Subgroups — C₃×#10618288 #14481494

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66040	C₂	1	2	yes	maximal, complemented
3	C₃×#66035	C₂	1	2	yes	maximal, complemented
4	C₃×#66014	C₂	1	2	yes	maximal, complemented
5	C₃×#66003	C₂	1	2	yes	maximal, complemented
6	C₃×#65996	C₂	1	2	yes	maximal, complemented
7	C₃×#65983	C₂	1	2	yes	maximal, complemented
8	C₃×#65979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65956	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65949	C₂	1	2	yes	maximal, complemented
11	C₃×#65936	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65934	C₂	1	2	yes	maximal, complemented
13	C₃×#65930	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65927	C₂	1	2	yes	maximal, complemented
15	C₃×#65920	C₂	1	2	yes	maximal, complemented
16	C₃×#65898	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×#711	C₂	1	2	yes	maximal, complemented
18	C₃×#65828	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
20	#10618288	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#711	C₂²	1	2	yes	—
23	C₃×C₅×#126	C₂²	1	2	yes	—
24	C₃×C₅×#124	C₂²	1	2	yes	—
25	C₃×C₅×#123	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₅×#121	C₂²	1	1	yes	characteristic
28	C₃×C₅×#121	C₂²	1	2	yes	—
29	C₃×C₅×#120	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×#4099	C₂²	1	2	yes	—
33	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
34	C₃×#4092	C₂²	1	2	yes	complemented
35	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
37	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
38	C₃×#4085	C₂²	1	2	yes	—
39	C₃×#4085	C₂²	1	2	yes	—
40	C₃×#4085	C₂²	1	2	yes	—
41	C₃×#4085	C₂²	1	2	yes	—
42	C₃×#4084	C₂²	1	2	yes	—
43	C₃×#4082	C₂²	1	2	yes	—
44	C₃×#4081	C₂²	1	2	yes	—
45	C₃×#4081	C₂²	1	2	yes	—
46	C₃×#4081	C₂²	1	2	yes	complemented
47	C₃×D₄×Dic₅	C₂²	1	2	yes	—
48	C₃×D₄×Dic₅	C₂²	1	2	yes	—
49	C₃×D₄×Dic₅	C₂²	1	2	yes	—
50	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
51	C₃×#4076	C₂²	1	1	yes	characteristic
52	C₃×#4075	C₂²	1	2	yes	complemented
53	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
54	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
55	C₃×#4070	C₂²	1	1	yes	characteristic
56	C₃×#4070	C₂²	1	2	yes	complemented
57	C₂×C₃×#683	C₂²	1	1	yes	characteristic
58	C₂×C₃×#683	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
60	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
62	C₃×#4044	C₂²	1	2	yes	complemented
63	C₃×#4042	C₂²	1	2	yes	complemented
64	C₃×#4040	C₂²	1	2	yes	complemented
65	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
66	C₃×#4038	C₂²	1	2	yes	complemented
67	C₃×#4036	C₂²	1	2	yes	complemented
68	C₃×#4035	C₂²	1	2	yes	complemented
69	C₃×#4035	C₂²	1	2	yes	complemented
70	C₃×#4035	C₂²	1	2	yes	complemented
71	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
72	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
73	C₃×#4033	C₂²	1	2	yes	complemented
74	C₃×#4033	C₂²	1	2	yes	complemented
75	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
76	C₃×#4032	C₂²	1	2	yes	—
77	C₃×#4031	C₂²	1	2	yes	—
78	C₃×#4031	C₂²	1	2	yes	—
79	C₃×#4031	C₂²	1	2	yes	complemented
80	C₃×#4030	C₂²	1	2	yes	—
81	C₃×#4029	C₂²	1	2	yes	—
82	C₃×#4029	C₂²	1	2	yes	—
83	C₃×#4029	C₂²	1	2	yes	complemented
84	C₃×#4027	C₂²	1	2	yes	—
85	C₃×#4027	C₂²	1	2	yes	—
86	C₃×#4027	C₂²	1	2	yes	—
87	C₃×#4027	C₂²	1	2	yes	complemented
88	C₃×#4027	C₂²	1	2	yes	complemented
89	C₃×#4025	C₂²	1	2	yes	—
90	C₃×#4025	C₂²	1	2	yes	—
91	C₃×#4025	C₂²	1	2	yes	—
92	C₃×#4025	C₂²	1	2	yes	complemented
93	C₃×#4025	C₂²	1	2	yes	complemented
94	C₃×#4024	C₂²	1	2	yes	—
95	C₃×#4024	C₂²	1	2	yes	—
96	C₃×#4024	C₂²	1	2	yes	—
97	C₃×#4024	C₂²	1	2	yes	complemented
98	C₃×#4023	C₂²	1	2	yes	—
99	C₃×#4023	C₂²	1	2	yes	—
100	C₃×#4023	C₂²	1	2	yes	—
101	C₃×#4023	C₂²	1	2	yes	—
102	C₃×#4023	C₂²	1	2	yes	—
103	C₃×#4023	C₂²	1	2	yes	complemented
104	C₃×#4022	C₂²	1	2	yes	complemented
105	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
106	C₃×#4016	C₂²	1	2	yes	complemented
107	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
108	C₃×#3455	—	5	1	no	maximal, Hall
109	C₅×#538	C₂×C₃	1	1	yes	characteristic, complemented
110	#66040	C₂×C₃	1	2	yes	complemented
111	#66035	C₂×C₃	1	2	yes	complemented
112	#66014	C₂×C₃	1	2	yes	complemented
113	#66003	C₂×C₃	1	2	yes	complemented
114	#65996	C₂×C₃	1	2	yes	complemented
115	#65983	C₂×C₃	1	2	yes	complemented
116	#65979	C₂×C₃	1	1	yes	characteristic, complemented
117	#65956	C₂×C₃	1	1	yes	characteristic, complemented
118	#65949	C₂×C₃	1	2	yes	complemented
119	#65936	C₂×C₃	1	1	yes	characteristic, complemented
120	#65934	C₂×C₃	1	2	yes	complemented
121	#65930	C₂×C₃	1	1	yes	characteristic, complemented
122	#65927	C₂×C₃	1	2	yes	complemented
123	#65920	C₂×C₃	1	2	yes	complemented
124	#65898	C₂×C₃	1	2	yes	complemented
125	C₄×#711	C₂×C₃	1	2	yes	complemented
126	#65828	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#4023	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
131	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
133	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
137	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
139	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
140	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂²×C₃×Dic₅	—	2	4	no	—
143	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
144	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
145	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
146	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
147	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
149	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
151	C₃×#711	—	2	8	no	—
152	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
154	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
155	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
157	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
158	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
159	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₃×C₄²×C₅	C₂³	1	2	yes	—
171	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
172	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
173	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
174	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
175	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
178	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
179	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
180	C₃×#685	C₂³	1	2	yes	—
181	C₃×#685	C₂³	1	2	yes	—
182	C₃×#685	C₂³	1	2	yes	—
183	C₃×#685	C₂³	1	2	yes	—
184	C₃×#685	C₂³	1	2	yes	—
185	C₃×#685	C₂³	1	2	yes	—
186	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
187	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
188	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
189	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
191	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₃×#683	C₂³	1	2	yes	—
193	C₃×#683	C₂³	1	2	yes	—
194	C₃×#683	C₂³	1	2	yes	—
195	C₃×#683	C₂³	1	2	yes	—
196	C₃×#683	C₂³	1	2	yes	—
197	C₃×#683	C₂³	1	2	yes	—
198	C₃×#683	C₂³	1	2	yes	—
199	C₃×#683	C₂³	1	2	yes	—
200	C₃×#683	C₂³	1	2	yes	—
201	C₃×#683	C₂³	1	2	yes	—
202	C₃×#683	C₂³	1	2	yes	—
203	C₃×#683	C₂³	1	2	yes	—
204	C₃×#683	C₂³	1	2	yes	—
205	C₃×#683	C₂³	1	2	yes	—
206	C₃×C₄×Dic₅	C₂³	1	2	yes	—
207	C₃×C₄×Dic₅	C₂³	1	2	yes	—
208	C₃×C₄×Dic₅	C₂³	1	2	yes	—
209	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
210	C₃×C₄×Dic₅	C₂³	1	2	yes	—
211	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
212	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
213	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
214	C₃×C₄×Dic₅	C₂³	1	2	yes	—
215	C₃×C₄×Dic₅	C₂³	1	2	yes	—
216	C₃×C₄×Dic₅	C₂³	1	2	yes	—
217	C₃×#542	—	5	2	no	—
218	C₃×#542	—	5	2	no	—
219	C₃×#541	—	5	2	no	—
220	C₃×#540	—	5	2	no	—
221	C₃×#539	—	5	1	no	—
222	C₃×#539	—	5	1	no	—
223	C₃×#539	—	5	2	no	—
224	C₃×#538	—	5	2	no	—
225	C₃×#538	—	5	1	no	—
226	C₃×#538	D₅	1	1	yes	characteristic, complemented
227	C₃×#533	—	5	1	no	—
228	C₃×#532	—	5	1	no	—
229	C₃×#529	—	5	2	no	—
230	C₃×#529	—	5	2	no	—
231	C₃×#529	—	5	2	no	—
232	C₃×#529	—	5	2	no	—
233	C₃×#525	—	5	2	no	—
234	C₃×C₄×#41	—	5	2	no	—
235	C₂×C₃×#117	—	5	1	no	—
236	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
237	C₂×#711	C₂²×C₃	1	2	yes	—
238	C₅×#126	C₂²×C₃	1	2	yes	—
239	C₅×#124	C₂²×C₃	1	2	yes	—
240	C₅×#123	C₂²×C₃	1	2	yes	—
241	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
242	C₅×#121	C₂²×C₃	1	1	yes	characteristic
243	C₅×#121	C₂²×C₃	1	2	yes	—
244	C₅×#120	C₂²×C₃	1	2	yes	—
245	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
246	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
247	#4099	C₂²×C₃	1	2	yes	—
248	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
249	#4092	C₂²×C₃	1	2	yes	complemented
250	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
251	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
252	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
253	#4085	C₂²×C₃	1	2	yes	—
254	#4085	C₂²×C₃	1	2	yes	—
255	#4085	C₂²×C₃	1	2	yes	—
256	#4085	C₂²×C₃	1	2	yes	—
257	#4084	C₂²×C₃	1	2	yes	—
258	#4082	C₂²×C₃	1	2	yes	—
259	#4081	C₂²×C₃	1	2	yes	—
260	#4081	C₂²×C₃	1	2	yes	—
261	#4081	C₂²×C₃	1	2	yes	complemented
262	D₄×Dic₅	C₂²×C₃	1	2	yes	—
263	D₄×Dic₅	C₂²×C₃	1	2	yes	—
264	D₄×Dic₅	C₂²×C₃	1	2	yes	—
265	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
266	#4076	C₂²×C₃	1	1	yes	characteristic
267	#4075	C₂²×C₃	1	2	yes	complemented
268	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
269	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
270	#4070	C₂²×C₃	1	1	yes	characteristic
271	#4070	C₂²×C₃	1	2	yes	complemented
272	C₂×#683	C₂²×C₃	1	1	yes	characteristic
273	C₂×#683	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
277	#4044	C₂²×C₃	1	2	yes	complemented
278	#4042	C₂²×C₃	1	2	yes	complemented
279	#4040	C₂²×C₃	1	2	yes	complemented
280	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
281	#4038	C₂²×C₃	1	2	yes	complemented
282	#4036	C₂²×C₃	1	2	yes	complemented
283	#4035	C₂²×C₃	1	2	yes	complemented
284	#4035	C₂²×C₃	1	2	yes	complemented
285	#4035	C₂²×C₃	1	2	yes	complemented
286	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
287	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
288	#4033	C₂²×C₃	1	2	yes	complemented
289	#4033	C₂²×C₃	1	2	yes	complemented
290	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
291	#4032	C₂²×C₃	1	2	yes	—
292	#4031	C₂²×C₃	1	2	yes	—
293	#4031	C₂²×C₃	1	2	yes	—
294	#4031	C₂²×C₃	1	2	yes	complemented
295	#4030	C₂²×C₃	1	2	yes	—
296	#4029	C₂²×C₃	1	2	yes	—
297	#4029	C₂²×C₃	1	2	yes	—
298	#4029	C₂²×C₃	1	2	yes	complemented
299	#4027	C₂²×C₃	1	2	yes	—
300	#4027	C₂²×C₃	1	2	yes	—
301	#4027	C₂²×C₃	1	2	yes	—
302	#4027	C₂²×C₃	1	2	yes	complemented
303	#4027	C₂²×C₃	1	2	yes	complemented
304	#4025	C₂²×C₃	1	2	yes	—
305	#4025	C₂²×C₃	1	2	yes	—
306	#4025	C₂²×C₃	1	2	yes	—
307	#4025	C₂²×C₃	1	2	yes	complemented
308	#4025	C₂²×C₃	1	2	yes	complemented
309	#4024	C₂²×C₃	1	2	yes	—
310	#4024	C₂²×C₃	1	2	yes	—
311	#4024	C₂²×C₃	1	2	yes	—
312	#4024	C₂²×C₃	1	2	yes	complemented
313	#4023	C₂²×C₃	1	2	yes	—
314	#4023	C₂²×C₃	1	2	yes	—
315	#4023	C₂²×C₃	1	2	yes	—
316	#4023	C₂²×C₃	1	2	yes	—
317	#4023	C₂²×C₃	1	2	yes	—
318	#4023	C₂²×C₃	1	2	yes	complemented
319	#4022	C₂²×C₃	1	2	yes	complemented
320	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
321	#4016	C₂²×C₃	1	2	yes	complemented
322	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
323	#3455	—	5	1	no	Sylow
324	C₂³×C₃×C₅	—	2	2	no	—
325	C₂³×C₃×C₅	—	4	1	no	—
326	C₂³×C₃×C₅	—	4	1	no	—
327	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
328	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
329	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
331	C₃×C₅×Q₈	—	4	1	no	—
332	C₃×C₅×D₄	—	2	4	no	—
333	C₃×C₅×D₄	—	4	2	no	—
334	C₃×C₅×D₄	—	4	2	no	—
335	C₃×C₅×D₄	—	4	1	no	—
336	C₂×C₃×C₄×C₅	—	4	2	no	—
337	C₂×C₃×C₄×C₅	—	4	1	no	—
338	C₂×C₃×C₄×C₅	—	4	1	no	—
339	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
340	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
342	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
343	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
344	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
345	C₃×C₂²⋊D₅	—	2	4	no	—
346	C₃×C₂²⋊D₅	—	2	4	no	—
347	C₃×C₂²⋊D₅	—	4	2	no	—
348	C₃×C₂²⋊D₅	—	4	2	no	—
349	C₃×C₂²⋊D₅	—	4	2	no	—
350	C₂×C₃×Dic₅	—	2	2	no	—
351	C₂×C₃×Dic₅	—	2	4	no	—
352	C₂×C₃×Dic₅	—	2	4	no	—
353	C₂×C₃×Dic₅	—	2	4	no	—
354	C₂×C₃×Dic₅	—	4	1	no	—
355	C₂×C₃×Dic₅	—	4	2	no	—
356	C₂×C₃×Dic₅	—	4	1	no	—
357	C₂×C₃×Dic₅	#41	1	4	yes	—
358	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
359	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
360	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
361	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
362	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
364	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
365	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
367	C₃×D₂₀	—	4	1	no	—
368	C₃×C₄×D₅	—	2	4	no	—
369	C₃×C₄×D₅	—	4	2	no	—
370	C₃×C₄×D₅	—	4	2	no	—
371	C₃×Dic₁₀	—	2	4	no	—
372	C₃×Dic₁₀	—	4	2	no	—
373	C₃×Dic₁₀	—	4	1	no	—
374	C₂×C₃×#41	—	5	2	no	—
375	C₂³×C₃×C₄	—	5	1	no	—
376	C₃×C₄⋊Q₈	—	5	1	no	—
377	C₃×C₄⋊Q₈	—	5	1	no	—
378	C₃×C₄⋊Q₈	—	5	1	no	—
379	C₃×#127	—	5	1	no	—
380	C₃×#126	—	5	2	no	—
381	C₃×#126	—	5	2	no	—
382	C₃×#126	—	5	2	no	—
383	C₃×#126	—	5	2	no	—
384	C₃×#126	—	5	2	no	—
385	C₃×#126	—	5	2	no	—
386	C₃×#126	—	5	2	no	—
387	C₃×#126	C₂×D₅	1	2	yes	—
388	C₃×#125	—	5	2	no	—
389	C₃×#125	—	5	2	no	—
390	C₃×#125	—	5	2	no	—
391	C₃×#125	—	5	2	no	—
392	C₃×#125	—	5	2	no	—
393	C₃×#124	—	5	2	no	—
394	C₃×#124	—	5	2	no	—
395	C₃×#124	—	5	2	no	—
396	C₃×#124	—	5	2	no	—
397	C₃×#124	C₂×D₅	1	2	yes	—
398	C₃×#123	—	5	2	no	—
399	C₃×#123	—	5	2	no	—
400	C₃×#123	—	5	2	no	—
401	C₃×#123	—	5	2	no	—
402	C₃×#123	—	5	2	no	—
403	C₃×#123	—	5	2	no	—
404	C₃×#123	—	5	2	no	—
405	C₃×#123	—	5	2	no	—
406	C₃×#123	—	5	2	no	—
407	C₃×#123	C₂×D₅	1	2	yes	—
408	C₃×C₂²⋊Q₈	—	5	2	no	—
409	C₃×C₂²⋊Q₈	—	5	2	no	—
410	C₃×C₂²⋊Q₈	—	5	1	no	—
411	C₃×C₂²⋊Q₈	—	5	2	no	—
412	C₃×C₂²⋊Q₈	—	5	2	no	—
413	C₃×C₂²⋊Q₈	—	5	2	no	—
414	C₃×C₂²⋊Q₈	—	5	2	no	—
415	C₃×C₂²⋊Q₈	—	5	2	no	—
416	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
417	C₃×#121	—	5	2	no	—
418	C₃×#121	—	5	2	no	—
419	C₃×#121	—	5	2	no	—
420	C₃×#121	—	5	2	no	—
421	C₃×#121	—	5	2	no	—
422	C₃×#121	—	5	1	no	—
423	C₃×#121	—	5	2	no	—
424	C₃×#121	C₂×D₅	1	2	yes	—
425	C₃×#121	C₂×D₅	1	1	yes	characteristic
426	C₃×#120	—	5	2	no	—
427	C₃×#120	C₂×D₅	1	2	yes	—
428	C₃×C₄×Q₈	—	5	1	no	—
429	C₃×C₄×Q₈	—	5	2	no	—
430	C₃×C₄×Q₈	—	5	1	no	—
431	C₃×C₄×Q₈	—	5	2	no	—
432	C₃×C₄×Q₈	—	5	2	no	—
433	C₃×C₄×D₄	—	5	2	no	—
434	C₃×C₄×D₄	—	5	2	no	—
435	C₃×C₄×D₄	—	5	2	no	—
436	C₃×C₄×D₄	—	5	1	no	—
437	C₃×C₄×D₄	—	5	2	no	—
438	C₃×C₄×D₄	—	5	2	no	—
439	C₃×C₄×D₄	—	5	1	no	—
440	C₃×C₄×D₄	—	5	2	no	—
441	C₃×C₄×D₄	—	5	2	no	—
442	C₃×C₄×D₄	—	5	2	no	—
443	C₃×C₄×D₄	—	5	2	no	—
444	C₃×C₄×D₄	—	5	2	no	—
445	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
446	C₃×#117	—	5	2	no	—
447	C₃×#117	—	5	2	no	—
448	C₃×#117	—	5	2	no	—
449	C₃×#117	—	5	2	no	—
450	C₃×#117	—	5	2	no	—
451	C₃×#117	—	5	2	no	—
452	C₃×#117	—	5	2	no	—
453	C₂×C₃×C₄⋊C₄	—	5	1	no	—
454	C₂×C₃×C₄⋊C₄	—	5	1	no	—
455	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
456	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
457	C₂×C₃×C₄²	—	5	1	no	—
458	C₂×C₃×C₄²	—	5	1	no	—
459	C₂×C₃×C₄²	—	5	2	no	—
460	C₂×C₃×C₄²	—	5	2	no	—
461	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
463	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
464	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
465	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
466	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
467	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
468	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
469	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
470	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
471	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
472	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
473	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
474	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
475	C₂²×Dic₅	—	2	4	no	—
476	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
477	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
478	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
479	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
480	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
481	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
482	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
483	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
484	#711	—	2	8	no	—
485	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
487	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
488	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
489	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
490	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
491	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
492	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₄²×C₅	C₂³×C₃	1	2	yes	—
504	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
505	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
506	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
507	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
508	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
509	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
510	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
511	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
512	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
513	#685	C₂³×C₃	1	2	yes	—
514	#685	C₂³×C₃	1	2	yes	—
515	#685	C₂³×C₃	1	2	yes	—
516	#685	C₂³×C₃	1	2	yes	—
517	#685	C₂³×C₃	1	2	yes	—
518	#685	C₂³×C₃	1	2	yes	—
519	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
520	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
521	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
522	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
523	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
524	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
525	#683	C₂³×C₃	1	2	yes	—
526	#683	C₂³×C₃	1	2	yes	—
527	#683	C₂³×C₃	1	2	yes	—
528	#683	C₂³×C₃	1	2	yes	—
529	#683	C₂³×C₃	1	2	yes	—
530	#683	C₂³×C₃	1	2	yes	—
531	#683	C₂³×C₃	1	2	yes	—
532	#683	C₂³×C₃	1	2	yes	—
533	#683	C₂³×C₃	1	2	yes	—
534	#683	C₂³×C₃	1	2	yes	—
535	#683	C₂³×C₃	1	2	yes	—
536	#683	C₂³×C₃	1	2	yes	—
537	#683	C₂³×C₃	1	2	yes	—
538	#683	C₂³×C₃	1	2	yes	—
539	C₄×Dic₅	C₂³×C₃	1	2	yes	—
540	C₄×Dic₅	C₂³×C₃	1	2	yes	—
541	C₄×Dic₅	C₂³×C₃	1	2	yes	—
542	C₄×Dic₅	C₂³×C₃	1	2	yes	—
543	C₄×Dic₅	C₂³×C₃	1	2	yes	—
544	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
545	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
546	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
547	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
548	C₄×Dic₅	C₂³×C₃	1	2	yes	—
549	C₄×Dic₅	C₂³×C₃	1	2	yes	—
550	#542	—	5	2	no	—
551	#542	—	5	2	no	—
552	#541	—	5	2	no	—
553	#540	—	5	2	no	—
554	#539	—	5	1	no	—
555	#539	—	5	1	no	—
556	#539	—	5	2	no	—
557	#538	—	5	2	no	—
558	#538	—	5	1	no	—
559	#538	C₃×D₅	1	1	yes	characteristic, complemented
560	#533	—	5	1	no	—
561	#532	—	5	1	no	—
562	#529	—	5	2	no	—
563	#529	—	5	2	no	—
564	#529	—	5	2	no	—
565	#529	—	5	2	no	—
566	#525	—	5	2	no	—
567	C₄×#41	—	5	2	no	—
568	C₂×#117	—	5	1	no	—
569	C₂²×C₃×C₅	—	2	1	no	—
570	C₂²×C₃×C₅	—	2	1	no	—
571	C₂²×C₃×C₅	—	2	2	no	—
572	C₂²×C₃×C₅	—	2	2	no	—
573	C₂²×C₃×C₅	—	2	2	no	—
574	C₂²×C₃×C₅	—	2	2	no	—
575	C₂²×C₃×C₅	—	2	2	no	—
576	C₂²×C₃×C₅	—	2	2	no	—
577	C₂²×C₃×C₅	—	4	4	no	—
578	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
579	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
580	C₂×C₃×D₅	—	2	2	no	—
581	C₂×C₃×D₅	—	2	2	no	—
582	C₂×C₃×D₅	—	2	2	no	—
583	C₃×C₄×C₅	—	2	2	no	—
584	C₃×C₄×C₅	—	2	2	no	—
585	C₃×C₄×C₅	—	2	1	no	—
586	C₃×C₄×C₅	—	2	2	no	—
587	C₃×C₄×C₅	—	2	2	no	—
588	C₃×C₄×C₅	—	2	1	no	—
589	C₃×Dic₅	—	2	2	no	—
590	C₃×Dic₅	—	2	2	no	—
591	C₃×Dic₅	—	2	1	no	—
592	C₃×Dic₅	—	2	2	no	—
593	C₃×Dic₅	—	2	2	no	—
594	C₃×Dic₅	—	2	2	no	—
595	C₃×Dic₅	—	2	1	no	—
596	C₃×Dic₅	C₂×#41	1	2	yes	—
597	C₃×Dic₅	C₂×#41	1	2	yes	—
598	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
599	C₃×#41	—	10	8	no	—
600	C₂×C₃×Q₈	—	5	2	no	—
601	C₂×C₃×Q₈	—	5	2	no	—
602	C₂×C₃×Q₈	—	5	1	no	—
603	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
604	C₂×C₃×D₄	—	5	2	no	—
605	C₂×C₃×D₄	—	5	2	no	—
606	C₂×C₃×D₄	—	5	2	no	—
607	C₂×C₃×D₄	—	5	2	no	—
608	C₂×C₃×D₄	—	5	2	no	—
609	C₂×C₃×D₄	—	5	1	no	—
610	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
611	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
612	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
613	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
614	C₂²×C₃×C₄	—	5	1	no	—
615	C₂²×C₃×C₄	—	5	2	no	—
616	C₂²×C₃×C₄	—	5	1	no	—
617	C₂²×C₃×C₄	—	5	2	no	—
618	C₂²×C₃×C₄	—	5	2	no	—
619	C₂²×C₃×C₄	—	5	1	no	—
620	C₂²×C₃×C₄	—	5	1	no	—
621	C₂²×C₃×C₄	—	5	2	no	—
622	C₂²×C₃×C₄	—	5	2	no	—
623	C₂²×C₃×C₄	—	5	2	no	—
624	C₂²×C₃×C₄	—	5	2	no	—
625	C₂²×C₃×C₄	—	10	4	no	—
626	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
627	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
628	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
629	C₃×C₄⋊C₄	—	5	2	no	—
630	C₃×C₄⋊C₄	—	5	2	no	—
631	C₃×C₄⋊C₄	—	5	2	no	—
632	C₃×C₄⋊C₄	—	5	2	no	—
633	C₃×C₄⋊C₄	—	5	2	no	—
634	C₃×C₄⋊C₄	—	5	2	no	—
635	C₃×C₄⋊C₄	—	5	2	no	—
636	C₃×C₄⋊C₄	—	5	2	no	—
637	C₃×C₄⋊C₄	—	5	2	no	—
638	C₃×C₄⋊C₄	—	5	2	no	—
639	C₃×C₄⋊C₄	—	5	2	no	—
640	C₃×C₄⋊C₄	—	5	2	no	—
641	C₃×C₄⋊C₄	—	5	2	no	—
642	C₃×C₄⋊C₄	—	5	2	no	—
643	C₃×C₄⋊C₄	—	5	2	no	—
644	C₃×C₄⋊C₄	—	5	1	no	—
645	C₃×C₄⋊C₄	—	5	2	no	—
646	C₃×C₄⋊C₄	—	5	2	no	—
647	C₃×C₄⋊C₄	—	5	2	no	—
648	C₃×C₄⋊C₄	—	5	1	no	—
649	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
650	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
651	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
652	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
653	C₃×C₂²⋊C₄	—	5	2	no	—
654	C₃×C₂²⋊C₄	—	5	2	no	—
655	C₃×C₂²⋊C₄	—	5	2	no	—
656	C₃×C₂²⋊C₄	—	5	2	no	—
657	C₃×C₂²⋊C₄	—	5	2	no	—
658	C₃×C₂²⋊C₄	—	5	2	no	—
659	C₃×C₂²⋊C₄	—	5	2	no	—
660	C₃×C₂²⋊C₄	—	5	2	no	—
661	C₃×C₂²⋊C₄	—	5	2	no	—
662	C₃×C₂²⋊C₄	—	5	2	no	—
663	C₃×C₂²⋊C₄	—	5	2	no	—
664	C₃×C₂²⋊C₄	—	5	2	no	—
665	C₃×C₂²⋊C₄	—	5	2	no	—
666	C₃×C₂²⋊C₄	—	5	2	no	—
667	C₃×C₂²⋊C₄	—	5	2	no	—
668	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
669	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
670	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
671	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
672	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
673	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
674	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
675	C₃×C₄²	—	5	2	no	—
676	C₃×C₄²	—	5	1	no	—
677	C₃×C₄²	—	5	2	no	—
678	C₃×C₄²	—	5	2	no	—
679	C₃×C₄²	—	5	1	no	—
680	C₃×C₄²	—	5	2	no	—
681	C₃×C₄²	—	5	1	no	—
682	C₃×C₄²	—	5	1	no	—
683	C₃×C₄²	—	5	2	no	—
684	C₃×C₄²	—	5	2	no	—
685	C₃×C₄²	—	5	2	no	—
686	C₃×C₄²	C₂²×D₅	1	2	yes	—
687	C₂³×C₅	—	2	2	no	—
688	C₂³×C₅	—	4	1	no	—
689	C₂³×C₅	—	4	1	no	—
690	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
691	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
692	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
693	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
694	C₅×Q₈	—	4	1	no	—
695	C₅×D₄	—	2	4	no	—
696	C₅×D₄	—	4	2	no	—
697	C₅×D₄	—	4	2	no	—
698	C₅×D₄	—	4	1	no	—
699	C₂×C₄×C₅	—	4	2	no	—
700	C₂×C₄×C₅	—	4	1	no	—
701	C₂×C₄×C₅	—	4	1	no	—
702	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
703	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
704	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
705	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
706	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
707	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
708	C₂²⋊D₅	—	2	4	no	—
709	C₂²⋊D₅	—	2	4	no	—
710	C₂²⋊D₅	—	4	2	no	—
711	C₂²⋊D₅	—	4	2	no	—
712	C₂²⋊D₅	—	4	2	no	—
713	C₂×Dic₅	—	2	2	no	—
714	C₂×Dic₅	—	2	4	no	—
715	C₂×Dic₅	—	2	4	no	—
716	C₂×Dic₅	—	2	4	no	—
717	C₂×Dic₅	—	4	1	no	—
718	C₂×Dic₅	—	4	2	no	—
719	C₂×Dic₅	—	4	1	no	—
720	C₂×Dic₅	C₃×#41	1	4	yes	—
721	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
722	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
723	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
724	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
725	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
726	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
727	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
728	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
729	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
730	D₂₀	—	4	1	no	—
731	C₄×D₅	—	2	4	no	—
732	C₄×D₅	—	4	2	no	—
733	C₄×D₅	—	4	2	no	—
734	Dic₁₀	—	2	4	no	—
735	Dic₁₀	—	4	2	no	—
736	Dic₁₀	—	4	1	no	—
737	C₂×#41	—	5	2	no	—
738	C₂³×C₄	—	5	1	no	—
739	C₄⋊Q₈	—	5	1	no	—
740	C₄⋊Q₈	—	5	1	no	—
741	C₄⋊Q₈	—	5	1	no	—
742	#127	—	5	1	no	—
743	#126	—	5	2	no	—
744	#126	—	5	2	no	—
745	#126	—	5	2	no	—
746	#126	—	5	2	no	—
747	#126	—	5	2	no	—
748	#126	—	5	2	no	—
749	#126	—	5	2	no	—
750	#126	C₂×C₃×D₅	1	2	yes	—
751	#125	—	5	2	no	—
752	#125	—	5	2	no	—
753	#125	—	5	2	no	—
754	#125	—	5	2	no	—
755	#125	—	5	2	no	—
756	#124	—	5	2	no	—
757	#124	—	5	2	no	—
758	#124	—	5	2	no	—
759	#124	—	5	2	no	—
760	#124	C₂×C₃×D₅	1	2	yes	—
761	#123	—	5	2	no	—
762	#123	—	5	2	no	—
763	#123	—	5	2	no	—
764	#123	—	5	2	no	—
765	#123	—	5	2	no	—
766	#123	—	5	2	no	—
767	#123	—	5	2	no	—
768	#123	—	5	2	no	—
769	#123	—	5	2	no	—
770	#123	C₂×C₃×D₅	1	2	yes	—
771	C₂²⋊Q₈	—	5	2	no	—
772	C₂²⋊Q₈	—	5	2	no	—
773	C₂²⋊Q₈	—	5	1	no	—
774	C₂²⋊Q₈	—	5	2	no	—
775	C₂²⋊Q₈	—	5	2	no	—
776	C₂²⋊Q₈	—	5	2	no	—
777	C₂²⋊Q₈	—	5	2	no	—
778	C₂²⋊Q₈	—	5	2	no	—
779	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
780	#121	—	5	2	no	—
781	#121	—	5	2	no	—
782	#121	—	5	2	no	—
783	#121	—	5	2	no	—
784	#121	—	5	2	no	—
785	#121	—	5	1	no	—
786	#121	—	5	2	no	—
787	#121	C₂×C₃×D₅	1	2	yes	—
788	#121	C₂×C₃×D₅	1	1	yes	characteristic
789	#120	—	5	2	no	—
790	#120	C₂×C₃×D₅	1	2	yes	—
791	C₄×Q₈	—	5	1	no	—
792	C₄×Q₈	—	5	2	no	—
793	C₄×Q₈	—	5	1	no	—
794	C₄×Q₈	—	5	2	no	—
795	C₄×Q₈	—	5	2	no	—
796	C₄×D₄	—	5	2	no	—
797	C₄×D₄	—	5	2	no	—
798	C₄×D₄	—	5	2	no	—
799	C₄×D₄	—	5	1	no	—
800	C₄×D₄	—	5	2	no	—
801	C₄×D₄	—	5	2	no	—
802	C₄×D₄	—	5	1	no	—
803	C₄×D₄	—	5	2	no	—
804	C₄×D₄	—	5	2	no	—
805	C₄×D₄	—	5	2	no	—
806	C₄×D₄	—	5	2	no	—
807	C₄×D₄	—	5	2	no	—
808	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
809	#117	—	5	2	no	—
810	#117	—	5	2	no	—
811	#117	—	5	2	no	—
812	#117	—	5	2	no	—
813	#117	—	5	2	no	—
814	#117	—	5	2	no	—
815	#117	—	5	2	no	—
816	C₂×C₄⋊C₄	—	5	1	no	—
817	C₂×C₄⋊C₄	—	5	1	no	—
818	C₂×C₂²⋊C₄	—	5	1	no	—
819	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
820	C₂×C₄²	—	5	1	no	—
821	C₂×C₄²	—	5	1	no	—
822	C₂×C₄²	—	5	2	no	—
823	C₂×C₄²	—	5	2	no	—
824	C₂×C₃×C₅	—	2	2	no	—
825	C₂×C₃×C₅	—	4	2	no	—
826	C₂×C₃×C₅	—	4	2	no	—
827	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
828	C₂×C₃×C₅	#585	1	1	yes	characteristic
829	C₂×C₃×C₅	#585	1	1	yes	characteristic
830	C₃×D₅	—	4	2	no	—
831	C₂³×C₃	—	2	2	no	—
832	C₂³×C₃	—	4	1	no	—
833	C₂³×C₃	—	4	1	no	—
834	C₂³×C₃	—	5	2	no	—
835	C₂³×C₃	C₂³×D₅	1	2	yes	—
836	C₂³×C₃	C₂³×D₅	1	2	yes	—
837	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
838	C₃×Q₈	—	4	1	no	—
839	C₃×Q₈	—	10	4	no	—
840	C₃×Q₈	—	20	2	no	—
841	C₃×Q₈	—	20	1	no	—
842	C₃×D₄	—	2	4	no	—
843	C₃×D₄	—	4	1	no	—
844	C₃×D₄	—	4	2	no	—
845	C₃×D₄	—	4	2	no	—
846	C₃×D₄	—	10	4	no	—
847	C₃×D₄	—	10	4	no	—
848	C₃×D₄	—	20	1	no	—
849	C₃×D₄	—	20	2	no	—
850	C₃×D₄	—	20	2	no	—
851	C₃×D₄	—	20	2	no	—
852	C₂×C₃×C₄	—	4	1	no	—
853	C₂×C₃×C₄	—	4	2	no	—
854	C₂×C₃×C₄	—	4	1	no	—
855	C₂×C₃×C₄	—	5	4	no	—
856	C₂×C₃×C₄	—	5	1	no	—
857	C₂×C₃×C₄	—	5	1	no	—
858	C₂×C₃×C₄	—	5	2	no	—
859	C₂×C₃×C₄	—	5	1	no	—
860	C₂×C₃×C₄	—	5	2	no	—
861	C₂×C₃×C₄	—	5	2	no	—
862	C₂×C₃×C₄	—	5	2	no	—
863	C₂×C₃×C₄	—	5	1	no	—
864	C₂×C₃×C₄	—	5	2	no	—
865	C₂×C₃×C₄	—	10	4	no	—
866	C₂×C₃×C₄	—	10	4	no	—
867	C₂×C₃×C₄	—	10	4	no	—
868	C₂×C₃×C₄	—	10	4	no	—
869	C₂×C₃×C₄	—	10	2	no	—
870	C₂×C₃×C₄	—	20	2	no	—
871	C₂×C₃×C₄	—	20	2	no	—
872	C₂×C₃×C₄	—	20	1	no	—
873	C₂×C₃×C₄	—	20	2	no	—
874	C₂×C₃×C₄	—	20	1	no	—
875	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
876	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
877	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
878	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
879	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
880	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
881	C₂²×C₅	—	2	1	no	—
882	C₂²×C₅	—	2	1	no	—
883	C₂²×C₅	—	2	2	no	—
884	C₂²×C₅	—	2	2	no	—
885	C₂²×C₅	—	2	2	no	—
886	C₂²×C₅	—	2	2	no	—
887	C₂²×C₅	—	2	2	no	—
888	C₂²×C₅	—	2	2	no	—
889	C₂²×C₅	—	4	4	no	—
890	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
891	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
892	C₂×D₅	—	2	2	no	—
893	C₂×D₅	—	2	2	no	—
894	C₂×D₅	—	2	2	no	—
895	C₄×C₅	—	2	2	no	—
896	C₄×C₅	—	2	2	no	—
897	C₄×C₅	—	2	1	no	—
898	C₄×C₅	—	2	2	no	—
899	C₄×C₅	—	2	2	no	—
900	C₄×C₅	—	2	1	no	—
901	Dic₅	—	2	2	no	—
902	Dic₅	—	2	2	no	—
903	Dic₅	—	2	1	no	—
904	Dic₅	—	2	2	no	—
905	Dic₅	—	2	2	no	—
906	Dic₅	—	2	2	no	—
907	Dic₅	—	2	1	no	—
908	Dic₅	C₂×C₃×#41	1	2	yes	—
909	Dic₅	C₂×C₃×#41	1	2	yes	—
910	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
911	#41	—	10	8	no	—
912	C₂×Q₈	—	5	2	no	—
913	C₂×Q₈	—	5	2	no	—
914	C₂×Q₈	—	5	1	no	—
915	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
916	C₂×D₄	—	5	2	no	—
917	C₂×D₄	—	5	2	no	—
918	C₂×D₄	—	5	2	no	—
919	C₂×D₄	—	5	2	no	—
920	C₂×D₄	—	5	2	no	—
921	C₂×D₄	—	5	1	no	—
922	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
923	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
924	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
925	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
926	C₂²×C₄	—	5	1	no	—
927	C₂²×C₄	—	5	2	no	—
928	C₂²×C₄	—	5	1	no	—
929	C₂²×C₄	—	5	2	no	—
930	C₂²×C₄	—	5	2	no	—
931	C₂²×C₄	—	5	1	no	—
932	C₂²×C₄	—	5	1	no	—
933	C₂²×C₄	—	5	2	no	—
934	C₂²×C₄	—	5	2	no	—
935	C₂²×C₄	—	5	2	no	—
936	C₂²×C₄	—	5	2	no	—
937	C₂²×C₄	—	10	4	no	—
938	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
940	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
941	C₄⋊C₄	—	5	2	no	—
942	C₄⋊C₄	—	5	2	no	—
943	C₄⋊C₄	—	5	2	no	—
944	C₄⋊C₄	—	5	2	no	—
945	C₄⋊C₄	—	5	2	no	—
946	C₄⋊C₄	—	5	2	no	—
947	C₄⋊C₄	—	5	2	no	—
948	C₄⋊C₄	—	5	2	no	—
949	C₄⋊C₄	—	5	2	no	—
950	C₄⋊C₄	—	5	2	no	—
951	C₄⋊C₄	—	5	1	no	—
952	C₄⋊C₄	—	5	2	no	—
953	C₄⋊C₄	—	5	2	no	—
954	C₄⋊C₄	—	5	2	no	—
955	C₄⋊C₄	—	5	2	no	—
956	C₄⋊C₄	—	5	2	no	—
957	C₄⋊C₄	—	5	2	no	—
958	C₄⋊C₄	—	5	2	no	—
959	C₄⋊C₄	—	5	2	no	—
960	C₄⋊C₄	—	5	1	no	—
961	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
962	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
963	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
964	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
965	C₂²⋊C₄	—	5	2	no	—
966	C₂²⋊C₄	—	5	2	no	—
967	C₂²⋊C₄	—	5	2	no	—
968	C₂²⋊C₄	—	5	2	no	—
969	C₂²⋊C₄	—	5	2	no	—
970	C₂²⋊C₄	—	5	2	no	—
971	C₂²⋊C₄	—	5	2	no	—
972	C₂²⋊C₄	—	5	2	no	—
973	C₂²⋊C₄	—	5	2	no	—
974	C₂²⋊C₄	—	5	2	no	—
975	C₂²⋊C₄	—	5	2	no	—
976	C₂²⋊C₄	—	5	2	no	—
977	C₂²⋊C₄	—	5	2	no	—
978	C₂²⋊C₄	—	5	2	no	—
979	C₂²⋊C₄	—	5	2	no	—
980	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
981	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
982	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
983	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
984	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
985	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
986	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
987	C₄²	—	5	2	no	—
988	C₄²	—	5	1	no	—
989	C₄²	—	5	2	no	—
990	C₄²	—	5	2	no	—
991	C₄²	—	5	1	no	—
992	C₄²	—	5	2	no	—
993	C₄²	—	5	1	no	—
994	C₄²	—	5	1	no	—
995	C₄²	—	5	2	no	—
996	C₄²	—	5	2	no	—
997	C₄²	—	5	2	no	—
998	C₄²	C₂²×C₃×D₅	1	2	yes	—
999	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
1000	C₂²×C₃	—	2	1	no	—
1001	C₂²×C₃	—	2	1	no	—
1002	C₂²×C₃	—	2	2	no	—
1003	C₂²×C₃	—	2	2	no	—
1004	C₂²×C₃	—	2	2	no	—
1005	C₂²×C₃	—	2	2	no	—
1006	C₂²×C₃	—	2	2	no	—
1007	C₂²×C₃	—	2	2	no	—
1008	C₂²×C₃	—	4	4	no	—
1009	C₂²×C₃	—	10	2	no	—
1010	C₂²×C₃	—	10	2	no	—
1011	C₂²×C₃	—	10	2	no	—
1012	C₂²×C₃	D₅×#41	1	2	yes	—
1013	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1014	C₃×C₄	—	2	2	no	—
1015	C₃×C₄	—	2	2	no	—
1016	C₃×C₄	—	2	1	no	—
1017	C₃×C₄	—	2	2	no	—
1018	C₃×C₄	—	2	1	no	—
1019	C₃×C₄	—	2	2	no	—
1020	C₃×C₄	—	5	2	no	—
1021	C₃×C₄	—	5	2	no	—
1022	C₃×C₄	—	10	2	no	—
1023	C₃×C₄	—	10	2	no	—
1024	C₃×C₄	—	10	2	no	—
1025	C₃×C₄	—	10	1	no	—
1026	C₃×C₄	—	10	2	no	—
1027	C₃×C₄	—	10	2	no	—
1028	C₃×C₄	—	10	1	no	—
1029	C₂×C₅	—	2	2	no	—
1030	C₂×C₅	—	4	2	no	—
1031	C₂×C₅	—	4	2	no	—
1032	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1033	C₂×C₅	C₃×#585	1	1	yes	characteristic
1034	C₂×C₅	C₃×#585	1	1	yes	characteristic
1035	D₅	—	4	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	5	2	no	—
1040	C₂³	C₂³×C₃×D₅	1	2	yes	—
1041	C₂³	C₂³×C₃×D₅	1	2	yes	—
1042	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1043	Q₈	—	4	1	no	—
1044	Q₈	—	10	4	no	—
1045	Q₈	—	20	2	no	—
1046	Q₈	—	20	1	no	—
1047	D₄	—	2	4	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	10	4	no	—
1052	D₄	—	10	4	no	—
1053	D₄	—	20	1	no	—
1054	D₄	—	20	2	no	—
1055	D₄	—	20	2	no	—
1056	D₄	—	20	2	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	5	4	no	—
1061	C₂×C₄	—	5	1	no	—
1062	C₂×C₄	—	5	1	no	—
1063	C₂×C₄	—	5	2	no	—
1064	C₂×C₄	—	5	1	no	—
1065	C₂×C₄	—	5	2	no	—
1066	C₂×C₄	—	5	2	no	—
1067	C₂×C₄	—	5	2	no	—
1068	C₂×C₄	—	5	1	no	—
1069	C₂×C₄	—	5	2	no	—
1070	C₂×C₄	—	10	4	no	—
1071	C₂×C₄	—	10	4	no	—
1072	C₂×C₄	—	10	4	no	—
1073	C₂×C₄	—	10	4	no	—
1074	C₂×C₄	—	10	2	no	—
1075	C₂×C₄	—	20	2	no	—
1076	C₂×C₄	—	20	2	no	—
1077	C₂×C₄	—	20	1	no	—
1078	C₂×C₄	—	20	2	no	—
1079	C₂×C₄	—	20	1	no	—
1080	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1081	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1082	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1083	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1084	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1085	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1086	C₂×C₃	—	2	2	no	—
1087	C₂×C₃	—	4	2	no	—
1088	C₂×C₃	—	4	2	no	—
1089	C₂×C₃	—	20	2	no	—
1090	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1091	C₂×C₃	#66285	1	1	yes	characteristic
1092	C₂×C₃	#66285	1	1	yes	characteristic
1093	C₅	C₃×#3455	1	1	yes	characteristic, complemented, Sylow
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	4	no	—
1103	C₂²	—	10	2	no	—
1104	C₂²	—	10	2	no	—
1105	C₂²	—	10	2	no	—
1106	C₂²	C₃×D₅×#41	1	2	yes	—
1107	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	5	2	no	—
1115	C₄	—	5	2	no	—
1116	C₄	—	10	2	no	—
1117	C₄	—	10	2	no	—
1118	C₄	—	10	2	no	—
1119	C₄	—	10	1	no	—
1120	C₄	—	10	2	no	—
1121	C₄	—	10	2	no	—
1122	C₄	—	10	1	no	—
1123	C₃	#10618288	1	1	yes	characteristic, direct product factor, Sylow
1124	C₂	—	2	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	20	2	no	—
1128	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1129	C₂	C₃×#66285	1	1	yes	characteristic
1130	C₂	C₃×#66285	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#538	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#538	D₅
hypocenter	C₅	C₃×#3455
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#538

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#538	C₂	semidirect
2. C₃×#66040	C₂	semidirect
3. C₃×#66035	C₂	semidirect
4. C₃×#66014	C₂	semidirect
5. C₃×#66003	C₂	semidirect
6. C₃×#65996	C₂	semidirect
7. C₃×#65983	C₂	semidirect
8. C₃×#65979	C₂	semidirect
9. C₃×#65956	C₂	semidirect
10. C₃×#65949	C₂	semidirect
11. C₃×#65936	C₂	semidirect
12. C₃×#65934	C₂	semidirect
13. C₃×#65930	C₂	semidirect
14. C₃×#65927	C₂	semidirect
15. C₃×#65920	C₂	semidirect
16. C₃×#65898	C₂	semidirect
17. C₃×C₄×#711	C₂	semidirect
18. C₃×#65828	C₂	semidirect
19. C₂×C₃×#4023	C₂	semidirect
20. #10618288	C₃	direct (N × H)
34. C₃×#4092	C₂²	semidirect
35. C₃×Q₈×Dic₅	C₂²	semidirect
36. C₃×#4090	C₂²	semidirect
37. C₃×#4086	C₂²	semidirect
46. C₃×#4081	C₂²	semidirect
50. C₃×D₄×Dic₅	C₂²	semidirect
52. C₃×#4075	C₂²	semidirect
54. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
56. C₃×#4070	C₂²	semidirect
61. C₂×C₃×C₄×Dic₅	C₂²	semidirect
62. C₃×#4044	C₂²	semidirect
63. C₃×#4042	C₂²	semidirect
64. C₃×#4040	C₂²	semidirect
65. C₃×#4039	C₂²	semidirect
66. C₃×#4038	C₂²	semidirect
67. C₃×#4036	C₂²	semidirect
68. C₃×#4035	C₂²	semidirect
69. C₃×#4035	C₂²	semidirect
70. C₃×#4035	C₂²	semidirect
71. C₃×#4034	C₂²	semidirect
72. C₃×#4034	C₂²	semidirect
73. C₃×#4033	C₂²	semidirect
74. C₃×#4033	C₂²	semidirect
75. C₃×#4033	C₂²	semidirect
79. C₃×#4031	C₂²	semidirect
83. C₃×#4029	C₂²	semidirect
87. C₃×#4027	C₂²	semidirect
88. C₃×#4027	C₂²	semidirect
92. C₃×#4025	C₂²	semidirect
93. C₃×#4025	C₂²	semidirect
97. C₃×#4024	C₂²	semidirect
103. C₃×#4023	C₂²	semidirect
104. C₃×#4022	C₂²	semidirect
105. C₃×C₄²×D₅	C₂²	semidirect
106. C₃×#4016	C₂²	semidirect
107. C₃×C₄×Dic₁₀	C₂²	semidirect
109. C₅×#538	C₂×C₃	semidirect
110. #66040	C₂×C₃	semidirect
111. #66035	C₂×C₃	semidirect
112. #66014	C₂×C₃	semidirect
113. #66003	C₂×C₃	semidirect
114. #65996	C₂×C₃	semidirect
115. #65983	C₂×C₃	semidirect
116. #65979	C₂×C₃	semidirect
117. #65956	C₂×C₃	semidirect
118. #65949	C₂×C₃	semidirect
119. #65936	C₂×C₃	semidirect
120. #65934	C₂×C₃	semidirect
121. #65930	C₂×C₃	semidirect
122. #65927	C₂×C₃	semidirect
123. #65920	C₂×C₃	semidirect
124. #65898	C₂×C₃	semidirect
125. C₄×#711	C₂×C₃	semidirect
126. #65828	C₂×C₃	semidirect
127. C₂×#4023	C₂×C₃	semidirect
226. C₃×#538	D₅	semidirect
249. #4092	C₂²×C₃	semidirect
250. Q₈×Dic₅	C₂²×C₃	semidirect
251. #4090	C₂²×C₃	semidirect
252. #4086	C₂²×C₃	semidirect
261. #4081	C₂²×C₃	semidirect
265. D₄×Dic₅	C₂²×C₃	semidirect
267. #4075	C₂²×C₃	semidirect
269. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
271. #4070	C₂²×C₃	semidirect
276. C₂×C₄×Dic₅	C₂²×C₃	semidirect
277. #4044	C₂²×C₃	semidirect
278. #4042	C₂²×C₃	semidirect
279. #4040	C₂²×C₃	semidirect
280. #4039	C₂²×C₃	semidirect
281. #4038	C₂²×C₃	semidirect
282. #4036	C₂²×C₃	semidirect
283. #4035	C₂²×C₃	semidirect
284. #4035	C₂²×C₃	semidirect
285. #4035	C₂²×C₃	semidirect
286. #4034	C₂²×C₃	semidirect
287. #4034	C₂²×C₃	semidirect
288. #4033	C₂²×C₃	semidirect
289. #4033	C₂²×C₃	semidirect
290. #4033	C₂²×C₃	semidirect
294. #4031	C₂²×C₃	semidirect
298. #4029	C₂²×C₃	semidirect
302. #4027	C₂²×C₃	semidirect
303. #4027	C₂²×C₃	semidirect
307. #4025	C₂²×C₃	semidirect
308. #4025	C₂²×C₃	semidirect
312. #4024	C₂²×C₃	semidirect
318. #4023	C₂²×C₃	semidirect
319. #4022	C₂²×C₃	semidirect
320. C₄²×D₅	C₂²×C₃	semidirect
321. #4016	C₂²×C₃	semidirect
322. C₄×Dic₁₀	C₂²×C₃	semidirect
559. #538	C₃×D₅	semidirect
999. C₃×C₅	#3455	semidirect
1093. C₅	C₃×#3455	semidirect
1123. C₃	#10618288	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×C₅×#538	2
C₃×#66040	2
C₃×#66035	2
C₃×#66014	2
C₃×#66003	2
C₃×#65996	2
C₃×#65983	2
C₃×#65979	2
C₃×#65956	2
C₃×#65949	2
C₃×#65936	2
C₃×#65934	2
C₃×#65930	2
C₃×#65927	2
C₃×#65920	2
C₃×#65898	2
C₃×C₄×#711	2
C₃×#65828	2
C₂×C₃×#4023	2
#10618288	3
C₃×#3455	5

Subgroups — C3×#10618288 #14481494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618288 #14481494