Subgroups — C₃×#10615407 #14472062

Order 1920.

672 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	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic
2	C₃×#65901	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65345	C₂	1	2	yes	maximal
6	C₃×#65343	C₂	1	2	yes	maximal
7	C₃×C₄×#689	C₂	1	2	yes	maximal, complemented
8	C₃×Q₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65311	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#687	C₂	1	1	yes	maximal, characteristic
11	C₃×#65296	C₂	1	1	yes	maximal, characteristic
12	#10615407	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#126	—	2	2	no	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₃×#4090	—	2	1	no	—
22	C₂×C₃×#689	C₂²	1	2	yes	—
23	C₂×C₃×#687	C₂²	1	1	yes	characteristic
24	C₃×#4035	—	2	2	no	—
25	C₃×#4033	—	2	1	no	—
26	C₃×#4016	C₂²	1	2	yes	—
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
30	C₃×#3967	C₂²	1	2	yes	—
31	C₃×#3967	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	1	yes	characteristic
35	C₃×#3942	C₂²	1	1	yes	characteristic
36	C₃×#3940	C₂²	1	1	yes	characteristic
37	C₃×#3939	C₂²	1	2	yes	—
38	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊#168	C₂²	1	2	yes	—
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	2	yes	—
42	C₃×#3364	—	5	1	no	maximal, Hall
43	C₅×#556	C₂×C₃	1	1	yes	characteristic
44	#65901	C₂×C₃	1	1	yes	characteristic, complemented
45	#65379	C₂×C₃	1	1	yes	characteristic, complemented
46	#65370	C₂×C₃	1	1	yes	characteristic, complemented
47	#65345	C₂×C₃	1	2	yes	—
48	#65343	C₂×C₃	1	2	yes	—
49	C₄×#689	C₂×C₃	1	2	yes	complemented
50	Q₈×#168	C₂×C₃	1	1	yes	characteristic, complemented
51	#65311	C₂×C₃	1	2	yes	complemented
52	C₄×#687	C₂×C₃	1	1	yes	characteristic
53	#65296	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₃×Dic₁₀	—	2	1	no	—
59	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	2	yes	—
72	C₃×#689	—	2	4	no	—
73	C₃×#687	—	2	2	no	—
74	C₃×C₄⋊Dic₅	—	2	1	no	—
75	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
77	C₃×#683	—	2	2	no	—
78	C₃×#683	—	2	2	no	—
79	C₃×#683	—	2	1	no	—
80	C₃×#683	—	2	2	no	—
81	C₃×C₄×Dic₅	—	2	1	no	—
82	C₃×C₄×Dic₅	—	2	2	no	—
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₃×#557	—	5	1	no	—
87	C₃×#556	D₅	1	1	yes	characteristic
88	C₃×#488	—	5	2	no	—
89	C₃×#487	—	5	1	no	—
90	C₃×#479	—	5	2	no	—
91	C₃×#474	—	5	1	no	—
92	C₃×#464	—	5	2	no	—
93	C₃×#462	—	5	1	no	—
94	C₃×C₈×Q₈	—	5	1	no	—
95	C₃×C₄×Q₁₆	—	5	2	no	—
96	C₃×C₄×SD₁₆	—	5	1	no	—
97	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₅×#126	—	2	2	no	—
99	C₅×#124	C₂²×C₃	1	2	yes	—
100	C₅×C₂²⋊Q₈	—	2	1	no	—
101	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
102	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₅×#117	—	2	1	no	—
105	#4090	—	2	1	no	—
106	C₂×#689	C₂²×C₃	1	2	yes	—
107	C₂×#687	C₂²×C₃	1	1	yes	characteristic
108	#4035	—	2	2	no	—
109	#4033	—	2	1	no	—
110	#4016	C₂²×C₃	1	2	yes	—
111	#4015	C₂²×C₃	1	1	yes	characteristic
112	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
114	#3967	C₂²×C₃	1	2	yes	—
115	#3967	C₂²×C₃	1	2	yes	—
116	#3967	C₂²×C₃	1	2	yes	—
117	#3964	C₂²×C₃	1	2	yes	—
118	#3964	C₂²×C₃	1	1	yes	characteristic
119	#3942	C₂²×C₃	1	1	yes	characteristic
120	#3940	C₂²×C₃	1	1	yes	characteristic
121	#3939	C₂²×C₃	1	2	yes	—
122	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊#168	C₂²×C₃	1	2	yes	—
124	C₄×#168	C₂²×C₃	1	1	yes	characteristic
125	C₄×#168	C₂²×C₃	1	2	yes	—
126	#3364	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×C₃×Dic₅	—	2	1	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₃×Dic₁₀	—	2	1	no	—
145	C₃×Dic₁₀	—	4	2	no	—
146	C₃×Dic₁₀	#41	1	2	yes	—
147	C₃×#168	—	2	1	no	—
148	C₃×#168	—	2	2	no	—
149	C₃×#168	—	2	1	no	—
150	C₂×C₃×Q₁₆	—	5	2	no	—
151	C₂×C₃×SD₁₆	—	5	1	no	—
152	C₃×C₄⋊Q₈	—	5	1	no	—
153	C₃×C₄⋊Q₈	—	10	1	no	—
154	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
155	C₃×#126	—	2	2	no	—
156	C₃×#125	—	5	2	no	—
157	C₃×#125	—	10	2	no	—
158	C₃×#124	C₂×D₅	1	2	yes	—
159	C₃×C₂²⋊Q₈	—	2	1	no	—
160	C₃×C₄×Q₈	—	5	1	no	—
161	C₃×C₄×Q₈	—	5	2	no	—
162	C₃×C₄×Q₈	—	10	1	no	—
163	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
164	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
166	C₃×#117	—	2	1	no	—
167	C₃×#107	—	5	2	no	—
168	C₃×#106	—	5	1	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₄⋊C₈	—	5	2	no	—
171	C₃×#103	—	5	2	no	—
172	C₃×#103	—	5	2	no	—
173	C₃×#103	—	5	2	no	—
174	C₃×#103	—	5	1	no	—
175	C₃×#102	—	5	1	no	—
176	C₃×#102	—	5	2	no	—
177	C₃×C₄×C₈	—	5	1	no	—
178	C₃×C₄×C₈	—	5	2	no	—
179	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
180	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
181	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂×Dic₁₀	—	2	1	no	—
184	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
190	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₄²×C₅	—	2	2	no	—
195	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₄²×C₅	C₂³×C₃	1	2	yes	—
197	#689	—	2	4	no	—
198	#687	—	2	2	no	—
199	C₄⋊Dic₅	—	2	1	no	—
200	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
201	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
202	#683	—	2	1	no	—
203	#683	—	2	2	no	—
204	#683	—	2	2	no	—
205	#683	—	2	2	no	—
206	C₄×Dic₅	—	2	2	no	—
207	C₄×Dic₅	—	2	1	no	—
208	C₂×#168	C₂³×C₃	1	1	yes	characteristic
209	C₂×#168	C₂³×C₃	1	2	yes	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	#557	—	5	1	no	—
212	#556	C₃×D₅	1	1	yes	characteristic
213	#488	—	5	2	no	—
214	#487	—	5	1	no	—
215	#479	—	5	2	no	—
216	#474	—	5	1	no	—
217	#464	—	5	2	no	—
218	#462	—	5	1	no	—
219	C₈×Q₈	—	5	1	no	—
220	C₄×Q₁₆	—	5	2	no	—
221	C₄×SD₁₆	—	5	1	no	—
222	C₂²×C₃×C₅	—	4	1	no	—
223	C₂²×C₃×C₅	—	4	1	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	1	no	—
231	C₃×C₄×C₅	#135	1	2	yes	—
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
234	C₃×Dic₅	—	2	2	no	—
235	C₃×Dic₅	—	4	2	no	—
236	C₃×Dic₅	—	4	1	no	—
237	C₂×C₃×Q₈	—	5	1	no	—
238	C₂×C₃×Q₈	—	10	1	no	—
239	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
240	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
241	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₃×Q₁₆	—	10	4	no	—
244	C₃×SD₁₆	—	10	2	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	2	no	—
247	C₂×C₃×C₈	—	5	1	no	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	5	1	no	—
252	C₃×C₄⋊C₄	—	5	2	no	—
253	C₃×C₄⋊C₄	—	10	1	no	—
254	C₃×C₄⋊C₄	—	10	2	no	—
255	C₃×C₄⋊C₄	—	10	2	no	—
256	C₃×C₄⋊C₄	—	10	2	no	—
257	C₃×C₄⋊C₄	—	10	1	no	—
258	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
260	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₂²⋊C₄	—	2	2	no	—
262	C₃×C₂²⋊C₄	—	2	1	no	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₄²	—	2	2	no	—
265	C₃×C₄²	—	10	2	no	—
266	C₃×C₄²	—	10	1	no	—
267	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
268	C₃×C₄²	C₂²×D₅	1	2	yes	—
269	C₂³×C₅	—	2	1	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	2	2	no	—
273	C₅×D₄	—	2	1	no	—
274	C₅×D₄	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
280	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
283	C₂×Dic₅	—	2	1	no	—
284	C₂×Dic₅	—	2	1	no	—
285	C₂×Dic₅	—	2	2	no	—
286	Dic₁₀	—	2	1	no	—
287	Dic₁₀	—	4	2	no	—
288	Dic₁₀	C₃×#41	1	2	yes	—
289	#168	—	2	1	no	—
290	#168	—	2	2	no	—
291	#168	—	2	1	no	—
292	C₂×Q₁₆	—	5	2	no	—
293	C₂×SD₁₆	—	5	1	no	—
294	C₄⋊Q₈	—	5	1	no	—
295	C₄⋊Q₈	—	10	1	no	—
296	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
297	#126	—	2	2	no	—
298	#125	—	5	2	no	—
299	#125	—	10	2	no	—
300	#124	C₂×C₃×D₅	1	2	yes	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₄×Q₈	—	5	1	no	—
303	C₄×Q₈	—	5	2	no	—
304	C₄×Q₈	—	10	1	no	—
305	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
306	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
307	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#107	—	5	2	no	—
310	#106	—	5	1	no	—
311	C₄⋊C₈	—	5	1	no	—
312	C₄⋊C₈	—	5	2	no	—
313	#103	—	5	2	no	—
314	#103	—	5	2	no	—
315	#103	—	5	2	no	—
316	#103	—	5	1	no	—
317	#102	—	5	1	no	—
318	#102	—	5	2	no	—
319	C₄×C₈	—	5	1	no	—
320	C₄×C₈	—	5	2	no	—
321	C₂×C₃×C₅	—	8	1	no	—
322	C₂×C₃×C₅	#548	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
324	C₂×C₃×C₅	#578	1	1	yes	characteristic
325	C₂³×C₃	—	2	1	no	—
326	C₃×Q₈	—	2	2	no	—
327	C₃×Q₈	—	2	2	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	5	2	no	—
330	C₃×Q₈	—	10	1	no	—
331	C₃×Q₈	—	20	2	no	—
332	C₃×D₄	—	2	1	no	—
333	C₃×D₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	4	2	no	—
337	C₂×C₃×C₄	—	10	1	no	—
338	C₂×C₃×C₄	—	10	1	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₃×C₈	—	10	1	no	—
346	C₃×C₈	—	10	2	no	—
347	C₃×C₈	—	10	1	no	—
348	C₂²×C₅	—	4	1	no	—
349	C₂²×C₅	—	4	1	no	—
350	C₂²×C₅	—	4	1	no	—
351	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	C₃×#135	1	2	yes	—
358	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
359	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
360	Dic₅	—	2	2	no	—
361	Dic₅	—	4	2	no	—
362	Dic₅	—	4	1	no	—
363	C₂×Q₈	—	5	1	no	—
364	C₂×Q₈	—	10	1	no	—
365	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
366	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
367	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	Q₁₆	—	10	4	no	—
370	SD₁₆	—	10	2	no	—
371	C₂×C₈	—	5	1	no	—
372	C₂×C₈	—	5	2	no	—
373	C₂×C₈	—	5	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	5	1	no	—
378	C₄⋊C₄	—	5	2	no	—
379	C₄⋊C₄	—	10	1	no	—
380	C₄⋊C₄	—	10	2	no	—
381	C₄⋊C₄	—	10	2	no	—
382	C₄⋊C₄	—	10	2	no	—
383	C₄⋊C₄	—	10	1	no	—
384	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
386	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	10	2	no	—
392	C₄²	—	10	1	no	—
393	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
394	C₄²	C₂²×C₃×D₅	1	2	yes	—
395	C₃×C₅	#3364	1	1	yes	characteristic, complemented, Hall
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	4	1	no	—
399	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	4	1	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	10	2	no	—
406	C₃×C₄	—	20	2	no	—
407	C₃×C₄	—	20	1	no	—
408	C₃×C₄	#4096	1	2	yes	—
409	C₃×C₄	D₅×#41	1	1	yes	characteristic
410	C₃×C₄	#4150	1	1	yes	characteristic
411	C₂×C₅	—	8	1	no	—
412	C₂×C₅	C₃×#548	1	1	yes	characteristic
413	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
414	C₂×C₅	C₃×#578	1	1	yes	characteristic
415	C₂³	—	2	1	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	5	2	no	—
420	Q₈	—	10	1	no	—
421	Q₈	—	20	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	10	1	no	—
428	C₂×C₄	—	10	1	no	—
429	C₂×C₄	—	10	2	no	—
430	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
431	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
432	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
433	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
434	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
435	C₈	—	10	1	no	—
436	C₈	—	10	2	no	—
437	C₈	—	10	1	no	—
438	C₂×C₃	—	8	1	no	—
439	C₂×C₃	C₂×#4096	1	1	yes	characteristic
440	C₂×C₃	#66165	1	1	yes	characteristic
441	C₂×C₃	#66172	1	1	yes	characteristic
442	C₅	C₃×#3364	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	10	2	no	—
453	C₄	—	20	2	no	—
454	C₄	—	20	1	no	—
455	C₄	C₃×#4096	1	2	yes	—
456	C₄	C₃×D₅×#41	1	1	yes	characteristic
457	C₄	C₃×#4150	1	1	yes	characteristic
458	C₃	#10615407	1	1	yes	characteristic, direct product factor, Sylow
459	C₂	—	8	1	no	—
460	C₂	C₂×C₃×#4096	1	1	yes	characteristic
461	C₂	C₃×#66165	1	1	yes	characteristic
462	C₂	C₃×#66172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×D₄	C₂³
hypercenter	C₃×#556	D₅
hypocenter	C₅	C₃×#3364
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
2. C₃×#65901	C₂	semidirect
3. C₃×#65379	C₂	semidirect
4. C₃×#65370	C₂	semidirect
7. C₃×C₄×#689	C₂	semidirect
8. C₃×Q₈×#168	C₂	semidirect
9. C₃×#65311	C₂	semidirect
12. #10615407	C₃	direct (N × H)
44. #65901	C₂×C₃	semidirect
45. #65379	C₂×C₃	semidirect
46. #65370	C₂×C₃	semidirect
49. C₄×#689	C₂×C₃	semidirect
50. Q₈×#168	C₂×C₃	semidirect
51. #65311	C₂×C₃	semidirect
395. C₃×C₅	#3364	semidirect
442. C₅	C₃×#3364	semidirect
458. C₃	#10615407	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×C₅×#556	2
C₃×#65901	2
C₃×#65379	2
C₃×#65370	2
C₃×#65345	2
C₃×#65343	2
C₃×C₄×#689	2
C₃×Q₈×#168	2
C₃×#65311	2
C₃×C₄×#687	2
C₃×#65296	2
#10615407	3
C₃×#3364	5

Subgroups — C3×#10615407 #14472062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615407 #14472062