Subgroups — C₃×#10611595 #14416539

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#711	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65441	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65307	C₂	1	2	yes	maximal, complemented
6	C₃×#65149	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65142	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65061	C₂	1	2	yes	maximal, complemented
9	C₃×#65046	C₂	1	2	yes	maximal, complemented
10	C₃×#65005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611595	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₃×D₄×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#687	C₂²	1	2	yes	—
18	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
19	C₂×C₃×C₄×Dic₅	—	2	2	no	—
20	C₃×#4058	C₄	1	8	yes	complemented
21	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4038	C₂²	1	2	yes	—
25	C₃×#4033	C₂²	1	2	yes	—
26	C₃×#4027	—	2	2	no	—
27	C₃×#4023	—	2	2	no	—
28	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3949	C₂²	1	1	yes	characteristic
35	C₃×#3948	C₂²	1	2	yes	—
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	C₃×#3947	C₂²	1	1	yes	characteristic
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×#3935	C₂²	1	1	yes	characteristic
41	C₃×#2943	—	5	1	no	maximal, Hall
42	C₂×#4058	C₂×C₃	1	1	yes	characteristic
43	C₄×#711	C₂×C₃	1	2	yes	complemented
44	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
45	#65441	C₂×C₃	1	1	yes	characteristic, complemented
46	#65307	C₂×C₃	1	2	yes	complemented
47	#65149	C₂×C₃	1	1	yes	characteristic, complemented
48	#65142	C₂×C₃	1	1	yes	characteristic, complemented
49	#65061	C₂×C₃	1	2	yes	complemented
50	#65046	C₂×C₃	1	2	yes	complemented
51	#65005	C₂×C₃	1	1	yes	characteristic, complemented
52	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
56	C₂²×C₃×Dic₅	—	2	2	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₃×#711	—	2	4	no	—
59	C₃×#711	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
61	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
63	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₂²⋊Dic₅	—	2	2	no	—
70	C₃×#687	C₂×C₄	1	8	yes	complemented
71	C₃×#685	—	2	2	no	—
72	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
73	C₃×#683	—	2	2	no	—
74	C₃×#683	—	2	2	no	—
75	C₃×C₄×Dic₅	—	2	2	no	—
76	C₃×C₄×Dic₅	—	2	2	no	—
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	D₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
83	C₃×C₈×D₅	—	2	2	no	—
84	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
85	C₂×C₃×#135	—	5	1	no	—
86	C₃×C₄×#41	—	5	2	no	—
87	C₃×#442	—	5	1	no	—
88	C₃×#442	D₅	1	1	yes	characteristic, complemented
89	C₃×#441	—	5	1	no	—
90	C₃×#441	—	5	1	no	—
91	C₃×#440	—	5	2	no	—
92	C₃×#440	—	5	2	no	—
93	C₃×#427	—	5	1	no	—
94	C₃×#416	—	5	2	no	—
95	C₂×C₃×#97	—	5	1	no	—
96	C₂×#711	C₂²×C₃	1	2	yes	—
97	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
99	D₄×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×#687	C₂²×C₃	1	2	yes	—
101	C₄×C₂²⋊D₅	—	2	2	no	—
102	C₂×C₄×Dic₅	—	2	2	no	—
103	#4058	C₃×C₄	1	8	yes	complemented
104	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	#4038	C₂²×C₃	1	2	yes	—
108	#4033	C₂²×C₃	1	2	yes	—
109	#4027	—	2	2	no	—
110	#4023	—	2	2	no	—
111	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
112	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
113	C₅×#106	C₂²×C₃	1	1	yes	characteristic
114	C₅×#102	C₂²×C₃	1	2	yes	—
115	C₅×#97	C₂²×C₃	1	1	yes	characteristic
116	#3964	C₂²×C₃	1	2	yes	—
117	#3949	C₂²×C₃	1	1	yes	characteristic
118	#3948	C₂²×C₃	1	2	yes	—
119	#3947	C₂²×C₃	1	1	yes	characteristic
120	#3947	C₂²×C₃	1	1	yes	characteristic
121	#3942	C₂²×C₃	1	2	yes	—
122	#3939	C₂²×C₃	1	2	yes	—
123	#3935	C₂²×C₃	1	1	yes	characteristic
124	#2943	—	5	1	no	Sylow
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	4	4	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₃×C₂²⋊D₅	—	2	8	no	—
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	—	2	8	no	—
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	—	4	4	no	—
138	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₄×D₅	—	4	2	no	—
141	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
142	C₃×C₄×D₅	#41	1	2	yes	—
143	C₃×Dic₁₀	—	2	2	no	—
144	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₃×#168	—	2	1	no	—
148	C₃×#168	C₂²×C₄	1	2	yes	—
149	C₂×C₃×#41	—	5	2	no	—
150	C₃×#135	—	5	8	no	—
151	C₂×C₃×Q₁₆	—	5	1	no	—
152	C₂×C₃×SD₁₆	—	5	2	no	—
153	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
154	C₂²×C₃×C₈	—	5	1	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₃×C₄×Q₈	—	5	2	no	—
157	C₃×C₄×Q₈	—	5	2	no	—
158	C₃×C₄×D₄	—	5	2	no	—
159	C₃×C₄×D₄	—	10	2	no	—
160	C₃×C₄×D₄	—	10	2	no	—
161	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
162	C₃×#117	—	5	2	no	—
163	C₃×#117	—	10	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×C₃×C₄²	—	10	2	no	—
166	C₃×#107	—	5	2	no	—
167	C₃×#106	—	5	1	no	—
168	C₃×#106	C₂×D₅	1	1	yes	characteristic
169	C₃×#103	—	5	2	no	—
170	C₃×#103	—	5	2	no	—
171	C₃×#102	—	5	2	no	—
172	C₃×#102	C₂×D₅	1	2	yes	—
173	C₃×#97	—	5	1	no	—
174	C₃×#97	—	5	1	no	—
175	C₃×#97	—	5	1	no	—
176	C₃×#97	C₂×D₅	1	1	yes	characteristic
177	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	—	2	2	no	—
179	C₂×C₂²⋊D₅	—	2	2	no	—
180	C₂²×Dic₅	—	2	2	no	—
181	C₂²×Dic₅	—	2	2	no	—
182	#711	—	2	4	no	—
183	#711	C₂×C₃×C₄	1	8	yes	complemented
184	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
185	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
186	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
187	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₂²⋊Dic₅	—	2	2	no	—
194	#687	C₂×C₃×C₄	1	8	yes	complemented
195	#685	—	2	2	no	—
196	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
197	#683	—	2	2	no	—
198	#683	—	2	2	no	—
199	C₄×Dic₅	—	2	2	no	—
200	C₄×Dic₅	—	2	2	no	—
201	C₄×Dic₅	—	2	2	no	—
202	C₄×Dic₅	C₃×D₄	1	2	yes	—
203	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
204	C₂×#168	C₂³×C₃	1	1	yes	characteristic
205	C₂×#168	C₂³×C₃	1	1	yes	characteristic
206	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
207	C₈×D₅	—	2	2	no	—
208	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
209	C₂×#135	—	5	1	no	—
210	C₄×#41	—	5	2	no	—
211	#442	—	5	1	no	—
212	#442	C₃×D₅	1	1	yes	characteristic, complemented
213	#441	—	5	1	no	—
214	#441	—	5	1	no	—
215	#440	—	5	2	no	—
216	#440	—	5	2	no	—
217	#427	—	5	1	no	—
218	#416	—	5	2	no	—
219	C₂×#97	—	5	1	no	—
220	C₂²×C₃×C₅	—	2	4	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₃×D₅	—	2	2	no	—
225	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	4	2	no	—
228	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₃×Dic₅	—	2	4	no	—
231	C₃×Dic₅	—	2	2	no	—
232	C₃×Dic₅	—	4	2	no	—
233	C₃×Dic₅	C₄×D₄	1	2	yes	—
234	C₃×#41	—	5	8	no	—
235	C₃×#41	—	10	4	no	—
236	C₂×C₃×Q₈	—	5	2	no	—
237	C₂×C₃×D₄	—	10	2	no	—
238	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	5	1	no	—
241	C₂²×C₃×C₄	—	5	2	no	—
242	C₂²×C₃×C₄	—	10	2	no	—
243	C₂²×C₃×C₄	—	10	2	no	—
244	C₃×Q₁₆	—	5	4	no	—
245	C₃×SD₁₆	—	5	8	no	—
246	C₃×D₈	C₄×D₅	1	4	yes	complemented
247	C₂×C₃×C₈	—	5	1	no	—
248	C₂×C₃×C₈	—	5	4	no	—
249	C₂×C₃×C₈	—	5	1	no	—
250	C₂×C₃×C₈	—	10	2	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	5	2	no	—
254	C₃×C₄⋊C₄	—	10	2	no	—
255	C₃×C₄⋊C₄	—	10	2	no	—
256	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₂²⋊C₄	—	10	2	no	—
259	C₃×C₂²⋊C₄	—	10	2	no	—
260	C₃×C₄²	—	5	2	no	—
261	C₃×C₄²	—	5	1	no	—
262	C₃×C₄²	—	10	2	no	—
263	C₃×C₄²	—	10	2	no	—
264	C₃×C₄²	—	10	2	no	—
265	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
266	C₂³×C₅	—	2	2	no	—
267	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	4	4	no	—
272	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
274	C₂²⋊D₅	—	2	8	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	—	2	8	no	—
277	C₂×Dic₅	—	2	2	no	—
278	C₂×Dic₅	—	4	4	no	—
279	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
280	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₄×D₅	—	4	2	no	—
282	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
283	C₄×D₅	C₃×#41	1	2	yes	—
284	Dic₁₀	—	2	2	no	—
285	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
286	C₅×C₈	—	2	1	no	—
287	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
288	#168	—	2	1	no	—
289	#168	C₂²×C₃×C₄	1	2	yes	—
290	C₂×#41	—	5	2	no	—
291	#135	—	5	8	no	—
292	C₂×Q₁₆	—	5	1	no	—
293	C₂×SD₁₆	—	5	2	no	—
294	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₄×Q₈	—	5	2	no	—
298	C₄×Q₈	—	5	2	no	—
299	C₄×D₄	—	5	2	no	—
300	C₄×D₄	—	10	2	no	—
301	C₄×D₄	—	10	2	no	—
302	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
303	#117	—	5	2	no	—
304	#117	—	10	2	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	10	2	no	—
307	#107	—	5	2	no	—
308	#106	—	5	1	no	—
309	#106	C₂×C₃×D₅	1	1	yes	characteristic
310	#103	—	5	2	no	—
311	#103	—	5	2	no	—
312	#102	—	5	2	no	—
313	#102	C₂×C₃×D₅	1	2	yes	—
314	#97	—	5	1	no	—
315	#97	—	5	1	no	—
316	#97	—	5	1	no	—
317	#97	C₂×C₃×D₅	1	1	yes	characteristic
318	C₂×C₃×C₅	—	4	4	no	—
319	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂×C₃×C₅	#575	1	2	yes	—
321	C₃×D₅	—	2	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂³×C₃	—	5	1	no	—
324	C₃×Q₈	—	5	4	no	—
325	C₃×Q₈	—	10	2	no	—
326	C₃×D₄	—	2	2	no	—
327	C₃×D₄	—	10	8	no	—
328	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	4	4	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	2	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	10	8	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	—	20	2	no	—
339	C₂×C₃×C₄	—	20	4	no	—
340	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	—	5	2	no	—
344	C₃×C₈	—	10	1	no	—
345	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
346	C₂²×C₅	—	2	4	no	—
347	C₂²×C₅	—	4	2	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
350	C₂×D₅	—	2	2	no	—
351	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
355	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
356	Dic₅	—	2	2	no	—
357	Dic₅	—	2	4	no	—
358	Dic₅	—	4	2	no	—
359	Dic₅	C₃×C₄×D₄	1	2	yes	—
360	#41	—	5	8	no	—
361	#41	—	10	4	no	—
362	C₂×Q₈	—	5	2	no	—
363	C₂×D₄	—	10	2	no	—
364	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	10	2	no	—
369	C₂²×C₄	—	10	2	no	—
370	Q₁₆	—	5	4	no	—
371	SD₁₆	—	5	8	no	—
372	D₈	C₃×C₄×D₅	1	4	yes	complemented
373	C₂×C₈	—	5	1	no	—
374	C₂×C₈	—	5	4	no	—
375	C₂×C₈	—	5	1	no	—
376	C₂×C₈	—	10	2	no	—
377	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
378	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₄⋊C₄	—	5	2	no	—
380	C₄⋊C₄	—	10	2	no	—
381	C₄⋊C₄	—	10	2	no	—
382	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	10	2	no	—
385	C₂²⋊C₄	—	10	2	no	—
386	C₄²	—	5	2	no	—
387	C₄²	—	5	1	no	—
388	C₄²	—	10	2	no	—
389	C₄²	—	10	2	no	—
390	C₄²	—	10	2	no	—
391	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₃×C₅	#2943	1	1	yes	characteristic, complemented, Hall
393	C₂²×C₃	—	2	4	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	5	2	no	—
397	C₂²×C₃	—	10	2	no	—
398	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	5	2	no	—
402	C₃×C₄	—	10	2	no	—
403	C₃×C₄	—	10	4	no	—
404	C₃×C₄	—	20	2	no	—
405	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
406	C₃×C₄	D₅×#41	1	1	yes	characteristic
407	C₂×C₅	—	4	4	no	—
408	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
409	C₂×C₅	C₃×#575	1	2	yes	—
410	D₅	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	5	1	no	—
413	Q₈	—	5	4	no	—
414	Q₈	—	10	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	10	8	no	—
417	D₄	C₂×C₃×C₄×D₅	1	4	yes	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	4	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	8	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	—	20	2	no	—
428	C₂×C₄	—	20	4	no	—
429	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
430	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	5	2	no	—
433	C₈	—	10	1	no	—
434	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
435	C₂×C₃	—	4	4	no	—
436	C₂×C₃	—	10	2	no	—
437	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
438	C₂×C₃	#66107	1	2	yes	—
439	C₅	C₃×#2943	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	2	4	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	5	2	no	—
444	C₂²	—	10	2	no	—
445	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	5	2	no	—
449	C₄	—	10	2	no	—
450	C₄	—	10	4	no	—
451	C₄	—	20	2	no	—
452	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
453	C₄	C₃×D₅×#41	1	1	yes	characteristic
454	C₃	#10611595	1	1	yes	characteristic, direct product factor, Sylow
455	C₂	—	4	4	no	—
456	C₂	—	10	2	no	—
457	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
458	C₂	C₃×#66107	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4058	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#442	D₅
hypocenter	C₅	C₃×#2943
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#442

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#711	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₃×#65441	C₂	semidirect
5. C₃×#65307	C₂	semidirect
6. C₃×#65149	C₂	semidirect
7. C₃×#65142	C₂	semidirect
8. C₃×#65061	C₂	semidirect
9. C₃×#65046	C₂	semidirect
10. C₃×#65005	C₂	semidirect
11. C₃×D₅×#97	C₂	semidirect
12. #10611595	C₃	direct (N × H)
20. C₃×#4058	C₄	semidirect
43. C₄×#711	C₂×C₃	semidirect
44. C₅×#442	C₂×C₃	semidirect
45. #65441	C₂×C₃	semidirect
46. #65307	C₂×C₃	semidirect
47. #65149	C₂×C₃	semidirect
48. #65142	C₂×C₃	semidirect
49. #65061	C₂×C₃	semidirect
50. #65046	C₂×C₃	semidirect
51. #65005	C₂×C₃	semidirect
52. D₅×#97	C₂×C₃	semidirect
59. C₃×#711	C₂×C₄	semidirect
63. C₃×C₅×D₈	C₂×C₄	semidirect
70. C₃×#687	C₂×C₄	semidirect
82. C₃×Dic₂₀	C₂×C₄	semidirect
84. C₃×C₈×D₅	C₂×C₄	semidirect
88. C₃×#442	D₅	semidirect
103. #4058	C₃×C₄	semidirect
183. #711	C₂×C₃×C₄	semidirect
187. C₅×D₈	C₂×C₃×C₄	semidirect
194. #687	C₂×C₃×C₄	semidirect
206. Dic₂₀	C₂×C₃×C₄	semidirect
208. C₈×D₅	C₂×C₃×C₄	semidirect
212. #442	C₃×D₅	semidirect
246. C₃×D₈	C₄×D₅	semidirect
372. D₈	C₃×C₄×D₅	semidirect
392. C₃×C₅	#2943	semidirect
439. C₅	C₃×#2943	semidirect
454. C₃	#10611595	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×#4058	2
C₃×C₄×#711	2
C₃×C₅×#442	2
C₃×#65441	2
C₃×#65307	2
C₃×#65149	2
C₃×#65142	2
C₃×#65061	2
C₃×#65046	2
C₃×#65005	2
C₃×D₅×#97	2
#10611595	3
C₃×#2943	5

Subgroups — C3×#10611595 #14416539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611595 #14416539