Subgroups — C₃×#10599833 #14303035

Order 1920.

680 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	C₃×#66079	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65859	C₂	1	1	yes	maximal, characteristic
3	C₃×#65421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64753	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599833	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₃×#681	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₃×#4053	—	2	2	no	—
17	C₃×D₅×M₁₆	—	2	2	no	—
18	C₃×#4047	—	2	2	no	—
19	C₃×#4041	—	2	2	no	—
20	C₃×#4028	C₄	1	4	yes	—
21	C₃×#4021	—	2	1	no	—
22	C₃×#4020	—	2	1	no	—
23	C₃×#3956	—	2	1	no	—
24	C₃×#3955	—	2	1	no	—
25	C₃×#3955	—	2	2	no	—
26	C₃×#3955	—	2	2	no	—
27	C₃×#1914	—	5	1	no	maximal, Hall
28	#66079	C₂×C₃	1	1	yes	characteristic, complemented
29	#65859	C₂×C₃	1	1	yes	characteristic
30	#65421	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#344	C₂×C₃	1	1	yes	characteristic, complemented
34	#64753	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
38	C₃×#709	—	2	1	no	—
39	C₃×#709	—	2	1	no	—
40	C₃×#709	—	2	1	no	—
41	C₃×#709	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	—	2	1	no	—
44	C₂×C₃×D₂₀	—	2	1	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×D₂₀	—	2	4	no	—
49	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
51	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₂×C₃×C₅×C₈	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₃×#685	—	2	4	no	—
62	C₃×#681	—	2	1	no	—
63	C₃×#681	—	2	1	no	—
64	C₃×#681	—	2	1	no	—
65	C₃×#681	D₄	1	2	yes	complemented
66	C₂×C₃×#168	—	2	1	no	—
67	C₂×C₃×#168	—	2	1	no	—
68	C₃×#676	—	2	4	no	—
69	C₃×C₈×D₅	—	2	4	no	—
70	C₃×#568	—	5	1	no	—
71	C₃×#535	—	5	1	no	—
72	C₃×#413	—	5	1	no	—
73	C₂×C₃×#100	—	5	1	no	—
74	C₂×C₃×#100	—	5	1	no	—
75	C₃×#344	—	5	1	no	—
76	C₃×#344	D₅	1	1	yes	characteristic, complemented
77	C₂×#709	C₂²×C₃	1	1	yes	characteristic
78	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
81	C₅×#117	C₂²×C₃	1	1	yes	characteristic
82	C₂×#681	C₂²×C₃	1	1	yes	characteristic
83	C₂×#681	C₂²×C₃	1	1	yes	characteristic
84	#4053	—	2	2	no	—
85	D₅×M₁₆	—	2	2	no	—
86	#4047	—	2	2	no	—
87	#4041	—	2	2	no	—
88	#4028	C₃×C₄	1	4	yes	—
89	#4021	—	2	1	no	—
90	#4020	—	2	1	no	—
91	#3956	—	2	1	no	—
92	#3955	—	2	1	no	—
93	#3955	—	2	2	no	—
94	#3955	—	2	2	no	—
95	#1914	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	2	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	2	2	no	—
100	C₂²×C₃×D₅	—	8	2	no	—
101	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₃×C₂²⋊D₅	—	2	2	no	—
110	C₃×C₂²⋊D₅	—	2	2	no	—
111	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
112	C₃×D₂₀	—	2	1	no	—
113	C₃×D₂₀	—	2	1	no	—
114	C₃×D₂₀	—	4	1	no	—
115	C₃×D₂₀	—	4	1	no	—
116	C₃×D₂₀	—	4	1	no	—
117	C₃×D₂₀	—	4	1	no	—
118	C₃×D₂₀	—	8	4	no	—
119	C₃×C₄×D₅	—	2	2	no	—
120	C₃×C₄×D₅	—	2	2	no	—
121	C₃×Dic₁₀	—	2	1	no	—
122	C₃×Dic₁₀	—	2	1	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₃×#168	—	2	2	no	—
126	C₃×#168	—	4	1	no	—
127	C₂×C₃×#41	—	5	1	no	—
128	C₂²×C₃×D₄	—	5	1	no	—
129	C₃×#131	—	10	2	no	—
130	C₃×#131	—	10	2	no	—
131	C₂×C₃×M₁₆	—	5	1	no	—
132	C₂×C₃×M₁₆	—	5	1	no	—
133	C₂×C₃×M₁₆	—	10	2	no	—
134	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
135	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
136	C₃×#127	—	10	1	no	—
137	C₃×#124	—	10	1	no	—
138	C₃×#121	—	10	2	no	—
139	C₃×#120	—	5	4	no	—
140	C₃×#117	C₂×D₅	1	1	yes	characteristic
141	C₃×#101	—	10	1	no	—
142	C₃×#100	—	10	2	no	—
143	C₃×#100	—	10	1	no	—
144	C₃×#100	—	10	2	no	—
145	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
148	#709	—	2	1	no	—
149	#709	—	2	1	no	—
150	#709	—	2	1	no	—
151	#709	—	2	1	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×D₂₀	—	2	1	no	—
154	C₂×D₂₀	—	2	1	no	—
155	C₂×D₂₀	—	2	1	no	—
156	C₂×D₂₀	—	2	1	no	—
157	C₂×D₂₀	—	2	1	no	—
158	C₂×D₂₀	—	2	4	no	—
159	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
160	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
161	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	2	1	no	—
164	C₅×M₁₆	—	2	1	no	—
165	C₅×M₁₆	C₃×D₄	1	2	yes	complemented
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
170	C₄²×C₅	—	2	1	no	—
171	#685	—	2	4	no	—
172	#681	—	2	1	no	—
173	#681	—	2	1	no	—
174	#681	—	2	1	no	—
175	#681	C₃×D₄	1	2	yes	complemented
176	C₂×#168	—	2	1	no	—
177	C₂×#168	—	2	1	no	—
178	#676	—	2	4	no	—
179	C₈×D₅	—	2	4	no	—
180	#568	—	5	1	no	—
181	#535	—	5	1	no	—
182	#413	—	5	1	no	—
183	C₂×#100	—	5	1	no	—
184	C₂×#100	—	5	1	no	—
185	#344	—	5	1	no	—
186	#344	C₃×D₅	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
191	C₂×C₃×D₅	—	2	2	no	—
192	C₂×C₃×D₅	—	4	2	no	—
193	C₂×C₃×D₅	—	4	4	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	8	2	no	—
196	C₂×C₃×D₅	—	8	2	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	#120	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#121	1	1	yes	characteristic
201	C₃×C₄×C₅	#123	1	1	yes	characteristic
202	C₃×Dic₅	—	2	2	no	—
203	C₂⁴×C₃	—	5	2	no	—
204	C₃×#41	—	10	1	no	—
205	C₃×#41	—	10	1	no	—
206	C₃×#41	—	10	1	no	—
207	C₃×#41	—	10	1	no	—
208	C₂×C₃×Q₈	—	5	1	no	—
209	C₂×C₃×D₄	—	5	2	no	—
210	C₂×C₃×D₄	—	5	1	no	—
211	C₂×C₃×D₄	—	10	4	no	—
212	C₂×C₃×D₄	—	10	1	no	—
213	C₂×C₃×D₄	—	10	1	no	—
214	C₂×C₃×D₄	—	10	1	no	—
215	C₂×C₃×D₄	—	10	1	no	—
216	C₂×C₃×D₄	—	10	1	no	—
217	C₂×C₃×D₄	—	10	1	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	2	1	no	—
223	C₃×M₁₆	—	5	2	no	—
224	C₃×M₁₆	—	10	4	no	—
225	C₃×M₁₆	—	10	1	no	—
226	C₃×M₁₆	—	10	1	no	—
227	C₃×M₁₆	—	10	1	no	—
228	C₃×M₁₆	D₂₀	1	2	yes	complemented
229	C₂×C₃×C₈	—	2	1	no	—
230	C₂×C₃×C₈	—	2	1	no	—
231	C₂×C₃×C₈	—	10	4	no	—
232	C₂×C₃×C₈	—	10	1	no	—
233	C₂×C₃×C₈	—	10	1	no	—
234	C₃×C₄⋊C₄	—	2	1	no	—
235	C₃×C₂²⋊C₄	—	10	4	no	—
236	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
237	C₃×C₄²	—	2	1	no	—
238	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂²×D₅	—	2	2	no	—
240	C₂²×D₅	—	2	2	no	—
241	C₂²×D₅	—	2	2	no	—
242	C₂²×D₅	—	8	2	no	—
243	C₂²×D₅	C₃×C₂²⋊C₄	1	2	yes	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
250	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
251	C₂²⋊D₅	—	2	2	no	—
252	C₂²⋊D₅	—	2	2	no	—
253	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
254	D₂₀	—	2	1	no	—
255	D₂₀	—	2	1	no	—
256	D₂₀	—	4	1	no	—
257	D₂₀	—	4	1	no	—
258	D₂₀	—	4	1	no	—
259	D₂₀	—	4	1	no	—
260	D₂₀	—	8	4	no	—
261	C₄×D₅	—	2	2	no	—
262	C₄×D₅	—	2	2	no	—
263	Dic₁₀	—	2	1	no	—
264	Dic₁₀	—	2	1	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	4	1	no	—
267	#168	—	2	2	no	—
268	#168	—	4	1	no	—
269	C₂×#41	—	5	1	no	—
270	C₂²×D₄	—	5	1	no	—
271	#131	—	10	2	no	—
272	#131	—	10	2	no	—
273	C₂×M₁₆	—	5	1	no	—
274	C₂×M₁₆	—	5	1	no	—
275	C₂×M₁₆	—	10	2	no	—
276	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
277	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
278	#127	—	10	1	no	—
279	#124	—	10	1	no	—
280	#121	—	10	2	no	—
281	#120	—	5	4	no	—
282	#117	C₂×C₃×D₅	1	1	yes	characteristic
283	#101	—	10	1	no	—
284	#100	—	10	2	no	—
285	#100	—	10	1	no	—
286	#100	—	10	2	no	—
287	C₂×C₃×C₅	—	2	1	no	—
288	C₂×C₃×C₅	—	2	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	#386	1	1	yes	characteristic
291	C₃×D₅	—	4	2	no	—
292	C₃×D₅	—	8	2	no	—
293	C₂³×C₃	—	5	2	no	—
294	C₂³×C₃	—	10	2	no	—
295	C₂³×C₃	—	10	2	no	—
296	C₂³×C₃	—	10	2	no	—
297	C₂³×C₃	—	40	2	no	—
298	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
299	C₃×Q₈	—	10	1	no	—
300	C₃×Q₈	—	10	1	no	—
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	10	2	no	—
303	C₃×D₄	—	10	1	no	—
304	C₃×D₄	—	10	1	no	—
305	C₃×D₄	—	20	1	no	—
306	C₃×D₄	—	20	1	no	—
307	C₃×D₄	—	20	1	no	—
308	C₃×D₄	—	20	1	no	—
309	C₃×D₄	—	40	4	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	5	2	no	—
312	C₂×C₃×C₄	—	10	2	no	—
313	C₂×C₃×C₄	—	10	2	no	—
314	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
315	C₂×C₃×C₄	#709	1	1	yes	characteristic
316	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
317	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
318	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
319	C₂×C₃×C₄	#713	1	1	yes	characteristic
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	4	1	no	—
322	C₃×C₈	—	10	2	no	—
323	C₃×C₈	—	20	1	no	—
324	C₂²×C₅	—	4	1	no	—
325	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
327	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
328	C₂×D₅	—	2	2	no	—
329	C₂×D₅	—	4	2	no	—
330	C₂×D₅	—	4	4	no	—
331	C₂×D₅	—	4	2	no	—
332	C₂×D₅	—	8	2	no	—
333	C₂×D₅	—	8	2	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	C₃×#120	1	1	yes	characteristic
336	C₄×C₅	C₃×#121	1	1	yes	characteristic
337	C₄×C₅	C₃×#121	1	1	yes	characteristic
338	C₄×C₅	C₃×#123	1	1	yes	characteristic
339	Dic₅	—	2	2	no	—
340	C₂⁴	—	5	2	no	—
341	#41	—	10	1	no	—
342	#41	—	10	1	no	—
343	#41	—	10	1	no	—
344	#41	—	10	1	no	—
345	C₂×Q₈	—	5	1	no	—
346	C₂×D₄	—	5	2	no	—
347	C₂×D₄	—	5	1	no	—
348	C₂×D₄	—	10	4	no	—
349	C₂×D₄	—	10	1	no	—
350	C₂×D₄	—	10	1	no	—
351	C₂×D₄	—	10	1	no	—
352	C₂×D₄	—	10	1	no	—
353	C₂×D₄	—	10	1	no	—
354	C₂×D₄	—	10	1	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	5	2	no	—
361	M₁₆	—	10	4	no	—
362	M₁₆	—	10	1	no	—
363	M₁₆	—	10	1	no	—
364	M₁₆	—	10	1	no	—
365	M₁₆	C₃×D₂₀	1	2	yes	complemented
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	10	4	no	—
369	C₂×C₈	—	10	1	no	—
370	C₂×C₈	—	10	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	10	4	no	—
373	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
374	C₄²	—	2	1	no	—
375	C₃×C₅	#1914	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	—	10	2	no	—
378	C₂²×C₃	—	20	2	no	—
379	C₂²×C₃	—	20	4	no	—
380	C₂²×C₃	—	20	2	no	—
381	C₂²×C₃	—	40	2	no	—
382	C₂²×C₃	—	40	2	no	—
383	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
384	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
385	C₂²×C₃	#4039	1	1	yes	characteristic
386	C₃×C₄	—	4	2	no	—
387	C₃×C₄	—	10	2	no	—
388	C₃×C₄	#4028	1	1	yes	characteristic
389	C₃×C₄	#4030	1	1	yes	characteristic
390	C₃×C₄	#4040	1	1	yes	characteristic
391	C₃×C₄	#4041	1	1	yes	characteristic
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	C₃×#386	1	1	yes	characteristic
396	D₅	—	4	2	no	—
397	D₅	—	8	2	no	—
398	C₂³	—	5	2	no	—
399	C₂³	—	10	2	no	—
400	C₂³	—	10	2	no	—
401	C₂³	—	10	2	no	—
402	C₂³	—	40	2	no	—
403	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
404	Q₈	—	10	1	no	—
405	Q₈	—	10	1	no	—
406	D₄	—	10	2	no	—
407	D₄	—	10	2	no	—
408	D₄	—	10	1	no	—
409	D₄	—	10	1	no	—
410	D₄	—	20	1	no	—
411	D₄	—	20	1	no	—
412	D₄	—	20	1	no	—
413	D₄	—	20	1	no	—
414	D₄	—	40	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	10	2	no	—
419	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
420	C₂×C₄	C₃×#709	1	1	yes	characteristic
421	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
422	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
423	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
424	C₂×C₄	C₃×#713	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	10	2	no	—
428	C₈	—	20	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	20	2	no	—
433	C₂×C₃	—	40	2	no	—
434	C₂×C₃	#64954	1	1	yes	characteristic
435	C₅	C₃×#1914	1	1	yes	characteristic, complemented, Sylow
436	C₂²	—	4	1	no	—
437	C₂²	—	10	2	no	—
438	C₂²	—	20	2	no	—
439	C₂²	—	20	4	no	—
440	C₂²	—	20	2	no	—
441	C₂²	—	40	2	no	—
442	C₂²	—	40	2	no	—
443	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
444	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
445	C₂²	C₃×#4039	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	10	2	no	—
448	C₄	C₃×#4028	1	1	yes	characteristic
449	C₄	C₃×#4030	1	1	yes	characteristic
450	C₄	C₃×#4040	1	1	yes	characteristic
451	C₄	C₃×#4041	1	1	yes	characteristic
452	C₃	#10599833	1	1	yes	characteristic, direct product factor, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	20	2	no	—
457	C₂	—	40	2	no	—
458	C₂	C₃×#64954	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#64954
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#344	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₃×#65859	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#344	D₅
hypocenter	C₅	C₃×#1914
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#344

Complements

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

N	H ≅ G/N	type
1. C₃×#66079	C₂	semidirect
3. C₃×#65421	C₂	semidirect
4. C₂×C₃×#3955	C₂	semidirect
5. C₂×C₃×#3955	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₃×#64753	C₂	semidirect
8. #10599833	C₃	direct (N × H)
28. #66079	C₂×C₃	semidirect
30. #65421	C₂×C₃	semidirect
31. C₂×#3955	C₂×C₃	semidirect
32. C₂×#3955	C₂×C₃	semidirect
33. C₅×#344	C₂×C₃	semidirect
34. #64753	C₂×C₃	semidirect
55. C₃×C₅×M₁₆	D₄	semidirect
65. C₃×#681	D₄	semidirect
76. C₃×#344	D₅	semidirect
165. C₅×M₁₆	C₃×D₄	semidirect
175. #681	C₃×D₄	semidirect
186. #344	C₃×D₅	semidirect
228. C₃×M₁₆	D₂₀	semidirect
365. M₁₆	C₃×D₂₀	semidirect
375. C₃×C₅	#1914	semidirect
435. C₅	C₃×#1914	semidirect
452. C₃	#10599833	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×#66079	2
C₃×#65859	2
C₃×#65421	2
C₂×C₃×#3955	2
C₃×C₅×#344	2
C₃×#64753	2
#10599833	3
C₃×#1914	5

Subgroups — C3×#10599833 #14303035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599833 #14303035