	1	yes	characteristic
120	C₂×C₃×M₁₆	—	5	1	no	—
121	C₂×C₃×M₁₆	—	10	1	no	—
122	C₂²×C₃×C₈	—	5	1	no	—
123	C₂²×C₃×C₈	—	10	1	no	—
124	C₃×M₃₂	—	5	2	no	—
125	C₃×M₃₂	—	10	1	no	—
126	C₂×C₃×C₁₆	—	5	2	no	—
127	C₂×C₃×C₁₆	—	10	1	no	—
128	C₂×C₃×C₁₆	—	10	1	no	—
129	C₂×C₃×C₁₆	—	10	1	no	—
130	C₅×#41	C₂×C₃×C₄	1	1	yes	characteristic
131	#713	C₃×C₈	1	1	yes	characteristic
132	Q₈×D₅	C₃×C₈	1	1	yes	characteristic
133	#711	—	2	1	no	—
134	#711	C₃×C₈	1	1	yes	characteristic
135	D₄×D₅	—	2	1	no	—
136	D₄×D₅	C₃×C₈	1	1	yes	characteristic
137	#709	—	2	1	no	—
138	#709	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	—	2	1	no	—
140	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
145	#681	—	2	1	no	—
146	#681	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×#168	—	2	1	no	—
148	C₂×#168	C₂³×C₃	1	1	yes	characteristic
149	#676	—	2	1	no	—
150	#676	—	2	1	no	—
151	#676	—	2	1	no	—
152	C₈×D₅	—	2	1	no	—
153	C₈×D₅	—	2	1	no	—
154	C₈×D₅	—	2	1	no	—
155	C₈×D₅	C₃×D₄	1	1	yes	characteristic
156	C₈×D₅	C₃×D₄	1	1	yes	characteristic
157	C₈×D₅	C₃×D₄	1	1	yes	characteristic
158	C₈×D₅	C₃×D₄	1	1	yes	characteristic
159	#674	—	2	2	no	—
160	#674	—	2	2	no	—
161	C₂×#131	—	5	1	no	—
162	C₂×M₃₂	—	5	1	no	—
163	C₂²×C₁₆	—	5	1	no	—
164	#350	—	5	2	no	—
165	#350	—	5	2	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₃×D₅	—	2	2	no	—
169	C₂×C₃×D₅	—	2	1	no	—
170	C₂×C₃×D₅	—	4	2	no	—
171	C₂×C₃×D₅	C₂²⋊C₈	1	1	yes	characteristic
172	C₂×C₃×D₅	C₂²⋊C₈	1	1	yes	characteristic
173	C₃×C₄×C₅	—	2	1	no	—
174	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
176	C₃×Dic₅	—	2	1	no	—
177	C₃×Dic₅	C₂²⋊C₈	1	1	yes	characteristic
178	C₃×Dic₅	C₂²⋊C₈	1	1	yes	characteristic
179	C₃×#41	—	5	1	no	—
180	C₃×#41	—	5	1	no	—
181	C₃×#41	—	5	1	no	—
182	C₃×#41	—	10	1	no	—
183	C₃×#41	—	10	1	no	—
184	C₃×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
185	C₂×C₃×Q₈	—	5	1	no	—
186	C₂×C₃×D₄	—	5	1	no	—
187	C₂×C₃×D₄	—	10	1	no	—
188	C₂²×C₃×C₄	—	5	1	no	—
189	C₂²×C₃×C₄	—	10	1	no	—
190	C₃×M₁₆	—	2	1	no	—
191	C₃×M₁₆	—	5	1	no	—
192	C₃×M₁₆	—	10	1	no	—
193	C₃×M₁₆	—	10	1	no	—
194	C₃×M₁₆	—	10	1	no	—
195	C₃×M₁₆	—	10	1	no	—
196	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
197	C₂×C₃×C₈	—	2	1	no	—
198	C₂×C₃×C₈	—	5	1	no	—
199	C₂×C₃×C₈	—	5	1	no	—
200	C₂×C₃×C₈	—	5	1	no	—
201	C₂×C₃×C₈	—	5	1	no	—
202	C₂×C₃×C₈	—	5	1	no	—
203	C₂×C₃×C₈	—	10	1	no	—
204	C₂×C₃×C₈	—	10	1	no	—
205	C₂×C₃×C₈	—	10	1	no	—
206	C₂×C₃×C₈	—	10	1	no	—
207	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₃×C₁₆	—	10	2	no	—
209	C₃×C₁₆	—	10	2	no	—
210	C₂²×D₅	—	2	1	no	—
211	C₂²×D₅	C₃×M₁₆	1	1	yes	characteristic
212	C₅×Q₈	C₂×C₃×C₈	1	1	yes	characteristic
213	C₅×D₄	—	2	1	no	—
214	C₅×D₄	C₂×C₃×C₈	1	1	yes	characteristic
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂²⋊D₅	—	2	1	no	—
218	C₂²⋊D₅	—	2	1	no	—
219	C₂²⋊D₅	—	2	1	no	—
220	C₂×Dic₅	—	2	1	no	—
221	C₂×Dic₅	C₃×M₁₆	1	1	yes	characteristic
222	D₂₀	—	2	1	no	—
223	D₂₀	C₂×C₃×C₈	1	1	yes	characteristic
224	C₄×D₅	—	2	1	no	—
225	C₄×D₅	—	2	1	no	—
226	C₄×D₅	—	2	1	no	—
227	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×D₅	C₂×C₃×C₈	1	1	yes	characteristic
230	C₄×D₅	C₂×C₃×C₈	1	1	yes	characteristic
231	Dic₁₀	—	2	1	no	—
232	Dic₁₀	C₂×C₃×C₈	1	1	yes	characteristic
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
235	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
236	#168	—	2	1	no	—
237	#168	C₂×C₃×D₄	1	1	yes	characteristic
238	#168	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×#41	—	5	1	no	—
240	#131	—	5	1	no	—
241	#131	—	5	1	no	—
242	#131	—	5	1	no	—
243	#131	—	10	1	no	—
244	#131	—	10	1	no	—
245	#131	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₂×M₁₆	—	5	1	no	—
247	C₂×M₁₆	—	10	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	10	1	no	—
250	M₃₂	—	5	2	no	—
251	M₃₂	—	10	1	no	—
252	C₂×C₁₆	—	5	2	no	—
253	C₂×C₁₆	—	10	1	no	—
254	C₂×C₁₆	—	10	1	no	—
255	C₂×C₁₆	—	10	1	no	—
256	C₂×C₃×C₅	—	2	1	no	—
257	C₂×C₃×C₅	—	4	1	no	—
258	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
259	C₃×D₅	—	2	1	no	—
260	C₃×D₅	—	4	1	no	—
261	C₃×D₅	#350	1	2	yes	complemented
262	C₂³×C₃	—	5	1	no	—
263	C₂³×C₃	—	10	1	no	—
264	C₃×Q₈	—	5	1	no	—
265	C₃×Q₈	—	10	1	no	—
266	C₃×Q₈	D₅⋊C₈	1	1	yes	characteristic
267	C₃×D₄	—	2	1	no	—
268	C₃×D₄	—	5	1	no	—
269	C₃×D₄	—	10	1	no	—
270	C₃×D₄	—	10	1	no	—
271	C₃×D₄	—	10	1	no	—
272	C₃×D₄	—	10	1	no	—
273	C₃×D₄	D₅⋊C₈	1	1	yes	characteristic
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	5	1	no	—
276	C₂×C₃×C₄	—	5	1	no	—
277	C₂×C₃×C₄	—	5	1	no	—
278	C₂×C₃×C₄	—	5	1	no	—
279	C₂×C₃×C₄	—	5	1	no	—
280	C₂×C₃×C₄	—	10	1	no	—
281	C₂×C₃×C₄	—	10	1	no	—
282	C₂×C₃×C₄	—	10	1	no	—
283	C₂×C₃×C₄	—	10	1	no	—
284	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₃×C₈	—	2	1	no	—
286	C₃×C₈	—	5	1	no	—
287	C₃×C₈	—	5	1	no	—
288	C₃×C₈	—	10	1	no	—
289	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
293	C₂×D₅	—	2	2	no	—
294	C₂×D₅	—	2	1	no	—
295	C₂×D₅	—	4	2	no	—
296	C₂×D₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
297	C₂×D₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
301	Dic₅	—	2	1	no	—
302	Dic₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
303	Dic₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
304	#41	—	5	1	no	—
305	#41	—	5	1	no	—
306	#41	—	5	1	no	—
307	#41	—	10	1	no	—
308	#41	—	10	1	no	—
309	#41	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
310	C₂×Q₈	—	5	1	no	—
311	C₂×D₄	—	5	1	no	—
312	C₂×D₄	—	10	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	10	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	5	1	no	—
317	M₁₆	—	10	1	no	—
318	M₁₆	—	10	1	no	—
319	M₁₆	—	10	1	no	—
320	M₁₆	—	10	1	no	—
321	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	5	1	no	—
324	C₂×C₈	—	5	1	no	—
325	C₂×C₈	—	5	1	no	—
326	C₂×C₈	—	5	1	no	—
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	10	1	no	—
329	C₂×C₈	—	10	1	no	—
330	C₂×C₈	—	10	1	no	—
331	C₂×C₈	—	10	1	no	—
332	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
333	C₁₆	—	10	2	no	—
334	C₁₆	—	10	2	no	—
335	C₃×C₅	C₂×#350	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	5	1	no	—
338	C₂²×C₃	—	5	1	no	—
339	C₂²×C₃	—	10	2	no	—
340	C₂²×C₃	—	10	1	no	—
341	C₂²×C₃	—	20	2	no	—
342	C₂²×C₃	D₅⋊M₁₆	1	1	yes	characteristic
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	5	1	no	—
345	C₃×C₄	—	5	1	no	—
346	C₃×C₄	—	10	1	no	—
347	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
348	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	4	1	no	—
351	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
352	D₅	—	2	1	no	—
353	D₅	—	4	1	no	—
354	D₅	C₃×#350	1	2	yes	complemented
355	C₂³	—	5	1	no	—
356	C₂³	—	10	1	no	—
357	Q₈	—	5	1	no	—
358	Q₈	—	10	1	no	—
359	Q₈	C₃×D₅⋊C₈	1	1	yes	characteristic
360	D₄	—	2	1	no	—
361	D₄	—	5	1	no	—
362	D₄	—	10	1	no	—
363	D₄	—	10	1	no	—
364	D₄	—	10	1	no	—
365	D₄	—	10	1	no	—
366	D₄	C₃×D₅⋊C₈	1	1	yes	characteristic
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	5	1	no	—
370	C₂×C₄	—	5	1	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	5	1	no	—
373	C₂×C₄	—	10	1	no	—
374	C₂×C₄	—	10	1	no	—
375	C₂×C₄	—	10	1	no	—
376	C₂×C₄	—	10	1	no	—
377	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	5	1	no	—
380	C₈	—	5	1	no	—
381	C₈	—	10	1	no	—
382	C₈	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₈	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	4	1	no	—
386	C₂×C₃	—	5	2	no	—
387	C₂×C₃	—	10	1	no	—
388	C₂×C₃	—	20	1	no	—
389	C₂×C₃	D₅⋊(C₂²⋊C₈)	1	1	yes	characteristic
390	C₅	C₂×C₃×#350	1	1	yes	characteristic, complemented, Sylow
391	C₂²	—	2	1	no	—
392	C₂²	—	5	1	no	—
393	C₂²	—	5	1	no	—
394	C₂²	—	10	2	no	—
395	C₂²	—	10	1	no	—
396	C₂²	—	20	2	no	—
397	C₂²	C₃×D₅⋊M₁₆	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	5	1	no	—
400	C₄	—	5	1	no	—
401	C₄	—	10	1	no	—
402	C₄	C₂×C₃×D₅⋊C₈	1	1	yes	characteristic
403	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₃	D₅⋊#350	1	1	yes	characteristic, direct product factor, Sylow
405	C₂	—	2	1	no	—
406	C₂	—	4	1	no	—
407	C₂	—	5	2	no	—
408	C₂	—	10	1	no	—
409	C₂	—	20	1	no	—
410	C₂	C₃×D₅⋊(C₂²⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂²⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#131	C₄
socle	C₂×C₃×C₅	C₂×C₂²⋊C₈
prime radical	C₃×D₅×#41	C₄
cosocle	C₂×#168	C₂³×C₃
hypercenter	C₃×#131	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#350
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×C₈ ◁ C₃×#131

Complements

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

N	H ≅ G/N	type
2. C₃×D₅⋊M₃₂	C₂	semidirect
3. C₂×C₃×D₅⋊C₁₆	C₂	semidirect
4. C₃×#64932	C₂	semidirect
5. C₃×#64898	C₂	semidirect
6. D₅⋊#350	C₃	direct (N × H)
18. C₃×#3998	C₂²	semidirect
19. C₂×C₃×#674	C₂²	semidirect
26. D₅⋊M₃₂	C₂×C₃	semidirect
27. C₂×D₅⋊C₁₆	C₂×C₃	semidirect
28. #64932	C₂×C₃	semidirect
29. #64898	C₂×C₃	semidirect
77. #3998	C₂²×C₃	semidirect
78. C₂×#674	C₂²×C₃	semidirect
261. C₃×D₅	#350	semidirect
335. C₃×C₅	C₂×#350	semidirect
354. D₅	C₃×#350	semidirect
390. C₅	C₂×C₃×#350	semidirect
404. C₃	D₅⋊#350	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×#131	2
C₃×D₅⋊M₃₂	2
C₂×C₃×D₅⋊C₁₆	2
C₃×#64932	2
C₃×#64898	2
D₅⋊#350	3
C₂×C₃×#350	5

Subgroups — C3×D5⋊#350 #14312972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅⋊#350 #14312972