Subgroups — C₃×#10615645 #14427790

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66162	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	2	yes	maximal, complemented
5	C₃×#65477	C₂	1	2	yes	maximal, complemented
6	C₃×#65460	C₂	1	4	yes	maximal, complemented
7	C₃×#65446	C₂	1	2	yes	maximal, complemented
8	C₃×#65395	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615645	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×#4092	C₂²	1	4	yes	—
18	C₃×#4084	C₂²	1	4	yes	—
19	C₃×#4083	—	2	2	no	—
20	C₃×#4081	—	2	2	no	—
21	C₃×C₄×C₂²⋊D₅	—	2	4	no	—
22	C₃×#4072	C₂²	1	2	yes	—
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₈×D₅	—	2	4	no	—
25	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
26	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
27	C₃×#3967	C₂²	1	4	yes	complemented
28	C₃×#3964	C₂²	1	4	yes	complemented
29	C₃×#3950	C₂²	1	2	yes	complemented
30	C₃×#3949	C₂²	1	2	yes	complemented
31	C₃×#3050	—	5	1	no	maximal, Hall
32	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
33	#66162	C₂×C₃	1	2	yes	complemented
34	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
35	#65522	C₂×C₃	1	2	yes	complemented
36	#65477	C₂×C₃	1	2	yes	complemented
37	#65460	C₂×C₃	1	4	yes	complemented
38	#65446	C₂×C₃	1	2	yes	complemented
39	#65395	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
49	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×C₄×D₅	—	2	2	no	—
52	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
53	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
54	C₃×C₅×Q₁₆	—	2	2	no	—
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₃×C₅×D₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₃×C₂²⋊Dic₅	—	2	2	no	—
61	C₃×C₂²⋊Dic₅	—	2	4	no	—
62	C₃×#685	—	2	4	no	—
63	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
64	C₃×#683	—	2	4	no	—
65	C₃×C₄×Dic₅	—	2	2	no	—
66	C₂×C₃×#168	—	2	2	no	—
67	C₂×C₃×#168	C₂³	1	2	yes	—
68	C₃×C₈×D₅	—	2	4	no	—
69	C₃×C₈×D₅	—	2	4	no	—
70	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
71	C₂³×C₃×C₈	—	5	1	no	—
72	C₃×#525	—	5	2	no	—
73	C₃×#467	—	5	2	no	—
74	C₃×#466	—	5	2	no	—
75	C₃×#465	—	5	4	no	—
76	C₃×#427	—	5	1	no	—
77	C₃×#416	—	5	2	no	—
78	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
79	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
83	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
85	#4092	C₂²×C₃	1	4	yes	—
86	#4084	C₂²×C₃	1	4	yes	—
87	#4083	—	2	2	no	—
88	#4081	—	2	2	no	—
89	C₄×C₂²⋊D₅	—	2	4	no	—
90	#4072	C₂²×C₃	1	2	yes	—
91	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₈×D₅	—	2	4	no	—
93	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
94	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
95	#3967	C₂²×C₃	1	4	yes	complemented
96	#3964	C₂²×C₃	1	4	yes	complemented
97	#3950	C₂²×C₃	1	2	yes	complemented
98	#3949	C₂²×C₃	1	2	yes	complemented
99	#3050	—	5	1	no	Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	—	2	2	no	—
103	C₂²×C₃×D₅	—	2	4	no	—
104	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	4	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	4	no	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₂²⋊D₅	—	4	8	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	—	2	4	no	—
119	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
120	C₃×C₄×D₅	—	2	4	no	—
121	C₃×C₄×D₅	—	2	2	no	—
122	C₃×C₄×D₅	—	2	2	no	—
123	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
124	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
125	C₃×#168	—	2	2	no	—
126	C₂×C₃×#41	C₂×D₅	1	2	yes	—
127	C₂³×C₃×C₄	—	5	1	no	—
128	C₃×#135	—	2	4	no	—
129	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
130	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
131	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₂²×C₃×C₈	—	5	2	no	—
134	C₂²×C₃×C₈	—	5	2	no	—
135	C₂²×C₃×C₈	—	10	4	no	—
136	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×#123	—	10	2	no	—
138	C₃×C₂²⋊Q₈	—	5	4	no	—
139	C₃×#121	—	5	4	no	—
140	C₃×#120	—	10	2	no	—
141	C₃×C₄×D₄	—	10	4	no	—
142	C₃×#117	—	5	2	no	—
143	C₃×#107	—	5	2	no	—
144	C₃×#106	—	5	2	no	—
145	C₃×#103	—	5	4	no	—
146	C₃×#102	—	5	4	no	—
147	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
148	C₅×#41	—	2	4	no	—
149	C₅×#41	—	2	4	no	—
150	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₂²⋊D₅	—	2	4	no	—
156	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
157	C₂×C₄×D₅	—	2	2	no	—
158	C₂×C₄×D₅	—	2	2	no	—
159	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
160	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
161	C₅×Q₁₆	—	2	2	no	—
162	C₅×SD₁₆	—	2	4	no	—
163	C₅×D₈	—	2	2	no	—
164	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
165	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
167	C₂²⋊Dic₅	—	2	2	no	—
168	C₂²⋊Dic₅	—	2	4	no	—
169	#685	—	2	4	no	—
170	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
171	#683	—	2	4	no	—
172	C₄×Dic₅	—	2	2	no	—
173	C₂×#168	—	2	2	no	—
174	C₂×#168	C₂³×C₃	1	2	yes	—
175	C₈×D₅	—	2	4	no	—
176	C₈×D₅	—	2	4	no	—
177	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
178	C₂³×C₈	—	5	1	no	—
179	#525	—	5	2	no	—
180	#467	—	5	2	no	—
181	#466	—	5	2	no	—
182	#465	—	5	4	no	—
183	#427	—	5	1	no	—
184	#416	—	5	2	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	—	4	4	no	—
188	C₂²×C₃×C₅	#121	1	2	yes	—
189	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₃×D₅	—	2	8	no	—
191	C₂×C₃×D₅	—	2	2	no	—
192	C₂×C₃×D₅	—	2	2	no	—
193	C₂×C₃×D₅	#135	1	4	yes	complemented
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	#121	1	2	yes	—
196	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₃×Dic₅	—	2	2	no	—
199	C₃×Dic₅	—	4	4	no	—
200	C₂⁴×C₃	—	5	1	no	—
201	C₃×#41	—	2	4	no	—
202	C₃×#41	—	2	4	no	—
203	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	—	10	4	no	—
206	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	—	5	2	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	10	2	no	—
212	C₂²×C₃×C₄	—	10	2	no	—
213	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
214	C₃×Q₁₆	—	2	2	no	—
215	C₃×SD₁₆	—	2	4	no	—
216	C₃×D₈	—	2	2	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	—	10	2	no	—
219	C₂×C₃×C₈	—	10	4	no	—
220	C₂×C₃×C₈	—	10	4	no	—
221	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
222	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
224	C₃×C₄⋊C₄	—	5	4	no	—
225	C₃×C₄⋊C₄	—	10	4	no	—
226	C₃×C₂²⋊C₄	—	10	4	no	—
227	C₃×C₂²⋊C₄	—	10	4	no	—
228	C₃×C₂²⋊C₄	—	10	2	no	—
229	C₃×C₄²	—	10	2	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂²×D₅	—	2	2	no	—
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
235	C₅×Q₈	—	2	2	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	4	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	4	4	no	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
244	C₂×C₄×C₅	C₃×#41	1	2	yes	—
245	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
246	C₂²⋊D₅	—	4	8	no	—
247	C₂×Dic₅	—	2	2	no	—
248	C₂×Dic₅	—	2	4	no	—
249	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
250	C₄×D₅	—	2	4	no	—
251	C₄×D₅	—	2	2	no	—
252	C₄×D₅	—	2	2	no	—
253	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
254	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
255	#168	—	2	2	no	—
256	C₂×#41	C₂×C₃×D₅	1	2	yes	—
257	C₂³×C₄	—	5	1	no	—
258	#135	—	2	4	no	—
259	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
260	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
261	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
262	C₂²×C₈	—	5	1	no	—
263	C₂²×C₈	—	5	2	no	—
264	C₂²×C₈	—	5	2	no	—
265	C₂²×C₈	—	10	4	no	—
266	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
267	#123	—	10	2	no	—
268	C₂²⋊Q₈	—	5	4	no	—
269	#121	—	5	4	no	—
270	#120	—	10	2	no	—
271	C₄×D₄	—	10	4	no	—
272	#117	—	5	2	no	—
273	#107	—	5	2	no	—
274	#106	—	5	2	no	—
275	#103	—	5	4	no	—
276	#102	—	5	4	no	—
277	C₂×C₃×C₅	—	2	2	no	—
278	C₂×C₃×C₅	—	8	2	no	—
279	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×#135	1	2	yes	—
281	C₃×D₅	—	2	4	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	5	2	no	—
284	C₂³×C₃	—	10	4	no	—
285	C₂³×C₃	—	10	2	no	—
286	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
287	C₃×Q₈	—	2	2	no	—
288	C₃×Q₈	—	2	2	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	—	2	2	no	—
291	C₃×D₄	—	4	4	no	—
292	C₃×D₄	—	20	8	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	4	4	no	—
295	C₂×C₃×C₄	—	5	2	no	—
296	C₂×C₃×C₄	—	10	2	no	—
297	C₂×C₃×C₄	—	10	2	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	D₄×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	#711	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
304	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
305	C₃×C₈	—	10	2	no	—
306	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
307	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	4	4	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	C₃×#121	1	2	yes	—
312	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₂×D₅	—	2	8	no	—
314	C₂×D₅	—	2	2	no	—
315	C₂×D₅	—	2	2	no	—
316	C₂×D₅	C₃×#135	1	4	yes	complemented
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	C₃×#121	1	2	yes	—
319	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
320	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
321	Dic₅	—	2	2	no	—
322	Dic₅	—	4	4	no	—
323	C₂⁴	—	5	1	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	10	4	no	—
329	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	2	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	10	2	no	—
335	C₂²×C₄	—	10	2	no	—
336	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
337	Q₁₆	—	2	2	no	—
338	SD₁₆	—	2	4	no	—
339	D₈	—	2	2	no	—
340	C₂×C₈	—	5	2	no	—
341	C₂×C₈	—	10	2	no	—
342	C₂×C₈	—	10	4	no	—
343	C₂×C₈	—	10	4	no	—
344	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
345	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
346	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
347	C₄⋊C₄	—	5	4	no	—
348	C₄⋊C₄	—	10	4	no	—
349	C₂²⋊C₄	—	10	4	no	—
350	C₂²⋊C₄	—	10	4	no	—
351	C₂²⋊C₄	—	10	2	no	—
352	C₄²	—	10	2	no	—
353	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	4	4	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	5	4	no	—
358	C₂²×C₃	—	10	8	no	—
359	C₂²×C₃	—	10	2	no	—
360	C₂²×C₃	—	10	2	no	—
361	C₂²×C₃	#4084	1	2	yes	—
362	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	10	2	no	—
365	C₃×C₄	—	20	4	no	—
366	C₃×C₄	#4084	1	2	yes	—
367	C₃×C₄	C₂×#711	1	1	yes	characteristic
368	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
369	C₂×C₅	—	2	2	no	—
370	C₂×C₅	—	8	2	no	—
371	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
372	C₂×C₅	C₂×C₃×#135	1	2	yes	—
373	D₅	—	2	4	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	5	2	no	—
376	C₂³	—	10	4	no	—
377	C₂³	—	10	2	no	—
378	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	20	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	5	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	—	10	4	no	—
390	C₂×C₄	—	10	2	no	—
391	C₂×C₄	—	10	2	no	—
392	C₂×C₄	—	10	4	no	—
393	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
394	C₂×C₄	C₃×#711	1	2	yes	—
395	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
396	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
397	C₈	—	10	2	no	—
398	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
399	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	8	2	no	—
402	C₂×C₃	—	10	4	no	—
403	C₂×C₃	D₅×#135	1	2	yes	—
404	C₂×C₃	C₂×#4084	1	1	yes	characteristic
405	C₅	C₃×#3050	1	1	yes	characteristic, complemented, Sylow
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	5	4	no	—
410	C₂²	—	10	8	no	—
411	C₂²	—	10	2	no	—
412	C₂²	—	10	2	no	—
413	C₂²	C₃×#4084	1	2	yes	—
414	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
415	C₄	—	4	2	no	—
416	C₄	—	10	2	no	—
417	C₄	—	20	4	no	—
418	C₄	C₃×#4084	1	2	yes	—
419	C₄	C₂×C₃×#711	1	1	yes	characteristic
420	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
421	C₃	#10615645	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	—	10	4	no	—
425	C₂	C₃×D₅×#135	1	2	yes	—
426	C₂	C₂×C₃×#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#3050
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×#66162	C₂	semidirect
3. C₂²×C₃×C₈×D₅	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65477	C₂	semidirect
6. C₃×#65460	C₂	semidirect
7. C₃×#65446	C₂	semidirect
8. C₃×#65395	C₂	semidirect
9. #10615645	C₃	direct (N × H)
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₃×#3967	C₂²	semidirect
28. C₃×#3964	C₂²	semidirect
29. C₃×#3950	C₂²	semidirect
30. C₃×#3949	C₂²	semidirect
32. C₂×C₅×#135	C₂×C₃	semidirect
33. #66162	C₂×C₃	semidirect
34. C₂²×C₈×D₅	C₂×C₃	semidirect
35. #65522	C₂×C₃	semidirect
36. #65477	C₂×C₃	semidirect
37. #65460	C₂×C₃	semidirect
38. #65446	C₂×C₃	semidirect
39. #65395	C₂×C₃	semidirect
57. C₂×C₃×C₅×C₈	D₄	semidirect
70. C₂×C₃×#135	D₅	semidirect
81. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
82. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
83. C₂×C₅×D₈	C₂²×C₃	semidirect
95. #3967	C₂²×C₃	semidirect
96. #3964	C₂²×C₃	semidirect
97. #3950	C₂²×C₃	semidirect
98. #3949	C₂²×C₃	semidirect
129. C₂×C₃×Q₁₆	C₂×D₅	semidirect
130. C₂×C₃×SD₁₆	C₂×D₅	semidirect
131. C₂×C₃×D₈	C₂×D₅	semidirect
164. C₂×C₅×C₈	C₃×D₄	semidirect
177. C₂×#135	C₃×D₅	semidirect
193. C₂×C₃×D₅	#135	semidirect
221. C₂×C₃×C₈	C₂²⋊D₅	semidirect
259. C₂×Q₁₆	C₂×C₃×D₅	semidirect
260. C₂×SD₁₆	C₂×C₃×D₅	semidirect
261. C₂×D₈	C₂×C₃×D₅	semidirect
316. C₂×D₅	C₃×#135	semidirect
344. C₂×C₈	C₃×C₂²⋊D₅	semidirect
353. C₃×C₅	#3050	semidirect
405. C₅	C₃×#3050	semidirect
421. C₃	#10615645	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×C₅×#135	2
C₃×#66162	2
C₂²×C₃×C₈×D₅	2
C₃×#65522	2
C₃×#65477	2
C₃×#65460	2
C₃×#65446	2
C₃×#65395	2
#10615645	3
C₃×#3050	5

Subgroups — C3×#10615645 #14427790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615645 #14427790