Subgroups — C₃×#10617309 #14415240

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4133	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66002	C₂	1	1	yes	maximal, characteristic
4	C₃×#65787	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65776	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65695	C₂	1	4	yes	maximal, complemented
7	C₃×#65692	C₂	1	4	yes	maximal, complemented
8	C₃×#65682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#10617309	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#713	C₂²	1	1	yes	characteristic
12	C₂×C₃×#711	C₂²	1	1	yes	characteristic
13	C₂×C₃×#704	C₂²	1	2	yes	—
14	C₂²×C₃×#170	C₂²	1	2	yes	—
15	C₃×#4133	—	2	4	no	—
16	C₃×#4131	—	2	4	no	—
17	C₂×C₃×#700	C₂²	1	1	yes	characteristic
18	C₂×C₃×#700	C₂²	1	1	yes	characteristic
19	C₂×C₃×#700	C₂²	1	2	yes	—
20	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₄	1	1	yes	characteristic
24	C₃×#4090	C₄	1	1	yes	characteristic
25	C₃×#4086	C₄	1	1	yes	characteristic
26	C₃×#4030	C₄	1	4	yes	—
27	C₃×#4027	C₂²	1	4	yes	—
28	C₃×#4021	C₄	1	1	yes	characteristic
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₂²⋊#170	C₂²	1	4	yes	—
31	C₃×#4004	C₂²	1	4	yes	—
32	C₃×#4003	C₂²	1	4	yes	—
33	C₃×C₄×#170	C₂²	1	2	yes	—
34	C₃×C₄×#170	C₂²	1	2	yes	—
35	C₃×#2931	—	5	1	no	maximal, Hall
36	C₂×#4133	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
38	#66002	C₂×C₃	1	1	yes	characteristic
39	#65787	C₂×C₃	1	1	yes	characteristic, complemented
40	#65776	C₂×C₃	1	1	yes	characteristic, complemented
41	#65695	C₂×C₃	1	4	yes	complemented
42	#65692	C₂×C₃	1	4	yes	complemented
43	#65682	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₃×#713	—	2	2	no	—
51	C₃×#713	—	2	2	no	—
52	C₃×#711	—	2	2	no	—
53	C₃×#711	—	2	2	no	—
54	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
60	C₃×#704	—	2	4	no	—
61	C₂×C₃×#170	—	2	4	no	—
62	C₂×C₃×#170	C₂³	1	2	yes	—
63	C₂×C₃×#170	C₂³	1	2	yes	—
64	C₂×C₃×#170	C₂³	1	2	yes	—
65	C₂×C₃×#170	C₂³	1	1	yes	characteristic
66	C₂×C₃×#170	C₂³	1	1	yes	characteristic
67	C₃×#700	—	2	2	no	—
68	C₃×#700	—	2	2	no	—
69	C₃×#700	—	2	4	no	—
70	C₃×D₅⋊C₈	—	2	2	no	—
71	C₃×D₅⋊C₈	—	2	4	no	—
72	C₃×D₅⋊C₈	D₄	1	4	yes	complemented
73	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
74	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₃×#685	C₂×C₄	1	4	yes	—
76	C₃×#683	C₂×C₄	1	4	yes	—
77	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂³	1	2	yes	—
79	C₂×C₃×#131	—	5	1	no	—
80	C₂×C₃×#131	—	5	1	no	—
81	C₃×#532	—	5	1	no	—
82	C₃×#436	—	5	4	no	—
83	C₃×C₈×D₄	—	5	4	no	—
84	C₃×#423	—	5	1	no	—
85	C₃×#408	—	5	1	no	—
86	C₃×#408	—	5	1	no	—
87	C₂×C₃×C₄×C₈	—	5	1	no	—
88	C₂×#713	C₂²×C₃	1	1	yes	characteristic
89	C₂×#711	C₂²×C₃	1	1	yes	characteristic
90	C₂×#704	C₂²×C₃	1	2	yes	—
91	C₂²×#170	C₂²×C₃	1	2	yes	—
92	#4133	—	2	4	no	—
93	#4131	—	2	4	no	—
94	C₂×#700	C₂²×C₃	1	1	yes	characteristic
95	C₂×#700	C₂²×C₃	1	1	yes	characteristic
96	C₂×#700	C₂²×C₃	1	2	yes	—
97	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
98	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
99	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
100	C₅×#124	C₃×C₄	1	1	yes	characteristic
101	#4090	C₃×C₄	1	1	yes	characteristic
102	#4086	C₃×C₄	1	1	yes	characteristic
103	#4030	C₃×C₄	1	4	yes	—
104	#4027	C₂²×C₃	1	4	yes	—
105	#4021	C₃×C₄	1	1	yes	characteristic
106	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂²⋊#170	C₂²×C₃	1	4	yes	—
108	#4004	C₂²×C₃	1	4	yes	—
109	#4003	C₂²×C₃	1	4	yes	—
110	C₄×#170	C₂²×C₃	1	2	yes	—
111	C₄×#170	C₂²×C₃	1	2	yes	—
112	#2931	—	5	1	no	Sylow
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
115	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₃×C₂²⋊D₅	—	2	4	no	—
122	C₃×C₂²⋊D₅	—	2	8	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
128	C₃×D₂₀	—	2	4	no	—
129	C₃×D₂₀	—	2	2	no	—
130	C₃×C₄×D₅	—	2	4	no	—
131	C₃×C₄×D₅	—	2	2	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
134	C₃×C₄×D₅	#41	1	2	yes	—
135	C₃×Dic₁₀	—	2	2	no	—
136	C₃×#170	—	2	2	no	—
137	C₃×#170	—	2	2	no	—
138	C₃×#170	—	2	2	no	—
139	C₃×#170	C₂×D₄	1	2	yes	—
140	C₃×#170	C₂×D₄	1	2	yes	—
141	C₂×C₃×#41	—	5	1	no	—
142	C₂×C₃×#41	—	5	1	no	—
143	C₃×#131	—	10	4	no	—
144	C₃×#131	—	10	4	no	—
145	C₂×C₃×M₁₆	—	5	1	no	—
146	C₂×C₃×M₁₆	—	5	1	no	—
147	C₂×C₃×M₁₆	—	5	2	no	—
148	C₂×C₃×M₁₆	—	5	2	no	—
149	C₂²×C₃×C₈	—	5	1	no	—
150	C₂²×C₃×C₈	—	5	2	no	—
151	C₂²×C₃×C₈	—	5	2	no	—
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₃×C₄⋊Q₈	—	5	1	no	—
154	C₃×#127	—	5	1	no	—
155	C₃×#124	—	5	1	no	—
156	C₃×#124	AGL(1,𝔽₅)	1	1	yes	characteristic
157	C₃×#121	—	5	4	no	—
158	C₃×C₄×D₄	—	5	4	no	—
159	C₂×C₃×C₄²	—	5	1	no	—
160	C₃×C₄⋊C₈	—	5	4	no	—
161	C₃×C₂²⋊C₈	—	5	4	no	—
162	C₃×C₂²⋊C₈	—	5	4	no	—
163	C₃×C₄×C₈	—	5	2	no	—
164	C₃×C₄×C₈	—	5	2	no	—
165	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
168	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
169	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
170	#713	—	2	2	no	—
171	#713	—	2	2	no	—
172	#711	—	2	2	no	—
173	#711	—	2	2	no	—
174	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
175	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
176	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
177	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
178	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
179	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
180	#704	—	2	4	no	—
181	C₂×#170	—	2	4	no	—
182	C₂×#170	C₂³×C₃	1	2	yes	—
183	C₂×#170	C₂³×C₃	1	2	yes	—
184	C₂×#170	C₂³×C₃	1	2	yes	—
185	C₂×#170	C₂³×C₃	1	1	yes	characteristic
186	C₂×#170	C₂³×C₃	1	1	yes	characteristic
187	#700	—	2	2	no	—
188	#700	—	2	2	no	—
189	#700	—	2	4	no	—
190	D₅⋊C₈	—	2	2	no	—
191	D₅⋊C₈	—	2	4	no	—
192	D₅⋊C₈	C₃×D₄	1	4	yes	complemented
193	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
194	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
195	#685	C₂×C₃×C₄	1	4	yes	—
196	#683	C₂×C₃×C₄	1	4	yes	—
197	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
198	C₄×Dic₅	C₂³×C₃	1	2	yes	—
199	C₂×#131	—	5	1	no	—
200	C₂×#131	—	5	1	no	—
201	#532	—	5	1	no	—
202	#436	—	5	4	no	—
203	C₈×D₄	—	5	4	no	—
204	#423	—	5	1	no	—
205	#408	—	5	1	no	—
206	#408	—	5	1	no	—
207	C₂×C₄×C₈	—	5	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₃×D₅	—	2	2	no	—
212	C₂×C₃×D₅	—	2	2	no	—
213	C₂×C₃×D₅	—	2	4	no	—
214	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
218	C₃×Dic₅	—	2	2	no	—
219	C₃×Dic₅	#131	1	4	yes	complemented
220	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
222	C₃×#41	—	10	2	no	—
223	C₃×#41	—	10	2	no	—
224	C₃×#41	—	10	2	no	—
225	C₃×#41	—	10	2	no	—
226	C₂×C₃×Q₈	—	5	1	no	—
227	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
228	C₂×C₃×D₄	—	5	4	no	—
229	C₂×C₃×D₄	—	5	2	no	—
230	C₂×C₃×D₄	—	5	2	no	—
231	C₂×C₃×D₄	—	5	1	no	—
232	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₂²×C₃×C₄	—	5	1	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	5	2	no	—
236	C₂²×C₃×C₄	—	5	2	no	—
237	C₃×M₁₆	—	10	4	no	—
238	C₃×M₁₆	—	10	4	no	—
239	C₃×M₁₆	—	10	2	no	—
240	C₃×M₁₆	—	10	2	no	—
241	C₂×C₃×C₈	—	5	1	no	—
242	C₂×C₃×C₈	—	5	1	no	—
243	C₂×C₃×C₈	—	5	4	no	—
244	C₂×C₃×C₈	—	5	2	no	—
245	C₂×C₃×C₈	—	5	2	no	—
246	C₂×C₃×C₈	—	5	2	no	—
247	C₂×C₃×C₈	—	10	4	no	—
248	C₂×C₃×C₈	—	10	4	no	—
249	C₂×C₃×C₈	—	10	2	no	—
250	C₃×C₄⋊C₄	—	5	4	no	—
251	C₃×C₂²⋊C₄	—	5	4	no	—
252	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	4	yes	—
253	C₃×C₄²	—	5	1	no	—
254	C₃×C₄²	—	5	2	no	—
255	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
256	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
258	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₅×Q₈	—	2	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₂²⋊D₅	—	2	4	no	—
265	C₂²⋊D₅	—	2	8	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
270	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
271	D₂₀	—	2	4	no	—
272	D₂₀	—	2	2	no	—
273	C₄×D₅	—	2	4	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
277	C₄×D₅	C₃×#41	1	2	yes	—
278	Dic₁₀	—	2	2	no	—
279	#170	—	2	2	no	—
280	#170	—	2	2	no	—
281	#170	—	2	2	no	—
282	#170	C₂×C₃×D₄	1	2	yes	—
283	#170	C₂×C₃×D₄	1	2	yes	—
284	C₂×#41	—	5	1	no	—
285	C₂×#41	—	5	1	no	—
286	#131	—	10	4	no	—
287	#131	—	10	4	no	—
288	C₂×M₁₆	—	5	1	no	—
289	C₂×M₁₆	—	5	1	no	—
290	C₂×M₁₆	—	5	2	no	—
291	C₂×M₁₆	—	5	2	no	—
292	C₂²×C₈	—	5	1	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₂²×C₈	—	5	1	no	—
295	C₂²×C₈	—	5	2	no	—
296	C₄⋊Q₈	—	5	1	no	—
297	#127	—	5	1	no	—
298	#124	—	5	1	no	—
299	#124	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
300	#121	—	5	4	no	—
301	C₄×D₄	—	5	4	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₄⋊C₈	—	5	4	no	—
304	C₂²⋊C₈	—	5	4	no	—
305	C₂²⋊C₈	—	5	4	no	—
306	C₄×C₈	—	5	2	no	—
307	C₄×C₈	—	5	2	no	—
308	C₂×C₃×C₅	—	4	2	no	—
309	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂×C₃×C₅	C₂×#131	1	2	yes	—
311	C₃×D₅	—	2	2	no	—
312	C₃×D₅	—	4	2	no	—
313	C₂³×C₃	—	5	1	no	—
314	C₂³×C₃	—	5	2	no	—
315	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	10	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	10	4	no	—
320	C₃×D₄	—	10	8	no	—
321	C₃×D₄	—	10	4	no	—
322	C₃×D₄	—	10	2	no	—
323	C₂×C₃×C₄	—	5	2	no	—
324	C₂×C₃×C₄	—	5	1	no	—
325	C₂×C₃×C₄	—	5	2	no	—
326	C₂×C₃×C₄	—	5	2	no	—
327	C₂×C₃×C₄	—	5	2	no	—
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	—	10	2	no	—
331	C₂×C₃×C₄	—	10	2	no	—
332	C₂×C₃×C₄	—	10	2	no	—
333	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
334	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
335	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₃×C₈	—	5	2	no	—
337	C₃×C₈	—	5	2	no	—
338	C₃×C₈	—	10	2	no	—
339	C₃×C₈	—	10	2	no	—
340	C₃×C₈	—	10	2	no	—
341	C₂²×C₅	—	2	4	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₂×D₅	—	2	2	no	—
345	C₂×D₅	—	2	4	no	—
346	C₂×D₅	—	2	2	no	—
347	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
351	Dic₅	—	2	2	no	—
352	Dic₅	C₃×#131	1	4	yes	complemented
353	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
354	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
355	#41	—	10	2	no	—
356	#41	—	10	2	no	—
357	#41	—	10	2	no	—
358	#41	—	10	2	no	—
359	C₂×Q₈	—	5	1	no	—
360	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₂×D₄	—	5	4	no	—
362	C₂×D₄	—	5	2	no	—
363	C₂×D₄	—	5	2	no	—
364	C₂×D₄	—	5	1	no	—
365	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	5	2	no	—
369	C₂²×C₄	—	5	2	no	—
370	M₁₆	—	10	4	no	—
371	M₁₆	—	10	4	no	—
372	M₁₆	—	10	2	no	—
373	M₁₆	—	10	2	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	5	1	no	—
376	C₂×C₈	—	5	4	no	—
377	C₂×C₈	—	5	2	no	—
378	C₂×C₈	—	5	2	no	—
379	C₂×C₈	—	5	2	no	—
380	C₂×C₈	—	10	4	no	—
381	C₂×C₈	—	10	4	no	—
382	C₂×C₈	—	10	2	no	—
383	C₄⋊C₄	—	5	4	no	—
384	C₂²⋊C₄	—	5	4	no	—
385	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
386	C₄²	—	5	2	no	—
387	C₄²	—	5	1	no	—
388	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	5	2	no	—
393	C₂²×C₃	—	10	2	no	—
394	C₂²×C₃	—	10	2	no	—
395	C₂²×C₃	—	10	4	no	—
396	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	5	1	no	—
400	C₃×C₄	—	5	1	no	—
401	C₃×C₄	—	5	4	no	—
402	C₃×C₄	—	10	2	no	—
403	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
404	C₂×C₅	—	4	2	no	—
405	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
406	C₂×C₅	C₂×C₃×#131	1	2	yes	—
407	D₅	—	2	2	no	—
408	D₅	—	4	2	no	—
409	C₂³	—	5	1	no	—
410	C₂³	—	5	2	no	—
411	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
412	Q₈	—	2	2	no	—
413	Q₈	—	10	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	10	4	no	—
416	D₄	—	10	8	no	—
417	D₄	—	10	4	no	—
418	D₄	—	10	2	no	—
419	C₂×C₄	—	5	2	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	4	no	—
427	C₂×C₄	—	10	2	no	—
428	C₂×C₄	—	10	2	no	—
429	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
430	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
431	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₈	—	5	2	no	—
433	C₈	—	5	2	no	—
434	C₈	—	10	2	no	—
435	C₈	—	10	2	no	—
436	C₈	—	10	2	no	—
437	C₂×C₃	—	4	2	no	—
438	C₂×C₃	—	10	2	no	—
439	C₂×C₃	—	20	2	no	—
440	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂×C₃	D₅⋊#131	1	2	yes	—
442	C₅	C₃×#2931	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	5	2	no	—
446	C₂²	—	10	2	no	—
447	C₂²	—	10	2	no	—
448	C₂²	—	10	4	no	—
449	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	5	1	no	—
453	C₄	—	5	1	no	—
454	C₄	—	5	4	no	—
455	C₄	—	10	2	no	—
456	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
457	C₃	#10617309	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	4	2	no	—
459	C₂	—	10	2	no	—
460	C₂	—	20	2	no	—
461	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
462	C₂	C₃×D₅⋊#131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#124	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66002	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#124	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2931
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4133	C₂	semidirect
2. C₂×C₃×#4131	C₂	semidirect
4. C₃×#65787	C₂	semidirect
5. C₃×#65776	C₂	semidirect
6. C₃×#65695	C₂	semidirect
7. C₃×#65692	C₂	semidirect
8. C₃×#65682	C₂	semidirect
9. C₃×C₄×D₅⋊C₈	C₂	semidirect
10. #10617309	C₃	direct (N × H)
36. C₂×#4133	C₂×C₃	semidirect
37. C₂×#4131	C₂×C₃	semidirect
39. #65787	C₂×C₃	semidirect
40. #65776	C₂×C₃	semidirect
41. #65695	C₂×C₃	semidirect
42. #65692	C₂×C₃	semidirect
43. #65682	C₂×C₃	semidirect
44. C₄×D₅⋊C₈	C₂×C₃	semidirect
72. C₃×D₅⋊C₈	D₄	semidirect
192. D₅⋊C₈	C₃×D₄	semidirect
219. C₃×Dic₅	#131	semidirect
352. Dic₅	C₃×#131	semidirect
389. C₃×C₅	#2931	semidirect
442. C₅	C₃×#2931	semidirect
457. C₃	#10617309	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×#4133	2
C₂×C₃×#4131	2
C₃×#66002	2
C₃×#65787	2
C₃×#65776	2
C₃×#65695	2
C₃×#65692	2
C₃×#65682	2
C₃×C₄×D₅⋊C₈	2
#10617309	3
C₃×#2931	5

Subgroups — C3×#10617309 #14415240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617309 #14415240