Subgroups — C₃×#10600803 #14297268

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66283	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65529	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65428	C₂	1	2	yes	maximal, complemented
5	C₃×#65402	C₂	1	2	yes	maximal, complemented
6	#10600803	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₃×#4150	—	2	2	no	—
9	C₃×#4149	—	2	2	no	—
10	C₃×D₅×#41	—	2	4	no	—
11	C₃×#4147	C₄	1	2	yes	complemented
12	C₃×#4144	—	2	2	no	—
13	C₃×#4144	C₄	1	2	yes	complemented
14	C₂×C₃×#709	—	2	2	no	—
15	C₂×C₃×#709	C₂²	1	2	yes	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×#4072	C₂²	1	2	yes	complemented
19	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
20	C₃×#3966	—	2	2	no	—
21	C₃×#3957	—	2	4	no	—
22	C₃×#3953	—	2	2	no	—
23	C₃×#3948	—	2	2	no	—
24	C₃×#1794	—	5	1	no	maximal, Hall
25	#66283	C₂×C₃	1	1	yes	characteristic
26	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
27	#65529	C₂×C₃	1	1	yes	characteristic, complemented
28	#65428	C₂×C₃	1	2	yes	complemented
29	#65402	C₂×C₃	1	2	yes	complemented
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
38	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
39	C₃×#713	—	2	4	no	—
40	C₃×Q₈×D₅	—	2	4	no	—
41	C₃×#711	—	2	8	no	—
42	C₃×#711	—	2	4	no	—
43	C₃×D₄×D₅	—	2	8	no	—
44	C₃×D₄×D₅	—	2	4	no	—
45	C₃×#709	—	2	4	no	—
46	C₃×#709	—	2	4	no	—
47	C₃×#709	—	2	4	no	—
48	C₃×#709	—	2	2	no	—
49	C₃×#709	—	2	2	no	—
50	C₃×#709	C₂×C₄	1	4	yes	—
51	C₃×#709	D₄	1	4	yes	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	D₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	—	2	4	no	—
55	C₂×C₃×C₄×D₅	—	2	2	no	—
56	C₂×C₃×Dic₁₀	—	2	2	no	—
57	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
58	C₃×C₅×M₁₆	—	2	2	no	—
59	C₂×C₃×C₅×C₈	—	2	2	no	—
60	C₂×C₃×C₅×C₈	—	2	1	no	—
61	C₂×C₃×C₅×C₈	—	2	1	no	—
62	C₃×C₂²⋊Dic₅	—	2	2	no	—
63	C₃×C₄⋊Dic₅	—	2	2	no	—
64	C₃×C₄×Dic₅	—	2	2	no	—
65	C₃×#585	—	5	1	no	—
66	C₃×#421	—	5	2	no	—
67	C₃×#416	—	5	2	no	—
68	C₃×#410	—	5	1	no	—
69	C₃×#408	D₅	1	1	yes	characteristic, complemented
70	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
71	#4150	—	2	2	no	—
72	#4149	—	2	2	no	—
73	D₅×#41	—	2	4	no	—
74	#4147	C₃×C₄	1	2	yes	complemented
75	#4144	—	2	2	no	—
76	#4144	C₃×C₄	1	2	yes	complemented
77	C₂×#709	—	2	2	no	—
78	C₂×#709	C₂²×C₃	1	2	yes	—
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
81	#4072	C₂²×C₃	1	2	yes	complemented
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	#3966	—	2	2	no	—
84	#3957	—	2	4	no	—
85	#3953	—	2	2	no	—
86	#3948	—	2	2	no	—
87	#1794	—	5	1	no	Sylow
88	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	4	no	—
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₃×C₅×Q₈	—	2	2	no	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₃×C₂²⋊D₅	—	2	8	no	—
103	C₃×C₂²⋊D₅	—	2	4	no	—
104	C₃×C₂²⋊D₅	—	2	4	no	—
105	C₂×C₃×Dic₅	—	2	4	no	—
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	4	2	no	—
108	C₃×D₂₀	—	2	4	no	—
109	C₃×D₂₀	—	2	2	no	—
110	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
111	C₃×C₄×D₅	—	2	8	no	—
112	C₃×C₄×D₅	—	2	4	no	—
113	C₃×C₄×D₅	—	2	4	no	—
114	C₃×Dic₁₀	—	2	4	no	—
115	C₃×Dic₁₀	—	2	2	no	—
116	C₃×Dic₁₀	C₂²⋊C₄	1	4	yes	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₃×C₅×C₈	—	4	1	no	—
119	C₃×2₋¹⁺⁴	—	5	2	no	—
120	C₃×2₋¹⁺⁴	—	10	2	no	—
121	C₃×H(5,𝔽₂)	—	5	2	no	—
122	C₃×H(5,𝔽₂)	—	10	2	no	—
123	C₃×H(5,𝔽₂)	—	10	2	no	—
124	C₂×C₃×#41	—	5	2	no	—
125	C₂×C₃×#41	—	10	4	no	—
126	C₂×C₃×#41	—	10	2	no	—
127	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
129	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
130	C₃×#117	—	5	2	no	—
131	C₃×#104	—	10	4	no	—
132	C₃×#103	—	10	2	no	—
133	C₃×#102	—	10	2	no	—
134	C₃×#99	—	10	2	no	—
135	C₃×C₂²⋊C₈	—	2	2	no	—
136	C₅×#41	—	2	2	no	—
137	C₅×#41	—	2	2	no	—
138	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
141	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₂²⋊D₅	—	2	4	no	—
144	C₂×C₂²⋊D₅	—	2	2	no	—
145	#713	—	2	4	no	—
146	Q₈×D₅	—	2	4	no	—
147	#711	—	2	8	no	—
148	#711	—	2	4	no	—
149	D₄×D₅	—	2	8	no	—
150	D₄×D₅	—	2	4	no	—
151	#709	—	2	4	no	—
152	#709	—	2	4	no	—
153	#709	—	2	4	no	—
154	#709	—	2	2	no	—
155	#709	—	2	2	no	—
156	#709	C₂×C₃×C₄	1	4	yes	—
157	#709	C₃×D₄	1	4	yes	—
158	C₂×D₂₀	—	2	2	no	—
159	C₂×D₂₀	C₃×D₄	1	2	yes	—
160	C₂×C₄×D₅	—	2	4	no	—
161	C₂×C₄×D₅	—	2	2	no	—
162	C₂×Dic₁₀	—	2	2	no	—
163	C₂×Dic₁₀	C₃×D₄	1	2	yes	—
164	C₅×M₁₆	—	2	2	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂²⋊Dic₅	—	2	2	no	—
169	C₄⋊Dic₅	—	2	2	no	—
170	C₄×Dic₅	—	2	2	no	—
171	#585	—	5	1	no	—
172	#421	—	5	2	no	—
173	#416	—	5	2	no	—
174	#410	—	5	1	no	—
175	#408	C₃×D₅	1	1	yes	characteristic, complemented
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	4	1	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	#120	1	2	yes	—
181	C₂×C₃×D₅	—	2	4	no	—
182	C₂×C₃×D₅	—	8	2	no	—
183	C₂×C₃×D₅	—	8	4	no	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
186	C₃×C₄×C₅	#120	1	1	yes	characteristic
187	C₃×C₄×C₅	#120	1	1	yes	characteristic
188	C₃×Dic₅	—	2	4	no	—
189	C₃×Dic₅	—	8	2	no	—
190	C₃×#41	—	2	2	no	—
191	C₃×#41	—	2	2	no	—
192	C₃×#41	—	5	4	no	—
193	C₃×#41	—	5	4	no	—
194	C₃×#41	—	10	4	no	—
195	C₃×#41	—	10	4	no	—
196	C₃×#41	—	10	4	no	—
197	C₃×#41	—	10	8	no	—
198	C₃×#41	—	10	4	no	—
199	C₃×#41	—	10	4	no	—
200	C₃×#41	—	10	2	no	—
201	C₃×#41	—	10	2	no	—
202	C₂×C₃×Q₈	—	5	2	no	—
203	C₂×C₃×Q₈	—	10	2	no	—
204	C₂×C₃×Q₈	—	10	4	no	—
205	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
206	C₂×C₃×D₄	—	5	2	no	—
207	C₂×C₃×D₄	—	10	2	no	—
208	C₂×C₃×D₄	—	10	4	no	—
209	C₂×C₃×D₄	—	10	8	no	—
210	C₂×C₃×D₄	—	10	4	no	—
211	C₂×C₃×D₄	—	10	2	no	—
212	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
213	C₂×C₃×D₄	D₂₀	1	2	yes	—
214	C₂²×C₃×C₄	—	10	4	no	—
215	C₂²×C₃×C₄	—	10	2	no	—
216	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
218	C₃×M₁₆	—	2	2	no	—
219	C₂×C₃×C₈	—	2	2	no	—
220	C₂×C₃×C₈	—	2	1	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₃×C₄⋊C₄	—	10	2	no	—
223	C₃×C₂²⋊C₄	—	10	2	no	—
224	C₃×C₄²	—	10	2	no	—
225	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
226	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂²×D₅	—	2	4	no	—
228	C₂²×D₅	—	2	2	no	—
229	C₅×Q₈	—	2	2	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
238	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂²⋊D₅	—	2	8	no	—
240	C₂²⋊D₅	—	2	4	no	—
241	C₂²⋊D₅	—	2	4	no	—
242	C₂×Dic₅	—	2	4	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	4	2	no	—
245	D₂₀	—	2	4	no	—
246	D₂₀	—	2	2	no	—
247	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
248	C₄×D₅	—	2	8	no	—
249	C₄×D₅	—	2	4	no	—
250	C₄×D₅	—	2	4	no	—
251	Dic₁₀	—	2	4	no	—
252	Dic₁₀	—	2	2	no	—
253	Dic₁₀	C₃×C₂²⋊C₄	1	4	yes	—
254	C₅×C₈	—	4	1	no	—
255	C₅×C₈	—	4	1	no	—
256	2₋¹⁺⁴	—	5	2	no	—
257	2₋¹⁺⁴	—	10	2	no	—
258	H(5,𝔽₂)	—	5	2	no	—
259	H(5,𝔽₂)	—	10	2	no	—
260	H(5,𝔽₂)	—	10	2	no	—
261	C₂×#41	—	5	2	no	—
262	C₂×#41	—	10	4	no	—
263	C₂×#41	—	10	2	no	—
264	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
265	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
266	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
267	#117	—	5	2	no	—
268	#104	—	10	4	no	—
269	#103	—	10	2	no	—
270	#102	—	10	2	no	—
271	#99	—	10	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	4	2	no	—
276	C₂×C₃×C₅	#379	1	1	yes	characteristic
277	C₃×D₅	—	4	4	no	—
278	C₂³×C₃	—	10	4	no	—
279	C₂³×C₃	—	10	2	no	—
280	C₂³×C₃	#685	1	2	yes	—
281	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
282	C₃×Q₈	—	2	2	no	—
283	C₃×Q₈	—	5	4	no	—
284	C₃×Q₈	—	10	4	no	—
285	C₃×Q₈	—	10	2	no	—
286	C₃×D₄	—	2	4	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	5	4	no	—
289	C₃×D₄	—	10	4	no	—
290	C₃×D₄	—	10	8	no	—
291	C₃×D₄	—	10	4	no	—
292	C₃×D₄	—	10	4	no	—
293	C₃×D₄	—	10	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	10	8	no	—
297	C₂×C₃×C₄	—	10	4	no	—
298	C₂×C₃×C₄	—	10	2	no	—
299	C₂×C₃×C₄	—	10	4	no	—
300	C₂×C₃×C₄	—	10	4	no	—
301	C₂×C₃×C₄	—	20	2	no	—
302	C₂×C₃×C₄	#685	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
304	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
305	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
307	C₃×C₈	—	4	1	no	—
308	C₃×C₈	—	4	1	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
313	C₂²×C₅	C₃×#120	1	2	yes	—
314	C₂×D₅	—	2	4	no	—
315	C₂×D₅	—	8	2	no	—
316	C₂×D₅	—	8	4	no	—
317	C₄×C₅	—	2	2	no	—
318	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
319	C₄×C₅	C₃×#120	1	1	yes	characteristic
320	C₄×C₅	C₃×#120	1	1	yes	characteristic
321	Dic₅	—	2	4	no	—
322	Dic₅	—	8	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	5	4	no	—
326	#41	—	5	4	no	—
327	#41	—	10	4	no	—
328	#41	—	10	4	no	—
329	#41	—	10	4	no	—
330	#41	—	10	8	no	—
331	#41	—	10	4	no	—
332	#41	—	10	4	no	—
333	#41	—	10	2	no	—
334	#41	—	10	2	no	—
335	C₂×Q₈	—	5	2	no	—
336	C₂×Q₈	—	10	2	no	—
337	C₂×Q₈	—	10	4	no	—
338	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
339	C₂×D₄	—	5	2	no	—
340	C₂×D₄	—	10	2	no	—
341	C₂×D₄	—	10	4	no	—
342	C₂×D₄	—	10	8	no	—
343	C₂×D₄	—	10	4	no	—
344	C₂×D₄	—	10	2	no	—
345	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
346	C₂×D₄	C₃×D₂₀	1	2	yes	—
347	C₂²×C₄	—	10	4	no	—
348	C₂²×C₄	—	10	2	no	—
349	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
350	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
351	M₁₆	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₄⋊C₄	—	10	2	no	—
356	C₂²⋊C₄	—	10	2	no	—
357	C₄²	—	10	2	no	—
358	C₃×C₅	#1794	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	4	1	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	10	4	no	—
363	C₂²×C₃	—	40	2	no	—
364	C₂²×C₃	—	40	4	no	—
365	C₂²×C₃	#4028	1	2	yes	—
366	C₂²×C₃	C₂×#685	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	10	4	no	—
369	C₃×C₄	—	40	2	no	—
370	C₃×C₄	D₅×C₂²⋊C₄	1	2	yes	—
371	C₃×C₄	#4083	1	1	yes	characteristic
372	C₃×C₄	#4083	1	1	yes	characteristic
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	—	2	1	no	—
375	C₂×C₅	—	4	2	no	—
376	C₂×C₅	C₃×#379	1	1	yes	characteristic
377	D₅	—	4	4	no	—
378	C₂³	—	10	4	no	—
379	C₂³	—	10	2	no	—
380	C₂³	C₃×#685	1	2	yes	—
381	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	5	4	no	—
384	Q₈	—	10	4	no	—
385	Q₈	—	10	2	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	2	no	—
388	D₄	—	5	4	no	—
389	D₄	—	10	4	no	—
390	D₄	—	10	8	no	—
391	D₄	—	10	4	no	—
392	D₄	—	10	4	no	—
393	D₄	—	10	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	10	8	no	—
397	C₂×C₄	—	10	4	no	—
398	C₂×C₄	—	10	2	no	—
399	C₂×C₄	—	10	4	no	—
400	C₂×C₄	—	10	4	no	—
401	C₂×C₄	—	20	2	no	—
402	C₂×C₄	C₃×#685	1	2	yes	—
403	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
404	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
405	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
406	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₂×C₃	—	2	2	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	—	20	4	no	—
413	C₂×C₃	#65244	1	1	yes	characteristic
414	C₅	C₃×#1794	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	2	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	10	4	no	—
419	C₂²	—	40	2	no	—
420	C₂²	—	40	4	no	—
421	C₂²	C₃×#4028	1	2	yes	—
422	C₂²	C₂×C₃×#685	1	1	yes	characteristic
423	C₄	—	2	2	no	—
424	C₄	—	10	4	no	—
425	C₄	—	40	2	no	—
426	C₄	C₃×D₅×C₂²⋊C₄	1	2	yes	—
427	C₄	C₃×#4083	1	1	yes	characteristic
428	C₄	C₃×#4083	1	1	yes	characteristic
429	C₃	#10600803	1	1	yes	characteristic, direct product factor, Sylow
430	C₂	—	2	2	no	—
431	C₂	—	2	1	no	—
432	C₂	—	4	2	no	—
433	C₂	—	20	4	no	—
434	C₂	C₃×#65244	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#4083
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#408	C₂
socle	C₂×C₃×C₅	#379
prime radical	C₃×#66283	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#408	D₅
hypocenter	C₅	C₃×#1794
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#408

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#408	C₂	semidirect
3. C₃×#65529	C₂	semidirect
4. C₃×#65428	C₂	semidirect
5. C₃×#65402	C₂	semidirect
6. #10600803	C₃	direct (N × H)
11. C₃×#4147	C₄	semidirect
13. C₃×#4144	C₄	semidirect
16. C₂×C₃×C₅×M₁₆	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×#4072	C₂²	semidirect
26. C₅×#408	C₂×C₃	semidirect
27. #65529	C₂×C₃	semidirect
28. #65428	C₂×C₃	semidirect
29. #65402	C₂×C₃	semidirect
69. C₃×#408	D₅	semidirect
74. #4147	C₃×C₄	semidirect
76. #4144	C₃×C₄	semidirect
79. C₂×C₅×M₁₆	C₂²×C₃	semidirect
80. C₂²×C₅×C₈	C₂²×C₃	semidirect
81. #4072	C₂²×C₃	semidirect
128. C₂×C₃×M₁₆	C₂×D₅	semidirect
129. C₂²×C₃×C₈	C₂×D₅	semidirect
175. #408	C₃×D₅	semidirect
265. C₂×M₁₆	C₂×C₃×D₅	semidirect
266. C₂²×C₈	C₂×C₃×D₅	semidirect
358. C₃×C₅	#1794	semidirect
414. C₅	C₃×#1794	semidirect
429. C₃	#10600803	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×#66283	2
C₃×C₅×#408	2
C₃×#65529	2
C₃×#65428	2
C₃×#65402	2
#10600803	3
C₃×#1794	5

Subgroups — C3×#10600803 #14297268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600803 #14297268