Subgroups — D₃×D₅⋊M₃₂ #14478107

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751741	C₂	1	2	yes	maximal, complemented
5	D₃×#3998	C₂	1	2	yes	maximal, complemented
6	#11751646	C₂	1	2	yes	maximal, complemented
7	D₅⋊#798	C₂	1	2	yes	maximal, complemented
8	D₃×#3990	C₂	1	2	yes	maximal, complemented
9	D₃×D₅⋊C₁₆	C₂	1	2	yes	maximal, complemented
10	C₂×D₅⋊M₃₂	—	3	1	no	maximal, Hall
11	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
12	C₂×C₈×D₁₅	C₄	1	1	yes	characteristic
13	C₂×C₅×D₃×C₈	C₄	1	1	yes	characteristic
14	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×#6648	C₂²	1	1	yes	characteristic
16	C₂×D₃×#168	C₂²	1	1	yes	characteristic
17	C₂×D₅×C₃⋊C₈	C₄	1	1	yes	characteristic
18	D₃×C₈×D₅	C₄	1	1	yes	characteristic
19	D₃×C₈×D₅	C₄	1	1	yes	characteristic
20	D₃×C₈×D₅	C₄	1	1	yes	characteristic
21	D₃×C₈×D₅	C₄	1	1	yes	characteristic
22	D₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	D₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	D₃×C₈×D₅	C₂²	1	1	yes	characteristic
25	D₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	#91227	C₂²	1	2	yes	complemented
27	#91219	C₂²	1	2	yes	complemented
28	D₅⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
29	C₃×#3998	C₂²	1	2	yes	complemented
30	C₃×#3990	C₂²	1	2	yes	complemented
31	C₃×D₅⋊C₁₆	C₂²	1	2	yes	complemented
32	#91166	C₂²	1	4	yes	complemented
33	#91165	C₂²	1	4	yes	complemented
34	#91164	C₂²	1	4	yes	complemented
35	D₃×#674	C₂²	1	4	yes	complemented
36	C₂×D₃×M₃₂	—	5	1	no	maximal, Hall
37	C₂²×C₈×D₅	—	3	1	no	—
38	C₂×#3998	—	3	2	no	—
39	D₅⋊M₃₂	—	3	1	no	—
40	D₅⋊M₃₂	—	3	2	no	—
41	D₅⋊M₃₂	—	3	2	no	—
42	D₅⋊M₃₂	—	3	2	no	—
43	D₅⋊M₃₂	D₃	1	1	yes	characteristic, direct product factor
44	C₂×#3990	—	3	2	no	—
45	C₂×D₅⋊C₁₆	—	3	2	no	—
46	C₂²×D₃×D₅	C₈	1	1	yes	characteristic
47	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×#1200	C₈	1	1	yes	characteristic
51	C₂×D₃×Dic₅	C₈	1	1	yes	characteristic
52	C₂×D₅×Dic₃	C₈	1	1	yes	characteristic
53	C₄×D₃×D₅	C₈	1	1	yes	characteristic
54	C₄×D₃×D₅	C₈	1	1	yes	characteristic
55	C₄×D₃×D₅	C₈	1	1	yes	characteristic
56	C₄×D₃×D₅	C₈	1	1	yes	characteristic
57	C₄×D₃×D₅	C₂×C₄	1	1	yes	characteristic
58	C₄×D₃×D₅	C₂×C₄	1	1	yes	characteristic
59	C₄×D₃×D₅	C₂×C₄	1	1	yes	characteristic
60	C₄×D₃×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
63	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
64	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
65	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
66	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
69	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
70	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
71	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×#168	C₂³	1	1	yes	characteristic
73	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
76	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
77	#6648	C₂×C₄	1	1	yes	characteristic
78	#6648	C₂×C₄	1	1	yes	characteristic
79	#6648	C₂³	1	1	yes	characteristic
80	#6648	C₂³	1	1	yes	characteristic
81	D₃×#168	C₂×C₄	1	1	yes	characteristic
82	D₃×#168	C₂×C₄	1	1	yes	characteristic
83	D₃×#168	C₂³	1	1	yes	characteristic
84	D₃×#168	C₂³	1	1	yes	characteristic
85	D₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	D₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
87	D₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
88	D₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₃⋊#674	C₂³	1	4	yes	complemented
90	C₃×#674	C₂³	1	4	yes	complemented
91	C₂²×D₃×C₈	—	5	1	no	—
92	C₂×C₃×M₃₂	—	5	1	no	—
93	C₂×#812	—	5	1	no	—
94	D₃×M₃₂	—	5	2	no	—
95	D₃×M₃₂	—	5	2	no	—
96	D₃×M₃₂	—	5	2	no	—
97	D₃×M₃₂	—	5	2	no	—
98	C₂×#798	—	5	2	no	—
99	C₂×D₃×C₁₆	—	5	2	no	—
100	C₂²×C₄×D₅	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	1	no	—
102	C₂²×#168	—	3	1	no	—
103	C₂×C₈×D₅	—	3	1	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	C₂×C₈×D₅	—	3	1	no	—
106	C₂×C₈×D₅	—	3	1	no	—
107	C₂×C₈×D₅	—	3	1	no	—
108	C₂×C₈×D₅	—	3	1	no	—
109	C₂×C₈×D₅	—	3	1	no	—
110	C₂×C₈×D₅	—	3	1	no	—
111	C₂×C₈×D₅	—	3	1	no	—
112	C₂×C₈×D₅	—	3	1	no	—
113	C₂×C₈×D₅	—	3	1	no	—
114	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
115	#3998	—	3	2	no	—
116	#3998	—	3	4	no	—
117	#3998	C₂×D₃	1	2	yes	complemented
118	C₂×#674	—	3	4	no	—
119	#3990	—	3	2	no	—
120	#3990	—	3	4	no	—
121	#3990	C₂×D₃	1	2	yes	complemented
122	D₅⋊C₁₆	—	3	2	no	—
123	D₅⋊C₁₆	—	3	4	no	—
124	D₅⋊C₁₆	C₂×D₃	1	2	yes	complemented
125	C₂²×M₃₂	—	15	1	no	Sylow
126	C₂²×D₁₅	C₂×C₈	1	1	yes	characteristic
127	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
128	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
129	C₂×D₃×D₅	—	2	4	no	—
130	C₂×D₃×D₅	C₂×C₈	1	1	yes	characteristic
131	C₂×D₃×D₅	C₂×C₈	1	1	yes	characteristic
132	C₂×D₃×D₅	C₂×C₈	1	1	yes	characteristic
133	C₂×D₃×D₅	C₂×C₈	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂×C₈	1	1	yes	characteristic
136	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
137	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
138	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
141	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
142	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
143	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
146	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
147	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
148	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
150	#1200	C₂×C₈	1	1	yes	characteristic
151	#1200	C₂×C₈	1	1	yes	characteristic
152	#1200	C₂×C₈	1	1	yes	characteristic
153	#1200	C₂×C₈	1	1	yes	characteristic
154	D₃×Dic₅	C₂×C₈	1	1	yes	characteristic
155	D₃×Dic₅	C₂×C₈	1	1	yes	characteristic
156	D₃×Dic₅	C₂×C₈	1	1	yes	characteristic
157	D₃×Dic₅	C₂×C₈	1	1	yes	characteristic
158	D₅×Dic₃	C₂×C₈	1	1	yes	characteristic
159	D₅×Dic₃	C₂×C₈	1	1	yes	characteristic
160	D₅×Dic₃	C₂×C₈	1	1	yes	characteristic
161	D₅×Dic₃	C₂×C₈	1	1	yes	characteristic
162	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
163	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
164	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
165	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
166	C₃×#168	C₂²×C₄	1	1	yes	characteristic
167	C₃×#168	C₂⁴	1	1	yes	characteristic
168	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×D₃	—	5	1	no	—
171	C₂²×C₃×C₈	—	5	1	no	—
172	C₂²×C₃⋊C₈	—	5	1	no	—
173	C₂×D₃×C₈	—	5	1	no	—
174	C₂×D₃×C₈	—	5	1	no	—
175	C₂×D₃×C₈	—	5	1	no	—
176	C₂×D₃×C₈	—	5	1	no	—
177	C₂×D₃×C₈	—	5	1	no	—
178	C₂×D₃×C₈	—	5	1	no	—
179	C₂×D₃×C₈	—	5	1	no	—
180	C₂×D₃×C₈	—	5	1	no	—
181	C₂×D₃×C₈	—	5	1	no	—
182	C₂×D₃×C₈	—	5	1	no	—
183	C₂×D₃×C₈	—	5	1	no	—
184	C₂×D₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
185	C₃×M₃₂	—	5	2	no	—
186	C₃×M₃₂	—	5	2	no	—
187	C₂×C₃×C₁₆	—	5	2	no	—
188	#812	—	5	2	no	—
189	#812	—	5	2	no	—
190	C₂×C₃⋊C₁₆	—	5	2	no	—
191	#798	—	5	4	no	—
192	#798	—	5	4	no	—
193	D₃×C₁₆	—	5	4	no	—
194	D₃×C₁₆	—	5	4	no	—
195	C₂³×D₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	3	1	no	—
197	C₂²×Dic₅	—	3	1	no	—
198	C₂×C₄×D₅	—	3	1	no	—
199	C₂×C₄×D₅	—	3	1	no	—
200	C₂×C₄×D₅	—	3	1	no	—
201	C₂×C₄×D₅	—	3	1	no	—
202	C₂×C₄×D₅	—	3	1	no	—
203	C₂×C₄×D₅	—	3	1	no	—
204	C₂×C₄×D₅	—	3	1	no	—
205	C₂×C₄×D₅	—	3	1	no	—
206	C₂×C₄×D₅	—	3	1	no	—
207	C₂×C₄×D₅	—	3	1	no	—
208	C₂×C₄×D₅	—	3	1	no	—
209	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	—	3	1	no	—
212	C₂×C₅×C₈	—	3	1	no	—
213	C₂×C₅×C₈	—	3	1	no	—
214	C₂×C₅×C₈	—	3	1	no	—
215	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
216	C₂×#168	—	3	1	no	—
217	C₂×#168	—	3	1	no	—
218	C₂×#168	—	3	1	no	—
219	C₂×#168	—	3	1	no	—
220	C₂×#168	—	3	1	no	—
221	C₂×#168	C₂²×D₃	1	1	yes	characteristic
222	C₈×D₅	—	3	1	no	—
223	C₈×D₅	—	3	1	no	—
224	C₈×D₅	—	3	1	no	—
225	C₈×D₅	—	3	1	no	—
226	C₈×D₅	—	3	1	no	—
227	C₈×D₅	—	3	1	no	—
228	C₈×D₅	—	3	1	no	—
229	C₈×D₅	—	3	1	no	—
230	C₈×D₅	—	3	1	no	—
231	C₈×D₅	—	3	1	no	—
232	C₈×D₅	—	3	1	no	—
233	C₈×D₅	—	3	1	no	—
234	C₈×D₅	C₄×D₃	1	1	yes	characteristic
235	C₈×D₅	C₄×D₃	1	1	yes	characteristic
236	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
237	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
238	#674	—	3	4	no	—
239	#674	C₂²×D₃	1	4	yes	complemented
240	C₂³×C₈	—	15	1	no	—
241	C₂×M₃₂	—	5	1	no	—
242	C₂×M₃₂	—	15	2	no	—
243	C₂×M₃₂	—	15	2	no	—
244	C₂×M₃₂	—	15	2	no	—
245	C₂×M₃₂	—	15	2	no	—
246	C₂×M₃₂	—	15	2	no	—
247	C₂×M₃₂	—	15	1	no	—
248	C₂²×C₁₆	—	15	2	no	—
249	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
250	C₂×D₁₅	—	2	2	no	—
251	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
252	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
253	C₂×C₅×D₃	—	2	2	no	—
254	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
255	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
256	C₂×C₃×D₅	—	2	2	no	—
257	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
258	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
259	D₃×D₅	—	2	2	no	—
260	D₃×D₅	—	2	2	no	—
261	D₃×D₅	—	2	2	no	—
262	D₃×D₅	M₃₂	1	4	yes	complemented
263	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
265	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
266	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
267	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
268	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
269	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
270	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
271	C₂³×D₃	—	5	1	no	—
272	C₂²×C₃×C₄	—	5	1	no	—
273	C₂²×Dic₃	—	5	1	no	—
274	C₂×C₄×D₃	—	5	1	no	—
275	C₂×C₄×D₃	—	5	1	no	—
276	C₂×C₄×D₃	—	5	1	no	—
277	C₂×C₄×D₃	—	5	1	no	—
278	C₂×C₄×D₃	—	5	1	no	—
279	C₂×C₄×D₃	—	5	1	no	—
280	C₂×C₄×D₃	—	5	1	no	—
281	C₂×C₄×D₃	—	5	1	no	—
282	C₂×C₄×D₃	—	5	1	no	—
283	C₂×C₄×D₃	—	5	1	no	—
284	C₂×C₄×D₃	—	5	1	no	—
285	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	5	1	no	—
288	C₂×C₃×C₈	—	5	1	no	—
289	C₂×C₃×C₈	—	5	1	no	—
290	C₂×C₃×C₈	—	5	1	no	—
291	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₂×C₃⋊C₈	—	5	1	no	—
293	C₂×C₃⋊C₈	—	5	1	no	—
294	C₂×C₃⋊C₈	—	5	1	no	—
295	C₂×C₃⋊C₈	—	5	1	no	—
296	C₂×C₃⋊C₈	—	5	1	no	—
297	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
298	D₃×C₈	—	5	1	no	—
299	D₃×C₈	—	5	1	no	—
300	D₃×C₈	—	5	1	no	—
301	D₃×C₈	—	5	1	no	—
302	D₃×C₈	—	5	1	no	—
303	D₃×C₈	—	5	1	no	—
304	D₃×C₈	—	5	1	no	—
305	D₃×C₈	—	5	1	no	—
306	D₃×C₈	—	5	1	no	—
307	D₃×C₈	—	5	1	no	—
308	D₃×C₈	—	5	1	no	—
309	D₃×C₈	—	5	1	no	—
310	D₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
311	D₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
312	D₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
313	D₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₃×C₁₆	—	5	4	no	—
315	C₃⋊C₁₆	—	5	4	no	—
316	C₂³×C₅	—	3	1	no	—
317	C₂²×D₅	—	3	1	no	—
318	C₂²×D₅	—	3	1	no	—
319	C₂²×D₅	—	3	1	no	—
320	C₂²×D₅	—	3	1	no	—
321	C₂²×D₅	—	3	1	no	—
322	C₂²×D₅	—	6	4	no	—
323	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
324	C₂×C₄×C₅	—	3	1	no	—
325	C₂×C₄×C₅	—	3	1	no	—
326	C₂×C₄×C₅	—	3	1	no	—
327	C₂×C₄×C₅	—	3	1	no	—
328	C₂×C₄×C₅	—	3	1	no	—
329	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂×Dic₅	—	3	1	no	—
331	C₂×Dic₅	—	3	1	no	—
332	C₂×Dic₅	—	3	1	no	—
333	C₂×Dic₅	—	3	1	no	—
334	C₂×Dic₅	—	3	1	no	—
335	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
336	C₄×D₅	—	3	1	no	—
337	C₄×D₅	—	3	1	no	—
338	C₄×D₅	—	3	1	no	—
339	C₄×D₅	—	3	1	no	—
340	C₄×D₅	—	3	1	no	—
341	C₄×D₅	—	3	1	no	—
342	C₄×D₅	—	3	1	no	—
343	C₄×D₅	—	3	1	no	—
344	C₄×D₅	—	3	1	no	—
345	C₄×D₅	—	3	1	no	—
346	C₄×D₅	—	3	1	no	—
347	C₄×D₅	—	3	1	no	—
348	C₄×D₅	D₃×C₈	1	1	yes	characteristic
349	C₄×D₅	D₃×C₈	1	1	yes	characteristic
350	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
351	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
352	C₅×C₈	—	3	1	no	—
353	C₅×C₈	—	3	1	no	—
354	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
355	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
356	#168	—	3	1	no	—
357	#168	—	3	1	no	—
358	#168	C₂×C₄×D₃	1	1	yes	characteristic
359	#168	C₂³×D₃	1	1	yes	characteristic
360	C₂³×C₄	—	15	1	no	—
361	C₂²×C₈	—	3	1	no	—
362	C₂²×C₈	—	5	1	no	—
363	C₂²×C₈	—	15	1	no	—
364	C₂²×C₈	—	15	1	no	—
365	C₂²×C₈	—	15	1	no	—
366	C₂²×C₈	—	15	1	no	—
367	C₂²×C₈	—	15	1	no	—
368	C₂²×C₈	—	15	1	no	—
369	C₂²×C₈	—	15	1	no	—
370	C₂²×C₈	—	15	1	no	—
371	C₂²×C₈	—	15	1	no	—
372	C₂²×C₈	—	15	1	no	—
373	C₂²×C₈	—	15	1	no	—
374	C₂²×C₈	—	15	1	no	—
375	M₃₂	—	5	2	no	—
376	M₃₂	—	5	2	no	—
377	M₃₂	—	15	4	no	—
378	M₃₂	—	15	4	no	—
379	M₃₂	—	15	2	no	—
380	M₃₂	—	15	2	no	—
381	C₂×C₁₆	—	5	2	no	—
382	C₂×C₁₆	—	15	4	no	—
383	C₂×C₁₆	—	15	4	no	—
384	C₂×C₁₆	—	15	2	no	—
385	C₂×C₃×C₅	—	2	1	no	—
386	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
387	D₁₅	—	2	1	no	—
388	D₁₅	C₂×M₃₂	1	2	yes	complemented
389	C₃×D₅	—	2	1	no	—
390	C₃×D₅	C₂×M₃₂	1	2	yes	complemented
391	C₅×D₃	—	2	1	no	—
392	C₅×D₃	C₂×M₃₂	1	2	yes	complemented
393	C₂³×C₃	—	5	1	no	—
394	C₂²×D₃	—	5	1	no	—
395	C₂²×D₃	—	5	1	no	—
396	C₂²×D₃	—	5	1	no	—
397	C₂²×D₃	—	5	1	no	—
398	C₂²×D₃	—	5	1	no	—
399	C₂²×D₃	—	10	4	no	—
400	C₂²×D₃	D₅⋊C₈	1	1	yes	characteristic
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	1	no	—
403	C₂×C₃×C₄	—	5	1	no	—
404	C₂×C₃×C₄	—	5	1	no	—
405	C₂×C₃×C₄	—	5	1	no	—
406	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
407	C₂×Dic₃	—	5	1	no	—
408	C₂×Dic₃	—	5	1	no	—
409	C₂×Dic₃	—	5	1	no	—
410	C₂×Dic₃	—	5	1	no	—
411	C₂×Dic₃	—	5	1	no	—
412	C₂×Dic₃	D₅⋊C₈	1	1	yes	characteristic
413	C₄×D₃	—	5	1	no	—
414	C₄×D₃	—	5	1	no	—
415	C₄×D₃	—	5	1	no	—
416	C₄×D₃	—	5	1	no	—
417	C₄×D₃	—	5	1	no	—
418	C₄×D₃	—	5	1	no	—
419	C₄×D₃	—	5	1	no	—
420	C₄×D₃	—	5	1	no	—
421	C₄×D₃	—	5	1	no	—
422	C₄×D₃	—	5	1	no	—
423	C₄×D₃	—	5	1	no	—
424	C₄×D₃	—	5	1	no	—
425	C₄×D₃	D₅⋊C₈	1	1	yes	characteristic
426	C₄×D₃	D₅⋊C₈	1	1	yes	characteristic
427	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
429	C₃×C₈	—	5	1	no	—
430	C₃×C₈	—	5	1	no	—
431	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₃⋊C₈	—	5	1	no	—
434	C₃⋊C₈	—	5	1	no	—
435	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
436	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
437	C₂²×C₅	—	3	1	no	—
438	C₂²×C₅	—	3	1	no	—
439	C₂²×C₅	—	6	2	no	—
440	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
441	C₂×D₅	—	2	2	no	—
442	C₂×D₅	—	3	1	no	—
443	C₂×D₅	—	3	4	no	—
444	C₂×D₅	—	3	1	no	—
445	C₂×D₅	—	6	2	no	—
446	C₂×D₅	—	6	2	no	—
447	C₂×D₅	—	6	2	no	—
448	C₂×D₅	—	6	2	no	—
449	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
450	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
451	C₄×C₅	—	3	1	no	—
452	C₄×C₅	—	3	1	no	—
453	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
454	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
455	Dic₅	—	3	1	no	—
456	Dic₅	—	3	1	no	—
457	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
458	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
459	C₂⁴	—	15	1	no	—
460	C₂²×C₄	—	3	1	no	—
461	C₂²×C₄	—	5	1	no	—
462	C₂²×C₄	—	15	1	no	—
463	C₂²×C₄	—	15	1	no	—
464	C₂²×C₄	—	15	1	no	—
465	C₂²×C₄	—	15	1	no	—
466	C₂²×C₄	—	15	1	no	—
467	C₂²×C₄	—	15	1	no	—
468	C₂²×C₄	—	15	1	no	—
469	C₂²×C₄	—	15	1	no	—
470	C₂²×C₄	—	15	1	no	—
471	C₂²×C₄	—	15	1	no	—
472	C₂²×C₄	—	15	1	no	—
473	C₂²×C₄	—	15	1	no	—
474	C₂×C₈	—	3	1	no	—
475	C₂×C₈	—	3	1	no	—
476	C₂×C₈	—	3	1	no	—
477	C₂×C₈	—	3	1	no	—
478	C₂×C₈	—	3	1	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	5	1	no	—
481	C₂×C₈	—	5	1	no	—
482	C₂×C₈	—	5	1	no	—
483	C₂×C₈	—	5	1	no	—
484	C₂×C₈	—	15	1	no	—
485	C₂×C₈	—	15	1	no	—
486	C₂×C₈	—	15	1	no	—
487	C₂×C₈	—	15	1	no	—
488	C₂×C₈	—	15	1	no	—
489	C₂×C₈	—	15	1	no	—
490	C₂×C₈	—	15	1	no	—
491	C₂×C₈	—	15	1	no	—
492	C₂×C₈	—	15	1	no	—
493	C₂×C₈	—	15	1	no	—
494	C₂×C₈	—	15	1	no	—
495	C₂×C₈	—	15	1	no	—
496	C₂×C₈	—	15	1	no	—
497	C₂×C₈	—	15	1	no	—
498	C₂×C₈	—	15	1	no	—
499	C₂×C₈	—	15	1	no	—
500	C₂×C₈	—	15	1	no	—
501	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
502	C₁₆	—	5	4	no	—
503	C₁₆	—	15	4	no	—
504	C₃×C₅	C₂²×M₃₂	1	1	yes	characteristic, complemented, Hall
505	C₂²×C₃	—	5	1	no	—
506	C₂²×C₃	—	5	1	no	—
507	C₂²×C₃	—	10	2	no	—
508	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	5	1	no	—
511	C₂×D₃	—	5	4	no	—
512	C₂×D₃	—	5	1	no	—
513	C₂×D₃	—	10	2	no	—
514	C₂×D₃	—	10	2	no	—
515	C₂×D₃	—	10	2	no	—
516	C₂×D₃	—	10	2	no	—
517	C₂×D₃	C₂×D₅⋊C₈	1	1	yes	characteristic
518	C₂×D₃	C₂×D₅⋊C₈	1	1	yes	characteristic
519	C₃×C₄	—	5	1	no	—
520	C₃×C₄	—	5	1	no	—
521	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
522	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
523	Dic₃	—	5	1	no	—
524	Dic₃	—	5	1	no	—
525	Dic₃	C₂×D₅⋊C₈	1	1	yes	characteristic
526	Dic₃	C₂×D₅⋊C₈	1	1	yes	characteristic
527	C₂×C₅	—	2	1	no	—
528	C₂×C₅	—	3	2	no	—
529	C₂×C₅	—	6	1	no	—
530	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
531	D₅	—	2	1	no	—
532	D₅	—	3	2	no	—
533	D₅	—	6	1	no	—
534	D₅	D₃×M₃₂	1	2	yes	complemented
535	C₂³	—	3	1	no	—
536	C₂³	—	5	1	no	—
537	C₂³	—	15	1	no	—
538	C₂³	—	15	1	no	—
539	C₂³	—	15	1	no	—
540	C₂³	—	15	1	no	—
541	C₂³	—	15	1	no	—
542	C₂³	—	30	4	no	—
543	C₂×C₄	—	3	1	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	3	1	no	—
546	C₂×C₄	—	3	1	no	—
547	C₂×C₄	—	3	1	no	—
548	C₂×C₄	—	5	1	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	1	no	—
551	C₂×C₄	—	5	1	no	—
552	C₂×C₄	—	5	1	no	—
553	C₂×C₄	—	15	1	no	—
554	C₂×C₄	—	15	1	no	—
555	C₂×C₄	—	15	1	no	—
556	C₂×C₄	—	15	1	no	—
557	C₂×C₄	—	15	1	no	—
558	C₂×C₄	—	15	1	no	—
559	C₂×C₄	—	15	1	no	—
560	C₂×C₄	—	15	1	no	—
561	C₂×C₄	—	15	1	no	—
562	C₂×C₄	—	15	1	no	—
563	C₂×C₄	—	15	1	no	—
564	C₂×C₄	—	15	1	no	—
565	C₂×C₄	—	15	1	no	—
566	C₂×C₄	—	15	1	no	—
567	C₂×C₄	—	15	1	no	—
568	C₂×C₄	—	15	1	no	—
569	C₂×C₄	—	15	1	no	—
570	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
571	C₈	—	3	1	no	—
572	C₈	—	3	1	no	—
573	C₈	—	5	1	no	—
574	C₈	—	5	1	no	—
575	C₈	—	15	1	no	—
576	C₈	—	15	1	no	—
577	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
578	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
579	C₂×C₃	—	2	1	no	—
580	C₂×C₃	—	5	2	no	—
581	C₂×C₃	—	10	1	no	—
582	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
583	D₃	—	2	1	no	—
584	D₃	—	5	2	no	—
585	D₃	—	10	1	no	—
586	D₃	D₅⋊M₃₂	1	2	yes	direct product factor
587	C₅	C₂×D₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
588	C₂²	—	3	1	no	—
589	C₂²	—	3	1	no	—
590	C₂²	—	5	1	no	—
591	C₂²	—	5	1	no	—
592	C₂²	—	6	2	no	—
593	C₂²	—	10	2	no	—
594	C₂²	—	15	4	no	—
595	C₂²	—	15	1	no	—
596	C₂²	—	15	1	no	—
597	C₂²	—	30	2	no	—
598	C₂²	—	30	2	no	—
599	C₂²	—	30	2	no	—
600	C₂²	—	30	2	no	—
601	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
602	C₄	—	3	1	no	—
603	C₄	—	3	1	no	—
604	C₄	—	5	1	no	—
605	C₄	—	5	1	no	—
606	C₄	—	15	1	no	—
607	C₄	—	15	1	no	—
608	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
609	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
610	C₃	C₂×D₅⋊M₃₂	1	1	yes	characteristic, complemented, Sylow
611	C₂	—	2	1	no	—
612	C₂	—	3	2	no	—
613	C₂	—	5	2	no	—
614	C₂	—	6	1	no	—
615	C₂	—	10	1	no	—
616	C₂	—	15	2	no	—
617	C₂	—	30	1	no	—
618	C₂	C₂×D₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	C₂²×D₃×D₅	C₈
cosocle	C₃×#168	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂²×M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. D₅⋊#812	C₂	semidirect
3. C₃×D₅⋊M₃₂	C₂	semidirect
4. #11751741	C₂	semidirect
5. D₃×#3998	C₂	semidirect
6. #11751646	C₂	semidirect
7. D₅⋊#798	C₂	semidirect
8. D₃×#3990	C₂	semidirect
9. D₃×D₅⋊C₁₆	C₂	semidirect
26. #91227	C₂²	semidirect
27. #91219	C₂²	semidirect
28. D₅⋊(C₃⋊C₁₆)	C₂²	semidirect
29. C₃×#3998	C₂²	semidirect
30. C₃×#3990	C₂²	semidirect
31. C₃×D₅⋊C₁₆	C₂²	semidirect
32. #91166	C₂²	semidirect
33. #91165	C₂²	semidirect
34. #91164	C₂²	semidirect
35. D₃×#674	C₂²	semidirect
43. D₅⋊M₃₂	D₃	direct (N × H)
89. C₃⋊#674	C₂³	semidirect
90. C₃×#674	C₂³	semidirect
117. #3998	C₂×D₃	semidirect
121. #3990	C₂×D₃	semidirect
124. D₅⋊C₁₆	C₂×D₃	semidirect
239. #674	C₂²×D₃	semidirect
262. D₃×D₅	M₃₂	semidirect
388. D₁₅	C₂×M₃₂	semidirect
390. C₃×D₅	C₂×M₃₂	semidirect
392. C₅×D₃	C₂×M₃₂	semidirect
504. C₃×C₅	C₂²×M₃₂	semidirect
534. D₅	D₃×M₃₂	semidirect
586. D₃	D₅⋊M₃₂	direct (N × H)
587. C₅	C₂×D₃×M₃₂	semidirect
610. C₃	C₂×D₅⋊M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈×D₅	2
D₅⋊#812	2
C₃×D₅⋊M₃₂	2
#11751741	2
D₃×#3998	2
#11751646	2
D₅⋊#798	2
D₃×#3990	2
D₃×D₅⋊C₁₆	2
C₂×D₅⋊M₃₂	3
C₂×D₃×M₃₂	5

Subgroups — D3×D5⋊M32 #14478107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₅⋊M₃₂ #14478107