Subgroups — C₃×#10611562 #14417535

Order 1920.

912 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	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#65906	C₂	1	2	yes	maximal
3	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#689	C₂	1	2	yes	maximal, complemented
6	C₃×#65149	C₂	1	1	yes	maximal, characteristic
7	C₃×#65142	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65091	C₂	1	2	yes	maximal
9	C₃×#65079	C₂	1	2	yes	maximal, complemented
10	C₃×#65005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64997	C₂	1	1	yes	maximal, characteristic
12	#10611562	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#689	C₂²	1	2	yes	—
18	C₃×D₅×Q₁₆	C₄	1	8	yes	complemented
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4038	—	2	2	no	—
23	C₃×#4038	C₂²	1	2	yes	—
24	C₃×#4033	—	2	2	no	—
25	C₃×#4033	C₂²	1	2	yes	—
26	C₃×#4018	—	2	2	no	—
27	C₃×#4018	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₁₀	—	2	2	no	—
29	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₃×#3967	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×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic
41	C₃×#2950	—	5	1	no	maximal, Hall
42	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
43	#65906	C₂×C₃	1	2	yes	—
44	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
45	#65473	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×#689	C₂×C₃	1	2	yes	complemented
47	#65149	C₂×C₃	1	1	yes	characteristic
48	#65142	C₂×C₃	1	1	yes	characteristic, complemented
49	#65091	C₂×C₃	1	2	yes	—
50	#65079	C₂×C₃	1	2	yes	complemented
51	#65005	C₂×C₃	1	1	yes	characteristic, complemented
52	#64997	C₂×C₃	1	1	yes	characteristic
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×Q₈×D₅	—	2	4	no	—
55	C₃×Q₈×D₅	C₂×C₄	1	8	yes	—
56	C₂×C₃×C₄×D₅	—	2	2	no	—
57	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	—	2	2	no	—
59	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
60	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×#689	C₂×C₄	1	8	yes	—
68	C₃×#685	—	2	2	no	—
69	C₃×#685	D₄	1	2	yes	—
70	C₃×C₄⋊Dic₅	—	2	2	no	—
71	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
72	C₃×#683	—	2	2	no	—
73	C₃×#683	—	2	2	no	—
74	C₃×#683	D₄	1	2	yes	—
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	—	2	2	no	—
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	—
83	C₃×#676	—	2	2	no	—
84	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
85	C₂²×C₃×Q₁₆	—	5	1	no	—
86	C₃×#519	—	5	2	no	—
87	C₃×#441	—	5	1	no	—
88	C₃×#441	—	5	1	no	—
89	C₃×#441	—	5	1	no	—
90	C₃×#441	D₅	1	1	yes	characteristic, complemented
91	C₃×C₄×Q₁₆	—	5	2	no	—
92	C₃×C₄×Q₁₆	—	5	2	no	—
93	C₃×#427	—	5	1	no	—
94	C₃×#419	—	5	2	no	—
95	C₃×#405	—	5	1	no	—
96	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
97	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
99	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×#689	C₂²×C₃	1	2	yes	—
101	D₅×Q₁₆	C₃×C₄	1	8	yes	complemented
102	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
103	C₂×#676	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
105	#4038	—	2	2	no	—
106	#4038	C₂²×C₃	1	2	yes	—
107	#4033	—	2	2	no	—
108	#4033	C₂²×C₃	1	2	yes	—
109	#4018	—	2	2	no	—
110	#4018	C₂²×C₃	1	1	yes	characteristic
111	C₄×Dic₁₀	—	2	2	no	—
112	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
113	C₅×#106	C₂²×C₃	1	1	yes	characteristic
114	C₅×#103	C₂²×C₃	1	2	yes	—
115	C₅×#97	C₂²×C₃	1	1	yes	characteristic
116	#3967	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	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
121	#3942	C₂²×C₃	1	2	yes	—
122	#3939	C₂²×C₃	1	2	yes	—
123	C₄×#168	C₂²×C₃	1	1	yes	characteristic
124	#2950	—	5	1	no	Sylow
125	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	—	2	2	no	—
134	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
136	C₃×C₄×D₅	—	2	8	no	—
137	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
138	C₃×C₄×D₅	#41	1	2	yes	—
139	C₃×Dic₁₀	—	2	2	no	—
140	C₃×Dic₁₀	—	2	8	no	—
141	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
142	C₃×C₅×C₈	—	2	1	no	—
143	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
144	C₃×#168	—	2	1	no	—
145	C₃×#168	C₂²×C₄	1	2	yes	—
146	C₂²×C₃×Q₈	—	5	2	no	—
147	C₂×C₃×Q₁₆	—	5	2	no	—
148	C₂×C₃×Q₁₆	—	5	8	no	—
149	C₂×C₃×Q₁₆	—	5	1	no	—
150	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
151	C₂×C₃×M₁₆	—	5	1	no	—
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₃×C₄×Q₈	—	5	2	no	—
154	C₃×C₄×Q₈	—	5	2	no	—
155	C₃×C₄×Q₈	—	5	2	no	—
156	C₃×C₄×Q₈	—	10	2	no	—
157	C₃×C₄×Q₈	—	10	2	no	—
158	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
159	C₃×#117	—	5	1	no	—
160	C₃×#117	—	5	2	no	—
161	C₃×#117	—	10	2	no	—
162	C₃×#117	—	10	2	no	—
163	C₃×#107	—	5	2	no	—
164	C₃×#106	—	5	1	no	—
165	C₃×#106	C₂×D₅	1	1	yes	characteristic
166	C₃×#103	—	5	2	no	—
167	C₃×#103	—	5	2	no	—
168	C₃×#103	—	5	2	no	—
169	C₃×#103	C₂×D₅	1	2	yes	—
170	C₃×#97	—	5	1	no	—
171	C₃×#97	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄×C₈	—	5	1	no	—
173	C₃×C₄×C₈	—	5	1	no	—
174	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
175	Q₈×D₅	—	2	4	no	—
176	Q₈×D₅	C₂×C₃×C₄	1	8	yes	—
177	C₂×C₄×D₅	—	2	2	no	—
178	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
179	C₂×Dic₁₀	—	2	2	no	—
180	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
181	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	—
182	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
188	#689	C₂×C₃×C₄	1	8	yes	—
189	#685	—	2	2	no	—
190	#685	C₃×D₄	1	2	yes	—
191	C₄⋊Dic₅	—	2	2	no	—
192	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
193	#683	—	2	2	no	—
194	#683	—	2	2	no	—
195	#683	C₃×D₄	1	2	yes	—
196	C₄×Dic₅	—	2	2	no	—
197	C₄×Dic₅	—	2	2	no	—
198	C₄×Dic₅	—	2	2	no	—
199	C₄×Dic₅	—	2	2	no	—
200	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
201	C₂×#168	C₂³×C₃	1	1	yes	characteristic
202	C₂×#168	C₂³×C₃	1	1	yes	characteristic
203	Dic₂₀	C₂×C₃×C₄	1	4	yes	—
204	#676	—	2	2	no	—
205	C₈×D₅	C₂×C₃×C₄	1	4	yes	—
206	C₂²×Q₁₆	—	5	1	no	—
207	#519	—	5	2	no	—
208	#441	—	5	1	no	—
209	#441	—	5	1	no	—
210	#441	—	5	1	no	—
211	#441	C₃×D₅	1	1	yes	characteristic, complemented
212	C₄×Q₁₆	—	5	2	no	—
213	C₄×Q₁₆	—	5	2	no	—
214	#427	—	5	1	no	—
215	#419	—	5	2	no	—
216	#405	—	5	1	no	—
217	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₃×D₅	—	2	2	no	—
219	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₃×Dic₅	—	2	4	no	—
226	C₃×Dic₅	—	2	2	no	—
227	C₃×Dic₅	—	4	2	no	—
228	C₃×Dic₅	C₄×D₄	1	2	yes	—
229	C₂×C₃×Q₈	—	5	8	no	—
230	C₂×C₃×Q₈	—	5	2	no	—
231	C₂×C₃×Q₈	—	10	2	no	—
232	C₂×C₃×Q₈	—	10	4	no	—
233	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
234	C₂²×C₃×C₄	—	5	1	no	—
235	C₂²×C₃×C₄	—	10	2	no	—
236	C₃×Q₁₆	—	5	8	no	—
237	C₃×Q₁₆	—	5	4	no	—
238	C₃×Q₁₆	C₄×D₅	1	4	yes	—
239	C₃×M₁₆	—	10	2	no	—
240	C₂×C₃×C₈	—	5	1	no	—
241	C₂×C₃×C₈	—	5	4	no	—
242	C₂×C₃×C₈	—	5	1	no	—
243	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
245	C₃×C₄⋊C₄	—	2	2	no	—
246	C₃×C₄⋊C₄	—	5	2	no	—
247	C₃×C₄⋊C₄	—	5	2	no	—
248	C₃×C₄⋊C₄	—	10	2	no	—
249	C₃×C₄⋊C₄	—	10	2	no	—
250	C₃×C₄⋊C₄	—	10	2	no	—
251	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
252	C₃×C₂²⋊C₄	—	5	2	no	—
253	C₃×C₂²⋊C₄	—	10	2	no	—
254	C₃×C₄²	—	2	2	no	—
255	C₃×C₄²	—	5	1	no	—
256	C₃×C₄²	—	10	2	no	—
257	C₃×C₄²	—	10	2	no	—
258	C₃×C₄²	—	10	2	no	—
259	C₃×C₄²	—	10	2	no	—
260	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
261	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
268	C₂×Dic₅	—	2	2	no	—
269	C₂×Dic₅	—	2	2	no	—
270	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
271	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
272	C₄×D₅	—	2	8	no	—
273	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
274	C₄×D₅	C₃×#41	1	2	yes	—
275	Dic₁₀	—	2	2	no	—
276	Dic₁₀	—	2	8	no	—
277	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
278	C₅×C₈	—	2	1	no	—
279	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
280	#168	—	2	1	no	—
281	#168	C₂²×C₃×C₄	1	2	yes	—
282	C₂²×Q₈	—	5	2	no	—
283	C₂×Q₁₆	—	5	2	no	—
284	C₂×Q₁₆	—	5	8	no	—
285	C₂×Q₁₆	—	5	1	no	—
286	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
287	C₂×M₁₆	—	5	1	no	—
288	C₂²×C₈	—	5	1	no	—
289	C₄×Q₈	—	5	2	no	—
290	C₄×Q₈	—	5	2	no	—
291	C₄×Q₈	—	5	2	no	—
292	C₄×Q₈	—	10	2	no	—
293	C₄×Q₈	—	10	2	no	—
294	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
295	#117	—	5	1	no	—
296	#117	—	5	2	no	—
297	#117	—	10	2	no	—
298	#117	—	10	2	no	—
299	#107	—	5	2	no	—
300	#106	—	5	1	no	—
301	#106	C₂×C₃×D₅	1	1	yes	characteristic
302	#103	—	5	2	no	—
303	#103	—	5	2	no	—
304	#103	—	5	2	no	—
305	#103	C₂×C₃×D₅	1	2	yes	—
306	#97	—	5	1	no	—
307	#97	C₂×C₃×D₅	1	1	yes	characteristic
308	C₄×C₈	—	5	1	no	—
309	C₄×C₈	—	5	1	no	—
310	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃×C₅	#578	1	2	yes	—
312	C₃×D₅	—	2	2	no	—
313	C₂³×C₃	—	5	1	no	—
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	—	5	4	no	—
316	C₃×Q₈	—	10	8	no	—
317	C₃×Q₈	—	10	2	no	—
318	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	5	1	no	—
322	C₂×C₃×C₄	—	5	2	no	—
323	C₂×C₃×C₄	—	5	2	no	—
324	C₂×C₃×C₄	—	5	2	no	—
325	C₂×C₃×C₄	—	10	8	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	2	no	—
328	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
329	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
330	C₃×C₈	—	2	1	no	—
331	C₃×C₈	—	5	2	no	—
332	C₃×C₈	—	10	1	no	—
333	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
334	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
335	C₂×D₅	—	2	2	no	—
336	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
342	Dic₅	—	2	2	no	—
343	Dic₅	—	2	4	no	—
344	Dic₅	—	4	2	no	—
345	Dic₅	C₃×C₄×D₄	1	2	yes	—
346	C₂×Q₈	—	5	8	no	—
347	C₂×Q₈	—	5	2	no	—
348	C₂×Q₈	—	10	2	no	—
349	C₂×Q₈	—	10	4	no	—
350	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
351	C₂²×C₄	—	5	1	no	—
352	C₂²×C₄	—	10	2	no	—
353	Q₁₆	—	5	8	no	—
354	Q₁₆	—	5	4	no	—
355	Q₁₆	C₃×C₄×D₅	1	4	yes	—
356	M₁₆	—	10	2	no	—
357	C₂×C₈	—	5	1	no	—
358	C₂×C₈	—	5	4	no	—
359	C₂×C₈	—	5	1	no	—
360	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
361	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	5	2	no	—
364	C₄⋊C₄	—	5	2	no	—
365	C₄⋊C₄	—	10	2	no	—
366	C₄⋊C₄	—	10	2	no	—
367	C₄⋊C₄	—	10	2	no	—
368	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
369	C₂²⋊C₄	—	5	2	no	—
370	C₂²⋊C₄	—	10	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	5	1	no	—
373	C₄²	—	10	2	no	—
374	C₄²	—	10	2	no	—
375	C₄²	—	10	2	no	—
376	C₄²	—	10	2	no	—
377	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
378	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	5	2	no	—
380	C₂²×C₃	—	10	2	no	—
381	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	4	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	5	2	no	—
386	C₃×C₄	—	10	2	no	—
387	C₃×C₄	—	10	4	no	—
388	C₃×C₄	—	20	2	no	—
389	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
390	C₃×C₄	D₅×#41	1	1	yes	characteristic
391	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
392	C₂×C₅	C₃×#578	1	2	yes	—
393	D₅	—	2	2	no	—
394	C₂³	—	5	1	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	5	4	no	—
397	Q₈	—	10	8	no	—
398	Q₈	—	10	2	no	—
399	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	2	no	—
404	C₂×C₄	—	5	2	no	—
405	C₂×C₄	—	5	2	no	—
406	C₂×C₄	—	10	8	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
410	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	5	2	no	—
413	C₈	—	10	1	no	—
414	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
415	C₂×C₃	—	10	2	no	—
416	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
417	C₂×C₃	#66113	1	2	yes	—
418	C₅	C₃×#2950	1	1	yes	characteristic, complemented, Sylow
419	C₂²	—	5	2	no	—
420	C₂²	—	10	2	no	—
421	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	5	2	no	—
426	C₄	—	10	2	no	—
427	C₄	—	10	4	no	—
428	C₄	—	20	2	no	—
429	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
430	C₄	C₃×D₅×#41	1	1	yes	characteristic
431	C₃	#10611562	1	1	yes	characteristic, direct product factor, Sylow
432	C₂	—	10	2	no	—
433	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
434	C₂	C₃×#66113	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×#441	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#441	D₅
hypocenter	C₅	C₃×#2950
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#441

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#441	C₂	semidirect
4. C₃×#65473	C₂	semidirect
5. C₃×C₄×#689	C₂	semidirect
7. C₃×#65142	C₂	semidirect
9. C₃×#65079	C₂	semidirect
10. C₃×#65005	C₂	semidirect
12. #10611562	C₃	direct (N × H)
18. C₃×D₅×Q₁₆	C₄	semidirect
44. C₅×#441	C₂×C₃	semidirect
45. #65473	C₂×C₃	semidirect
46. C₄×#689	C₂×C₃	semidirect
48. #65142	C₂×C₃	semidirect
50. #65079	C₂×C₃	semidirect
51. #65005	C₂×C₃	semidirect
90. C₃×#441	D₅	semidirect
101. D₅×Q₁₆	C₃×C₄	semidirect
211. #441	C₃×D₅	semidirect
378. C₃×C₅	#2950	semidirect
418. C₅	C₃×#2950	semidirect
431. C₃	#10611562	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×D₅×Q₁₆	2
C₃×#65906	2
C₃×C₅×#441	2
C₃×#65473	2
C₃×C₄×#689	2
C₃×#65149	2
C₃×#65142	2
C₃×#65091	2
C₃×#65079	2
C₃×#65005	2
C₃×#64997	2
#10611562	3
C₃×#2950	5

Subgroups — C3×#10611562 #14417535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611562 #14417535