Subgroups — C₃×#10615719 #14454451

Order 1920.

956 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66158	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4062	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65527	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65517	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65471	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65454	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65416	C₂	1	1	yes	maximal, characteristic, complemented
16	#10615719	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×#713	C₂²	1	1	yes	characteristic
20	C₂×C₃×#711	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	—	2	4	no	—
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
27	C₃×#4093	—	2	1	no	—
28	C₃×#4093	C₂²	1	1	yes	characteristic
29	C₃×#4092	—	2	1	no	—
30	C₃×#4092	C₂²	1	1	yes	characteristic
31	C₃×#4092	C₂²	1	1	yes	characteristic
32	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
33	C₃×#4090	C₂²	1	1	yes	characteristic
34	C₂×C₃×#689	C₂²	1	1	yes	characteristic
35	C₂×C₃×#689	C₂²	1	1	yes	characteristic
36	C₂×C₃×#688	C₂²	1	1	yes	characteristic
37	C₃×#4085	—	2	1	no	—
38	C₃×#4081	—	2	1	no	—
39	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₂×C₃×#686	C₂²	1	1	yes	characteristic
41	C₃×#4076	—	2	1	no	—
42	C₃×#4076	C₂²	1	1	yes	characteristic
43	C₃×#4075	—	2	1	no	—
44	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
45	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
46	C₃×#4070	C₂²	1	1	yes	characteristic
47	C₂×C₃×#683	—	2	1	no	—
48	C₃×#4062	—	2	4	no	—
49	C₂×C₃×#677	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₃×#3967	C₂²	1	1	yes	characteristic
52	C₃×#3967	C₂²	1	1	yes	characteristic
53	C₃×#3967	C₂²	1	1	yes	characteristic
54	C₃×#3964	C₂²	1	1	yes	characteristic
55	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
56	C₃×#3953	C₂²	1	1	yes	characteristic
57	C₃×#3952	C₂²	1	1	yes	characteristic
58	C₃×#3950	C₂²	1	1	yes	characteristic
59	C₃×#3948	C₂²	1	1	yes	characteristic
60	C₃×#3947	C₂²	1	1	yes	characteristic
61	C₃×#3946	C₂²	1	1	yes	characteristic
62	C₃×#3269	—	5	1	no	maximal, Hall
63	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
64	#66158	C₂×C₃	1	1	yes	characteristic, complemented
65	#66151	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#4062	C₂×C₃	1	1	yes	characteristic, complemented
67	#65527	C₂×C₃	1	1	yes	characteristic, complemented
68	#65517	C₂×C₃	1	1	yes	characteristic, complemented
69	#65479	C₂×C₃	1	1	yes	characteristic, complemented
70	#65477	C₂×C₃	1	1	yes	characteristic, complemented
71	#65476	C₂×C₃	1	1	yes	characteristic, complemented
72	#65471	C₂×C₃	1	1	yes	characteristic, complemented
73	#65462	C₂×C₃	1	1	yes	characteristic, complemented
74	#65454	C₂×C₃	1	1	yes	characteristic, complemented
75	#65453	C₂×C₃	1	1	yes	characteristic, complemented
76	#65423	C₂×C₃	1	1	yes	characteristic, complemented
77	#65416	C₂×C₃	1	1	yes	characteristic, complemented
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	4	1	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	2	2	no	—
82	C₂×C₃×C₅×Q₈	—	4	1	no	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
93	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
94	C₂²×C₃×Dic₅	—	2	1	no	—
95	C₂²×C₃×Dic₅	—	2	1	no	—
96	C₃×#713	—	2	2	no	—
97	C₃×#713	—	4	1	no	—
98	C₃×#711	—	2	2	no	—
99	C₃×#711	—	4	1	no	—
100	C₂×C₃×D₂₀	—	2	1	no	—
101	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄×D₅	—	2	1	no	—
103	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
104	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
105	C₃×C₅×Q₁₆	—	2	2	no	—
106	C₃×C₅×Q₁₆	—	2	2	no	—
107	C₃×C₅×SD₁₆	—	2	2	no	—
108	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
109	C₃×C₅×M₁₆	—	2	2	no	—
110	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₃×C₂²⋊Dic₅	—	2	1	no	—
113	C₃×C₂²⋊Dic₅	—	2	1	no	—
114	C₃×C₂²⋊Dic₅	D₄	1	1	yes	characteristic
115	C₃×#689	—	2	2	no	—
116	C₃×#689	—	4	1	no	—
117	C₃×#688	—	4	1	no	—
118	C₃×#686	—	2	2	no	—
119	C₃×#685	—	2	1	no	—
120	C₃×#685	—	2	1	no	—
121	C₃×#685	—	2	1	no	—
122	C₃×#685	—	2	1	no	—
123	C₃×#685	—	2	1	no	—
124	C₃×#685	D₄	1	1	yes	characteristic
125	C₃×C₄⋊Dic₅	—	2	1	no	—
126	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
128	C₃×#683	—	2	1	no	—
129	C₃×#683	—	2	1	no	—
130	C₃×#683	—	2	1	no	—
131	C₃×#683	—	2	1	no	—
132	C₃×#683	—	2	1	no	—
133	C₃×#683	D₄	1	1	yes	characteristic
134	C₃×C₄×Dic₅	—	2	1	no	—
135	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
136	C₂×C₃×#168	C₂³	1	1	yes	characteristic
137	C₂×C₃×#168	C₂³	1	1	yes	characteristic
138	C₃×#677	—	2	2	no	—
139	C₃×C₈×D₅	—	2	2	no	—
140	C₂×C₃×#137	D₅	1	1	yes	characteristic, complemented
141	C₂×C₃×#135	—	5	1	no	—
142	C₃×#548	—	5	1	no	—
143	C₃×#547	—	5	1	no	—
144	C₃×#497	—	5	1	no	—
145	C₃×#468	—	5	1	no	—
146	C₃×#467	—	5	1	no	—
147	C₃×#463	—	5	1	no	—
148	C₃×#462	—	5	1	no	—
149	C₃×#452	—	5	1	no	—
150	C₃×#452	—	5	1	no	—
151	C₃×#451	—	5	1	no	—
152	C₃×#449	—	5	1	no	—
153	C₃×#440	—	5	1	no	—
154	C₃×#435	—	5	1	no	—
155	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×#713	C₂²×C₃	1	1	yes	characteristic
158	C₂×#711	C₂²×C₃	1	1	yes	characteristic
159	C₅×#137	—	2	4	no	—
160	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
165	#4093	—	2	1	no	—
166	#4093	C₂²×C₃	1	1	yes	characteristic
167	#4092	—	2	1	no	—
168	#4092	C₂²×C₃	1	1	yes	characteristic
169	#4092	C₂²×C₃	1	1	yes	characteristic
170	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
171	#4090	C₂²×C₃	1	1	yes	characteristic
172	C₂×#689	C₂²×C₃	1	1	yes	characteristic
173	C₂×#689	C₂²×C₃	1	1	yes	characteristic
174	C₂×#688	C₂²×C₃	1	1	yes	characteristic
175	#4085	—	2	1	no	—
176	#4081	—	2	1	no	—
177	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
178	C₂×#686	C₂²×C₃	1	1	yes	characteristic
179	#4076	—	2	1	no	—
180	#4076	C₂²×C₃	1	1	yes	characteristic
181	#4075	—	2	1	no	—
182	C₄×C₂²⋊D₅	—	2	1	no	—
183	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
184	#4070	C₂²×C₃	1	1	yes	characteristic
185	C₂×#683	—	2	1	no	—
186	#4062	—	2	4	no	—
187	C₂×#677	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
189	#3967	C₂²×C₃	1	1	yes	characteristic
190	#3967	C₂²×C₃	1	1	yes	characteristic
191	#3967	C₂²×C₃	1	1	yes	characteristic
192	#3964	C₂²×C₃	1	1	yes	characteristic
193	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
194	#3953	C₂²×C₃	1	1	yes	characteristic
195	#3952	C₂²×C₃	1	1	yes	characteristic
196	#3950	C₂²×C₃	1	1	yes	characteristic
197	#3948	C₂²×C₃	1	1	yes	characteristic
198	#3947	C₂²×C₃	1	1	yes	characteristic
199	#3946	C₂²×C₃	1	1	yes	characteristic
200	#3269	—	5	1	no	Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₃×D₅	—	2	1	no	—
204	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×Q₈	—	2	1	no	—
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	4	2	no	—
211	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	4	2	no	—
214	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	4	2	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₃×C₂²⋊D₅	—	4	1	no	—
225	C₃×C₂²⋊D₅	—	4	2	no	—
226	C₃×C₂²⋊D₅	—	4	2	no	—
227	C₂×C₃×Dic₅	—	2	1	no	—
228	C₂×C₃×Dic₅	—	2	1	no	—
229	C₂×C₃×Dic₅	—	2	1	no	—
230	C₂×C₃×Dic₅	—	4	2	no	—
231	C₂×C₃×Dic₅	—	4	2	no	—
232	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
233	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
234	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
235	C₃×D₂₀	—	2	1	no	—
236	C₃×D₂₀	—	2	1	no	—
237	C₃×D₂₀	—	4	2	no	—
238	C₃×C₄×D₅	—	2	1	no	—
239	C₃×C₄×D₅	—	2	1	no	—
240	C₃×C₄×D₅	—	4	2	no	—
241	C₃×Dic₁₀	—	2	1	no	—
242	C₃×Dic₁₀	—	2	1	no	—
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
245	C₃×#168	—	2	1	no	—
246	C₃×#168	—	2	1	no	—
247	C₂×C₃×#41	—	5	1	no	—
248	C₂×C₃×#41	—	5	1	no	—
249	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
250	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
251	C₃×#137	—	2	4	no	—
252	C₃×#135	—	10	4	no	—
253	C₂×C₃×Q₁₆	—	5	1	no	—
254	C₂×C₃×Q₁₆	—	5	1	no	—
255	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
256	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
257	C₂×C₃×SD₁₆	—	5	1	no	—
258	C₂×C₃×SD₁₆	—	5	1	no	—
259	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
260	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
261	C₂×C₃×D₈	—	5	1	no	—
262	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
263	C₂²×C₃×C₈	—	5	1	no	—
264	C₃×C₄⋊Q₈	—	5	1	no	—
265	C₃×#124	—	5	1	no	—
266	C₃×#124	—	10	1	no	—
267	C₃×#123	—	10	1	no	—
268	C₃×#123	—	10	1	no	—
269	C₃×C₂²⋊Q₈	—	5	1	no	—
270	C₃×C₂²⋊Q₈	—	5	1	no	—
271	C₃×C₂²⋊Q₈	—	5	1	no	—
272	C₃×C₂²⋊Q₈	—	10	1	no	—
273	C₃×#121	—	5	1	no	—
274	C₃×#121	—	10	1	no	—
275	C₃×#121	—	10	1	no	—
276	C₃×C₄×Q₈	—	5	1	no	—
277	C₃×C₄×D₄	—	5	1	no	—
278	C₃×C₄×D₄	—	5	1	no	—
279	C₃×C₄×D₄	—	10	1	no	—
280	C₂×C₃×C₄⋊C₄	—	10	1	no	—
281	C₃×#107	—	5	1	no	—
282	C₃×C₄⋊C₈	—	5	1	no	—
283	C₃×#103	—	5	1	no	—
284	C₃×#103	—	5	1	no	—
285	C₃×#103	—	5	1	no	—
286	C₃×#103	—	5	1	no	—
287	C₃×#102	—	5	1	no	—
288	C₃×#102	—	5	1	no	—
289	C₃×C₂²⋊C₈	—	5	1	no	—
290	C₃×C₂²⋊C₈	—	5	1	no	—
291	C₃×#97	—	5	1	no	—
292	C₅×#41	—	2	2	no	—
293	C₅×#41	—	4	1	no	—
294	C₂×C₅×Q₈	—	2	1	no	—
295	C₂×C₅×Q₈	—	2	2	no	—
296	C₂×C₅×Q₈	—	4	1	no	—
297	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₅×D₄	—	2	1	no	—
301	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	—	2	1	no	—
303	C₂²×C₄×C₅	—	2	1	no	—
304	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₂²⋊D₅	—	2	1	no	—
306	C₂×C₂²⋊D₅	—	2	1	no	—
307	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
308	C₂²×Dic₅	—	2	1	no	—
309	C₂²×Dic₅	—	2	1	no	—
310	#713	—	2	2	no	—
311	#713	—	4	1	no	—
312	#711	—	2	2	no	—
313	#711	—	4	1	no	—
314	C₂×D₂₀	—	2	1	no	—
315	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄×D₅	—	2	1	no	—
317	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
318	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
319	C₅×Q₁₆	—	2	2	no	—
320	C₅×Q₁₆	—	2	2	no	—
321	C₅×SD₁₆	—	2	2	no	—
322	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
323	C₅×M₁₆	—	2	2	no	—
324	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
325	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
326	C₂²⋊Dic₅	—	2	1	no	—
327	C₂²⋊Dic₅	—	2	1	no	—
328	C₂²⋊Dic₅	C₃×D₄	1	1	yes	characteristic
329	#689	—	2	2	no	—
330	#689	—	4	1	no	—
331	#688	—	4	1	no	—
332	#686	—	2	2	no	—
333	#685	—	2	1	no	—
334	#685	—	2	1	no	—
335	#685	—	2	1	no	—
336	#685	—	2	1	no	—
337	#685	—	2	1	no	—
338	#685	C₃×D₄	1	1	yes	characteristic
339	C₄⋊Dic₅	—	2	1	no	—
340	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
341	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
342	#683	—	2	1	no	—
343	#683	—	2	1	no	—
344	#683	—	2	1	no	—
345	#683	—	2	1	no	—
346	#683	—	2	1	no	—
347	#683	C₃×D₄	1	1	yes	characteristic
348	C₄×Dic₅	—	2	1	no	—
349	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
350	C₂×#168	C₂³×C₃	1	1	yes	characteristic
351	C₂×#168	C₂³×C₃	1	1	yes	characteristic
352	#677	—	2	2	no	—
353	C₈×D₅	—	2	2	no	—
354	C₂×#137	C₃×D₅	1	1	yes	characteristic, complemented
355	C₂×#135	—	5	1	no	—
356	#548	—	5	1	no	—
357	#547	—	5	1	no	—
358	#497	—	5	1	no	—
359	#468	—	5	1	no	—
360	#467	—	5	1	no	—
361	#463	—	5	1	no	—
362	#462	—	5	1	no	—
363	#452	—	5	1	no	—
364	#452	—	5	1	no	—
365	#451	—	5	1	no	—
366	#449	—	5	1	no	—
367	#440	—	5	1	no	—
368	#435	—	5	1	no	—
369	C₂²×C₃×C₅	—	2	2	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₃×D₅	—	2	1	no	—
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	—	4	1	no	—
380	C₂×C₃×D₅	—	4	1	no	—
381	C₂×C₃×D₅	—	4	1	no	—
382	C₃×C₄×C₅	—	2	2	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	—	4	1	no	—
386	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
387	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
388	C₃×Dic₅	—	2	1	no	—
389	C₃×Dic₅	—	2	1	no	—
390	C₃×Dic₅	—	2	1	no	—
391	C₃×Dic₅	—	4	1	no	—
392	C₃×Dic₅	—	4	1	no	—
393	C₃×Dic₅	—	4	1	no	—
394	C₃×#41	—	2	2	no	—
395	C₃×#41	—	4	1	no	—
396	C₃×#41	—	10	2	no	—
397	C₃×#41	—	10	2	no	—
398	C₃×#41	—	20	1	no	—
399	C₃×#41	—	20	1	no	—
400	C₂×C₃×Q₈	—	2	1	no	—
401	C₂×C₃×Q₈	—	2	2	no	—
402	C₂×C₃×Q₈	—	4	1	no	—
403	C₂×C₃×Q₈	—	5	1	no	—
404	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
405	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
406	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
407	C₂×C₃×D₄	—	2	1	no	—
408	C₂×C₃×D₄	—	5	1	no	—
409	C₂×C₃×D₄	—	5	1	no	—
410	C₂×C₃×D₄	—	10	1	no	—
411	C₂×C₃×D₄	—	10	1	no	—
412	C₂×C₃×D₄	—	10	1	no	—
413	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	—	2	1	no	—
415	C₂²×C₃×C₄	—	2	1	no	—
416	C₂²×C₃×C₄	—	5	1	no	—
417	C₂²×C₃×C₄	—	10	1	no	—
418	C₂²×C₃×C₄	—	10	1	no	—
419	C₂²×C₃×C₄	—	10	1	no	—
420	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
421	C₃×Q₁₆	—	2	2	no	—
422	C₃×Q₁₆	—	2	2	no	—
423	C₃×Q₁₆	—	10	2	no	—
424	C₃×Q₁₆	—	20	1	no	—
425	C₃×SD₁₆	—	2	2	no	—
426	C₃×SD₁₆	—	10	2	no	—
427	C₃×SD₁₆	—	20	1	no	—
428	C₃×SD₁₆	C₂²⋊D₅	1	4	yes	complemented
429	C₃×D₈	—	10	2	no	—
430	C₃×M₁₆	—	2	2	no	—
431	C₂×C₃×C₈	—	5	1	no	—
432	C₂×C₃×C₈	—	5	1	no	—
433	C₂×C₃×C₈	—	10	2	no	—
434	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
435	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
436	C₃×C₄⋊C₄	—	5	1	no	—
437	C₃×C₄⋊C₄	—	5	1	no	—
438	C₃×C₄⋊C₄	—	5	1	no	—
439	C₃×C₄⋊C₄	—	10	1	no	—
440	C₃×C₄⋊C₄	—	10	1	no	—
441	C₃×C₄⋊C₄	—	10	1	no	—
442	C₃×C₄⋊C₄	—	10	1	no	—
443	C₃×C₄⋊C₄	—	10	1	no	—
444	C₃×C₄⋊C₄	—	10	1	no	—
445	C₃×C₂²⋊C₄	—	5	1	no	—
446	C₃×C₂²⋊C₄	—	5	1	no	—
447	C₃×C₂²⋊C₄	—	10	1	no	—
448	C₃×C₂²⋊C₄	—	10	1	no	—
449	C₃×C₂²⋊C₄	—	10	1	no	—
450	C₃×C₂²⋊C₄	—	10	1	no	—
451	C₃×C₂²⋊C₄	—	10	1	no	—
452	C₃×C₂²⋊C₄	—	10	1	no	—
453	C₃×C₂²⋊C₄	—	10	1	no	—
454	C₃×C₄²	—	5	1	no	—
455	C₃×C₄²	—	10	1	no	—
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂²×D₅	—	2	1	no	—
459	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
460	C₅×Q₈	—	2	1	no	—
461	C₅×Q₈	—	2	1	no	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	—	2	1	no	—
464	C₅×Q₈	—	2	1	no	—
465	C₅×Q₈	—	4	2	no	—
466	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
467	C₅×D₄	—	2	1	no	—
468	C₅×D₄	—	4	2	no	—
469	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	4	2	no	—
476	C₂×C₄×C₅	—	4	2	no	—
477	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
478	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
479	C₂²⋊D₅	—	4	1	no	—
480	C₂²⋊D₅	—	4	2	no	—
481	C₂²⋊D₅	—	4	2	no	—
482	C₂×Dic₅	—	2	1	no	—
483	C₂×Dic₅	—	2	1	no	—
484	C₂×Dic₅	—	2	1	no	—
485	C₂×Dic₅	—	4	2	no	—
486	C₂×Dic₅	—	4	2	no	—
487	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
488	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
489	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
490	D₂₀	—	2	1	no	—
491	D₂₀	—	2	1	no	—
492	D₂₀	—	4	2	no	—
493	C₄×D₅	—	2	1	no	—
494	C₄×D₅	—	2	1	no	—
495	C₄×D₅	—	4	2	no	—
496	Dic₁₀	—	2	1	no	—
497	Dic₁₀	—	2	1	no	—
498	C₅×C₈	—	2	1	no	—
499	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
500	#168	—	2	1	no	—
501	#168	—	2	1	no	—
502	C₂×#41	—	5	1	no	—
503	C₂×#41	—	5	1	no	—
504	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
505	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
506	#137	—	2	4	no	—
507	#135	—	10	4	no	—
508	C₂×Q₁₆	—	5	1	no	—
509	C₂×Q₁₆	—	5	1	no	—
510	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
511	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
512	C₂×SD₁₆	—	5	1	no	—
513	C₂×SD₁₆	—	5	1	no	—
514	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
515	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
516	C₂×D₈	—	5	1	no	—
517	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
518	C₂²×C₈	—	5	1	no	—
519	C₄⋊Q₈	—	5	1	no	—
520	#124	—	5	1	no	—
521	#124	—	10	1	no	—
522	#123	—	10	1	no	—
523	#123	—	10	1	no	—
524	C₂²⋊Q₈	—	5	1	no	—
525	C₂²⋊Q₈	—	5	1	no	—
526	C₂²⋊Q₈	—	5	1	no	—
527	C₂²⋊Q₈	—	10	1	no	—
528	#121	—	5	1	no	—
529	#121	—	10	1	no	—
530	#121	—	10	1	no	—
531	C₄×Q₈	—	5	1	no	—
532	C₄×D₄	—	5	1	no	—
533	C₄×D₄	—	5	1	no	—
534	C₄×D₄	—	10	1	no	—
535	C₂×C₄⋊C₄	—	10	1	no	—
536	#107	—	5	1	no	—
537	C₄⋊C₈	—	5	1	no	—
538	#103	—	5	1	no	—
539	#103	—	5	1	no	—
540	#103	—	5	1	no	—
541	#103	—	5	1	no	—
542	#102	—	5	1	no	—
543	#102	—	5	1	no	—
544	C₂²⋊C₈	—	5	1	no	—
545	C₂²⋊C₈	—	5	1	no	—
546	#97	—	5	1	no	—
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	2	no	—
549	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
550	C₂×C₃×C₅	#575	1	1	yes	characteristic
551	C₂×C₃×C₅	#578	1	1	yes	characteristic
552	C₃×D₅	—	4	1	no	—
553	C₃×D₅	—	8	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	5	1	no	—
556	C₂³×C₃	—	10	1	no	—
557	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
558	C₃×Q₈	—	2	1	no	—
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×Q₈	—	2	1	no	—
562	C₃×Q₈	—	2	1	no	—
563	C₃×Q₈	—	4	2	no	—
564	C₃×Q₈	—	10	1	no	—
565	C₃×Q₈	—	10	1	no	—
566	C₃×Q₈	C₂×C₂²⋊D₅	1	2	yes	—
567	C₃×D₄	—	2	1	no	—
568	C₃×D₄	—	4	2	no	—
569	C₃×D₄	—	10	1	no	—
570	C₃×D₄	—	10	1	no	—
571	C₃×D₄	—	20	2	no	—
572	C₃×D₄	—	20	1	no	—
573	C₃×D₄	—	20	2	no	—
574	C₃×D₄	—	20	2	no	—
575	C₃×D₄	C₂×C₂²⋊D₅	1	2	yes	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	4	2	no	—
582	C₂×C₃×C₄	—	4	2	no	—
583	C₂×C₃×C₄	—	5	1	no	—
584	C₂×C₃×C₄	—	5	1	no	—
585	C₂×C₃×C₄	—	5	1	no	—
586	C₂×C₃×C₄	—	10	1	no	—
587	C₂×C₃×C₄	—	10	1	no	—
588	C₂×C₃×C₄	—	10	1	no	—
589	C₂×C₃×C₄	—	10	1	no	—
590	C₂×C₃×C₄	—	10	1	no	—
591	C₂×C₃×C₄	—	20	2	no	—
592	C₂×C₃×C₄	—	20	2	no	—
593	C₂×C₃×C₄	—	20	2	no	—
594	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
596	C₃×C₈	—	2	1	no	—
597	C₃×C₈	—	10	1	no	—
598	C₃×C₈	—	10	1	no	—
599	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	2	no	—
603	C₂²×C₅	—	2	1	no	—
604	C₂²×C₅	—	4	1	no	—
605	C₂²×C₅	—	4	1	no	—
606	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
607	C₂×D₅	—	2	1	no	—
608	C₂×D₅	—	2	1	no	—
609	C₂×D₅	—	2	1	no	—
610	C₂×D₅	—	4	1	no	—
611	C₂×D₅	—	4	1	no	—
612	C₂×D₅	—	4	1	no	—
613	C₄×C₅	—	2	2	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
618	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
619	Dic₅	—	2	1	no	—
620	Dic₅	—	2	1	no	—
621	Dic₅	—	2	1	no	—
622	Dic₅	—	4	1	no	—
623	Dic₅	—	4	1	no	—
624	Dic₅	—	4	1	no	—
625	#41	—	2	2	no	—
626	#41	—	4	1	no	—
627	#41	—	10	2	no	—
628	#41	—	10	2	no	—
629	#41	—	20	1	no	—
630	#41	—	20	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	4	1	no	—
634	C₂×Q₈	—	5	1	no	—
635	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
636	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
637	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	5	1	no	—
640	C₂×D₄	—	5	1	no	—
641	C₂×D₄	—	10	1	no	—
642	C₂×D₄	—	10	1	no	—
643	C₂×D₄	—	10	1	no	—
644	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	5	1	no	—
648	C₂²×C₄	—	10	1	no	—
649	C₂²×C₄	—	10	1	no	—
650	C₂²×C₄	—	10	1	no	—
651	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
652	Q₁₆	—	2	2	no	—
653	Q₁₆	—	2	2	no	—
654	Q₁₆	—	10	2	no	—
655	Q₁₆	—	20	1	no	—
656	SD₁₆	—	2	2	no	—
657	SD₁₆	—	10	2	no	—
658	SD₁₆	—	20	1	no	—
659	SD₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
660	D₈	—	10	2	no	—
661	M₁₆	—	2	2	no	—
662	C₂×C₈	—	5	1	no	—
663	C₂×C₈	—	5	1	no	—
664	C₂×C₈	—	10	2	no	—
665	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
666	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
667	C₄⋊C₄	—	5	1	no	—
668	C₄⋊C₄	—	5	1	no	—
669	C₄⋊C₄	—	5	1	no	—
670	C₄⋊C₄	—	10	1	no	—
671	C₄⋊C₄	—	10	1	no	—
672	C₄⋊C₄	—	10	1	no	—
673	C₄⋊C₄	—	10	1	no	—
674	C₄⋊C₄	—	10	1	no	—
675	C₄⋊C₄	—	10	1	no	—
676	C₂²⋊C₄	—	5	1	no	—
677	C₂²⋊C₄	—	5	1	no	—
678	C₂²⋊C₄	—	10	1	no	—
679	C₂²⋊C₄	—	10	1	no	—
680	C₂²⋊C₄	—	10	1	no	—
681	C₂²⋊C₄	—	10	1	no	—
682	C₂²⋊C₄	—	10	1	no	—
683	C₂²⋊C₄	—	10	1	no	—
684	C₂²⋊C₄	—	10	1	no	—
685	C₄²	—	5	1	no	—
686	C₄²	—	10	1	no	—
687	C₃×C₅	#3269	1	1	yes	characteristic, complemented, Hall
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	—	2	2	no	—
692	C₂²×C₃	—	4	1	no	—
693	C₂²×C₃	—	4	1	no	—
694	C₂²×C₃	—	10	1	no	—
695	C₂²×C₃	—	10	1	no	—
696	C₂²×C₃	—	10	1	no	—
697	C₂²×C₃	—	20	1	no	—
698	C₂²×C₃	—	20	1	no	—
699	C₂²×C₃	—	20	1	no	—
700	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	2	no	—
703	C₃×C₄	—	4	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	10	1	no	—
706	C₃×C₄	—	10	1	no	—
707	C₃×C₄	—	10	1	no	—
708	C₃×C₄	—	20	1	no	—
709	C₃×C₄	—	20	1	no	—
710	C₃×C₄	—	20	1	no	—
711	C₃×C₄	#4144	1	1	yes	characteristic
712	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
713	C₂×C₅	—	4	1	no	—
714	C₂×C₅	—	4	2	no	—
715	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
716	C₂×C₅	C₃×#575	1	1	yes	characteristic
717	C₂×C₅	C₃×#578	1	1	yes	characteristic
718	D₅	—	4	1	no	—
719	D₅	—	8	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	5	1	no	—
722	C₂³	—	10	1	no	—
723	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	10	1	no	—
731	Q₈	—	10	1	no	—
732	Q₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
733	D₄	—	2	1	no	—
734	D₄	—	4	2	no	—
735	D₄	—	10	1	no	—
736	D₄	—	10	1	no	—
737	D₄	—	20	2	no	—
738	D₄	—	20	1	no	—
739	D₄	—	20	2	no	—
740	D₄	—	20	2	no	—
741	D₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	5	1	no	—
750	C₂×C₄	—	5	1	no	—
751	C₂×C₄	—	5	1	no	—
752	C₂×C₄	—	10	1	no	—
753	C₂×C₄	—	10	1	no	—
754	C₂×C₄	—	10	1	no	—
755	C₂×C₄	—	10	1	no	—
756	C₂×C₄	—	10	1	no	—
757	C₂×C₄	—	20	2	no	—
758	C₂×C₄	—	20	2	no	—
759	C₂×C₄	—	20	2	no	—
760	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
761	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	10	1	no	—
764	C₈	—	10	1	no	—
765	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	2	no	—
768	C₂×C₃	—	20	1	no	—
769	C₂×C₃	—	40	1	no	—
770	C₂×C₃	#66111	1	1	yes	characteristic
771	C₂×C₃	#66113	1	1	yes	characteristic
772	C₂×C₃	D₄×C₂²⋊D₅	1	1	yes	characteristic
773	C₅	C₃×#3269	1	1	yes	characteristic, complemented, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	10	1	no	—
781	C₂²	—	10	1	no	—
782	C₂²	—	10	1	no	—
783	C₂²	—	20	1	no	—
784	C₂²	—	20	1	no	—
785	C₂²	—	20	1	no	—
786	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	2	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	10	1	no	—
792	C₄	—	10	1	no	—
793	C₄	—	10	1	no	—
794	C₄	—	20	1	no	—
795	C₄	—	20	1	no	—
796	C₄	—	20	1	no	—
797	C₄	C₃×#4144	1	1	yes	characteristic
798	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
799	C₃	#10615719	1	1	yes	characteristic, direct product factor, Sylow
800	C₂	—	4	1	no	—
801	C₂	—	4	2	no	—
802	C₂	—	20	1	no	—
803	C₂	—	40	1	no	—
804	C₂	C₃×#66111	1	1	yes	characteristic
805	C₂	C₃×#66113	1	1	yes	characteristic
806	C₂	C₃×D₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#137	D₅
hypocenter	C₅	C₃×#3269
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
2. C₃×#66158	C₂	semidirect
3. C₃×#66151	C₂	semidirect
4. C₂×C₃×#4062	C₂	semidirect
5. C₃×#65527	C₂	semidirect
6. C₃×#65517	C₂	semidirect
7. C₃×#65479	C₂	semidirect
8. C₃×#65477	C₂	semidirect
9. C₃×#65476	C₂	semidirect
10. C₃×#65471	C₂	semidirect
11. C₃×#65462	C₂	semidirect
12. C₃×#65454	C₂	semidirect
13. C₃×#65453	C₂	semidirect
14. C₃×#65423	C₂	semidirect
15. C₃×#65416	C₂	semidirect
16. #10615719	C₃	direct (N × H)
63. C₂×C₅×#137	C₂×C₃	semidirect
64. #66158	C₂×C₃	semidirect
65. #66151	C₂×C₃	semidirect
66. C₂×#4062	C₂×C₃	semidirect
67. #65527	C₂×C₃	semidirect
68. #65517	C₂×C₃	semidirect
69. #65479	C₂×C₃	semidirect
70. #65477	C₂×C₃	semidirect
71. #65476	C₂×C₃	semidirect
72. #65471	C₂×C₃	semidirect
73. #65462	C₂×C₃	semidirect
74. #65454	C₂×C₃	semidirect
75. #65453	C₂×C₃	semidirect
76. #65423	C₂×C₃	semidirect
77. #65416	C₂×C₃	semidirect
108. C₃×C₅×SD₁₆	D₄	semidirect
140. C₂×C₃×#137	D₅	semidirect
322. C₅×SD₁₆	C₃×D₄	semidirect
354. C₂×#137	C₃×D₅	semidirect
428. C₃×SD₁₆	C₂²⋊D₅	semidirect
659. SD₁₆	C₃×C₂²⋊D₅	semidirect
687. C₃×C₅	#3269	semidirect
773. C₅	C₃×#3269	semidirect
799. C₃	#10615719	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×#137	2
C₃×#66158	2
C₃×#66151	2
C₂×C₃×#4062	2
C₃×#65527	2
C₃×#65517	2
C₃×#65479	2
C₃×#65477	2
C₃×#65476	2
C₃×#65471	2
C₃×#65462	2
C₃×#65454	2
C₃×#65453	2
C₃×#65423	2
C₃×#65416	2
#10615719	3
C₃×#3269	5

Subgroups — C3×#10615719 #14454451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615719 #14454451