Subgroups — C₃×#65943 #11755620

Order 960.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4083	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4030	C₂	1	2	yes	maximal, complemented
11	C₃×#4028	C₂	1	2	yes	maximal, complemented
12	#65943	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₅	C₂²	1	2	yes	complemented
14	C₂³×C₃×D₅	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
20	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₃×D₄×D₅	—	2	8	no	—
23	C₃×D₄×D₅	—	2	4	no	—
24	C₂×C₃×D₂₀	—	2	4	no	—
25	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×D₂₀	C₂²	1	2	yes	complemented
28	C₂×C₃×D₂₀	C₂²	1	2	yes	complemented
29	C₂×C₃×C₄×D₅	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
34	C₃×#685	C₂²	1	2	yes	complemented
35	C₃×#685	C₂²	1	2	yes	complemented
36	C₃×#685	C₂²	1	1	yes	characteristic, complemented
37	C₃×#683	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
39	C₃×D₄²	—	5	1	no	maximal, Hall
40	C₂×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×D₄×D₅	C₂×C₃	1	2	yes	complemented
42	C₂²×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
44	#4086	C₂×C₃	1	1	yes	characteristic, complemented
45	#4083	C₂×C₃	1	2	yes	complemented
46	C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
47	#4041	C₂×C₃	1	1	yes	characteristic, complemented
48	#4039	C₂×C₃	1	1	yes	characteristic, complemented
49	#4030	C₂×C₃	1	2	yes	complemented
50	#4028	C₂×C₃	1	2	yes	complemented
51	C₂³×C₃×C₅	C₂³	1	2	yes	—
52	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×D₅	—	2	4	no	—
54	C₂²×C₃×D₅	—	2	4	no	—
55	C₂²×C₃×D₅	—	2	4	no	—
56	C₂²×C₃×D₅	—	2	4	no	—
57	C₂²×C₃×D₅	—	4	2	no	—
58	C₂²×C₃×D₅	—	4	2	no	—
59	C₂²×C₃×D₅	C₂³	1	2	yes	—
60	C₂²×C₃×D₅	C₂³	1	2	yes	—
61	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×D₄	—	2	4	no	—
63	C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₄×C₅	—	2	2	no	—
65	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₂²⋊D₅	—	2	4	no	—
69	C₃×C₂²⋊D₅	—	2	4	no	—
70	C₃×C₂²⋊D₅	—	4	2	no	—
71	C₃×C₂²⋊D₅	D₄	1	4	yes	complemented
72	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
75	C₃×D₂₀	—	2	4	no	—
76	C₃×D₂₀	—	2	4	no	—
77	C₃×D₂₀	—	2	2	no	—
78	C₃×D₂₀	D₄	1	4	yes	complemented
79	C₃×C₄×D₅	—	2	2	no	—
80	C₃×C₄×D₅	—	2	4	no	—
81	C₂²×C₃×D₄	—	5	2	no	—
82	C₂²×C₃×D₄	—	5	1	no	—
83	C₂²×C₃×D₄	—	5	1	no	—
84	C₃×#127	—	5	1	no	—
85	C₃×#121	—	5	1	no	—
86	C₃×#121	—	5	2	no	—
87	C₃×#121	D₅	1	1	yes	characteristic, complemented
88	C₃×#120	—	5	2	no	—
89	C₃×#120	—	5	2	no	—
90	C₃×C₄×D₄	—	5	1	no	—
91	C₃×C₄×D₄	—	5	1	no	—
92	C₂³×D₅	C₂²×C₃	1	2	yes	complemented
93	C₂³×D₅	C₂²×C₃	1	2	yes	complemented
94	C₂×C₅×D₄	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
99	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
100	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
101	D₄×D₅	—	2	8	no	—
102	D₄×D₅	—	2	4	no	—
103	C₂×D₂₀	—	2	4	no	—
104	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×D₂₀	C₂²×C₃	1	2	yes	complemented
106	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂×D₂₀	C₂²×C₃	1	2	yes	complemented
108	C₂×C₄×D₅	C₂²×C₃	1	2	yes	complemented
109	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
112	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
113	#685	C₂²×C₃	1	1	yes	characteristic, complemented
114	#685	C₂²×C₃	1	2	yes	complemented
115	#685	C₂²×C₃	1	2	yes	complemented
116	#683	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
118	D₄²	—	5	1	no	Sylow
119	C₂²×C₃×C₅	—	2	1	no	—
120	C₂²×C₃×C₅	—	2	1	no	—
121	C₂²×C₃×C₅	—	2	2	no	—
122	C₂²×C₃×C₅	—	2	2	no	—
123	C₂²×C₃×C₅	—	2	2	no	—
124	C₂²×C₃×C₅	C₂×D₄	1	2	yes	complemented
125	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
126	C₂×C₃×D₅	—	2	1	no	—
127	C₂×C₃×D₅	—	2	2	no	—
128	C₂×C₃×D₅	—	2	2	no	—
129	C₂×C₃×D₅	—	2	1	no	—
130	C₂×C₃×D₅	—	2	2	no	—
131	C₂×C₃×D₅	—	2	2	no	—
132	C₂×C₃×D₅	—	2	2	no	—
133	C₂×C₃×D₅	—	4	8	no	—
134	C₂×C₃×D₅	—	4	8	no	—
135	C₂×C₃×D₅	C₂×D₄	1	2	yes	complemented
136	C₂×C₃×D₅	C₂×D₄	1	4	yes	complemented
137	C₃×C₄×C₅	—	2	2	no	—
138	C₃×C₄×C₅	—	2	1	no	—
139	C₃×C₄×C₅	C₂×D₄	1	2	yes	complemented
140	C₃×Dic₅	—	2	1	no	—
141	C₃×Dic₅	—	2	1	no	—
142	C₃×Dic₅	C₂×D₄	1	2	yes	complemented
143	C₂⁴×C₃	—	5	2	no	—
144	C₂⁴×C₃	—	5	2	no	—
145	C₂×C₃×D₄	—	5	1	no	—
146	C₂×C₃×D₄	—	5	2	no	—
147	C₂×C₃×D₄	—	5	2	no	—
148	C₂×C₃×D₄	—	5	2	no	—
149	C₂×C₃×D₄	—	5	1	no	—
150	C₂×C₃×D₄	—	5	2	no	—
151	C₂×C₃×D₄	—	5	2	no	—
152	C₂×C₃×D₄	—	5	1	no	—
153	C₂×C₃×D₄	—	10	4	no	—
154	C₂×C₃×D₄	—	10	8	no	—
155	C₂×C₃×D₄	—	10	4	no	—
156	C₂×C₃×D₄	C₂×D₅	1	2	yes	complemented
157	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
158	C₂²×C₃×C₄	—	5	2	no	—
159	C₂²×C₃×C₄	—	5	1	no	—
160	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
161	C₃×C₄⋊C₄	—	5	1	no	—
162	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
163	C₃×C₂²⋊C₄	—	5	1	no	—
164	C₃×C₂²⋊C₄	—	5	2	no	—
165	C₃×C₂²⋊C₄	—	5	1	no	—
166	C₃×C₂²⋊C₄	—	5	2	no	—
167	C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
168	C₃×C₄²	—	5	1	no	—
169	C₂³×C₅	C₂³×C₃	1	2	yes	—
170	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×D₅	—	2	4	no	—
172	C₂²×D₅	—	2	4	no	—
173	C₂²×D₅	—	2	4	no	—
174	C₂²×D₅	—	2	4	no	—
175	C₂²×D₅	—	4	2	no	—
176	C₂²×D₅	—	4	2	no	—
177	C₂²×D₅	C₂³×C₃	1	2	yes	—
178	C₂²×D₅	C₂³×C₃	1	2	yes	—
179	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
180	C₅×D₄	—	2	4	no	—
181	C₅×D₄	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
185	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂²⋊D₅	—	2	4	no	—
187	C₂²⋊D₅	—	2	4	no	—
188	C₂²⋊D₅	—	4	2	no	—
189	C₂²⋊D₅	C₃×D₄	1	4	yes	complemented
190	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
193	D₂₀	—	2	4	no	—
194	D₂₀	—	2	4	no	—
195	D₂₀	—	2	2	no	—
196	D₂₀	C₃×D₄	1	4	yes	complemented
197	C₄×D₅	—	2	2	no	—
198	C₄×D₅	—	2	4	no	—
199	C₂²×D₄	—	5	2	no	—
200	C₂²×D₄	—	5	1	no	—
201	C₂²×D₄	—	5	1	no	—
202	#127	—	5	1	no	—
203	#121	—	5	1	no	—
204	#121	—	5	2	no	—
205	#121	C₃×D₅	1	1	yes	characteristic, complemented
206	#120	—	5	2	no	—
207	#120	—	5	2	no	—
208	C₄×D₄	—	5	1	no	—
209	C₄×D₄	—	5	1	no	—
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	—	4	2	no	—
212	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
215	C₃×D₅	—	2	2	no	—
216	C₃×D₅	—	2	4	no	—
217	C₃×D₅	—	4	2	no	—
218	C₂³×C₃	—	5	2	no	—
219	C₂³×C₃	—	5	1	no	—
220	C₂³×C₃	—	5	2	no	—
221	C₂³×C₃	—	10	4	no	—
222	C₂³×C₃	—	10	4	no	—
223	C₂³×C₃	—	10	4	no	—
224	C₂³×C₃	—	10	4	no	—
225	C₂³×C₃	—	20	2	no	—
226	C₂³×C₃	—	20	2	no	—
227	C₂³×C₃	C₂²×D₅	1	2	yes	—
228	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
229	C₃×D₄	—	2	4	no	—
230	C₃×D₄	—	2	2	no	—
231	C₃×D₄	—	5	4	no	—
232	C₃×D₄	—	5	4	no	—
233	C₃×D₄	—	10	4	no	—
234	C₃×D₄	—	10	4	no	—
235	C₃×D₄	—	10	4	no	—
236	C₃×D₄	—	10	4	no	—
237	C₃×D₄	—	10	2	no	—
238	C₃×D₄	—	20	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	5	1	no	—
241	C₂×C₃×C₄	—	5	1	no	—
242	C₂×C₃×C₄	—	5	1	no	—
243	C₂×C₃×C₄	—	10	4	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
246	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	C₂×C₃×D₄	1	2	yes	complemented
254	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
255	C₂×D₅	—	2	1	no	—
256	C₂×D₅	—	2	2	no	—
257	C₂×D₅	—	2	2	no	—
258	C₂×D₅	—	2	1	no	—
259	C₂×D₅	—	2	2	no	—
260	C₂×D₅	—	2	2	no	—
261	C₂×D₅	—	2	2	no	—
262	C₂×D₅	—	4	8	no	—
263	C₂×D₅	—	4	8	no	—
264	C₂×D₅	C₂×C₃×D₄	1	2	yes	complemented
265	C₂×D₅	C₂×C₃×D₄	1	4	yes	complemented
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	C₂×C₃×D₄	1	2	yes	complemented
269	Dic₅	—	2	1	no	—
270	Dic₅	—	2	1	no	—
271	Dic₅	C₂×C₃×D₄	1	2	yes	complemented
272	C₂⁴	—	5	2	no	—
273	C₂⁴	—	5	2	no	—
274	C₂×D₄	—	5	1	no	—
275	C₂×D₄	—	5	2	no	—
276	C₂×D₄	—	5	2	no	—
277	C₂×D₄	—	5	2	no	—
278	C₂×D₄	—	5	1	no	—
279	C₂×D₄	—	5	2	no	—
280	C₂×D₄	—	5	2	no	—
281	C₂×D₄	—	5	1	no	—
282	C₂×D₄	—	10	4	no	—
283	C₂×D₄	—	10	8	no	—
284	C₂×D₄	—	10	4	no	—
285	C₂×D₄	C₂×C₃×D₅	1	2	yes	complemented
286	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
290	C₄⋊C₄	—	5	1	no	—
291	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
292	C₂²⋊C₄	—	5	1	no	—
293	C₂²⋊C₄	—	5	2	no	—
294	C₂²⋊C₄	—	5	1	no	—
295	C₂²⋊C₄	—	5	2	no	—
296	C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
297	C₄²	—	5	1	no	—
298	C₃×C₅	D₄²	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	2	no	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	5	2	no	—
305	C₂²×C₃	—	5	4	no	—
306	C₂²×C₃	—	10	2	no	—
307	C₂²×C₃	—	10	1	no	—
308	C₂²×C₃	—	10	2	no	—
309	C₂²×C₃	—	10	1	no	—
310	C₂²×C₃	—	10	2	no	—
311	C₂²×C₃	—	10	2	no	—
312	C₂²×C₃	—	10	2	no	—
313	C₂²×C₃	—	20	8	no	—
314	C₂²×C₃	—	20	8	no	—
315	C₂²×C₃	D₄×D₅	1	2	yes	complemented
316	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	5	2	no	—
320	C₃×C₄	—	10	1	no	—
321	C₃×C₄	—	10	1	no	—
322	C₃×C₄	D₄×D₅	1	2	yes	complemented
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	4	2	no	—
325	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
326	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
327	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
328	D₅	—	2	2	no	—
329	D₅	—	2	4	no	—
330	D₅	—	4	2	no	—
331	C₂³	—	5	1	no	—
332	C₂³	—	5	2	no	—
333	C₂³	—	5	2	no	—
334	C₂³	—	10	4	no	—
335	C₂³	—	10	4	no	—
336	C₂³	—	10	4	no	—
337	C₂³	—	10	4	no	—
338	C₂³	—	20	2	no	—
339	C₂³	—	20	2	no	—
340	C₂³	C₂²×C₃×D₅	1	2	yes	—
341	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	5	4	no	—
345	D₄	—	5	4	no	—
346	D₄	—	10	4	no	—
347	D₄	—	10	4	no	—
348	D₄	—	10	4	no	—
349	D₄	—	10	4	no	—
350	D₄	—	10	2	no	—
351	D₄	—	20	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	5	1	no	—
354	C₂×C₄	—	5	1	no	—
355	C₂×C₄	—	5	1	no	—
356	C₂×C₄	—	10	4	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
359	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	4	2	no	—
363	C₂×C₃	—	10	4	no	—
364	C₂×C₃	—	10	2	no	—
365	C₂×C₃	—	20	2	no	—
366	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
367	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
368	C₂×C₃	#4149	1	1	yes	characteristic
369	C₅	C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	5	2	no	—
376	C₂²	—	5	4	no	—
377	C₂²	—	10	2	no	—
378	C₂²	—	10	1	no	—
379	C₂²	—	10	2	no	—
380	C₂²	—	10	1	no	—
381	C₂²	—	10	2	no	—
382	C₂²	—	10	2	no	—
383	C₂²	—	10	2	no	—
384	C₂²	—	20	8	no	—
385	C₂²	—	20	8	no	—
386	C₂²	C₃×D₄×D₅	1	2	yes	complemented
387	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	5	2	no	—
391	C₄	—	10	1	no	—
392	C₄	—	10	1	no	—
393	C₄	C₃×D₄×D₅	1	2	yes	complemented
394	C₃	#65943	1	1	yes	characteristic, direct product factor, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	4	2	no	—
397	C₂	—	10	4	no	—
398	C₂	—	10	2	no	—
399	C₂	—	20	2	no	—
400	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic
401	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic
402	C₂	C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#121	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₃×#121	D₅
hypocenter	C₅	C₃×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₅	C₂	semidirect
2. C₂×C₃×D₄×D₅	C₂	semidirect
3. C₂²×C₃×D₂₀	C₂	semidirect
4. C₃×C₅×#121	C₂	semidirect
5. C₃×#4086	C₂	semidirect
6. C₃×#4083	C₂	semidirect
7. C₃×C₄×C₂²⋊D₅	C₂	semidirect
8. C₃×#4041	C₂	semidirect
9. C₃×#4039	C₂	semidirect
10. C₃×#4030	C₂	semidirect
11. C₃×#4028	C₂	semidirect
12. #65943	C₃	direct (N × H)
13. C₂³×C₃×D₅	C₂²	semidirect
14. C₂³×C₃×D₅	C₂²	semidirect
15. C₂×C₃×C₅×D₄	C₂²	semidirect
16. C₂×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₃×C₄×C₅	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
21. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
26. C₂×C₃×D₂₀	C₂²	semidirect
27. C₂×C₃×D₂₀	C₂²	semidirect
28. C₂×C₃×D₂₀	C₂²	semidirect
29. C₂×C₃×C₄×D₅	C₂²	semidirect
30. C₂×C₃×C₄×D₅	C₂²	semidirect
31. C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₃×C₂²⋊Dic₅	C₂²	semidirect
34. C₃×#685	C₂²	semidirect
35. C₃×#685	C₂²	semidirect
36. C₃×#685	C₂²	semidirect
37. C₃×#683	C₂²	semidirect
38. C₃×C₄×Dic₅	C₂²	semidirect
40. C₂×D₄×D₅	C₂×C₃	semidirect
41. C₂×D₄×D₅	C₂×C₃	semidirect
42. C₂²×D₂₀	C₂×C₃	semidirect
43. C₅×#121	C₂×C₃	semidirect
44. #4086	C₂×C₃	semidirect
45. #4083	C₂×C₃	semidirect
46. C₄×C₂²⋊D₅	C₂×C₃	semidirect
47. #4041	C₂×C₃	semidirect
48. #4039	C₂×C₃	semidirect
49. #4030	C₂×C₃	semidirect
50. #4028	C₂×C₃	semidirect
71. C₃×C₂²⋊D₅	D₄	semidirect
78. C₃×D₂₀	D₄	semidirect
87. C₃×#121	D₅	semidirect
92. C₂³×D₅	C₂²×C₃	semidirect
93. C₂³×D₅	C₂²×C₃	semidirect
94. C₂×C₅×D₄	C₂²×C₃	semidirect
95. C₂×C₅×D₄	C₂²×C₃	semidirect
96. C₂²×C₄×C₅	C₂²×C₃	semidirect
98. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
99. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
100. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
105. C₂×D₂₀	C₂²×C₃	semidirect
106. C₂×D₂₀	C₂²×C₃	semidirect
107. C₂×D₂₀	C₂²×C₃	semidirect
108. C₂×C₄×D₅	C₂²×C₃	semidirect
109. C₂×C₄×D₅	C₂²×C₃	semidirect
110. C₅×C₄⋊C₄	C₂²×C₃	semidirect
111. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
112. C₂²⋊Dic₅	C₂²×C₃	semidirect
113. #685	C₂²×C₃	semidirect
114. #685	C₂²×C₃	semidirect
115. #685	C₂²×C₃	semidirect
116. #683	C₂²×C₃	semidirect
117. C₄×Dic₅	C₂²×C₃	semidirect
124. C₂²×C₃×C₅	C₂×D₄	semidirect
135. C₂×C₃×D₅	C₂×D₄	semidirect
136. C₂×C₃×D₅	C₂×D₄	semidirect
139. C₃×C₄×C₅	C₂×D₄	semidirect
142. C₃×Dic₅	C₂×D₄	semidirect
156. C₂×C₃×D₄	C₂×D₅	semidirect
157. C₂×C₃×D₄	C₂×D₅	semidirect
160. C₂²×C₃×C₄	C₂×D₅	semidirect
162. C₃×C₄⋊C₄	C₂×D₅	semidirect
167. C₃×C₂²⋊C₄	C₂×D₅	semidirect
189. C₂²⋊D₅	C₃×D₄	semidirect
196. D₂₀	C₃×D₄	semidirect
205. #121	C₃×D₅	semidirect
253. C₂²×C₅	C₂×C₃×D₄	semidirect
264. C₂×D₅	C₂×C₃×D₄	semidirect
265. C₂×D₅	C₂×C₃×D₄	semidirect
268. C₄×C₅	C₂×C₃×D₄	semidirect
271. Dic₅	C₂×C₃×D₄	semidirect
285. C₂×D₄	C₂×C₃×D₅	semidirect
286. C₂×D₄	C₂×C₃×D₅	semidirect
289. C₂²×C₄	C₂×C₃×D₅	semidirect
291. C₄⋊C₄	C₂×C₃×D₅	semidirect
296. C₂²⋊C₄	C₂×C₃×D₅	semidirect
298. C₃×C₅	D₄²	semidirect
315. C₂²×C₃	D₄×D₅	semidirect
322. C₃×C₄	D₄×D₅	semidirect
369. C₅	C₃×D₄²	semidirect
386. C₂²	C₃×D₄×D₅	semidirect
393. C₄	C₃×D₄×D₅	semidirect
394. C₃	#65943	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×D₅	2
C₂²×C₃×D₂₀	2
C₃×C₅×#121	2
C₃×#4086	2
C₃×#4083	2
C₃×C₄×C₂²⋊D₅	2
C₃×#4041	2
C₃×#4039	2
C₃×#4030	2
C₃×#4028	2
#65943	3
C₃×D₄²	5

Subgroups — C3×#65943 #11755620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65943 #11755620