Subgroups — C₃×D₅×#556 #14483983

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66066	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#126	C₂	1	4	yes	maximal, complemented
5	C₃×#66036	C₂	1	4	yes	maximal, complemented
6	C₃×D₅×#124	C₂	1	2	yes	maximal
7	C₃×#66005	C₂	1	2	yes	maximal, complemented
8	C₃×#65975	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₃×#65918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×Q₈×D₅	C₂	1	2	yes	maximal, complemented
13	C₃×#65902	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
15	C₃×#65876	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65867	C₂	1	2	yes	maximal, complemented
17	C₃×D₅×#117	C₂	1	2	yes	maximal, complemented
18	D₅×#556	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
21	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#126	C₂²	1	4	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	complemented
31	C₃×#4093	C₂²	1	2	yes	—
32	C₃×#4092	C₂²	1	2	yes	complemented
33	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
34	C₃×Q₈×Dic₅	C₂²	1	2	yes	complemented
35	C₃×#4090	C₂²	1	2	yes	complemented
36	C₃×#4082	C₂²	1	2	yes	—
37	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
39	C₃×#4072	C₂²	1	2	yes	complemented
40	C₃×#4070	C₂²	1	2	yes	complemented
41	C₃×#4044	C₂²	1	4	yes	complemented
42	C₃×#4044	C₂²	1	4	yes	complemented
43	C₃×#4044	C₂²	1	4	yes	complemented
44	C₃×#4043	C₂²	1	2	yes	complemented
45	C₃×#4042	C₂²	1	4	yes	complemented
46	C₃×#4039	C₂²	1	1	yes	characteristic
47	C₃×#4038	C₂²	1	2	yes	complemented
48	C₃×#4038	C₂²	1	2	yes	complemented
49	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
51	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
53	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
54	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
55	C₃×#4034	C₂²	1	2	yes	complemented
56	C₃×#4034	C₂²	1	2	yes	complemented
57	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
58	C₃×#4033	C₂²	1	2	yes	complemented
59	C₃×#4033	C₂²	1	4	yes	complemented
60	C₃×#4033	C₂²	1	2	yes	complemented
61	C₃×#4031	C₂²	1	4	yes	—
62	C₃×#4031	C₂²	1	4	yes	—
63	C₃×#4027	C₂²	1	2	yes	—
64	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₃×#4025	C₂²	1	4	yes	complemented
68	C₃×#4025	C₂²	1	4	yes	complemented
69	C₃×#4025	C₂²	1	4	yes	complemented
70	C₃×#4024	C₂²	1	4	yes	complemented
71	C₃×#4023	C₂²	1	4	yes	complemented
72	C₃×#4022	C₂²	1	4	yes	complemented
73	C₃×#4021	C₂²	1	2	yes	—
74	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
75	C₃×#4018	C₂²	1	4	yes	complemented
76	C₃×C₄²×D₅	C₂²	1	4	yes	—
77	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
78	C₃×C₄²×D₅	C₂²	1	2	yes	—
79	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
80	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
81	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
84	C₂×C₃×#556	—	5	1	no	maximal, Hall
85	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
86	#66066	C₂×C₃	1	1	yes	characteristic, complemented
87	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
88	D₅×#126	C₂×C₃	1	4	yes	complemented
89	#66036	C₂×C₃	1	4	yes	complemented
90	D₅×#124	C₂×C₃	1	2	yes	—
91	#66005	C₂×C₃	1	2	yes	complemented
92	#65975	C₂×C₃	1	2	yes	complemented
93	D₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
94	#65918	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×Q₈×D₅	C₂×C₃	1	2	yes	complemented
96	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
97	#65902	C₂×C₃	1	2	yes	complemented
98	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
99	#65876	C₂×C₃	1	1	yes	characteristic, complemented
100	#65867	C₂×C₃	1	2	yes	complemented
101	D₅×#117	C₂×C₃	1	2	yes	complemented
102	C₂³×C₃×D₅	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
104	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
107	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
108	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
109	C₃×Q₈×D₅	—	2	4	no	—
110	C₃×Q₈×D₅	—	2	8	no	—
111	C₃×D₄×D₅	—	2	4	no	—
112	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₄×D₅	—	2	8	no	—
114	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
115	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
116	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
117	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
118	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
119	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
120	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
123	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
124	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
125	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
126	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃×C₄²×C₅	C₂³	1	2	yes	—
137	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₃×C₄²×C₅	C₂³	1	4	yes	—
139	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
140	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
141	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
142	C₃×#685	C₂³	1	4	yes	—
143	C₃×#685	C₂³	1	4	yes	—
144	C₃×#685	C₂³	1	4	yes	—
145	C₃×#685	C₂³	1	4	yes	—
146	C₃×#685	C₂³	1	2	yes	—
147	C₃×#685	C₂³	1	2	yes	—
148	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
149	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
151	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
152	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
153	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
154	C₃×#683	C₂³	1	4	yes	—
155	C₃×#683	C₂³	1	4	yes	—
156	C₃×#683	C₂³	1	4	yes	—
157	C₃×#683	C₂³	1	2	yes	—
158	C₃×#683	C₂³	1	2	yes	—
159	C₃×#683	C₂³	1	2	yes	—
160	C₃×#683	C₂³	1	4	yes	—
161	C₃×#683	C₂³	1	2	yes	—
162	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
163	C₃×C₄×Dic₅	C₂³	1	2	yes	—
164	C₃×C₄×Dic₅	C₂³	1	4	yes	—
165	C₃×C₄×Dic₅	C₂³	1	2	yes	—
166	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
167	C₃×C₄×Dic₅	C₂³	1	4	yes	—
168	C₃×C₄×Dic₅	C₂³	1	2	yes	—
169	C₃×C₄×Dic₅	C₂³	1	4	yes	—
170	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
171	C₃×#556	—	5	1	no	—
172	C₃×#556	—	5	4	no	—
173	C₃×#556	—	5	2	no	—
174	C₃×#556	—	5	2	no	—
175	C₃×#556	—	5	2	no	—
176	C₃×#556	—	5	1	no	—
177	C₃×#556	—	5	1	no	—
178	C₃×#556	—	5	2	no	—
179	C₃×#556	D₅	1	1	yes	characteristic, direct product factor
180	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
181	C₂×C₃×#126	—	5	4	no	—
182	C₂×C₃×#124	—	5	2	no	—
183	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
184	C₂×C₃×C₄×Q₈	—	5	2	no	—
185	C₂×C₃×C₄×Q₈	—	5	1	no	—
186	C₂×C₃×C₄×D₄	—	5	1	no	—
187	C₂×C₃×#117	—	5	2	no	—
188	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
189	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
191	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
192	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#126	C₂²×C₃	1	4	yes	complemented
194	C₅×#124	C₂²×C₃	1	2	yes	—
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
196	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
197	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₅×#117	C₂²×C₃	1	2	yes	complemented
200	#4093	C₂²×C₃	1	2	yes	—
201	#4092	C₂²×C₃	1	2	yes	complemented
202	Q₈×Dic₅	C₂²×C₃	1	2	yes	complemented
203	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
204	#4090	C₂²×C₃	1	2	yes	complemented
205	#4082	C₂²×C₃	1	2	yes	—
206	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
207	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
208	#4072	C₂²×C₃	1	2	yes	complemented
209	#4070	C₂²×C₃	1	2	yes	complemented
210	#4044	C₂²×C₃	1	4	yes	complemented
211	#4044	C₂²×C₃	1	4	yes	complemented
212	#4044	C₂²×C₃	1	4	yes	complemented
213	#4043	C₂²×C₃	1	2	yes	complemented
214	#4042	C₂²×C₃	1	4	yes	complemented
215	#4039	C₂²×C₃	1	1	yes	characteristic
216	#4038	C₂²×C₃	1	2	yes	complemented
217	#4038	C₂²×C₃	1	2	yes	complemented
218	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
219	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
220	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
221	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
222	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
223	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
224	#4034	C₂²×C₃	1	2	yes	complemented
225	#4034	C₂²×C₃	1	2	yes	complemented
226	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
227	#4033	C₂²×C₃	1	2	yes	complemented
228	#4033	C₂²×C₃	1	4	yes	complemented
229	#4033	C₂²×C₃	1	2	yes	complemented
230	#4031	C₂²×C₃	1	4	yes	—
231	#4031	C₂²×C₃	1	4	yes	—
232	#4027	C₂²×C₃	1	2	yes	—
233	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
234	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
235	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
236	#4025	C₂²×C₃	1	4	yes	complemented
237	#4025	C₂²×C₃	1	4	yes	complemented
238	#4025	C₂²×C₃	1	4	yes	complemented
239	#4024	C₂²×C₃	1	4	yes	complemented
240	#4023	C₂²×C₃	1	4	yes	complemented
241	#4022	C₂²×C₃	1	4	yes	complemented
242	#4021	C₂²×C₃	1	2	yes	—
243	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
244	#4018	C₂²×C₃	1	4	yes	complemented
245	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
246	C₄²×D₅	C₂²×C₃	1	4	yes	—
247	C₄²×D₅	C₂²×C₃	1	2	yes	—
248	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
249	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
251	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
252	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
253	C₂×#556	—	5	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂²×C₃×D₅	—	2	4	no	—
256	C₂²×C₃×D₅	—	2	4	no	—
257	C₂²×C₃×D₅	—	2	4	no	—
258	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
259	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
260	C₃×C₅×Q₈	—	2	4	no	—
261	C₃×C₅×Q₈	—	2	2	no	—
262	C₃×C₅×D₄	—	2	2	no	—
263	C₂×C₃×C₄×C₅	—	2	4	no	—
264	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₃×C₂²⋊D₅	—	2	4	no	—
272	C₂×C₃×Dic₅	—	2	4	no	—
273	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
274	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
275	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
277	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
278	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₃×D₂₀	—	2	2	no	—
281	C₃×C₄×D₅	—	2	4	no	—
282	C₃×C₄×D₅	—	2	4	no	—
283	C₃×C₄×D₅	—	2	8	no	—
284	C₃×C₄×D₅	—	2	4	no	—
285	C₃×C₄×D₅	—	2	2	no	—
286	C₃×C₄×D₅	—	2	4	no	—
287	C₃×C₄×D₅	—	2	4	no	—
288	C₃×C₄×D₅	#41	1	4	yes	—
289	C₃×C₄×D₅	#41	1	4	yes	—
290	C₃×Dic₁₀	—	2	4	no	—
291	C₃×Dic₁₀	—	2	2	no	—
292	C₃×Dic₁₀	—	2	8	no	—
293	C₃×Dic₁₀	—	2	4	no	—
294	C₂²×C₃×Q₈	—	5	1	no	—
295	C₂²×C₃×Q₈	—	5	2	no	—
296	C₂²×C₃×D₄	—	5	1	no	—
297	C₂³×C₃×C₄	—	5	2	no	—
298	C₃×C₄⋊Q₈	—	5	2	no	—
299	C₃×C₄⋊Q₈	—	5	2	no	—
300	C₃×C₄⋊Q₈	—	5	2	no	—
301	C₃×C₄⋊Q₈	—	5	1	no	—
302	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
303	C₃×#126	—	5	4	no	—
304	C₃×#126	—	5	4	no	—
305	C₃×#126	—	5	4	no	—
306	C₃×#126	—	5	4	no	—
307	C₃×#126	—	5	4	no	—
308	C₃×#126	—	5	4	no	—
309	C₃×#126	—	5	4	no	—
310	C₃×#126	C₂×D₅	1	4	yes	complemented
311	C₃×#124	—	5	2	no	—
312	C₃×#124	—	5	2	no	—
313	C₃×#124	—	5	4	no	—
314	C₃×#124	—	5	4	no	—
315	C₃×#124	—	5	2	no	—
316	C₃×#124	C₂×D₅	1	2	yes	—
317	C₃×C₂²⋊Q₈	—	5	2	no	—
318	C₃×C₂²⋊Q₈	—	5	2	no	—
319	C₃×C₂²⋊Q₈	—	5	4	no	—
320	C₃×C₂²⋊Q₈	—	5	2	no	—
321	C₃×C₂²⋊Q₈	—	5	4	no	—
322	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
323	C₃×C₄×Q₈	—	5	2	no	—
324	C₃×C₄×Q₈	—	5	1	no	—
325	C₃×C₄×Q₈	—	5	4	no	—
326	C₃×C₄×Q₈	—	5	2	no	—
327	C₃×C₄×Q₈	—	5	2	no	—
328	C₃×C₄×Q₈	—	5	1	no	—
329	C₃×C₄×Q₈	—	5	2	no	—
330	C₃×C₄×Q₈	—	5	4	no	—
331	C₃×C₄×Q₈	—	5	2	no	—
332	C₃×C₄×Q₈	—	5	1	no	—
333	C₃×C₄×Q₈	C₂×D₅	1	2	yes	complemented
334	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
335	C₃×C₄×D₄	—	5	1	no	—
336	C₃×C₄×D₄	—	5	2	no	—
337	C₃×C₄×D₄	—	5	1	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	1	no	—
340	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
341	C₃×#117	—	5	2	no	—
342	C₃×#117	—	5	2	no	—
343	C₃×#117	—	5	2	no	—
344	C₃×#117	—	5	4	no	—
345	C₃×#117	—	5	4	no	—
346	C₃×#117	C₂×D₅	1	2	yes	complemented
347	C₂×C₃×C₄⋊C₄	—	5	1	no	—
348	C₂×C₃×C₄⋊C₄	—	5	2	no	—
349	C₂×C₃×C₄⋊C₄	—	5	1	no	—
350	C₂×C₃×C₄⋊C₄	—	5	4	no	—
351	C₂×C₃×C₄⋊C₄	—	5	2	no	—
352	C₂×C₃×C₄⋊C₄	—	5	2	no	—
353	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
354	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
355	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
356	C₂×C₃×C₄²	—	5	4	no	—
357	C₂×C₃×C₄²	—	5	1	no	—
358	C₂×C₃×C₄²	—	5	2	no	—
359	C₂³×D₅	C₂³×C₃	1	2	yes	—
360	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
361	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
362	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
364	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
365	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
366	Q₈×D₅	—	2	4	no	—
367	Q₈×D₅	—	2	8	no	—
368	D₄×D₅	—	2	4	no	—
369	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
370	C₂×C₄×D₅	—	2	8	no	—
371	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
372	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
373	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
374	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
375	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
376	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
377	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
378	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
380	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
381	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
382	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
383	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
384	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
385	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
387	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
388	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
390	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
392	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
393	C₄²×C₅	C₂³×C₃	1	4	yes	—
394	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
395	C₄²×C₅	C₂³×C₃	1	2	yes	—
396	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
397	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
398	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
399	#685	C₂³×C₃	1	4	yes	—
400	#685	C₂³×C₃	1	4	yes	—
401	#685	C₂³×C₃	1	2	yes	—
402	#685	C₂³×C₃	1	4	yes	—
403	#685	C₂³×C₃	1	2	yes	—
404	#685	C₂³×C₃	1	4	yes	—
405	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
406	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
407	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
408	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
409	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
410	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
411	#683	C₂³×C₃	1	2	yes	—
412	#683	C₂³×C₃	1	2	yes	—
413	#683	C₂³×C₃	1	2	yes	—
414	#683	C₂³×C₃	1	4	yes	—
415	#683	C₂³×C₃	1	4	yes	—
416	#683	C₂³×C₃	1	2	yes	—
417	#683	C₂³×C₃	1	4	yes	—
418	#683	C₂³×C₃	1	4	yes	—
419	C₄×Dic₅	C₂³×C₃	1	4	yes	—
420	C₄×Dic₅	C₂³×C₃	1	2	yes	—
421	C₄×Dic₅	C₂³×C₃	1	2	yes	—
422	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
423	C₄×Dic₅	C₂³×C₃	1	4	yes	—
424	C₄×Dic₅	C₂³×C₃	1	4	yes	—
425	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
426	C₄×Dic₅	C₂³×C₃	1	2	yes	—
427	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
428	#556	—	5	1	no	—
429	#556	—	5	4	no	—
430	#556	—	5	2	no	—
431	#556	—	5	2	no	—
432	#556	—	5	2	no	—
433	#556	—	5	1	no	—
434	#556	—	5	1	no	—
435	#556	—	5	2	no	—
436	#556	C₃×D₅	1	1	yes	characteristic, direct product factor
437	C₂×C₄⋊Q₈	—	5	1	no	—
438	C₂×#126	—	5	4	no	—
439	C₂×#124	—	5	2	no	—
440	C₂×C₂²⋊Q₈	—	5	2	no	—
441	C₂×C₄×Q₈	—	5	2	no	—
442	C₂×C₄×Q₈	—	5	1	no	—
443	C₂×C₄×D₄	—	5	1	no	—
444	C₂×#117	—	5	2	no	—
445	C₂²×C₃×C₅	—	2	2	no	—
446	C₂²×C₃×C₅	—	2	2	no	—
447	C₂²×C₃×C₅	—	2	2	no	—
448	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
449	C₂×C₃×D₅	—	2	2	no	—
450	C₂×C₃×D₅	—	2	2	no	—
451	C₂×C₃×D₅	—	2	2	no	—
452	C₂×C₃×D₅	—	4	8	no	—
453	C₂×C₃×D₅	C₂×#41	1	2	yes	—
454	C₂×C₃×D₅	C₂×#41	1	2	yes	—
455	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
456	C₃×C₄×C₅	—	2	4	no	—
457	C₃×C₄×C₅	—	2	2	no	—
458	C₃×C₄×C₅	—	2	2	no	—
459	C₃×C₄×C₅	—	2	2	no	—
460	C₃×C₄×C₅	—	2	1	no	—
461	C₃×C₄×C₅	C₂×#41	1	2	yes	—
462	C₃×C₄×C₅	C₂×#41	1	2	yes	—
463	C₃×Dic₅	—	2	4	no	—
464	C₃×Dic₅	—	2	2	no	—
465	C₃×Dic₅	—	2	2	no	—
466	C₃×Dic₅	—	2	2	no	—
467	C₃×Dic₅	—	2	1	no	—
468	C₃×Dic₅	C₂×#41	1	2	yes	—
469	C₃×Dic₅	C₂×#41	1	2	yes	—
470	C₂⁴×C₃	—	5	2	no	—
471	C₂×C₃×Q₈	—	5	2	no	—
472	C₂×C₃×Q₈	—	5	1	no	—
473	C₂×C₃×Q₈	—	5	4	no	—
474	C₂×C₃×Q₈	—	5	2	no	—
475	C₂×C₃×Q₈	—	10	4	no	—
476	C₂×C₃×Q₈	—	10	8	no	—
477	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
478	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
479	C₂×C₃×D₄	—	5	2	no	—
480	C₂×C₃×D₄	—	5	1	no	—
481	C₂×C₃×D₄	—	10	4	no	—
482	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
483	C₂²×C₃×C₄	—	5	1	no	—
484	C₂²×C₃×C₄	—	5	1	no	—
485	C₂²×C₃×C₄	—	5	2	no	—
486	C₂²×C₃×C₄	—	5	2	no	—
487	C₂²×C₃×C₄	—	5	2	no	—
488	C₂²×C₃×C₄	—	5	1	no	—
489	C₂²×C₃×C₄	—	5	4	no	—
490	C₂²×C₃×C₄	—	5	2	no	—
491	C₂²×C₃×C₄	—	5	2	no	—
492	C₂²×C₃×C₄	—	5	2	no	—
493	C₂²×C₃×C₄	—	10	8	no	—
494	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
495	C₃×C₄⋊C₄	—	5	2	no	—
496	C₃×C₄⋊C₄	—	5	4	no	—
497	C₃×C₄⋊C₄	—	5	2	no	—
498	C₃×C₄⋊C₄	—	5	4	no	—
499	C₃×C₄⋊C₄	—	5	4	no	—
500	C₃×C₄⋊C₄	—	5	2	no	—
501	C₃×C₄⋊C₄	—	5	2	no	—
502	C₃×C₄⋊C₄	—	5	4	no	—
503	C₃×C₄⋊C₄	—	5	1	no	—
504	C₃×C₄⋊C₄	—	5	2	no	—
505	C₃×C₄⋊C₄	—	5	1	no	—
506	C₃×C₄⋊C₄	—	5	4	no	—
507	C₃×C₄⋊C₄	—	5	2	no	—
508	C₃×C₄⋊C₄	—	5	2	no	—
509	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
511	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
512	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
513	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
514	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
515	C₃×C₂²⋊C₄	—	5	4	no	—
516	C₃×C₂²⋊C₄	—	5	2	no	—
517	C₃×C₂²⋊C₄	—	5	4	no	—
518	C₃×C₂²⋊C₄	—	5	4	no	—
519	C₃×C₂²⋊C₄	—	5	4	no	—
520	C₃×C₂²⋊C₄	—	5	2	no	—
521	C₃×C₂²⋊C₄	—	5	2	no	—
522	C₃×C₂²⋊C₄	—	5	4	no	—
523	C₃×C₂²⋊C₄	—	5	4	no	—
524	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
525	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
526	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
527	C₃×C₄²	—	5	4	no	—
528	C₃×C₄²	—	5	4	no	—
529	C₃×C₄²	—	5	4	no	—
530	C₃×C₄²	—	5	1	no	—
531	C₃×C₄²	—	5	1	no	—
532	C₃×C₄²	—	5	1	no	—
533	C₃×C₄²	—	5	2	no	—
534	C₃×C₄²	—	5	2	no	—
535	C₃×C₄²	—	5	2	no	—
536	C₃×C₄²	C₂²×D₅	1	4	yes	—
537	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₃×C₄²	C₂²×D₅	1	2	yes	—
539	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
540	C₂²×D₅	—	2	4	no	—
541	C₂²×D₅	—	2	4	no	—
542	C₂²×D₅	—	2	4	no	—
543	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
544	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
545	C₅×Q₈	—	2	4	no	—
546	C₅×Q₈	—	2	2	no	—
547	C₅×D₄	—	2	2	no	—
548	C₂×C₄×C₅	—	2	4	no	—
549	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
550	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
551	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
552	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
553	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
554	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
555	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
556	C₂²⋊D₅	—	2	4	no	—
557	C₂×Dic₅	—	2	4	no	—
558	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
559	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
560	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
561	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
562	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
563	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
564	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
565	D₂₀	—	2	2	no	—
566	C₄×D₅	—	2	4	no	—
567	C₄×D₅	—	2	4	no	—
568	C₄×D₅	—	2	8	no	—
569	C₄×D₅	—	2	4	no	—
570	C₄×D₅	—	2	2	no	—
571	C₄×D₅	—	2	4	no	—
572	C₄×D₅	—	2	4	no	—
573	C₄×D₅	C₃×#41	1	4	yes	—
574	C₄×D₅	C₃×#41	1	4	yes	—
575	Dic₁₀	—	2	4	no	—
576	Dic₁₀	—	2	2	no	—
577	Dic₁₀	—	2	8	no	—
578	Dic₁₀	—	2	4	no	—
579	C₂²×Q₈	—	5	1	no	—
580	C₂²×Q₈	—	5	2	no	—
581	C₂²×D₄	—	5	1	no	—
582	C₂³×C₄	—	5	2	no	—
583	C₄⋊Q₈	—	5	2	no	—
584	C₄⋊Q₈	—	5	2	no	—
585	C₄⋊Q₈	—	5	2	no	—
586	C₄⋊Q₈	—	5	1	no	—
587	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
588	#126	—	5	4	no	—
589	#126	—	5	4	no	—
590	#126	—	5	4	no	—
591	#126	—	5	4	no	—
592	#126	—	5	4	no	—
593	#126	—	5	4	no	—
594	#126	—	5	4	no	—
595	#126	C₂×C₃×D₅	1	4	yes	complemented
596	#124	—	5	2	no	—
597	#124	—	5	2	no	—
598	#124	—	5	4	no	—
599	#124	—	5	4	no	—
600	#124	—	5	2	no	—
601	#124	C₂×C₃×D₅	1	2	yes	—
602	C₂²⋊Q₈	—	5	2	no	—
603	C₂²⋊Q₈	—	5	2	no	—
604	C₂²⋊Q₈	—	5	4	no	—
605	C₂²⋊Q₈	—	5	2	no	—
606	C₂²⋊Q₈	—	5	4	no	—
607	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
608	C₄×Q₈	—	5	2	no	—
609	C₄×Q₈	—	5	1	no	—
610	C₄×Q₈	—	5	4	no	—
611	C₄×Q₈	—	5	2	no	—
612	C₄×Q₈	—	5	2	no	—
613	C₄×Q₈	—	5	1	no	—
614	C₄×Q₈	—	5	2	no	—
615	C₄×Q₈	—	5	4	no	—
616	C₄×Q₈	—	5	2	no	—
617	C₄×Q₈	—	5	1	no	—
618	C₄×Q₈	C₂×C₃×D₅	1	2	yes	complemented
619	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
620	C₄×D₄	—	5	1	no	—
621	C₄×D₄	—	5	2	no	—
622	C₄×D₄	—	5	1	no	—
623	C₄×D₄	—	5	2	no	—
624	C₄×D₄	—	5	1	no	—
625	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
626	#117	—	5	2	no	—
627	#117	—	5	2	no	—
628	#117	—	5	2	no	—
629	#117	—	5	4	no	—
630	#117	—	5	4	no	—
631	#117	C₂×C₃×D₅	1	2	yes	complemented
632	C₂×C₄⋊C₄	—	5	1	no	—
633	C₂×C₄⋊C₄	—	5	2	no	—
634	C₂×C₄⋊C₄	—	5	1	no	—
635	C₂×C₄⋊C₄	—	5	4	no	—
636	C₂×C₄⋊C₄	—	5	2	no	—
637	C₂×C₄⋊C₄	—	5	2	no	—
638	C₂×C₂²⋊C₄	—	5	4	no	—
639	C₂×C₂²⋊C₄	—	5	2	no	—
640	C₂×C₂²⋊C₄	—	5	4	no	—
641	C₂×C₄²	—	5	4	no	—
642	C₂×C₄²	—	5	1	no	—
643	C₂×C₄²	—	5	2	no	—
644	C₂×C₃×C₅	—	4	2	no	—
645	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
646	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
647	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
648	C₃×D₅	—	4	2	no	—
649	C₃×D₅	#556	1	4	yes	direct product factor
650	C₂³×C₃	—	5	1	no	—
651	C₂³×C₃	—	5	2	no	—
652	C₂³×C₃	—	10	4	no	—
653	C₂³×C₃	—	10	4	no	—
654	C₂³×C₃	—	10	4	no	—
655	C₂³×C₃	C₂³×D₅	1	2	yes	—
656	C₃×Q₈	—	2	2	no	—
657	C₃×Q₈	—	2	4	no	—
658	C₃×Q₈	—	10	4	no	—
659	C₃×Q₈	—	10	8	no	—
660	C₃×Q₈	—	10	2	no	—
661	C₃×Q₈	—	10	4	no	—
662	C₃×D₄	—	2	2	no	—
663	C₃×D₄	—	10	4	no	—
664	C₃×D₄	—	10	2	no	—
665	C₂×C₃×C₄	—	2	4	no	—
666	C₂×C₃×C₄	—	5	1	no	—
667	C₂×C₃×C₄	—	5	1	no	—
668	C₂×C₃×C₄	—	5	4	no	—
669	C₂×C₃×C₄	—	5	4	no	—
670	C₂×C₃×C₄	—	5	2	no	—
671	C₂×C₃×C₄	—	5	2	no	—
672	C₂×C₃×C₄	—	5	1	no	—
673	C₂×C₃×C₄	—	5	4	no	—
674	C₂×C₃×C₄	—	5	2	no	—
675	C₂×C₃×C₄	—	10	4	no	—
676	C₂×C₃×C₄	—	10	4	no	—
677	C₂×C₃×C₄	—	10	2	no	—
678	C₂×C₃×C₄	—	10	4	no	—
679	C₂×C₃×C₄	—	10	4	no	—
680	C₂×C₃×C₄	—	10	8	no	—
681	C₂×C₃×C₄	—	10	4	no	—
682	C₂×C₃×C₄	—	10	4	no	—
683	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
684	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
685	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
686	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
687	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
688	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
689	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
690	C₂²×C₅	—	2	2	no	—
691	C₂²×C₅	—	2	2	no	—
692	C₂²×C₅	—	2	2	no	—
693	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
694	C₂×D₅	—	2	2	no	—
695	C₂×D₅	—	2	2	no	—
696	C₂×D₅	—	2	2	no	—
697	C₂×D₅	—	4	8	no	—
698	C₂×D₅	C₂×C₃×#41	1	2	yes	—
699	C₂×D₅	C₂×C₃×#41	1	2	yes	—
700	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
701	C₄×C₅	—	2	4	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	2	2	no	—
705	C₄×C₅	—	2	1	no	—
706	C₄×C₅	C₂×C₃×#41	1	2	yes	—
707	C₄×C₅	C₂×C₃×#41	1	2	yes	—
708	Dic₅	—	2	4	no	—
709	Dic₅	—	2	2	no	—
710	Dic₅	—	2	2	no	—
711	Dic₅	—	2	2	no	—
712	Dic₅	—	2	1	no	—
713	Dic₅	C₂×C₃×#41	1	2	yes	—
714	Dic₅	C₂×C₃×#41	1	2	yes	—
715	C₂⁴	—	5	2	no	—
716	C₂×Q₈	—	5	2	no	—
717	C₂×Q₈	—	5	1	no	—
718	C₂×Q₈	—	5	4	no	—
719	C₂×Q₈	—	5	2	no	—
720	C₂×Q₈	—	10	4	no	—
721	C₂×Q₈	—	10	8	no	—
722	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
723	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
724	C₂×D₄	—	5	2	no	—
725	C₂×D₄	—	5	1	no	—
726	C₂×D₄	—	10	4	no	—
727	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
728	C₂²×C₄	—	5	1	no	—
729	C₂²×C₄	—	5	1	no	—
730	C₂²×C₄	—	5	2	no	—
731	C₂²×C₄	—	5	2	no	—
732	C₂²×C₄	—	5	2	no	—
733	C₂²×C₄	—	5	1	no	—
734	C₂²×C₄	—	5	4	no	—
735	C₂²×C₄	—	5	2	no	—
736	C₂²×C₄	—	5	2	no	—
737	C₂²×C₄	—	5	2	no	—
738	C₂²×C₄	—	10	8	no	—
739	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
740	C₄⋊C₄	—	5	2	no	—
741	C₄⋊C₄	—	5	1	no	—
742	C₄⋊C₄	—	5	4	no	—
743	C₄⋊C₄	—	5	2	no	—
744	C₄⋊C₄	—	5	2	no	—
745	C₄⋊C₄	—	5	1	no	—
746	C₄⋊C₄	—	5	4	no	—
747	C₄⋊C₄	—	5	4	no	—
748	C₄⋊C₄	—	5	4	no	—
749	C₄⋊C₄	—	5	2	no	—
750	C₄⋊C₄	—	5	2	no	—
751	C₄⋊C₄	—	5	2	no	—
752	C₄⋊C₄	—	5	4	no	—
753	C₄⋊C₄	—	5	2	no	—
754	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
756	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
758	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
759	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
760	C₂²⋊C₄	—	5	4	no	—
761	C₂²⋊C₄	—	5	2	no	—
762	C₂²⋊C₄	—	5	4	no	—
763	C₂²⋊C₄	—	5	4	no	—
764	C₂²⋊C₄	—	5	4	no	—
765	C₂²⋊C₄	—	5	2	no	—
766	C₂²⋊C₄	—	5	2	no	—
767	C₂²⋊C₄	—	5	4	no	—
768	C₂²⋊C₄	—	5	4	no	—
769	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
770	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
771	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
772	C₄²	—	5	4	no	—
773	C₄²	—	5	4	no	—
774	C₄²	—	5	4	no	—
775	C₄²	—	5	1	no	—
776	C₄²	—	5	1	no	—
777	C₄²	—	5	1	no	—
778	C₄²	—	5	2	no	—
779	C₄²	—	5	2	no	—
780	C₄²	—	5	2	no	—
781	C₄²	C₂²×C₃×D₅	1	4	yes	—
782	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
783	C₄²	C₂²×C₃×D₅	1	2	yes	—
784	C₃×C₅	C₂×#556	1	1	yes	characteristic, complemented, Hall
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	5	2	no	—
789	C₂²×C₃	—	5	2	no	—
790	C₂²×C₃	—	5	2	no	—
791	C₂²×C₃	—	10	2	no	—
792	C₂²×C₃	—	10	2	no	—
793	C₂²×C₃	—	10	2	no	—
794	C₂²×C₃	—	20	8	no	—
795	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
796	C₃×C₄	—	2	2	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	4	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	—	5	2	no	—
802	C₃×C₄	—	5	2	no	—
803	C₃×C₄	—	10	2	no	—
804	C₃×C₄	—	10	2	no	—
805	C₃×C₄	—	10	4	no	—
806	C₃×C₄	—	10	2	no	—
807	C₃×C₄	—	10	1	no	—
808	C₃×C₄	D₅×#41	1	2	yes	—
809	C₃×C₄	D₅×#41	1	2	yes	—
810	C₂×C₅	—	4	2	no	—
811	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
812	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
813	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
814	D₅	—	4	2	no	—
815	D₅	C₃×#556	1	4	yes	direct product factor
816	C₂³	—	5	1	no	—
817	C₂³	—	5	2	no	—
818	C₂³	—	10	4	no	—
819	C₂³	—	10	4	no	—
820	C₂³	—	10	4	no	—
821	C₂³	C₂³×C₃×D₅	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	10	4	no	—
825	Q₈	—	10	8	no	—
826	Q₈	—	10	2	no	—
827	Q₈	—	10	4	no	—
828	D₄	—	2	2	no	—
829	D₄	—	10	4	no	—
830	D₄	—	10	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	5	1	no	—
833	C₂×C₄	—	5	1	no	—
834	C₂×C₄	—	5	4	no	—
835	C₂×C₄	—	5	4	no	—
836	C₂×C₄	—	5	2	no	—
837	C₂×C₄	—	5	2	no	—
838	C₂×C₄	—	5	1	no	—
839	C₂×C₄	—	5	4	no	—
840	C₂×C₄	—	5	2	no	—
841	C₂×C₄	—	10	4	no	—
842	C₂×C₄	—	10	4	no	—
843	C₂×C₄	—	10	4	no	—
844	C₂×C₄	—	10	8	no	—
845	C₂×C₄	—	10	4	no	—
846	C₂×C₄	—	10	2	no	—
847	C₂×C₄	—	10	4	no	—
848	C₂×C₄	—	10	4	no	—
849	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
850	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
851	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
852	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
853	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
854	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
855	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
856	C₂×C₃	—	4	2	no	—
857	C₂×C₃	—	5	4	no	—
858	C₂×C₃	—	20	2	no	—
859	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
860	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
861	C₂×C₃	D₅×2₋¹⁺⁴	1	1	yes	characteristic
862	C₅	C₂×C₃×#556	1	1	yes	characteristic, complemented, Sylow
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	5	2	no	—
867	C₂²	—	5	2	no	—
868	C₂²	—	5	2	no	—
869	C₂²	—	10	2	no	—
870	C₂²	—	10	2	no	—
871	C₂²	—	10	2	no	—
872	C₂²	—	20	8	no	—
873	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	5	2	no	—
880	C₄	—	5	2	no	—
881	C₄	—	10	2	no	—
882	C₄	—	10	2	no	—
883	C₄	—	10	4	no	—
884	C₄	—	10	2	no	—
885	C₄	—	10	1	no	—
886	C₄	C₃×D₅×#41	1	2	yes	—
887	C₄	C₃×D₅×#41	1	2	yes	—
888	C₃	D₅×#556	1	1	yes	characteristic, direct product factor, Sylow
889	C₂	—	4	2	no	—
890	C₂	—	5	4	no	—
891	C₂	—	20	2	no	—
892	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
893	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
894	C₂	C₃×D₅×2₋¹⁺⁴	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×#556	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₃×D₄×D₅	C₂²
hypercenter	C₃×#556	D₅
hypocenter	C₅	C₂×C₃×#556
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
2. C₃×#66066	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×D₅×#126	C₂	semidirect
5. C₃×#66036	C₂	semidirect
7. C₃×#66005	C₂	semidirect
8. C₃×#65975	C₂	semidirect
9. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
10. C₃×#65918	C₂	semidirect
11. C₃×C₄×Q₈×D₅	C₂	semidirect
12. C₃×C₄×Q₈×D₅	C₂	semidirect
13. C₃×#65902	C₂	semidirect
15. C₃×#65876	C₂	semidirect
16. C₃×#65867	C₂	semidirect
17. C₃×D₅×#117	C₂	semidirect
18. D₅×#556	C₃	direct (N × H)
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₅×#126	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₄×C₅×Q₈	C₂²	semidirect
28. C₃×C₄×C₅×Q₈	C₂²	semidirect
30. C₃×C₅×#117	C₂²	semidirect
32. C₃×#4092	C₂²	semidirect
33. C₃×Q₈×Dic₅	C₂²	semidirect
34. C₃×Q₈×Dic₅	C₂²	semidirect
35. C₃×#4090	C₂²	semidirect
39. C₃×#4072	C₂²	semidirect
40. C₃×#4070	C₂²	semidirect
41. C₃×#4044	C₂²	semidirect
42. C₃×#4044	C₂²	semidirect
43. C₃×#4044	C₂²	semidirect
44. C₃×#4043	C₂²	semidirect
45. C₃×#4042	C₂²	semidirect
47. C₃×#4038	C₂²	semidirect
48. C₃×#4038	C₂²	semidirect
55. C₃×#4034	C₂²	semidirect
56. C₃×#4034	C₂²	semidirect
57. C₃×#4033	C₂²	semidirect
58. C₃×#4033	C₂²	semidirect
59. C₃×#4033	C₂²	semidirect
60. C₃×#4033	C₂²	semidirect
67. C₃×#4025	C₂²	semidirect
68. C₃×#4025	C₂²	semidirect
69. C₃×#4025	C₂²	semidirect
70. C₃×#4024	C₂²	semidirect
71. C₃×#4023	C₂²	semidirect
72. C₃×#4022	C₂²	semidirect
75. C₃×#4018	C₂²	semidirect
79. C₃×#4015	C₂²	semidirect
80. C₃×C₄×Dic₁₀	C₂²	semidirect
81. C₃×C₄×Dic₁₀	C₂²	semidirect
82. C₃×C₄×Dic₁₀	C₂²	semidirect
83. C₃×C₄×Dic₁₀	C₂²	semidirect
85. C₅×#556	C₂×C₃	semidirect
86. #66066	C₂×C₃	semidirect
87. D₅×C₄⋊Q₈	C₂×C₃	semidirect
88. D₅×#126	C₂×C₃	semidirect
89. #66036	C₂×C₃	semidirect
91. #66005	C₂×C₃	semidirect
92. #65975	C₂×C₃	semidirect
93. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
94. #65918	C₂×C₃	semidirect
95. C₄×Q₈×D₅	C₂×C₃	semidirect
96. C₄×Q₈×D₅	C₂×C₃	semidirect
97. #65902	C₂×C₃	semidirect
99. #65876	C₂×C₃	semidirect
100. #65867	C₂×C₃	semidirect
101. D₅×#117	C₂×C₃	semidirect
179. C₃×#556	D₅	direct (N × H)
192. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
193. C₅×#126	C₂²×C₃	semidirect
195. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₄×C₅×Q₈	C₂²×C₃	semidirect
197. C₄×C₅×Q₈	C₂²×C₃	semidirect
199. C₅×#117	C₂²×C₃	semidirect
201. #4092	C₂²×C₃	semidirect
202. Q₈×Dic₅	C₂²×C₃	semidirect
203. Q₈×Dic₅	C₂²×C₃	semidirect
204. #4090	C₂²×C₃	semidirect
208. #4072	C₂²×C₃	semidirect
209. #4070	C₂²×C₃	semidirect
210. #4044	C₂²×C₃	semidirect
211. #4044	C₂²×C₃	semidirect
212. #4044	C₂²×C₃	semidirect
213. #4043	C₂²×C₃	semidirect
214. #4042	C₂²×C₃	semidirect
216. #4038	C₂²×C₃	semidirect
217. #4038	C₂²×C₃	semidirect
224. #4034	C₂²×C₃	semidirect
225. #4034	C₂²×C₃	semidirect
226. #4033	C₂²×C₃	semidirect
227. #4033	C₂²×C₃	semidirect
228. #4033	C₂²×C₃	semidirect
229. #4033	C₂²×C₃	semidirect
236. #4025	C₂²×C₃	semidirect
237. #4025	C₂²×C₃	semidirect
238. #4025	C₂²×C₃	semidirect
239. #4024	C₂²×C₃	semidirect
240. #4023	C₂²×C₃	semidirect
241. #4022	C₂²×C₃	semidirect
244. #4018	C₂²×C₃	semidirect
248. #4015	C₂²×C₃	semidirect
249. C₄×Dic₁₀	C₂²×C₃	semidirect
250. C₄×Dic₁₀	C₂²×C₃	semidirect
251. C₄×Dic₁₀	C₂²×C₃	semidirect
252. C₄×Dic₁₀	C₂²×C₃	semidirect
302. C₃×C₄⋊Q₈	C₂×D₅	semidirect
310. C₃×#126	C₂×D₅	semidirect
322. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
333. C₃×C₄×Q₈	C₂×D₅	semidirect
334. C₃×C₄×Q₈	C₂×D₅	semidirect
346. C₃×#117	C₂×D₅	semidirect
436. #556	C₃×D₅	direct (N × H)
587. C₄⋊Q₈	C₂×C₃×D₅	semidirect
595. #126	C₂×C₃×D₅	semidirect
607. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
618. C₄×Q₈	C₂×C₃×D₅	semidirect
619. C₄×Q₈	C₂×C₃×D₅	semidirect
631. #117	C₂×C₃×D₅	semidirect
649. C₃×D₅	#556	direct (N × H)
784. C₃×C₅	C₂×#556	semidirect
815. D₅	C₃×#556	direct (N × H)
862. C₅	C₂×C₃×#556	semidirect
888. C₃	D₅×#556	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×#556	2
C₃×#66066	2
C₃×D₅×C₄⋊Q₈	2
C₃×D₅×#126	2
C₃×#66036	2
C₃×D₅×#124	2
C₃×#66005	2
C₃×#65975	2
C₃×D₅×C₂²⋊Q₈	2
C₃×#65918	2
C₃×C₄×Q₈×D₅	2
C₃×#65902	2
C₃×C₄×D₄×D₅	2
C₃×#65876	2
C₃×#65867	2
C₃×D₅×#117	2
D₅×#556	3
C₂×C₃×#556	5

Subgroups — C3×D5×#556 #14483983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#556 #14483983