Subgroups — C₃×D₅×#554 #14483785

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66064	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66024	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×#125	C₂	1	2	yes	maximal, complemented
6	C₃×#65970	C₂	1	4	yes	maximal, complemented
7	C₃×#65969	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
10	C₃×#65913	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
13	C₃×C₄×D₄×D₅	C₂	1	2	yes	maximal
14	C₃×#65877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65873	C₂	1	2	yes	maximal, complemented
16	C₃×#65845	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×D₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
18	D₅×#554	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	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#125	C₂²	1	2	yes	complemented
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₃×#4092	C₂²	1	2	yes	complemented
33	C₃×#4092	C₂²	1	4	yes	complemented
34	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
35	C₃×#4090	C₂²	1	2	yes	complemented
36	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
37	C₃×D₄×Dic₅	C₂²	1	2	yes	—
38	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
39	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
40	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
41	C₃×#4070	C₂²	1	4	yes	complemented
42	C₃×#4070	C₂²	1	2	yes	complemented
43	C₂×C₃×#683	C₂²	1	4	yes	complemented
44	C₃×#4043	C₂²	1	2	yes	complemented
45	C₃×#4043	C₂²	1	4	yes	complemented
46	C₃×#4042	C₂²	1	4	yes	complemented
47	C₃×#4042	C₂²	1	4	yes	complemented
48	C₃×#4042	C₂²	1	4	yes	complemented
49	C₃×#4039	C₂²	1	1	yes	characteristic
50	C₃×#4039	C₂²	1	2	yes	—
51	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
53	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
54	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
56	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
57	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
58	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	complemented
61	C₃×#4036	C₂²	1	2	yes	complemented
62	C₃×#4036	C₂²	1	2	yes	complemented
63	C₃×#4035	C₂²	1	4	yes	complemented
64	C₃×#4035	C₂²	1	4	yes	complemented
65	C₃×#4034	C₂²	1	2	yes	complemented
66	C₃×#4034	C₂²	1	2	yes	complemented
67	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
68	C₃×#4033	C₂²	1	2	yes	complemented
69	C₃×#4027	C₂²	1	4	yes	—
70	C₃×#4027	C₂²	1	2	yes	—
71	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₃×#4024	C₂²	1	4	yes	complemented
74	C₃×#4024	C₂²	1	4	yes	complemented
75	C₃×#4024	C₂²	1	4	yes	complemented
76	C₃×C₄×D₂₀	C₂²	1	2	yes	—
77	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
78	C₃×C₄²×D₅	C₂²	1	2	yes	—
79	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
80	C₃×#4016	C₂²	1	2	yes	complemented
81	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₃×#554	—	5	1	no	maximal, Hall
85	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
86	#66064	C₂×C₃	1	1	yes	characteristic, complemented
87	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
88	#66024	C₂×C₃	1	2	yes	complemented
89	D₅×#125	C₂×C₃	1	2	yes	complemented
90	#65970	C₂×C₃	1	4	yes	complemented
91	#65969	C₂×C₃	1	2	yes	complemented
92	D₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
93	D₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
94	#65913	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
96	C₄×D₄×D₅	C₂×C₃	1	2	yes	—
97	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
98	#65877	C₂×C₃	1	1	yes	characteristic, complemented
99	#65873	C₂×C₃	1	2	yes	complemented
100	#65845	C₂×C₃	1	2	yes	complemented
101	C₂×D₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
102	C₂³×C₃×D₅	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
108	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
109	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
110	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
111	C₃×Q₈×D₅	—	2	4	no	—
112	C₃×Q₈×D₅	—	4	4	no	—
113	C₃×D₄×D₅	Q₈	1	8	yes	complemented
114	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₄×D₅	—	2	8	no	—
116	C₂×C₃×C₄×D₅	—	4	8	no	—
117	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
118	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
119	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
120	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
121	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
122	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
124	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
125	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
126	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
128	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
129	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
130	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
131	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₃×C₄²×C₅	C₂³	1	2	yes	—
143	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
144	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
145	C₃×#685	C₂³	1	2	yes	—
146	C₃×#685	C₂³	1	4	yes	—
147	C₃×#685	C₂³	1	4	yes	—
148	C₃×#685	C₂³	1	2	yes	—
149	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
151	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
152	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
153	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
154	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
155	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
156	C₃×#683	C₂³	1	4	yes	—
157	C₃×#683	C₂³	1	4	yes	—
158	C₃×#683	C₂³	1	2	yes	—
159	C₃×#683	C₂³	1	4	yes	—
160	C₃×#683	C₂³	1	4	yes	—
161	C₃×#683	C₂³	1	2	yes	—
162	C₃×#683	C₂³	1	2	yes	—
163	C₃×#683	C₂³	1	4	yes	—
164	C₃×#683	C₂³	1	4	yes	—
165	C₃×#683	C₂³	1	2	yes	—
166	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
167	C₃×C₄×Dic₅	C₂³	1	2	yes	—
168	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
169	C₃×C₄×Dic₅	C₂³	1	2	yes	—
170	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
171	C₃×C₄×Dic₅	C₂³	1	2	yes	—
172	C₃×#554	—	5	1	no	—
173	C₃×#554	—	5	2	no	—
174	C₃×#554	—	5	2	no	—
175	C₃×#554	—	5	4	no	—
176	C₃×#554	—	5	1	no	—
177	C₃×#554	—	5	2	no	—
178	C₃×#554	—	5	1	no	—
179	C₃×#554	—	5	2	no	—
180	C₃×#554	D₅	1	1	yes	characteristic, direct product factor
181	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
182	C₂×C₃×#125	—	5	2	no	—
183	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
184	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
185	C₂×C₃×C₄×Q₈	—	5	1	no	—
186	C₂×C₃×C₄×D₄	—	5	2	no	—
187	C₂×C₃×C₄×D₄	—	5	1	no	—
188	C₂²×C₃×C₄⋊C₄	—	5	2	no	—
189	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
191	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
192	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
193	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
194	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₅×#125	C₂²×C₃	1	2	yes	complemented
196	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
197	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
198	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
200	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
201	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
202	#4092	C₂²×C₃	1	4	yes	complemented
203	#4092	C₂²×C₃	1	2	yes	complemented
204	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
205	#4090	C₂²×C₃	1	2	yes	complemented
206	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
207	D₄×Dic₅	C₂²×C₃	1	2	yes	—
208	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
209	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
210	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
211	#4070	C₂²×C₃	1	4	yes	complemented
212	#4070	C₂²×C₃	1	2	yes	complemented
213	C₂×#683	C₂²×C₃	1	4	yes	complemented
214	#4043	C₂²×C₃	1	2	yes	complemented
215	#4043	C₂²×C₃	1	4	yes	complemented
216	#4042	C₂²×C₃	1	4	yes	complemented
217	#4042	C₂²×C₃	1	4	yes	complemented
218	#4042	C₂²×C₃	1	4	yes	complemented
219	#4039	C₂²×C₃	1	2	yes	—
220	#4039	C₂²×C₃	1	1	yes	characteristic
221	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
222	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
223	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
224	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
225	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
226	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
227	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
228	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
229	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
230	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
231	#4036	C₂²×C₃	1	2	yes	complemented
232	#4036	C₂²×C₃	1	2	yes	complemented
233	#4035	C₂²×C₃	1	4	yes	complemented
234	#4035	C₂²×C₃	1	4	yes	complemented
235	#4034	C₂²×C₃	1	2	yes	complemented
236	#4034	C₂²×C₃	1	2	yes	complemented
237	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
238	#4033	C₂²×C₃	1	2	yes	complemented
239	#4027	C₂²×C₃	1	4	yes	—
240	#4027	C₂²×C₃	1	2	yes	—
241	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
242	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
243	#4024	C₂²×C₃	1	4	yes	complemented
244	#4024	C₂²×C₃	1	4	yes	complemented
245	#4024	C₂²×C₃	1	4	yes	complemented
246	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
247	C₄×D₂₀	C₂²×C₃	1	2	yes	—
248	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
249	C₄²×D₅	C₂²×C₃	1	2	yes	—
250	#4016	C₂²×C₃	1	2	yes	complemented
251	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
252	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
254	C₂×#554	—	5	1	no	Sylow
255	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
256	C₂²×C₃×D₅	—	2	4	no	—
257	C₂²×C₃×D₅	—	2	4	no	—
258	C₂²×C₃×D₅	C₂×Q₈	1	8	yes	—
259	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
260	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
261	C₃×C₅×Q₈	—	2	2	no	—
262	C₃×C₅×Q₈	—	4	2	no	—
263	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
264	C₂×C₃×C₄×C₅	—	2	4	no	—
265	C₂×C₃×C₄×C₅	—	4	4	no	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₃×C₂²⋊D₅	C₂×Q₈	1	8	yes	complemented
274	C₂×C₃×Dic₅	—	2	4	no	—
275	C₂×C₃×Dic₅	—	4	4	no	—
276	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
277	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
278	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
280	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
281	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₃×D₂₀	C₂×Q₈	1	4	yes	complemented
284	C₃×C₄×D₅	—	2	4	no	—
285	C₃×C₄×D₅	—	2	4	no	—
286	C₃×C₄×D₅	—	2	4	no	—
287	C₃×C₄×D₅	—	2	8	no	—
288	C₃×C₄×D₅	—	2	2	no	—
289	C₃×C₄×D₅	—	2	4	no	—
290	C₃×C₄×D₅	—	2	4	no	—
291	C₃×C₄×D₅	—	4	4	no	—
292	C₃×C₄×D₅	—	4	4	no	—
293	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
294	C₃×C₄×D₅	#41	1	4	yes	—
295	C₃×Dic₁₀	—	2	2	no	—
296	C₃×Dic₁₀	—	2	4	no	—
297	C₃×Dic₁₀	—	4	4	no	—
298	C₃×Dic₁₀	—	4	2	no	—
299	C₂²×C₃×Q₈	—	5	1	no	—
300	C₂²×C₃×Q₈	—	5	2	no	—
301	C₂²×C₃×D₄	—	5	1	no	—
302	C₂³×C₃×C₄	—	5	2	no	—
303	C₂³×C₃×C₄	—	5	4	no	—
304	C₃×C₄⋊Q₈	—	5	2	no	—
305	C₃×C₄⋊Q₈	—	5	2	no	—
306	C₃×C₄⋊Q₈	—	5	2	no	—
307	C₃×C₄⋊Q₈	—	5	1	no	—
308	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
309	C₃×#125	—	5	4	no	—
310	C₃×#125	—	5	4	no	—
311	C₃×#125	—	5	2	no	—
312	C₃×#125	—	5	2	no	—
313	C₃×#125	—	5	2	no	—
314	C₃×#125	C₂×D₅	1	2	yes	complemented
315	C₃×C₂²⋊Q₈	—	5	4	no	—
316	C₃×C₂²⋊Q₈	—	5	2	no	—
317	C₃×C₂²⋊Q₈	—	5	4	no	—
318	C₃×C₂²⋊Q₈	—	5	2	no	—
319	C₃×C₂²⋊Q₈	—	5	4	no	—
320	C₃×C₂²⋊Q₈	—	5	4	no	—
321	C₃×C₂²⋊Q₈	—	5	4	no	—
322	C₃×C₂²⋊Q₈	—	5	4	no	—
323	C₃×C₂²⋊Q₈	—	5	2	no	—
324	C₃×C₂²⋊Q₈	—	5	4	no	—
325	C₃×C₂²⋊Q₈	—	5	4	no	—
326	C₃×C₂²⋊Q₈	—	5	4	no	—
327	C₃×C₂²⋊Q₈	C₂×D₅	1	4	yes	complemented
328	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
329	C₃×C₄×Q₈	—	5	1	no	—
330	C₃×C₄×Q₈	—	5	2	no	—
331	C₃×C₄×Q₈	—	5	1	no	—
332	C₃×C₄×Q₈	—	5	1	no	—
333	C₃×C₄×Q₈	—	5	2	no	—
334	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
335	C₃×C₄×D₄	—	5	2	no	—
336	C₃×C₄×D₄	—	5	1	no	—
337	C₃×C₄×D₄	—	5	4	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	2	no	—
340	C₃×C₄×D₄	—	5	1	no	—
341	C₃×C₄×D₄	—	5	4	no	—
342	C₃×C₄×D₄	—	5	2	no	—
343	C₃×C₄×D₄	—	5	2	no	—
344	C₃×C₄×D₄	—	5	1	no	—
345	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
346	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
347	C₂×C₃×C₄⋊C₄	—	5	4	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	4	no	—
353	C₂×C₃×C₄⋊C₄	—	5	2	no	—
354	C₂×C₃×C₄⋊C₄	—	5	2	no	—
355	C₂×C₃×C₄⋊C₄	—	5	1	no	—
356	C₂×C₃×C₄⋊C₄	—	5	2	no	—
357	C₂×C₃×C₄⋊C₄	—	5	2	no	—
358	C₂×C₃×C₄⋊C₄	—	5	4	no	—
359	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
360	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
361	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
362	C₂×C₃×C₄²	—	5	2	no	—
363	C₂×C₃×C₄²	—	5	1	no	—
364	C₂³×D₅	C₂³×C₃	1	2	yes	—
365	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
367	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
369	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
370	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
371	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
372	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
373	Q₈×D₅	—	2	4	no	—
374	Q₈×D₅	—	4	4	no	—
375	D₄×D₅	C₃×Q₈	1	8	yes	complemented
376	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₄×D₅	—	2	8	no	—
378	C₂×C₄×D₅	—	4	8	no	—
379	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
380	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
381	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
382	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
383	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
384	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
386	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
387	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
388	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
390	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
391	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
392	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
393	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
394	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
395	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
396	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
398	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
402	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
403	C₄²×C₅	C₂³×C₃	1	2	yes	—
404	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
405	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
406	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
407	#685	C₂³×C₃	1	4	yes	—
408	#685	C₂³×C₃	1	2	yes	—
409	#685	C₂³×C₃	1	2	yes	—
410	#685	C₂³×C₃	1	4	yes	—
411	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
412	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
413	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
414	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
415	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
416	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
417	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
418	#683	C₂³×C₃	1	2	yes	—
419	#683	C₂³×C₃	1	2	yes	—
420	#683	C₂³×C₃	1	2	yes	—
421	#683	C₂³×C₃	1	4	yes	—
422	#683	C₂³×C₃	1	4	yes	—
423	#683	C₂³×C₃	1	4	yes	—
424	#683	C₂³×C₃	1	4	yes	—
425	#683	C₂³×C₃	1	4	yes	—
426	#683	C₂³×C₃	1	4	yes	—
427	#683	C₂³×C₃	1	2	yes	—
428	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
429	C₄×Dic₅	C₂³×C₃	1	2	yes	—
430	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
431	C₄×Dic₅	C₂³×C₃	1	2	yes	—
432	C₄×Dic₅	C₂³×C₃	1	2	yes	—
433	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
434	#554	—	5	1	no	—
435	#554	—	5	2	no	—
436	#554	—	5	2	no	—
437	#554	—	5	4	no	—
438	#554	—	5	1	no	—
439	#554	—	5	2	no	—
440	#554	—	5	1	no	—
441	#554	—	5	2	no	—
442	#554	C₃×D₅	1	1	yes	characteristic, direct product factor
443	C₂×C₄⋊Q₈	—	5	1	no	—
444	C₂×#125	—	5	2	no	—
445	C₂×C₂²⋊Q₈	—	5	4	no	—
446	C₂×C₂²⋊Q₈	—	5	2	no	—
447	C₂×C₄×Q₈	—	5	1	no	—
448	C₂×C₄×D₄	—	5	2	no	—
449	C₂×C₄×D₄	—	5	1	no	—
450	C₂²×C₄⋊C₄	—	5	2	no	—
451	C₂²×C₃×C₅	—	2	2	no	—
452	C₂²×C₃×C₅	—	2	2	no	—
453	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	—
454	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
455	C₂×C₃×D₅	—	2	2	no	—
456	C₂×C₃×D₅	—	2	2	no	—
457	C₂×C₃×D₅	—	2	16	no	—
458	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
459	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
460	C₂×C₃×D₅	C₂×#41	1	2	yes	—
461	C₂×C₃×D₅	H(5,𝔽₂)	1	2	yes	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	2	no	—
464	C₃×C₄×C₅	—	2	1	no	—
465	C₃×C₄×C₅	—	2	4	no	—
466	C₃×C₄×C₅	—	2	2	no	—
467	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
468	C₃×C₄×C₅	C₂×#41	1	2	yes	—
469	C₃×Dic₅	—	2	2	no	—
470	C₃×Dic₅	—	2	2	no	—
471	C₃×Dic₅	—	2	1	no	—
472	C₃×Dic₅	—	2	4	no	—
473	C₃×Dic₅	—	2	2	no	—
474	C₃×Dic₅	C₂²×Q₈	1	2	yes	—
475	C₃×Dic₅	C₂×#41	1	2	yes	—
476	C₂⁴×C₃	—	5	2	no	—
477	C₂×C₃×Q₈	—	5	2	no	—
478	C₂×C₃×Q₈	—	5	1	no	—
479	C₂×C₃×Q₈	—	5	4	no	—
480	C₂×C₃×Q₈	—	5	2	no	—
481	C₂×C₃×Q₈	—	10	4	no	—
482	C₂×C₃×Q₈	—	20	4	no	—
483	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
484	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
485	C₂×C₃×D₄	—	5	2	no	—
486	C₂×C₃×D₄	—	5	8	no	—
487	C₂×C₃×D₄	—	5	1	no	—
488	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
489	C₂²×C₃×C₄	—	5	1	no	—
490	C₂²×C₃×C₄	—	5	1	no	—
491	C₂²×C₃×C₄	—	5	2	no	—
492	C₂²×C₃×C₄	—	5	4	no	—
493	C₂²×C₃×C₄	—	5	2	no	—
494	C₂²×C₃×C₄	—	5	1	no	—
495	C₂²×C₃×C₄	—	5	2	no	—
496	C₂²×C₃×C₄	—	5	2	no	—
497	C₂²×C₃×C₄	—	5	4	no	—
498	C₂²×C₃×C₄	—	5	2	no	—
499	C₂²×C₃×C₄	—	5	2	no	—
500	C₂²×C₃×C₄	—	5	4	no	—
501	C₂²×C₃×C₄	—	5	4	no	—
502	C₂²×C₃×C₄	—	10	8	no	—
503	C₂²×C₃×C₄	—	20	8	no	—
504	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
505	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
506	C₃×C₄⋊C₄	—	5	2	no	—
507	C₃×C₄⋊C₄	—	5	4	no	—
508	C₃×C₄⋊C₄	—	5	4	no	—
509	C₃×C₄⋊C₄	—	5	4	no	—
510	C₃×C₄⋊C₄	—	5	2	no	—
511	C₃×C₄⋊C₄	—	5	4	no	—
512	C₃×C₄⋊C₄	—	5	2	no	—
513	C₃×C₄⋊C₄	—	5	2	no	—
514	C₃×C₄⋊C₄	—	5	4	no	—
515	C₃×C₄⋊C₄	—	5	4	no	—
516	C₃×C₄⋊C₄	—	5	1	no	—
517	C₃×C₄⋊C₄	—	5	4	no	—
518	C₃×C₄⋊C₄	—	5	2	no	—
519	C₃×C₄⋊C₄	—	5	1	no	—
520	C₃×C₄⋊C₄	—	5	2	no	—
521	C₃×C₄⋊C₄	—	5	2	no	—
522	C₃×C₄⋊C₄	—	5	4	no	—
523	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
524	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
525	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
526	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
527	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
528	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
529	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
530	C₃×C₂²⋊C₄	—	5	4	no	—
531	C₃×C₂²⋊C₄	—	5	2	no	—
532	C₃×C₂²⋊C₄	—	5	4	no	—
533	C₃×C₂²⋊C₄	—	5	2	no	—
534	C₃×C₂²⋊C₄	—	5	2	no	—
535	C₃×C₂²⋊C₄	—	5	4	no	—
536	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
537	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
538	C₃×C₄²	—	5	2	no	—
539	C₃×C₄²	—	5	2	no	—
540	C₃×C₄²	—	5	2	no	—
541	C₃×C₄²	—	5	1	no	—
542	C₃×C₄²	—	5	1	no	—
543	C₃×C₄²	—	5	1	no	—
544	C₃×C₄²	C₂²×D₅	1	2	yes	—
545	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
546	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
547	C₂²×D₅	—	2	4	no	—
548	C₂²×D₅	—	2	4	no	—
549	C₂²×D₅	C₂×C₃×Q₈	1	8	yes	—
550	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
551	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
552	C₅×Q₈	—	2	2	no	—
553	C₅×Q₈	—	4	2	no	—
554	C₅×D₄	C₂×C₃×Q₈	1	4	yes	complemented
555	C₂×C₄×C₅	—	2	4	no	—
556	C₂×C₄×C₅	—	4	4	no	—
557	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
558	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
559	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
560	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
561	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
562	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
563	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
564	C₂²⋊D₅	C₂×C₃×Q₈	1	8	yes	complemented
565	C₂×Dic₅	—	2	4	no	—
566	C₂×Dic₅	—	4	4	no	—
567	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
568	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
569	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
570	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
571	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
572	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
573	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
574	D₂₀	C₂×C₃×Q₈	1	4	yes	complemented
575	C₄×D₅	—	2	4	no	—
576	C₄×D₅	—	2	4	no	—
577	C₄×D₅	—	2	4	no	—
578	C₄×D₅	—	2	8	no	—
579	C₄×D₅	—	2	2	no	—
580	C₄×D₅	—	2	4	no	—
581	C₄×D₅	—	2	4	no	—
582	C₄×D₅	—	4	4	no	—
583	C₄×D₅	—	4	4	no	—
584	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
585	C₄×D₅	C₃×#41	1	4	yes	—
586	Dic₁₀	—	2	2	no	—
587	Dic₁₀	—	2	4	no	—
588	Dic₁₀	—	4	4	no	—
589	Dic₁₀	—	4	2	no	—
590	C₂²×Q₈	—	5	1	no	—
591	C₂²×Q₈	—	5	2	no	—
592	C₂²×D₄	—	5	1	no	—
593	C₂³×C₄	—	5	2	no	—
594	C₂³×C₄	—	5	4	no	—
595	C₄⋊Q₈	—	5	2	no	—
596	C₄⋊Q₈	—	5	2	no	—
597	C₄⋊Q₈	—	5	2	no	—
598	C₄⋊Q₈	—	5	1	no	—
599	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
600	#125	—	5	4	no	—
601	#125	—	5	4	no	—
602	#125	—	5	2	no	—
603	#125	—	5	2	no	—
604	#125	—	5	2	no	—
605	#125	C₂×C₃×D₅	1	2	yes	complemented
606	C₂²⋊Q₈	—	5	4	no	—
607	C₂²⋊Q₈	—	5	2	no	—
608	C₂²⋊Q₈	—	5	4	no	—
609	C₂²⋊Q₈	—	5	2	no	—
610	C₂²⋊Q₈	—	5	4	no	—
611	C₂²⋊Q₈	—	5	4	no	—
612	C₂²⋊Q₈	—	5	4	no	—
613	C₂²⋊Q₈	—	5	4	no	—
614	C₂²⋊Q₈	—	5	2	no	—
615	C₂²⋊Q₈	—	5	4	no	—
616	C₂²⋊Q₈	—	5	4	no	—
617	C₂²⋊Q₈	—	5	4	no	—
618	C₂²⋊Q₈	C₂×C₃×D₅	1	4	yes	complemented
619	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
620	C₄×Q₈	—	5	1	no	—
621	C₄×Q₈	—	5	2	no	—
622	C₄×Q₈	—	5	1	no	—
623	C₄×Q₈	—	5	1	no	—
624	C₄×Q₈	—	5	2	no	—
625	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
626	C₄×D₄	—	5	2	no	—
627	C₄×D₄	—	5	1	no	—
628	C₄×D₄	—	5	4	no	—
629	C₄×D₄	—	5	2	no	—
630	C₄×D₄	—	5	2	no	—
631	C₄×D₄	—	5	1	no	—
632	C₄×D₄	—	5	4	no	—
633	C₄×D₄	—	5	2	no	—
634	C₄×D₄	—	5	2	no	—
635	C₄×D₄	—	5	1	no	—
636	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
637	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
638	C₂×C₄⋊C₄	—	5	4	no	—
639	C₂×C₄⋊C₄	—	5	2	no	—
640	C₂×C₄⋊C₄	—	5	1	no	—
641	C₂×C₄⋊C₄	—	5	4	no	—
642	C₂×C₄⋊C₄	—	5	2	no	—
643	C₂×C₄⋊C₄	—	5	4	no	—
644	C₂×C₄⋊C₄	—	5	2	no	—
645	C₂×C₄⋊C₄	—	5	2	no	—
646	C₂×C₄⋊C₄	—	5	1	no	—
647	C₂×C₄⋊C₄	—	5	2	no	—
648	C₂×C₄⋊C₄	—	5	2	no	—
649	C₂×C₄⋊C₄	—	5	4	no	—
650	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
651	C₂×C₂²⋊C₄	—	5	4	no	—
652	C₂×C₂²⋊C₄	—	5	2	no	—
653	C₂×C₄²	—	5	2	no	—
654	C₂×C₄²	—	5	1	no	—
655	C₂×C₃×C₅	—	2	4	no	—
656	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
657	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
658	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₃×D₅	—	2	4	no	—
660	C₃×D₅	#554	1	4	yes	direct product factor
661	C₂³×C₃	—	5	1	no	—
662	C₂³×C₃	—	5	8	no	—
663	C₂³×C₃	—	5	2	no	—
664	C₂³×C₃	—	10	4	no	—
665	C₂³×C₃	—	10	4	no	—
666	C₂³×C₃	C₂³×D₅	1	2	yes	—
667	C₃×Q₈	—	2	2	no	—
668	C₃×Q₈	—	4	2	no	—
669	C₃×Q₈	—	10	4	no	—
670	C₃×Q₈	—	10	2	no	—
671	C₃×Q₈	—	20	4	no	—
672	C₃×Q₈	—	20	2	no	—
673	C₃×D₄	—	5	8	no	—
674	C₃×D₄	—	5	4	no	—
675	C₃×D₄	Q₈×D₅	1	4	yes	complemented
676	C₂×C₃×C₄	—	2	4	no	—
677	C₂×C₃×C₄	—	4	4	no	—
678	C₂×C₃×C₄	—	5	1	no	—
679	C₂×C₃×C₄	—	5	1	no	—
680	C₂×C₃×C₄	—	5	4	no	—
681	C₂×C₃×C₄	—	5	4	no	—
682	C₂×C₃×C₄	—	5	2	no	—
683	C₂×C₃×C₄	—	5	1	no	—
684	C₂×C₃×C₄	—	5	2	no	—
685	C₂×C₃×C₄	—	5	2	no	—
686	C₂×C₃×C₄	—	5	4	no	—
687	C₂×C₃×C₄	—	10	4	no	—
688	C₂×C₃×C₄	—	10	4	no	—
689	C₂×C₃×C₄	—	10	4	no	—
690	C₂×C₃×C₄	—	10	8	no	—
691	C₂×C₃×C₄	—	10	4	no	—
692	C₂×C₃×C₄	—	10	2	no	—
693	C₂×C₃×C₄	—	10	4	no	—
694	C₂×C₃×C₄	—	10	4	no	—
695	C₂×C₃×C₄	—	20	4	no	—
696	C₂×C₃×C₄	—	20	4	no	—
697	C₂×C₃×C₄	—	20	4	no	—
698	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
699	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
700	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
701	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
702	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
703	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
705	C₂²×C₅	—	2	2	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	C₂²×C₃×Q₈	1	4	yes	—
708	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
709	C₂×D₅	—	2	2	no	—
710	C₂×D₅	—	2	2	no	—
711	C₂×D₅	—	2	16	no	—
712	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
713	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
714	C₂×D₅	C₂×C₃×#41	1	2	yes	—
715	C₂×D₅	C₃×H(5,𝔽₂)	1	2	yes	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	1	no	—
719	C₄×C₅	—	2	4	no	—
720	C₄×C₅	—	2	2	no	—
721	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
722	C₄×C₅	C₂×C₃×#41	1	2	yes	—
723	Dic₅	—	2	2	no	—
724	Dic₅	—	2	2	no	—
725	Dic₅	—	2	1	no	—
726	Dic₅	—	2	4	no	—
727	Dic₅	—	2	2	no	—
728	Dic₅	C₂²×C₃×Q₈	1	2	yes	—
729	Dic₅	C₂×C₃×#41	1	2	yes	—
730	C₂⁴	—	5	2	no	—
731	C₂×Q₈	—	5	2	no	—
732	C₂×Q₈	—	5	1	no	—
733	C₂×Q₈	—	5	4	no	—
734	C₂×Q₈	—	5	2	no	—
735	C₂×Q₈	—	10	4	no	—
736	C₂×Q₈	—	20	4	no	—
737	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
739	C₂×D₄	—	5	2	no	—
740	C₂×D₄	—	5	8	no	—
741	C₂×D₄	—	5	1	no	—
742	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
743	C₂²×C₄	—	5	1	no	—
744	C₂²×C₄	—	5	1	no	—
745	C₂²×C₄	—	5	2	no	—
746	C₂²×C₄	—	5	4	no	—
747	C₂²×C₄	—	5	2	no	—
748	C₂²×C₄	—	5	1	no	—
749	C₂²×C₄	—	5	2	no	—
750	C₂²×C₄	—	5	2	no	—
751	C₂²×C₄	—	5	4	no	—
752	C₂²×C₄	—	5	2	no	—
753	C₂²×C₄	—	5	2	no	—
754	C₂²×C₄	—	5	4	no	—
755	C₂²×C₄	—	5	4	no	—
756	C₂²×C₄	—	10	8	no	—
757	C₂²×C₄	—	20	8	no	—
758	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
759	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
760	C₄⋊C₄	—	5	2	no	—
761	C₄⋊C₄	—	5	1	no	—
762	C₄⋊C₄	—	5	4	no	—
763	C₄⋊C₄	—	5	4	no	—
764	C₄⋊C₄	—	5	4	no	—
765	C₄⋊C₄	—	5	4	no	—
766	C₄⋊C₄	—	5	2	no	—
767	C₄⋊C₄	—	5	2	no	—
768	C₄⋊C₄	—	5	1	no	—
769	C₄⋊C₄	—	5	4	no	—
770	C₄⋊C₄	—	5	2	no	—
771	C₄⋊C₄	—	5	2	no	—
772	C₄⋊C₄	—	5	2	no	—
773	C₄⋊C₄	—	5	2	no	—
774	C₄⋊C₄	—	5	4	no	—
775	C₄⋊C₄	—	5	4	no	—
776	C₄⋊C₄	—	5	4	no	—
777	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
779	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
780	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
782	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
783	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
784	C₂²⋊C₄	—	5	4	no	—
785	C₂²⋊C₄	—	5	2	no	—
786	C₂²⋊C₄	—	5	4	no	—
787	C₂²⋊C₄	—	5	2	no	—
788	C₂²⋊C₄	—	5	2	no	—
789	C₂²⋊C₄	—	5	4	no	—
790	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
791	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
792	C₄²	—	5	2	no	—
793	C₄²	—	5	2	no	—
794	C₄²	—	5	2	no	—
795	C₄²	—	5	1	no	—
796	C₄²	—	5	1	no	—
797	C₄²	—	5	1	no	—
798	C₄²	C₂²×C₃×D₅	1	2	yes	—
799	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
800	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	5	2	no	—
804	C₂²×C₃	—	5	2	no	—
805	C₂²×C₃	—	5	2	no	—
806	C₂²×C₃	—	5	4	no	—
807	C₂²×C₃	—	10	16	no	—
808	C₂²×C₃	—	10	2	no	—
809	C₂²×C₃	—	10	2	no	—
810	C₂²×C₃	C₂×Q₈×D₅	1	4	yes	—
811	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
812	C₃×C₄	—	2	2	no	—
813	C₃×C₄	—	2	2	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	4	no	—
816	C₃×C₄	—	2	1	no	—
817	C₃×C₄	—	5	2	no	—
818	C₃×C₄	—	5	2	no	—
819	C₃×C₄	—	10	2	no	—
820	C₃×C₄	—	10	2	no	—
821	C₃×C₄	—	10	2	no	—
822	C₃×C₄	—	10	4	no	—
823	C₃×C₄	—	10	1	no	—
824	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
825	C₃×C₄	D₅×#41	1	2	yes	—
826	C₂×C₅	—	2	4	no	—
827	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
828	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
829	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
830	D₅	—	2	4	no	—
831	D₅	C₃×#554	1	4	yes	direct product factor
832	C₂³	—	5	1	no	—
833	C₂³	—	5	8	no	—
834	C₂³	—	5	2	no	—
835	C₂³	—	10	4	no	—
836	C₂³	—	10	4	no	—
837	C₂³	C₂³×C₃×D₅	1	2	yes	—
838	Q₈	—	2	2	no	—
839	Q₈	—	4	2	no	—
840	Q₈	—	10	4	no	—
841	Q₈	—	10	2	no	—
842	Q₈	—	20	4	no	—
843	Q₈	—	20	2	no	—
844	D₄	—	5	8	no	—
845	D₄	—	5	4	no	—
846	D₄	C₃×Q₈×D₅	1	4	yes	complemented
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	5	1	no	—
850	C₂×C₄	—	5	1	no	—
851	C₂×C₄	—	5	4	no	—
852	C₂×C₄	—	5	4	no	—
853	C₂×C₄	—	5	2	no	—
854	C₂×C₄	—	5	1	no	—
855	C₂×C₄	—	5	2	no	—
856	C₂×C₄	—	5	2	no	—
857	C₂×C₄	—	5	4	no	—
858	C₂×C₄	—	10	4	no	—
859	C₂×C₄	—	10	4	no	—
860	C₂×C₄	—	10	4	no	—
861	C₂×C₄	—	10	8	no	—
862	C₂×C₄	—	10	4	no	—
863	C₂×C₄	—	10	2	no	—
864	C₂×C₄	—	10	4	no	—
865	C₂×C₄	—	10	4	no	—
866	C₂×C₄	—	20	4	no	—
867	C₂×C₄	—	20	4	no	—
868	C₂×C₄	—	20	4	no	—
869	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
870	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
871	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
872	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
873	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
874	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
876	C₂×C₃	—	2	4	no	—
877	C₂×C₃	—	5	4	no	—
878	C₂×C₃	—	10	4	no	—
879	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
880	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
881	C₂×C₃	D₅×H(5,𝔽₂)	1	1	yes	characteristic
882	C₅	C₂×C₃×#554	1	1	yes	characteristic, complemented, Sylow
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	5	2	no	—
886	C₂²	—	5	2	no	—
887	C₂²	—	5	2	no	—
888	C₂²	—	5	4	no	—
889	C₂²	—	10	16	no	—
890	C₂²	—	10	2	no	—
891	C₂²	—	10	2	no	—
892	C₂²	C₂×C₃×Q₈×D₅	1	4	yes	—
893	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	1	no	—
899	C₄	—	5	2	no	—
900	C₄	—	5	2	no	—
901	C₄	—	10	2	no	—
902	C₄	—	10	2	no	—
903	C₄	—	10	2	no	—
904	C₄	—	10	4	no	—
905	C₄	—	10	1	no	—
906	C₄	C₂×C₃×Q₈×D₅	1	2	yes	—
907	C₄	C₃×D₅×#41	1	2	yes	—
908	C₃	D₅×#554	1	1	yes	characteristic, direct product factor, Sylow
909	C₂	—	2	4	no	—
910	C₂	—	5	4	no	—
911	C₂	—	10	4	no	—
912	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
913	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
914	C₂	C₃×D₅×H(5,𝔽₂)	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×#554	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₃×D₄×D₅	C₂²
hypercenter	C₃×#554	D₅
hypocenter	C₅	C₂×C₃×#554
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#554

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
2. C₃×#66064	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×#66024	C₂	semidirect
5. C₃×D₅×#125	C₂	semidirect
6. C₃×#65970	C₂	semidirect
7. C₃×#65969	C₂	semidirect
8. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
9. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
10. C₃×#65913	C₂	semidirect
11. C₃×C₄×Q₈×D₅	C₂	semidirect
14. C₃×#65877	C₂	semidirect
15. C₃×#65873	C₂	semidirect
16. C₃×#65845	C₂	semidirect
17. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
18. D₅×#554	C₃	direct (N × H)
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#125	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₃×C₄×C₅×Q₈	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₃×#4092	C₂²	semidirect
33. C₃×#4092	C₂²	semidirect
34. C₃×Q₈×Dic₅	C₂²	semidirect
35. C₃×#4090	C₂²	semidirect
40. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
41. C₃×#4070	C₂²	semidirect
42. C₃×#4070	C₂²	semidirect
43. C₂×C₃×#683	C₂²	semidirect
44. C₃×#4043	C₂²	semidirect
45. C₃×#4043	C₂²	semidirect
46. C₃×#4042	C₂²	semidirect
47. C₃×#4042	C₂²	semidirect
48. C₃×#4042	C₂²	semidirect
58. C₃×D₅×C₄⋊C₄	C₂²	semidirect
59. C₃×D₅×C₄⋊C₄	C₂²	semidirect
60. C₃×D₅×C₄⋊C₄	C₂²	semidirect
61. C₃×#4036	C₂²	semidirect
62. C₃×#4036	C₂²	semidirect
63. C₃×#4035	C₂²	semidirect
64. C₃×#4035	C₂²	semidirect
65. C₃×#4034	C₂²	semidirect
66. C₃×#4034	C₂²	semidirect
67. C₃×#4033	C₂²	semidirect
68. C₃×#4033	C₂²	semidirect
73. C₃×#4024	C₂²	semidirect
74. C₃×#4024	C₂²	semidirect
75. C₃×#4024	C₂²	semidirect
80. C₃×#4016	C₂²	semidirect
81. C₃×#4015	C₂²	semidirect
82. C₃×C₄×Dic₁₀	C₂²	semidirect
83. C₃×C₄×Dic₁₀	C₂²	semidirect
85. C₅×#554	C₂×C₃	semidirect
86. #66064	C₂×C₃	semidirect
87. D₅×C₄⋊Q₈	C₂×C₃	semidirect
88. #66024	C₂×C₃	semidirect
89. D₅×#125	C₂×C₃	semidirect
90. #65970	C₂×C₃	semidirect
91. #65969	C₂×C₃	semidirect
92. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
93. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
94. #65913	C₂×C₃	semidirect
95. C₄×Q₈×D₅	C₂×C₃	semidirect
98. #65877	C₂×C₃	semidirect
99. #65873	C₂×C₃	semidirect
100. #65845	C₂×C₃	semidirect
101. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
113. C₃×D₄×D₅	Q₈	semidirect
180. C₃×#554	D₅	direct (N × H)
194. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
195. C₅×#125	C₂²×C₃	semidirect
196. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
197. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
198. C₄×C₅×Q₈	C₂²×C₃	semidirect
201. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
202. #4092	C₂²×C₃	semidirect
203. #4092	C₂²×C₃	semidirect
204. Q₈×Dic₅	C₂²×C₃	semidirect
205. #4090	C₂²×C₃	semidirect
210. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
211. #4070	C₂²×C₃	semidirect
212. #4070	C₂²×C₃	semidirect
213. C₂×#683	C₂²×C₃	semidirect
214. #4043	C₂²×C₃	semidirect
215. #4043	C₂²×C₃	semidirect
216. #4042	C₂²×C₃	semidirect
217. #4042	C₂²×C₃	semidirect
218. #4042	C₂²×C₃	semidirect
228. D₅×C₄⋊C₄	C₂²×C₃	semidirect
229. D₅×C₄⋊C₄	C₂²×C₃	semidirect
230. D₅×C₄⋊C₄	C₂²×C₃	semidirect
231. #4036	C₂²×C₃	semidirect
232. #4036	C₂²×C₃	semidirect
233. #4035	C₂²×C₃	semidirect
234. #4035	C₂²×C₃	semidirect
235. #4034	C₂²×C₃	semidirect
236. #4034	C₂²×C₃	semidirect
237. #4033	C₂²×C₃	semidirect
238. #4033	C₂²×C₃	semidirect
243. #4024	C₂²×C₃	semidirect
244. #4024	C₂²×C₃	semidirect
245. #4024	C₂²×C₃	semidirect
250. #4016	C₂²×C₃	semidirect
251. #4015	C₂²×C₃	semidirect
252. C₄×Dic₁₀	C₂²×C₃	semidirect
253. C₄×Dic₁₀	C₂²×C₃	semidirect
263. C₃×C₅×D₄	C₂×Q₈	semidirect
273. C₃×C₂²⋊D₅	C₂×Q₈	semidirect
283. C₃×D₂₀	C₂×Q₈	semidirect
308. C₃×C₄⋊Q₈	C₂×D₅	semidirect
314. C₃×#125	C₂×D₅	semidirect
327. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
328. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
334. C₃×C₄×Q₈	C₂×D₅	semidirect
359. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
375. D₄×D₅	C₃×Q₈	semidirect
442. #554	C₃×D₅	direct (N × H)
554. C₅×D₄	C₂×C₃×Q₈	semidirect
564. C₂²⋊D₅	C₂×C₃×Q₈	semidirect
574. D₂₀	C₂×C₃×Q₈	semidirect
599. C₄⋊Q₈	C₂×C₃×D₅	semidirect
605. #125	C₂×C₃×D₅	semidirect
618. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
619. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
625. C₄×Q₈	C₂×C₃×D₅	semidirect
650. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
660. C₃×D₅	#554	direct (N × H)
675. C₃×D₄	Q₈×D₅	semidirect
800. C₃×C₅	C₂×#554	semidirect
831. D₅	C₃×#554	direct (N × H)
846. D₄	C₃×Q₈×D₅	semidirect
882. C₅	C₂×C₃×#554	semidirect
908. C₃	D₅×#554	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×#554	2
C₃×#66064	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66024	2
C₃×D₅×#125	2
C₃×#65970	2
C₃×#65969	2
C₃×D₅×C₂²⋊Q₈	2
C₃×#65913	2
C₃×C₄×Q₈×D₅	2
C₃×C₄×D₄×D₅	2
C₃×#65877	2
C₃×#65873	2
C₃×#65845	2
C₂×C₃×D₅×C₄⋊C₄	2
D₅×#554	3
C₂×C₃×#554	5

Subgroups — C3×D5×#554 #14483785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#554 #14483785