Subgroups — C₃×#10610723 #14412909

Order 1920.

1476 conjugacy classes of subgroups.

The subgroup lattice has 744 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×#66079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65294	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65110	C₂	1	4	yes	maximal, complemented
9	C₃×D₅×#104	C₂	1	4	yes	maximal, complemented
10	#10610723	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₃×#4150	—	2	1	no	—
13	C₃×#4150	C₄	1	2	yes	complemented
14	C₃×#4149	—	2	1	no	—
15	C₃×#4149	C₄	1	2	yes	complemented
16	C₃×D₅×#41	—	2	2	no	—
17	C₃×D₅×#41	C₂²	1	4	yes	—
18	C₃×#4147	C₄	1	2	yes	complemented
19	C₃×#4144	—	2	2	no	—
20	C₃×#4144	C₄	1	2	yes	complemented
21	C₂×C₃×#709	—	2	2	no	—
22	C₂×C₃×#709	C₂²	1	1	yes	characteristic
23	C₂×C₃×#709	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4053	—	2	2	no	—
29	C₃×D₅×M₁₆	C₂²	1	4	yes	complemented
30	C₃×#4047	—	2	2	no	—
31	C₃×#4039	—	2	1	no	—
32	C₃×#4033	—	2	1	no	—
33	C₃×#4027	—	2	2	no	—
34	C₃×#4018	C₂²	1	2	yes	complemented
35	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
36	C₃×C₅×#104	C₂²	1	4	yes	complemented
37	C₃×#3969	C₂²	1	2	yes	complemented
38	C₃×#3969	C₂²	1	2	yes	complemented
39	C₃×#3957	C₂²	1	2	yes	complemented
40	C₃×#3957	C₂²	1	2	yes	complemented
41	C₃×#3937	C₂²	1	4	yes	complemented
42	C₃×#2901	—	5	1	no	maximal, Hall
43	#66283	C₂×C₃	1	1	yes	characteristic
44	#66079	C₂×C₃	1	1	yes	characteristic, complemented
45	#65856	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#421	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3969	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#3957	C₂×C₃	1	1	yes	characteristic, complemented
49	#65294	C₂×C₃	1	1	yes	characteristic, complemented
50	#65110	C₂×C₃	1	4	yes	complemented
51	D₅×#104	C₂×C₃	1	4	yes	complemented
52	C₃×C₅×#41	—	2	1	no	—
53	C₃×C₅×#41	—	2	1	no	—
54	C₃×C₅×#41	C₂×C₄	1	2	yes	complemented
55	C₃×C₅×#41	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
62	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
63	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
64	C₂²×C₃×Dic₅	—	2	1	no	—
65	C₃×#713	—	2	2	no	—
66	C₃×#713	C₂×C₄	1	4	yes	complemented
67	C₃×Q₈×D₅	—	2	2	no	—
68	C₃×Q₈×D₅	C₂×C₄	1	4	yes	complemented
69	C₃×#711	—	2	4	no	—
70	C₃×#711	—	2	4	no	—
71	C₃×#711	—	2	2	no	—
72	C₃×#711	C₂×C₄	1	4	yes	complemented
73	C₃×D₄×D₅	—	2	4	no	—
74	C₃×D₄×D₅	—	2	4	no	—
75	C₃×D₄×D₅	—	2	2	no	—
76	C₃×D₄×D₅	C₂×C₄	1	4	yes	complemented
77	C₃×#709	—	2	1	no	—
78	C₃×#709	—	2	1	no	—
79	C₃×#709	—	2	4	no	—
80	C₃×#709	—	2	2	no	—
81	C₃×#709	—	2	4	no	—
82	C₃×#709	—	2	2	no	—
83	C₃×#709	C₂×C₄	1	2	yes	—
84	C₃×#709	C₂×C₄	1	2	yes	—
85	C₃×#709	C₂×C₄	1	2	yes	complemented
86	C₃×#709	D₄	1	2	yes	—
87	C₃×#709	D₄	1	2	yes	—
88	C₃×#709	C₂³	1	2	yes	—
89	C₂×C₃×D₂₀	—	2	2	no	—
90	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×D₅	—	2	1	no	—
93	C₂×C₃×C₄×D₅	—	2	4	no	—
94	C₂×C₃×C₄×D₅	—	2	2	no	—
95	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
96	C₂×C₃×Dic₁₀	—	2	2	no	—
97	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
99	C₃×C₅×M₁₆	—	2	1	no	—
100	C₃×C₅×M₁₆	C₂³	1	2	yes	—
101	C₂×C₃×C₅×C₈	—	2	1	no	—
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₄²×C₅	C₂³	1	2	yes	—
105	C₃×#685	—	2	2	no	—
106	C₃×#683	—	2	2	no	—
107	C₃×C₄×Dic₅	—	2	1	no	—
108	C₃×C₄×Dic₅	—	2	2	no	—
109	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
110	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
111	C₃×#681	—	2	1	no	—
112	C₃×#681	C₂³	1	2	yes	—
113	C₂×C₃×#168	—	2	1	no	—
114	C₃×#676	—	2	4	no	—
115	C₃×C₈×D₅	—	2	4	no	—
116	C₃×#585	—	5	1	no	—
117	C₃×#568	—	5	1	no	—
118	C₃×C₄×#41	—	5	1	no	—
119	C₃×#421	—	5	1	no	—
120	C₃×#421	—	5	4	no	—
121	C₃×#421	D₅	1	1	yes	characteristic, complemented
122	C₂×C₃×#104	—	5	1	no	—
123	C₂×C₃×#104	—	5	1	no	—
124	C₂×C₃×#104	—	5	4	no	—
125	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
126	#4150	—	2	1	no	—
127	#4150	C₃×C₄	1	2	yes	complemented
128	#4149	—	2	1	no	—
129	#4149	C₃×C₄	1	2	yes	complemented
130	D₅×#41	—	2	2	no	—
131	D₅×#41	C₂²×C₃	1	4	yes	—
132	#4147	C₃×C₄	1	2	yes	complemented
133	#4144	—	2	2	no	—
134	#4144	C₃×C₄	1	2	yes	complemented
135	C₂×#709	—	2	2	no	—
136	C₂×#709	C₂²×C₃	1	1	yes	characteristic
137	C₂×#709	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
142	#4053	—	2	2	no	—
143	D₅×M₁₆	C₂²×C₃	1	4	yes	complemented
144	#4047	—	2	2	no	—
145	#4039	—	2	1	no	—
146	#4033	—	2	1	no	—
147	#4027	—	2	2	no	—
148	#4018	C₂²×C₃	1	2	yes	complemented
149	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
150	C₅×#104	C₂²×C₃	1	4	yes	complemented
151	#3969	C₂²×C₃	1	2	yes	complemented
152	#3969	C₂²×C₃	1	2	yes	complemented
153	#3957	C₂²×C₃	1	2	yes	complemented
154	#3957	C₂²×C₃	1	2	yes	complemented
155	#3937	C₂²×C₃	1	4	yes	complemented
156	#2901	—	5	1	no	Sylow
157	C₂³×C₃×C₅	—	2	1	no	—
158	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₃×D₅	—	2	1	no	—
160	C₂²×C₃×D₅	—	2	4	no	—
161	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
162	C₃×C₅×Q₈	—	2	1	no	—
163	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
164	C₃×C₅×D₄	—	2	2	no	—
165	C₃×C₅×D₄	—	2	2	no	—
166	C₃×C₅×D₄	—	2	1	no	—
167	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₃×C₂²⋊D₅	—	2	2	no	—
179	C₃×C₂²⋊D₅	—	2	2	no	—
180	C₃×C₂²⋊D₅	—	2	4	no	—
181	C₃×C₂²⋊D₅	—	2	4	no	—
182	C₃×C₂²⋊D₅	C₂²⋊C₄	1	4	yes	—
183	C₃×C₂²⋊D₅	C₂²⋊C₄	1	4	yes	—
184	C₂×C₃×Dic₅	—	2	1	no	—
185	C₂×C₃×Dic₅	—	2	1	no	—
186	C₂×C₃×Dic₅	—	2	4	no	—
187	C₂×C₃×Dic₅	—	2	1	no	—
188	C₂×C₃×Dic₅	—	4	2	no	—
189	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
190	C₃×D₂₀	—	2	4	no	—
191	C₃×D₂₀	—	2	1	no	—
192	C₃×D₂₀	C₂²⋊C₄	1	2	yes	—
193	C₃×D₂₀	C₂²⋊C₄	1	2	yes	—
194	C₃×D₂₀	C₂²×C₄	1	2	yes	—
195	C₃×C₄×D₅	—	2	4	no	—
196	C₃×C₄×D₅	—	2	2	no	—
197	C₃×C₄×D₅	—	2	2	no	—
198	C₃×C₄×D₅	—	2	4	no	—
199	C₃×C₄×D₅	—	4	4	no	—
200	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
201	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
202	C₃×Dic₁₀	—	2	1	no	—
203	C₃×Dic₁₀	—	2	4	no	—
204	C₃×Dic₁₀	C₂²⋊C₄	1	2	yes	—
205	C₃×Dic₁₀	C₂²⋊C₄	1	2	yes	—
206	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
207	C₃×C₅×C₈	—	2	2	no	—
208	C₃×#168	—	2	2	no	—
209	C₃×2₋¹⁺⁴	—	5	2	no	—
210	C₃×2₋¹⁺⁴	—	5	2	no	—
211	C₃×2₋¹⁺⁴	—	10	1	no	—
212	C₃×H(5,𝔽₂)	—	5	2	no	—
213	C₃×H(5,𝔽₂)	—	5	2	no	—
214	C₃×H(5,𝔽₂)	—	10	2	no	—
215	C₃×H(5,𝔽₂)	—	10	1	no	—
216	C₂×C₃×#41	—	5	1	no	—
217	C₂×C₃×#41	—	5	4	no	—
218	C₂×C₃×#41	—	5	1	no	—
219	C₂×C₃×#41	—	10	2	no	—
220	C₂×C₃×#41	—	10	2	no	—
221	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
222	C₃×#131	—	10	2	no	—
223	C₃×#131	—	10	2	no	—
224	C₂×C₃×M₁₆	—	5	1	no	—
225	C₂×C₃×M₁₆	—	5	4	no	—
226	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
227	C₃×C₄×Q₈	—	10	1	no	—
228	C₃×C₄×D₄	—	10	2	no	—
229	C₃×C₄×D₄	—	10	1	no	—
230	C₃×#117	—	5	2	no	—
231	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
232	C₂×C₃×C₄²	—	5	1	no	—
233	C₂×C₃×C₄²	—	5	2	no	—
234	C₃×#104	—	5	2	no	—
235	C₃×#104	—	5	2	no	—
236	C₃×#104	—	5	2	no	—
237	C₃×#104	—	5	2	no	—
238	C₃×#104	—	5	4	no	—
239	C₃×#104	C₂×D₅	1	4	yes	complemented
240	C₅×#41	—	2	1	no	—
241	C₅×#41	—	2	1	no	—
242	C₅×#41	C₂×C₃×C₄	1	2	yes	complemented
243	C₅×#41	C₂³×C₃	1	2	yes	—
244	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
245	C₂×C₅×D₄	—	2	1	no	—
246	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
247	C₂²×C₄×C₅	—	2	1	no	—
248	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₂²⋊D₅	—	2	1	no	—
250	C₂×C₂²⋊D₅	—	2	4	no	—
251	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
252	C₂²×Dic₅	—	2	1	no	—
253	#713	—	2	2	no	—
254	#713	C₂×C₃×C₄	1	4	yes	complemented
255	Q₈×D₅	—	2	2	no	—
256	Q₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
257	#711	—	2	4	no	—
258	#711	—	2	4	no	—
259	#711	—	2	2	no	—
260	#711	C₂×C₃×C₄	1	4	yes	complemented
261	D₄×D₅	—	2	4	no	—
262	D₄×D₅	—	2	4	no	—
263	D₄×D₅	—	2	2	no	—
264	D₄×D₅	C₂×C₃×C₄	1	4	yes	complemented
265	#709	—	2	1	no	—
266	#709	—	2	1	no	—
267	#709	—	2	4	no	—
268	#709	—	2	2	no	—
269	#709	—	2	4	no	—
270	#709	—	2	2	no	—
271	#709	C₂×C₃×C₄	1	2	yes	—
272	#709	C₂×C₃×C₄	1	2	yes	—
273	#709	C₂×C₃×C₄	1	2	yes	complemented
274	#709	C₃×D₄	1	2	yes	—
275	#709	C₃×D₄	1	2	yes	—
276	#709	C₂³×C₃	1	2	yes	—
277	C₂×D₂₀	—	2	2	no	—
278	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
279	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
280	C₂×C₄×D₅	—	2	1	no	—
281	C₂×C₄×D₅	—	2	4	no	—
282	C₂×C₄×D₅	—	2	2	no	—
283	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
284	C₂×Dic₁₀	—	2	2	no	—
285	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
286	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
287	C₅×M₁₆	—	2	1	no	—
288	C₅×M₁₆	C₂³×C₃	1	2	yes	—
289	C₂×C₅×C₈	—	2	1	no	—
290	C₅×C₄⋊C₄	—	2	1	no	—
291	C₅×C₂²⋊C₄	—	2	1	no	—
292	C₄²×C₅	C₂³×C₃	1	2	yes	—
293	#685	—	2	2	no	—
294	#683	—	2	2	no	—
295	C₄×Dic₅	—	2	1	no	—
296	C₄×Dic₅	—	2	2	no	—
297	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
298	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
299	#681	—	2	1	no	—
300	#681	C₂³×C₃	1	2	yes	—
301	C₂×#168	—	2	1	no	—
302	#676	—	2	4	no	—
303	C₈×D₅	—	2	4	no	—
304	#585	—	5	1	no	—
305	#568	—	5	1	no	—
306	C₄×#41	—	5	1	no	—
307	#421	—	5	1	no	—
308	#421	—	5	4	no	—
309	#421	C₃×D₅	1	1	yes	characteristic, complemented
310	C₂×#104	—	5	1	no	—
311	C₂×#104	—	5	1	no	—
312	C₂×#104	—	5	4	no	—
313	C₂²×C₃×C₅	—	2	2	no	—
314	C₂²×C₃×C₅	—	4	1	no	—
315	C₂²×C₃×C₅	—	8	1	no	—
316	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₃×D₅	—	2	2	no	—
320	C₂×C₃×D₅	—	4	2	no	—
321	C₂×C₃×D₅	—	8	4	no	—
322	C₂×C₃×D₅	—	8	1	no	—
323	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
324	C₃×C₄×C₅	—	2	2	no	—
325	C₃×C₄×C₅	—	4	2	no	—
326	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
329	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₃×Dic₅	—	2	2	no	—
331	C₃×Dic₅	—	2	2	no	—
332	C₃×Dic₅	—	4	1	no	—
333	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
334	C₃×#41	—	2	1	no	—
335	C₃×#41	—	2	1	no	—
336	C₃×#41	—	5	2	no	—
337	C₃×#41	—	5	2	no	—
338	C₃×#41	—	5	2	no	—
339	C₃×#41	—	5	2	no	—
340	C₃×#41	—	5	4	no	—
341	C₃×#41	—	5	4	no	—
342	C₃×#41	—	5	2	no	—
343	C₃×#41	—	5	2	no	—
344	C₃×#41	—	10	4	no	—
345	C₃×#41	—	10	4	no	—
346	C₃×#41	—	10	2	no	—
347	C₃×#41	—	10	2	no	—
348	C₃×#41	—	10	4	no	—
349	C₃×#41	—	10	4	no	—
350	C₃×#41	—	10	2	no	—
351	C₃×#41	—	10	2	no	—
352	C₃×#41	—	10	1	no	—
353	C₃×#41	—	10	1	no	—
354	C₃×#41	C₄×D₅	1	2	yes	complemented
355	C₃×#41	C₂²×D₅	1	2	yes	—
356	C₂×C₃×Q₈	—	5	1	no	—
357	C₂×C₃×Q₈	—	5	4	no	—
358	C₂×C₃×Q₈	—	5	1	no	—
359	C₂×C₃×Q₈	—	10	2	no	—
360	C₂×C₃×Q₈	—	10	2	no	—
361	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic, complemented
362	C₂×C₃×D₄	—	2	1	no	—
363	C₂×C₃×D₄	—	5	2	no	—
364	C₂×C₃×D₄	—	5	4	no	—
365	C₂×C₃×D₄	—	5	1	no	—
366	C₂×C₃×D₄	—	5	1	no	—
367	C₂×C₃×D₄	—	10	2	no	—
368	C₂×C₃×D₄	—	10	4	no	—
369	C₂×C₃×D₄	—	10	2	no	—
370	C₂×C₃×D₄	—	10	4	no	—
371	C₂×C₃×D₄	—	10	4	no	—
372	C₂×C₃×D₄	—	10	1	no	—
373	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic, complemented
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂²×C₃×C₄	—	5	2	no	—
376	C₂²×C₃×C₄	—	10	4	no	—
377	C₂²×C₃×C₄	—	10	2	no	—
378	C₂²×C₃×C₄	—	10	1	no	—
379	C₂²×C₃×C₄	—	10	1	no	—
380	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
381	C₃×M₁₆	—	2	1	no	—
382	C₃×M₁₆	—	5	2	no	—
383	C₃×M₁₆	—	10	4	no	—
384	C₃×M₁₆	—	10	1	no	—
385	C₃×M₁₆	C₂²×D₅	1	2	yes	—
386	C₂×C₃×C₈	—	2	1	no	—
387	C₂×C₃×C₈	—	10	4	no	—
388	C₂×C₃×C₈	—	10	1	no	—
389	C₃×C₄⋊C₄	—	2	1	no	—
390	C₃×C₄⋊C₄	—	10	2	no	—
391	C₃×C₂²⋊C₄	—	2	1	no	—
392	C₃×C₂²⋊C₄	—	10	2	no	—
393	C₃×C₄²	—	5	1	no	—
394	C₃×C₄²	—	5	1	no	—
395	C₃×C₄²	—	10	2	no	—
396	C₃×C₄²	—	10	1	no	—
397	C₃×C₄²	C₂²×D₅	1	2	yes	—
398	C₂³×C₅	—	2	1	no	—
399	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
400	C₂²×D₅	—	2	1	no	—
401	C₂²×D₅	—	2	4	no	—
402	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
403	C₅×Q₈	—	2	1	no	—
404	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
405	C₅×D₄	—	2	2	no	—
406	C₅×D₄	—	2	2	no	—
407	C₅×D₄	—	2	1	no	—
408	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	2	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
414	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
415	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
416	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
419	C₂²⋊D₅	—	2	2	no	—
420	C₂²⋊D₅	—	2	2	no	—
421	C₂²⋊D₅	—	2	4	no	—
422	C₂²⋊D₅	—	2	4	no	—
423	C₂²⋊D₅	C₃×C₂²⋊C₄	1	4	yes	—
424	C₂²⋊D₅	C₃×C₂²⋊C₄	1	4	yes	—
425	C₂×Dic₅	—	2	1	no	—
426	C₂×Dic₅	—	2	1	no	—
427	C₂×Dic₅	—	2	4	no	—
428	C₂×Dic₅	—	2	1	no	—
429	C₂×Dic₅	—	4	2	no	—
430	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
431	D₂₀	—	2	4	no	—
432	D₂₀	—	2	1	no	—
433	D₂₀	C₃×C₂²⋊C₄	1	2	yes	—
434	D₂₀	C₃×C₂²⋊C₄	1	2	yes	—
435	D₂₀	C₂²×C₃×C₄	1	2	yes	—
436	C₄×D₅	—	2	4	no	—
437	C₄×D₅	—	2	2	no	—
438	C₄×D₅	—	2	2	no	—
439	C₄×D₅	—	2	4	no	—
440	C₄×D₅	—	4	4	no	—
441	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
442	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
443	Dic₁₀	—	2	1	no	—
444	Dic₁₀	—	2	4	no	—
445	Dic₁₀	C₃×C₂²⋊C₄	1	2	yes	—
446	Dic₁₀	C₃×C₂²⋊C₄	1	2	yes	—
447	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
448	C₅×C₈	—	2	2	no	—
449	#168	—	2	2	no	—
450	2₋¹⁺⁴	—	5	2	no	—
451	2₋¹⁺⁴	—	5	2	no	—
452	2₋¹⁺⁴	—	10	1	no	—
453	H(5,𝔽₂)	—	5	2	no	—
454	H(5,𝔽₂)	—	5	2	no	—
455	H(5,𝔽₂)	—	10	2	no	—
456	H(5,𝔽₂)	—	10	1	no	—
457	C₂×#41	—	5	1	no	—
458	C₂×#41	—	5	4	no	—
459	C₂×#41	—	5	1	no	—
460	C₂×#41	—	10	2	no	—
461	C₂×#41	—	10	2	no	—
462	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
463	#131	—	10	2	no	—
464	#131	—	10	2	no	—
465	C₂×M₁₆	—	5	1	no	—
466	C₂×M₁₆	—	5	4	no	—
467	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
468	C₄×Q₈	—	10	1	no	—
469	C₄×D₄	—	10	2	no	—
470	C₄×D₄	—	10	1	no	—
471	#117	—	5	2	no	—
472	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
473	C₂×C₄²	—	5	1	no	—
474	C₂×C₄²	—	5	2	no	—
475	#104	—	5	2	no	—
476	#104	—	5	2	no	—
477	#104	—	5	2	no	—
478	#104	—	5	2	no	—
479	#104	—	5	4	no	—
480	#104	C₂×C₃×D₅	1	4	yes	complemented
481	C₂×C₃×C₅	—	2	1	no	—
482	C₂×C₃×C₅	—	2	1	no	—
483	C₂×C₃×C₅	—	2	1	no	—
484	C₂×C₃×C₅	—	4	2	no	—
485	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
486	C₃×D₅	—	2	4	no	—
487	C₃×D₅	—	4	2	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	5	2	no	—
490	C₂³×C₃	—	10	4	no	—
491	C₂³×C₃	—	10	1	no	—
492	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
493	C₃×Q₈	—	2	1	no	—
494	C₃×Q₈	—	5	2	no	—
495	C₃×Q₈	—	5	2	no	—
496	C₃×Q₈	—	5	2	no	—
497	C₃×Q₈	—	10	4	no	—
498	C₃×Q₈	—	10	1	no	—
499	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
500	C₃×D₄	—	2	2	no	—
501	C₃×D₄	—	2	2	no	—
502	C₃×D₄	—	2	1	no	—
503	C₃×D₄	—	5	4	no	—
504	C₃×D₄	—	5	4	no	—
505	C₃×D₄	—	5	2	no	—
506	C₃×D₄	—	5	2	no	—
507	C₃×D₄	—	5	2	no	—
508	C₃×D₄	—	10	4	no	—
509	C₃×D₄	—	10	4	no	—
510	C₃×D₄	—	10	4	no	—
511	C₃×D₄	—	10	2	no	—
512	C₃×D₄	—	10	2	no	—
513	C₃×D₄	—	10	1	no	—
514	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	5	2	no	—
520	C₂×C₃×C₄	—	5	4	no	—
521	C₂×C₃×C₄	—	5	4	no	—
522	C₂×C₃×C₄	—	10	4	no	—
523	C₂×C₃×C₄	—	10	4	no	—
524	C₂×C₃×C₄	—	10	4	no	—
525	C₂×C₃×C₄	—	10	1	no	—
526	C₂×C₃×C₄	—	10	1	no	—
527	C₂×C₃×C₄	—	10	2	no	—
528	C₂×C₃×C₄	—	10	2	no	—
529	C₂×C₃×C₄	—	10	1	no	—
530	C₂×C₃×C₄	—	20	4	no	—
531	C₂×C₃×C₄	—	20	2	no	—
532	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
534	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
535	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
536	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
538	C₃×C₈	—	2	2	no	—
539	C₃×C₈	—	10	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	8	1	no	—
543	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
544	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
545	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
546	C₂×D₅	—	2	2	no	—
547	C₂×D₅	—	4	2	no	—
548	C₂×D₅	—	8	4	no	—
549	C₂×D₅	—	8	1	no	—
550	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
551	C₄×C₅	—	2	2	no	—
552	C₄×C₅	—	4	2	no	—
553	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
554	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
555	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
556	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
557	Dic₅	—	2	2	no	—
558	Dic₅	—	2	2	no	—
559	Dic₅	—	4	1	no	—
560	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
561	#41	—	2	1	no	—
562	#41	—	2	1	no	—
563	#41	—	5	2	no	—
564	#41	—	5	2	no	—
565	#41	—	5	2	no	—
566	#41	—	5	2	no	—
567	#41	—	5	4	no	—
568	#41	—	5	4	no	—
569	#41	—	5	2	no	—
570	#41	—	5	2	no	—
571	#41	—	10	4	no	—
572	#41	—	10	4	no	—
573	#41	—	10	2	no	—
574	#41	—	10	2	no	—
575	#41	—	10	4	no	—
576	#41	—	10	4	no	—
577	#41	—	10	2	no	—
578	#41	—	10	2	no	—
579	#41	—	10	1	no	—
580	#41	—	10	1	no	—
581	#41	C₃×C₄×D₅	1	2	yes	complemented
582	#41	C₂²×C₃×D₅	1	2	yes	—
583	C₂×Q₈	—	5	1	no	—
584	C₂×Q₈	—	5	4	no	—
585	C₂×Q₈	—	5	1	no	—
586	C₂×Q₈	—	10	2	no	—
587	C₂×Q₈	—	10	2	no	—
588	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic, complemented
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	5	2	no	—
591	C₂×D₄	—	5	4	no	—
592	C₂×D₄	—	5	1	no	—
593	C₂×D₄	—	5	1	no	—
594	C₂×D₄	—	10	2	no	—
595	C₂×D₄	—	10	4	no	—
596	C₂×D₄	—	10	2	no	—
597	C₂×D₄	—	10	4	no	—
598	C₂×D₄	—	10	4	no	—
599	C₂×D₄	—	10	1	no	—
600	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic, complemented
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	5	2	no	—
603	C₂²×C₄	—	10	4	no	—
604	C₂²×C₄	—	10	2	no	—
605	C₂²×C₄	—	10	1	no	—
606	C₂²×C₄	—	10	1	no	—
607	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
608	M₁₆	—	2	1	no	—
609	M₁₆	—	5	2	no	—
610	M₁₆	—	10	4	no	—
611	M₁₆	—	10	1	no	—
612	M₁₆	C₂²×C₃×D₅	1	2	yes	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	10	4	no	—
615	C₂×C₈	—	10	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	10	2	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	10	2	no	—
620	C₄²	—	5	1	no	—
621	C₄²	—	5	1	no	—
622	C₄²	—	10	2	no	—
623	C₄²	—	10	1	no	—
624	C₄²	C₂²×C₃×D₅	1	2	yes	—
625	C₃×C₅	#2901	1	1	yes	characteristic, complemented, Hall
626	C₂²×C₃	—	2	2	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	5	4	no	—
629	C₂²×C₃	—	8	1	no	—
630	C₂²×C₃	—	10	2	no	—
631	C₂²×C₃	—	20	2	no	—
632	C₂²×C₃	—	40	1	no	—
633	C₂²×C₃	—	40	4	no	—
634	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
635	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
636	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	4	2	no	—
639	C₃×C₄	—	5	4	no	—
640	C₃×C₄	—	10	2	no	—
641	C₃×C₄	—	10	2	no	—
642	C₃×C₄	—	20	1	no	—
643	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
644	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
645	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
646	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
647	C₂×C₅	—	2	1	no	—
648	C₂×C₅	—	2	1	no	—
649	C₂×C₅	—	2	1	no	—
650	C₂×C₅	—	4	2	no	—
651	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
652	D₅	—	2	4	no	—
653	D₅	—	4	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	5	2	no	—
656	C₂³	—	10	4	no	—
657	C₂³	—	10	1	no	—
658	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
659	Q₈	—	2	1	no	—
660	Q₈	—	5	2	no	—
661	Q₈	—	5	2	no	—
662	Q₈	—	5	2	no	—
663	Q₈	—	10	4	no	—
664	Q₈	—	10	1	no	—
665	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	1	no	—
669	D₄	—	5	4	no	—
670	D₄	—	5	4	no	—
671	D₄	—	5	2	no	—
672	D₄	—	5	2	no	—
673	D₄	—	5	2	no	—
674	D₄	—	10	4	no	—
675	D₄	—	10	4	no	—
676	D₄	—	10	4	no	—
677	D₄	—	10	2	no	—
678	D₄	—	10	2	no	—
679	D₄	—	10	1	no	—
680	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	5	2	no	—
686	C₂×C₄	—	5	4	no	—
687	C₂×C₄	—	5	4	no	—
688	C₂×C₄	—	10	4	no	—
689	C₂×C₄	—	10	4	no	—
690	C₂×C₄	—	10	4	no	—
691	C₂×C₄	—	10	1	no	—
692	C₂×C₄	—	10	1	no	—
693	C₂×C₄	—	10	2	no	—
694	C₂×C₄	—	10	2	no	—
695	C₂×C₄	—	10	1	no	—
696	C₂×C₄	—	20	4	no	—
697	C₂×C₄	—	20	2	no	—
698	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
699	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
700	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
701	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
702	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
703	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
704	C₈	—	2	2	no	—
705	C₈	—	10	2	no	—
706	C₂×C₃	—	2	1	no	—
707	C₂×C₃	—	2	1	no	—
708	C₂×C₃	—	2	1	no	—
709	C₂×C₃	—	4	2	no	—
710	C₂×C₃	—	10	4	no	—
711	C₂×C₃	—	20	2	no	—
712	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
713	C₅	C₃×#2901	1	1	yes	characteristic, complemented, Sylow
714	C₂²	—	2	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	5	4	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	10	2	no	—
719	C₂²	—	20	2	no	—
720	C₂²	—	40	1	no	—
721	C₂²	—	40	4	no	—
722	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
723	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
724	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
725	C₄	—	2	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	5	4	no	—
728	C₄	—	10	2	no	—
729	C₄	—	10	2	no	—
730	C₄	—	20	1	no	—
731	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
732	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
733	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
734	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
735	C₃	#10610723	1	1	yes	characteristic, direct product factor, Sylow
736	C₂	—	2	1	no	—
737	C₂	—	2	1	no	—
738	C₂	—	2	1	no	—
739	C₂	—	4	2	no	—
740	C₂	—	10	4	no	—
741	C₂	—	20	2	no	—
742	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#421	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₃×#66283	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#421	D₅
hypocenter	C₅	C₃×#2901
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#421

Complements

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

N	H ≅ G/N	type
2. C₃×#66079	C₂	semidirect
3. C₃×#65856	C₂	semidirect
4. C₃×C₅×#421	C₂	semidirect
5. C₂×C₃×#3969	C₂	semidirect
6. C₂×C₃×#3957	C₂	semidirect
7. C₃×#65294	C₂	semidirect
8. C₃×#65110	C₂	semidirect
9. C₃×D₅×#104	C₂	semidirect
10. #10610723	C₃	direct (N × H)
13. C₃×#4150	C₄	semidirect
15. C₃×#4149	C₄	semidirect
18. C₃×#4147	C₄	semidirect
20. C₃×#4144	C₄	semidirect
24. C₂×C₃×C₅×M₁₆	C₂²	semidirect
25. C₃×C₅×#117	C₂²	semidirect
26. C₂×C₃×C₄×Dic₅	C₂²	semidirect
27. C₂×C₃×#681	C₂²	semidirect
29. C₃×D₅×M₁₆	C₂²	semidirect
34. C₃×#4018	C₂²	semidirect
35. C₃×C₄²×D₅	C₂²	semidirect
36. C₃×C₅×#104	C₂²	semidirect
37. C₃×#3969	C₂²	semidirect
38. C₃×#3969	C₂²	semidirect
39. C₃×#3957	C₂²	semidirect
40. C₃×#3957	C₂²	semidirect
41. C₃×#3937	C₂²	semidirect
44. #66079	C₂×C₃	semidirect
45. #65856	C₂×C₃	semidirect
46. C₅×#421	C₂×C₃	semidirect
47. C₂×#3969	C₂×C₃	semidirect
48. C₂×#3957	C₂×C₃	semidirect
49. #65294	C₂×C₃	semidirect
50. #65110	C₂×C₃	semidirect
51. D₅×#104	C₂×C₃	semidirect
54. C₃×C₅×#41	C₂×C₄	semidirect
56. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
58. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
66. C₃×#713	C₂×C₄	semidirect
68. C₃×Q₈×D₅	C₂×C₄	semidirect
72. C₃×#711	C₂×C₄	semidirect
76. C₃×D₄×D₅	C₂×C₄	semidirect
85. C₃×#709	C₂×C₄	semidirect
90. C₂×C₃×D₂₀	C₂×C₄	semidirect
97. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
121. C₃×#421	D₅	semidirect
127. #4150	C₃×C₄	semidirect
129. #4149	C₃×C₄	semidirect
132. #4147	C₃×C₄	semidirect
134. #4144	C₃×C₄	semidirect
138. C₂×C₅×M₁₆	C₂²×C₃	semidirect
139. C₅×#117	C₂²×C₃	semidirect
140. C₂×C₄×Dic₅	C₂²×C₃	semidirect
141. C₂×#681	C₂²×C₃	semidirect
143. D₅×M₁₆	C₂²×C₃	semidirect
148. #4018	C₂²×C₃	semidirect
149. C₄²×D₅	C₂²×C₃	semidirect
150. C₅×#104	C₂²×C₃	semidirect
151. #3969	C₂²×C₃	semidirect
152. #3969	C₂²×C₃	semidirect
153. #3957	C₂²×C₃	semidirect
154. #3957	C₂²×C₃	semidirect
155. #3937	C₂²×C₃	semidirect
226. C₂×C₃×M₁₆	C₂×D₅	semidirect
231. C₃×#117	C₂×D₅	semidirect
239. C₃×#104	C₂×D₅	semidirect
242. C₅×#41	C₂×C₃×C₄	semidirect
244. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
246. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
254. #713	C₂×C₃×C₄	semidirect
256. Q₈×D₅	C₂×C₃×C₄	semidirect
260. #711	C₂×C₃×C₄	semidirect
264. D₄×D₅	C₂×C₃×C₄	semidirect
273. #709	C₂×C₃×C₄	semidirect
278. C₂×D₂₀	C₂×C₃×C₄	semidirect
285. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
309. #421	C₃×D₅	semidirect
354. C₃×#41	C₄×D₅	semidirect
361. C₂×C₃×Q₈	C₄×D₅	semidirect
373. C₂×C₃×D₄	C₄×D₅	semidirect
467. C₂×M₁₆	C₂×C₃×D₅	semidirect
472. #117	C₂×C₃×D₅	semidirect
480. #104	C₂×C₃×D₅	semidirect
581. #41	C₃×C₄×D₅	semidirect
588. C₂×Q₈	C₃×C₄×D₅	semidirect
600. C₂×D₄	C₃×C₄×D₅	semidirect
625. C₃×C₅	#2901	semidirect
713. C₅	C₃×#2901	semidirect
735. C₃	#10610723	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×#66079	2
C₃×#65856	2
C₃×C₅×#421	2
C₂×C₃×#3969	2
C₂×C₃×#3957	2
C₃×#65294	2
C₃×#65110	2
C₃×D₅×#104	2
#10610723	3
C₃×#2901	5

Subgroups — C3×#10610723 #14412909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610723 #14412909