Subgroups — C₅×D₃×#556 #14483982

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	C₅×#5732	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#126	C₂	1	4	yes	maximal, complemented
5	C₅×#5702	C₂	1	4	yes	maximal, complemented
6	C₅×D₃×#124	C₂	1	2	yes	maximal
7	C₅×#5671	C₂	1	2	yes	maximal, complemented
8	C₅×#5641	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₅×#5584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×D₃×Q₈	C₂	1	2	yes	maximal, complemented
13	C₅×#5568	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
15	C₅×#5542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5533	C₂	1	2	yes	maximal, complemented
17	C₅×D₃×#117	C₂	1	2	yes	maximal, complemented
18	C₂×C₅×#556	—	3	1	no	maximal, Hall
19	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
20	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	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	C₅×#947	C₂²	1	2	yes	—
32	C₅×#946	C₂²	1	2	yes	complemented
33	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
34	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₅×#944	C₂²	1	2	yes	complemented
36	C₅×#936	C₂²	1	2	yes	—
37	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
38	C₄×C₅×#67	C₂²	1	2	yes	—
39	C₅×#926	C₂²	1	2	yes	complemented
40	C₅×#924	C₂²	1	2	yes	complemented
41	C₅×#898	C₂²	1	4	yes	complemented
42	C₅×#898	C₂²	1	4	yes	complemented
43	C₅×#898	C₂²	1	4	yes	complemented
44	C₅×#897	C₂²	1	2	yes	complemented
45	C₅×#896	C₂²	1	4	yes	complemented
46	C₅×#893	C₂²	1	1	yes	characteristic
47	C₅×#892	C₂²	1	2	yes	complemented
48	C₅×#892	C₂²	1	2	yes	complemented
49	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
51	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
52	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
53	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₅×#888	C₂²	1	2	yes	complemented
56	C₅×#888	C₂²	1	2	yes	complemented
57	C₅×#887	C₂²	1	2	yes	complemented
58	C₅×#887	C₂²	1	4	yes	complemented
59	C₅×#887	C₂²	1	1	yes	characteristic, complemented
60	C₅×#887	C₂²	1	2	yes	complemented
61	C₅×#885	C₂²	1	4	yes	—
62	C₅×#885	C₂²	1	4	yes	—
63	C₅×#67⋊C₄	C₂²	1	2	yes	—
64	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₅×#879	C₂²	1	4	yes	complemented
68	C₅×#879	C₂²	1	4	yes	complemented
69	C₅×#879	C₂²	1	4	yes	complemented
70	C₅×#878	C₂²	1	4	yes	complemented
71	C₅×#877	C₂²	1	4	yes	complemented
72	C₅×#876	C₂²	1	4	yes	complemented
73	C₅×#875	C₂²	1	2	yes	—
74	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
75	C₅×#872	C₂²	1	4	yes	complemented
76	C₄²×C₅×D₃	C₂²	1	2	yes	—
77	C₄²×C₅×D₃	C₂²	1	4	yes	—
78	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
79	C₅×#869	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
81	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
82	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
83	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	D₃×#556	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#556	—	3	1	no	—
86	C₅×#556	—	3	4	no	—
87	C₅×#556	—	3	2	no	—
88	C₅×#556	—	3	2	no	—
89	C₅×#556	—	3	2	no	—
90	C₅×#556	—	3	1	no	—
91	C₅×#556	—	3	1	no	—
92	C₅×#556	—	3	2	no	—
93	C₅×#556	D₃	1	1	yes	characteristic, direct product factor
94	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
95	C₂×C₅×#126	—	3	4	no	—
96	C₂×C₅×#124	—	3	2	no	—
97	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
98	C₂×C₄×C₅×Q₈	—	3	2	no	—
99	C₂×C₄×C₅×Q₈	—	3	1	no	—
100	C₂×C₄×C₅×D₄	—	3	1	no	—
101	C₂×C₅×#117	—	3	2	no	—
102	C₂³×C₅×D₃	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×C₅×#67	C₂³	1	2	yes	—
108	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
109	C₅×D₃×Q₈	—	2	4	no	—
110	C₅×D₃×Q₈	—	2	8	no	—
111	C₅×D₃×D₄	—	2	4	no	—
112	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
113	C₂×C₄×C₅×D₃	—	2	8	no	—
114	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
115	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
116	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
117	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
118	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
119	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
120	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
121	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
122	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
123	C₂×C₅×Dic₆	C₂³	1	2	yes	—
124	C₂×C₅×Dic₆	C₂³	1	2	yes	—
125	C₂×C₅×Dic₆	C₂³	1	4	yes	—
126	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	2	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	4	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	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	C₅×#217	C₂³	1	4	yes	—
140	C₅×#217	C₂³	1	4	yes	—
141	C₅×#217	C₂³	1	2	yes	—
142	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
143	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
145	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
149	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
150	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
151	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
152	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
153	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
154	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
155	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
156	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
157	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
158	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
159	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
160	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₄×C₅×Dic₃	C₂³	1	4	yes	—
163	C₄×C₅×Dic₃	C₂³	1	2	yes	—
164	C₄×C₅×Dic₃	C₂³	1	2	yes	—
165	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
166	C₄×C₅×Dic₃	C₂³	1	4	yes	—
167	C₄×C₅×Dic₃	C₂³	1	4	yes	—
168	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
169	C₄×C₅×Dic₃	C₂³	1	2	yes	—
170	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
171	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
172	#5732	C₂×C₅	1	1	yes	characteristic, complemented
173	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
174	D₃×#126	C₂×C₅	1	4	yes	complemented
175	#5702	C₂×C₅	1	4	yes	complemented
176	D₃×#124	C₂×C₅	1	2	yes	—
177	#5671	C₂×C₅	1	2	yes	complemented
178	#5641	C₂×C₅	1	2	yes	complemented
179	D₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
180	#5584	C₂×C₅	1	1	yes	characteristic, complemented
181	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
182	C₄×D₃×Q₈	C₂×C₅	1	2	yes	complemented
183	#5568	C₂×C₅	1	2	yes	complemented
184	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
185	#5542	C₂×C₅	1	1	yes	characteristic, complemented
186	#5533	C₂×C₅	1	2	yes	complemented
187	D₃×#117	C₂×C₅	1	2	yes	complemented
188	C₂²×C₅×Q₈	—	3	1	no	—
189	C₂²×C₅×Q₈	—	3	2	no	—
190	C₂²×C₅×D₄	—	3	1	no	—
191	C₂³×C₄×C₅	—	3	2	no	—
192	C₅×C₄⋊Q₈	—	3	2	no	—
193	C₅×C₄⋊Q₈	—	3	2	no	—
194	C₅×C₄⋊Q₈	—	3	2	no	—
195	C₅×C₄⋊Q₈	—	3	1	no	—
196	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
197	C₅×#126	—	3	4	no	—
198	C₅×#126	—	3	4	no	—
199	C₅×#126	—	3	4	no	—
200	C₅×#126	—	3	4	no	—
201	C₅×#126	—	3	4	no	—
202	C₅×#126	—	3	4	no	—
203	C₅×#126	—	3	4	no	—
204	C₅×#126	C₂×D₃	1	4	yes	complemented
205	C₅×#124	—	3	2	no	—
206	C₅×#124	—	3	2	no	—
207	C₅×#124	—	3	4	no	—
208	C₅×#124	—	3	4	no	—
209	C₅×#124	—	3	2	no	—
210	C₅×#124	C₂×D₃	1	2	yes	—
211	C₅×C₂²⋊Q₈	—	3	2	no	—
212	C₅×C₂²⋊Q₈	—	3	2	no	—
213	C₅×C₂²⋊Q₈	—	3	4	no	—
214	C₅×C₂²⋊Q₈	—	3	2	no	—
215	C₅×C₂²⋊Q₈	—	3	4	no	—
216	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
217	C₄×C₅×Q₈	—	3	2	no	—
218	C₄×C₅×Q₈	—	3	1	no	—
219	C₄×C₅×Q₈	—	3	4	no	—
220	C₄×C₅×Q₈	—	3	2	no	—
221	C₄×C₅×Q₈	—	3	2	no	—
222	C₄×C₅×Q₈	—	3	1	no	—
223	C₄×C₅×Q₈	—	3	2	no	—
224	C₄×C₅×Q₈	—	3	4	no	—
225	C₄×C₅×Q₈	—	3	2	no	—
226	C₄×C₅×Q₈	—	3	1	no	—
227	C₄×C₅×Q₈	C₂×D₃	1	2	yes	complemented
228	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
229	C₄×C₅×D₄	—	3	1	no	—
230	C₄×C₅×D₄	—	3	2	no	—
231	C₄×C₅×D₄	—	3	1	no	—
232	C₄×C₅×D₄	—	3	2	no	—
233	C₄×C₅×D₄	—	3	1	no	—
234	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
235	C₅×#117	—	3	2	no	—
236	C₅×#117	—	3	2	no	—
237	C₅×#117	—	3	2	no	—
238	C₅×#117	—	3	4	no	—
239	C₅×#117	—	3	4	no	—
240	C₅×#117	C₂×D₃	1	2	yes	complemented
241	C₂×C₅×C₄⋊C₄	—	3	1	no	—
242	C₂×C₅×C₄⋊C₄	—	3	2	no	—
243	C₂×C₅×C₄⋊C₄	—	3	1	no	—
244	C₂×C₅×C₄⋊C₄	—	3	4	no	—
245	C₂×C₅×C₄⋊C₄	—	3	2	no	—
246	C₂×C₅×C₄⋊C₄	—	3	2	no	—
247	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
248	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
249	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
250	C₂×C₄²×C₅	—	3	4	no	—
251	C₂×C₄²×C₅	—	3	1	no	—
252	C₂×C₄²×C₅	—	3	2	no	—
253	C₂×#556	—	3	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂²×C₅×D₃	—	2	4	no	—
256	C₂²×C₅×D₃	—	2	4	no	—
257	C₂²×C₅×D₃	—	2	4	no	—
258	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
259	C₂²×C₅×D₃	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	C₅×#67	—	2	4	no	—
272	C₂×C₅×Dic₃	—	2	4	no	—
273	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
274	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
275	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
277	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
278	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
280	C₅×D₁₂	—	2	2	no	—
281	C₄×C₅×D₃	—	2	4	no	—
282	C₄×C₅×D₃	—	2	4	no	—
283	C₄×C₅×D₃	—	2	8	no	—
284	C₄×C₅×D₃	—	2	4	no	—
285	C₄×C₅×D₃	—	2	2	no	—
286	C₄×C₅×D₃	—	2	4	no	—
287	C₄×C₅×D₃	—	2	4	no	—
288	C₄×C₅×D₃	#41	1	4	yes	—
289	C₄×C₅×D₃	#41	1	4	yes	—
290	C₅×Dic₆	—	2	4	no	—
291	C₅×Dic₆	—	2	2	no	—
292	C₅×Dic₆	—	2	8	no	—
293	C₅×Dic₆	—	2	4	no	—
294	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
295	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
296	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
297	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
298	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₃×#126	C₂²×C₅	1	4	yes	complemented
300	C₃×#124	C₂²×C₅	1	2	yes	—
301	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
302	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
303	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
305	C₃×#117	C₂²×C₅	1	2	yes	complemented
306	#947	C₂²×C₅	1	2	yes	—
307	#946	C₂²×C₅	1	2	yes	complemented
308	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
309	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
310	#944	C₂²×C₅	1	2	yes	complemented
311	#936	C₂²×C₅	1	2	yes	—
312	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
313	C₄×#67	C₂²×C₅	1	2	yes	—
314	#926	C₂²×C₅	1	2	yes	complemented
315	#924	C₂²×C₅	1	2	yes	complemented
316	#898	C₂²×C₅	1	4	yes	complemented
317	#898	C₂²×C₅	1	4	yes	complemented
318	#898	C₂²×C₅	1	4	yes	complemented
319	#897	C₂²×C₅	1	2	yes	complemented
320	#896	C₂²×C₅	1	4	yes	complemented
321	#893	C₂²×C₅	1	1	yes	characteristic
322	#892	C₂²×C₅	1	2	yes	complemented
323	#892	C₂²×C₅	1	2	yes	complemented
324	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
325	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
326	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
327	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
328	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
329	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
330	#888	C₂²×C₅	1	2	yes	complemented
331	#888	C₂²×C₅	1	2	yes	complemented
332	#887	C₂²×C₅	1	4	yes	complemented
333	#887	C₂²×C₅	1	2	yes	complemented
334	#887	C₂²×C₅	1	1	yes	characteristic, complemented
335	#887	C₂²×C₅	1	2	yes	complemented
336	#885	C₂²×C₅	1	4	yes	—
337	#885	C₂²×C₅	1	4	yes	—
338	#67⋊C₄	C₂²×C₅	1	2	yes	—
339	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
340	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
341	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
342	#879	C₂²×C₅	1	4	yes	complemented
343	#879	C₂²×C₅	1	4	yes	complemented
344	#879	C₂²×C₅	1	4	yes	complemented
345	#878	C₂²×C₅	1	4	yes	complemented
346	#877	C₂²×C₅	1	4	yes	complemented
347	#876	C₂²×C₅	1	4	yes	complemented
348	#875	C₂²×C₅	1	2	yes	—
349	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
350	#872	C₂²×C₅	1	4	yes	complemented
351	C₄²×D₃	C₂²×C₅	1	2	yes	—
352	C₄²×D₃	C₂²×C₅	1	4	yes	—
353	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
354	#869	C₂²×C₅	1	1	yes	characteristic, complemented
355	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
356	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
357	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
358	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
359	C₂⁴×C₅	—	3	2	no	—
360	C₂×C₅×Q₈	—	3	2	no	—
361	C₂×C₅×Q₈	—	3	1	no	—
362	C₂×C₅×Q₈	—	3	4	no	—
363	C₂×C₅×Q₈	—	3	2	no	—
364	C₂×C₅×Q₈	—	6	4	no	—
365	C₂×C₅×Q₈	—	6	8	no	—
366	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
367	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
368	C₂×C₅×D₄	—	3	2	no	—
369	C₂×C₅×D₄	—	3	1	no	—
370	C₂×C₅×D₄	—	6	4	no	—
371	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
372	C₂²×C₄×C₅	—	3	1	no	—
373	C₂²×C₄×C₅	—	3	1	no	—
374	C₂²×C₄×C₅	—	3	2	no	—
375	C₂²×C₄×C₅	—	3	2	no	—
376	C₂²×C₄×C₅	—	3	2	no	—
377	C₂²×C₄×C₅	—	3	1	no	—
378	C₂²×C₄×C₅	—	3	4	no	—
379	C₂²×C₄×C₅	—	3	2	no	—
380	C₂²×C₄×C₅	—	3	2	no	—
381	C₂²×C₄×C₅	—	3	2	no	—
382	C₂²×C₄×C₅	—	6	8	no	—
383	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
384	C₅×C₄⋊C₄	—	3	2	no	—
385	C₅×C₄⋊C₄	—	3	1	no	—
386	C₅×C₄⋊C₄	—	3	4	no	—
387	C₅×C₄⋊C₄	—	3	2	no	—
388	C₅×C₄⋊C₄	—	3	2	no	—
389	C₅×C₄⋊C₄	—	3	1	no	—
390	C₅×C₄⋊C₄	—	3	4	no	—
391	C₅×C₄⋊C₄	—	3	4	no	—
392	C₅×C₄⋊C₄	—	3	4	no	—
393	C₅×C₄⋊C₄	—	3	2	no	—
394	C₅×C₄⋊C₄	—	3	2	no	—
395	C₅×C₄⋊C₄	—	3	2	no	—
396	C₅×C₄⋊C₄	—	3	4	no	—
397	C₅×C₄⋊C₄	—	3	2	no	—
398	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
399	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
400	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
401	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
402	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
403	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
404	C₅×C₂²⋊C₄	—	3	4	no	—
405	C₅×C₂²⋊C₄	—	3	2	no	—
406	C₅×C₂²⋊C₄	—	3	4	no	—
407	C₅×C₂²⋊C₄	—	3	4	no	—
408	C₅×C₂²⋊C₄	—	3	4	no	—
409	C₅×C₂²⋊C₄	—	3	2	no	—
410	C₅×C₂²⋊C₄	—	3	2	no	—
411	C₅×C₂²⋊C₄	—	3	4	no	—
412	C₅×C₂²⋊C₄	—	3	4	no	—
413	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
414	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
415	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
416	C₄²×C₅	—	3	4	no	—
417	C₄²×C₅	—	3	4	no	—
418	C₄²×C₅	—	3	4	no	—
419	C₄²×C₅	—	3	1	no	—
420	C₄²×C₅	—	3	1	no	—
421	C₄²×C₅	—	3	1	no	—
422	C₄²×C₅	—	3	2	no	—
423	C₄²×C₅	—	3	2	no	—
424	C₄²×C₅	—	3	2	no	—
425	C₄²×C₅	C₂²×D₃	1	4	yes	—
426	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
427	C₄²×C₅	C₂²×D₃	1	2	yes	—
428	#556	—	3	1	no	—
429	#556	—	3	4	no	—
430	#556	—	3	2	no	—
431	#556	—	3	2	no	—
432	#556	—	3	2	no	—
433	#556	—	3	1	no	—
434	#556	—	3	1	no	—
435	#556	—	3	2	no	—
436	#556	C₅×D₃	1	1	yes	characteristic, direct product factor
437	C₂×C₄⋊Q₈	—	3	1	no	—
438	C₂×#126	—	3	4	no	—
439	C₂×#124	—	3	2	no	—
440	C₂×C₂²⋊Q₈	—	3	2	no	—
441	C₂×C₄×Q₈	—	3	2	no	—
442	C₂×C₄×Q₈	—	3	1	no	—
443	C₂×C₄×D₄	—	3	1	no	—
444	C₂×#117	—	3	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×C₅×D₃	—	2	2	no	—
450	C₂×C₅×D₃	—	2	2	no	—
451	C₂×C₅×D₃	—	2	2	no	—
452	C₂×C₅×D₃	—	4	8	no	—
453	C₂×C₅×D₃	C₂×#41	1	2	yes	—
454	C₂×C₅×D₃	C₂×#41	1	2	yes	—
455	C₂×C₅×D₃	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	C₅×Dic₃	—	2	4	no	—
464	C₅×Dic₃	—	2	2	no	—
465	C₅×Dic₃	—	2	2	no	—
466	C₅×Dic₃	—	2	2	no	—
467	C₅×Dic₃	—	2	1	no	—
468	C₅×Dic₃	C₂×#41	1	2	yes	—
469	C₅×Dic₃	C₂×#41	1	2	yes	—
470	C₂³×D₃	C₂³×C₅	1	2	yes	—
471	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
472	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
473	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
475	C₂×#67	C₂³×C₅	1	2	yes	—
476	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
477	D₃×Q₈	—	2	4	no	—
478	D₃×Q₈	—	2	8	no	—
479	D₃×D₄	—	2	4	no	—
480	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₄×D₃	—	2	8	no	—
482	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
483	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
484	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
485	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
486	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
487	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
488	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
489	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
490	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
491	C₂×Dic₆	C₂³×C₅	1	2	yes	—
492	C₂×Dic₆	C₂³×C₅	1	2	yes	—
493	C₂×Dic₆	C₂³×C₅	1	4	yes	—
494	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
495	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
496	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
497	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
498	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
499	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
500	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
504	C₃×C₄²	C₂³×C₅	1	2	yes	—
505	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
506	C₃×C₄²	C₂³×C₅	1	4	yes	—
507	#217	C₂³×C₅	1	4	yes	—
508	#217	C₂³×C₅	1	4	yes	—
509	#217	C₂³×C₅	1	2	yes	—
510	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
511	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
512	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
513	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
516	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
517	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
518	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
519	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
520	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
521	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
522	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
523	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
524	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
525	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
526	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
527	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
528	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
529	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
530	C₄×Dic₃	C₂³×C₅	1	4	yes	—
531	C₄×Dic₃	C₂³×C₅	1	2	yes	—
532	C₄×Dic₃	C₂³×C₅	1	2	yes	—
533	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
534	C₄×Dic₃	C₂³×C₅	1	4	yes	—
535	C₄×Dic₃	C₂³×C₅	1	4	yes	—
536	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
537	C₄×Dic₃	C₂³×C₅	1	2	yes	—
538	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
539	C₂³×C₅	—	3	1	no	—
540	C₂³×C₅	—	3	2	no	—
541	C₂³×C₅	—	6	4	no	—
542	C₂³×C₅	—	6	4	no	—
543	C₂³×C₅	—	6	4	no	—
544	C₂³×C₅	C₂³×D₃	1	2	yes	—
545	C₅×Q₈	—	2	2	no	—
546	C₅×Q₈	—	2	4	no	—
547	C₅×Q₈	—	6	4	no	—
548	C₅×Q₈	—	6	8	no	—
549	C₅×Q₈	—	6	2	no	—
550	C₅×Q₈	—	6	4	no	—
551	C₅×D₄	—	2	2	no	—
552	C₅×D₄	—	6	4	no	—
553	C₅×D₄	—	6	2	no	—
554	C₂×C₄×C₅	—	2	4	no	—
555	C₂×C₄×C₅	—	3	1	no	—
556	C₂×C₄×C₅	—	3	1	no	—
557	C₂×C₄×C₅	—	3	4	no	—
558	C₂×C₄×C₅	—	3	4	no	—
559	C₂×C₄×C₅	—	3	2	no	—
560	C₂×C₄×C₅	—	3	2	no	—
561	C₂×C₄×C₅	—	3	1	no	—
562	C₂×C₄×C₅	—	3	4	no	—
563	C₂×C₄×C₅	—	3	2	no	—
564	C₂×C₄×C₅	—	6	4	no	—
565	C₂×C₄×C₅	—	6	4	no	—
566	C₂×C₄×C₅	—	6	2	no	—
567	C₂×C₄×C₅	—	6	4	no	—
568	C₂×C₄×C₅	—	6	4	no	—
569	C₂×C₄×C₅	—	6	8	no	—
570	C₂×C₄×C₅	—	6	4	no	—
571	C₂×C₄×C₅	—	6	4	no	—
572	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
573	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
574	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
575	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
576	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
577	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
578	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
579	C₂²×Q₈	—	3	1	no	—
580	C₂²×Q₈	—	3	2	no	—
581	C₂²×D₄	—	3	1	no	—
582	C₂³×C₄	—	3	2	no	—
583	C₄⋊Q₈	—	3	2	no	—
584	C₄⋊Q₈	—	3	2	no	—
585	C₄⋊Q₈	—	3	2	no	—
586	C₄⋊Q₈	—	3	1	no	—
587	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
588	#126	—	3	4	no	—
589	#126	—	3	4	no	—
590	#126	—	3	4	no	—
591	#126	—	3	4	no	—
592	#126	—	3	4	no	—
593	#126	—	3	4	no	—
594	#126	—	3	4	no	—
595	#126	C₂×C₅×D₃	1	4	yes	complemented
596	#124	—	3	2	no	—
597	#124	—	3	2	no	—
598	#124	—	3	4	no	—
599	#124	—	3	4	no	—
600	#124	—	3	2	no	—
601	#124	C₂×C₅×D₃	1	2	yes	—
602	C₂²⋊Q₈	—	3	2	no	—
603	C₂²⋊Q₈	—	3	2	no	—
604	C₂²⋊Q₈	—	3	4	no	—
605	C₂²⋊Q₈	—	3	2	no	—
606	C₂²⋊Q₈	—	3	4	no	—
607	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
608	C₄×Q₈	—	3	2	no	—
609	C₄×Q₈	—	3	1	no	—
610	C₄×Q₈	—	3	4	no	—
611	C₄×Q₈	—	3	2	no	—
612	C₄×Q₈	—	3	2	no	—
613	C₄×Q₈	—	3	1	no	—
614	C₄×Q₈	—	3	2	no	—
615	C₄×Q₈	—	3	4	no	—
616	C₄×Q₈	—	3	2	no	—
617	C₄×Q₈	—	3	1	no	—
618	C₄×Q₈	C₂×C₅×D₃	1	2	yes	complemented
619	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
620	C₄×D₄	—	3	1	no	—
621	C₄×D₄	—	3	2	no	—
622	C₄×D₄	—	3	1	no	—
623	C₄×D₄	—	3	2	no	—
624	C₄×D₄	—	3	1	no	—
625	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
626	#117	—	3	2	no	—
627	#117	—	3	2	no	—
628	#117	—	3	2	no	—
629	#117	—	3	4	no	—
630	#117	—	3	4	no	—
631	#117	C₂×C₅×D₃	1	2	yes	complemented
632	C₂×C₄⋊C₄	—	3	1	no	—
633	C₂×C₄⋊C₄	—	3	2	no	—
634	C₂×C₄⋊C₄	—	3	1	no	—
635	C₂×C₄⋊C₄	—	3	4	no	—
636	C₂×C₄⋊C₄	—	3	2	no	—
637	C₂×C₄⋊C₄	—	3	2	no	—
638	C₂×C₂²⋊C₄	—	3	4	no	—
639	C₂×C₂²⋊C₄	—	3	2	no	—
640	C₂×C₂²⋊C₄	—	3	4	no	—
641	C₂×C₄²	—	3	4	no	—
642	C₂×C₄²	—	3	1	no	—
643	C₂×C₄²	—	3	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	C₅×D₃	—	4	2	no	—
649	C₅×D₃	#556	1	4	yes	direct product factor
650	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
651	C₂²×D₃	—	2	4	no	—
652	C₂²×D₃	—	2	4	no	—
653	C₂²×D₃	—	2	4	no	—
654	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
655	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
656	C₃×Q₈	—	2	4	no	—
657	C₃×Q₈	—	2	2	no	—
658	C₃×D₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	4	no	—
660	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
661	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
662	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
663	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
664	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
665	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
666	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
667	#67	—	2	4	no	—
668	C₂×Dic₃	—	2	4	no	—
669	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
670	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
671	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
672	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
673	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
674	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
675	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
676	D₁₂	—	2	2	no	—
677	C₄×D₃	—	2	4	no	—
678	C₄×D₃	—	2	4	no	—
679	C₄×D₃	—	2	8	no	—
680	C₄×D₃	—	2	4	no	—
681	C₄×D₃	—	2	2	no	—
682	C₄×D₃	—	2	4	no	—
683	C₄×D₃	—	2	4	no	—
684	C₄×D₃	C₅×#41	1	4	yes	—
685	C₄×D₃	C₅×#41	1	4	yes	—
686	Dic₆	—	2	4	no	—
687	Dic₆	—	2	2	no	—
688	Dic₆	—	2	8	no	—
689	Dic₆	—	2	4	no	—
690	C₂²×C₅	—	2	2	no	—
691	C₂²×C₅	—	2	2	no	—
692	C₂²×C₅	—	2	2	no	—
693	C₂²×C₅	—	3	2	no	—
694	C₂²×C₅	—	3	2	no	—
695	C₂²×C₅	—	3	2	no	—
696	C₂²×C₅	—	6	2	no	—
697	C₂²×C₅	—	6	2	no	—
698	C₂²×C₅	—	6	2	no	—
699	C₂²×C₅	—	12	8	no	—
700	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
701	C₄×C₅	—	2	2	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	4	no	—
704	C₄×C₅	—	2	2	no	—
705	C₄×C₅	—	2	1	no	—
706	C₄×C₅	—	3	2	no	—
707	C₄×C₅	—	3	2	no	—
708	C₄×C₅	—	6	2	no	—
709	C₄×C₅	—	6	2	no	—
710	C₄×C₅	—	6	4	no	—
711	C₄×C₅	—	6	2	no	—
712	C₄×C₅	—	6	1	no	—
713	C₄×C₅	D₃×#41	1	2	yes	—
714	C₄×C₅	D₃×#41	1	2	yes	—
715	C₂⁴	—	3	2	no	—
716	C₂×Q₈	—	3	2	no	—
717	C₂×Q₈	—	3	1	no	—
718	C₂×Q₈	—	3	4	no	—
719	C₂×Q₈	—	3	2	no	—
720	C₂×Q₈	—	6	4	no	—
721	C₂×Q₈	—	6	8	no	—
722	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
723	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
724	C₂×D₄	—	3	2	no	—
725	C₂×D₄	—	3	1	no	—
726	C₂×D₄	—	6	4	no	—
727	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
728	C₂²×C₄	—	3	1	no	—
729	C₂²×C₄	—	3	1	no	—
730	C₂²×C₄	—	3	2	no	—
731	C₂²×C₄	—	3	2	no	—
732	C₂²×C₄	—	3	2	no	—
733	C₂²×C₄	—	3	1	no	—
734	C₂²×C₄	—	3	4	no	—
735	C₂²×C₄	—	3	2	no	—
736	C₂²×C₄	—	3	2	no	—
737	C₂²×C₄	—	3	2	no	—
738	C₂²×C₄	—	6	8	no	—
739	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
740	C₄⋊C₄	—	3	2	no	—
741	C₄⋊C₄	—	3	1	no	—
742	C₄⋊C₄	—	3	4	no	—
743	C₄⋊C₄	—	3	2	no	—
744	C₄⋊C₄	—	3	2	no	—
745	C₄⋊C₄	—	3	1	no	—
746	C₄⋊C₄	—	3	4	no	—
747	C₄⋊C₄	—	3	4	no	—
748	C₄⋊C₄	—	3	4	no	—
749	C₄⋊C₄	—	3	2	no	—
750	C₄⋊C₄	—	3	2	no	—
751	C₄⋊C₄	—	3	2	no	—
752	C₄⋊C₄	—	3	4	no	—
753	C₄⋊C₄	—	3	2	no	—
754	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
756	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
758	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
759	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
760	C₂²⋊C₄	—	3	4	no	—
761	C₂²⋊C₄	—	3	2	no	—
762	C₂²⋊C₄	—	3	4	no	—
763	C₂²⋊C₄	—	3	4	no	—
764	C₂²⋊C₄	—	3	4	no	—
765	C₂²⋊C₄	—	3	2	no	—
766	C₂²⋊C₄	—	3	2	no	—
767	C₂²⋊C₄	—	3	4	no	—
768	C₂²⋊C₄	—	3	4	no	—
769	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
770	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
771	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
772	C₄²	—	3	4	no	—
773	C₄²	—	3	4	no	—
774	C₄²	—	3	4	no	—
775	C₄²	—	3	1	no	—
776	C₄²	—	3	1	no	—
777	C₄²	—	3	1	no	—
778	C₄²	—	3	2	no	—
779	C₄²	—	3	2	no	—
780	C₄²	—	3	2	no	—
781	C₄²	C₂²×C₅×D₃	1	4	yes	—
782	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
783	C₄²	C₂²×C₅×D₃	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	C₂⁵×C₅	1	1	yes	characteristic
789	C₂×D₃	—	2	2	no	—
790	C₂×D₃	—	2	2	no	—
791	C₂×D₃	—	2	2	no	—
792	C₂×D₃	—	4	8	no	—
793	C₂×D₃	C₂×C₅×#41	1	2	yes	—
794	C₂×D₃	C₂×C₅×#41	1	2	yes	—
795	C₂×D₃	C₅×2₋¹⁺⁴	1	2	yes	—
796	C₃×C₄	—	2	4	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	C₂×C₅×#41	1	2	yes	—
802	C₃×C₄	C₂×C₅×#41	1	2	yes	—
803	Dic₃	—	2	4	no	—
804	Dic₃	—	2	2	no	—
805	Dic₃	—	2	2	no	—
806	Dic₃	—	2	2	no	—
807	Dic₃	—	2	1	no	—
808	Dic₃	C₂×C₅×#41	1	2	yes	—
809	Dic₃	C₂×C₅×#41	1	2	yes	—
810	C₂×C₅	—	3	4	no	—
811	C₂×C₅	—	4	2	no	—
812	C₂×C₅	—	12	2	no	—
813	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
814	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
815	C₂×C₅	D₃×2₋¹⁺⁴	1	1	yes	characteristic
816	C₂³	—	3	1	no	—
817	C₂³	—	3	2	no	—
818	C₂³	—	6	4	no	—
819	C₂³	—	6	4	no	—
820	C₂³	—	6	4	no	—
821	C₂³	C₂³×C₅×D₃	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	6	4	no	—
825	Q₈	—	6	8	no	—
826	Q₈	—	6	2	no	—
827	Q₈	—	6	4	no	—
828	D₄	—	2	2	no	—
829	D₄	—	6	4	no	—
830	D₄	—	6	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	3	1	no	—
833	C₂×C₄	—	3	1	no	—
834	C₂×C₄	—	3	4	no	—
835	C₂×C₄	—	3	4	no	—
836	C₂×C₄	—	3	2	no	—
837	C₂×C₄	—	3	2	no	—
838	C₂×C₄	—	3	1	no	—
839	C₂×C₄	—	3	4	no	—
840	C₂×C₄	—	3	2	no	—
841	C₂×C₄	—	6	4	no	—
842	C₂×C₄	—	6	4	no	—
843	C₂×C₄	—	6	4	no	—
844	C₂×C₄	—	6	8	no	—
845	C₂×C₄	—	6	4	no	—
846	C₂×C₄	—	6	2	no	—
847	C₂×C₄	—	6	4	no	—
848	C₂×C₄	—	6	4	no	—
849	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
850	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
851	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
852	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
853	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
854	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
855	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
856	C₂×C₃	—	4	2	no	—
857	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
858	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
859	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
860	D₃	—	4	2	no	—
861	D₃	C₅×#556	1	4	yes	direct product factor
862	C₅	D₃×#556	1	1	yes	characteristic, direct product factor, Sylow
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	3	2	no	—
867	C₂²	—	3	2	no	—
868	C₂²	—	3	2	no	—
869	C₂²	—	6	2	no	—
870	C₂²	—	6	2	no	—
871	C₂²	—	6	2	no	—
872	C₂²	—	12	8	no	—
873	C₂²	C₂⁴×C₅×D₃	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	—	3	2	no	—
880	C₄	—	3	2	no	—
881	C₄	—	6	2	no	—
882	C₄	—	6	2	no	—
883	C₄	—	6	4	no	—
884	C₄	—	6	2	no	—
885	C₄	—	6	1	no	—
886	C₄	C₅×D₃×#41	1	2	yes	—
887	C₄	C₅×D₃×#41	1	2	yes	—
888	C₃	C₂×C₅×#556	1	1	yes	characteristic, complemented, Sylow
889	C₂	—	3	4	no	—
890	C₂	—	4	2	no	—
891	C₂	—	12	2	no	—
892	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
893	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
894	C₂	C₅×D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#556	D₃
hypocenter	C₃	C₂×C₅×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
2. C₅×#5732	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₅×D₃×#126	C₂	semidirect
5. C₅×#5702	C₂	semidirect
7. C₅×#5671	C₂	semidirect
8. C₅×#5641	C₂	semidirect
9. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₅×#5584	C₂	semidirect
11. C₄×C₅×D₃×Q₈	C₂	semidirect
12. C₄×C₅×D₃×Q₈	C₂	semidirect
13. C₅×#5568	C₂	semidirect
15. C₅×#5542	C₂	semidirect
16. C₅×#5533	C₂	semidirect
17. C₅×D₃×#117	C₂	semidirect
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. C₅×#946	C₂²	semidirect
33. C₅×Q₈×Dic₃	C₂²	semidirect
34. C₅×Q₈×Dic₃	C₂²	semidirect
35. C₅×#944	C₂²	semidirect
39. C₅×#926	C₂²	semidirect
40. C₅×#924	C₂²	semidirect
41. C₅×#898	C₂²	semidirect
42. C₅×#898	C₂²	semidirect
43. C₅×#898	C₂²	semidirect
44. C₅×#897	C₂²	semidirect
45. C₅×#896	C₂²	semidirect
47. C₅×#892	C₂²	semidirect
48. C₅×#892	C₂²	semidirect
55. C₅×#888	C₂²	semidirect
56. C₅×#888	C₂²	semidirect
57. C₅×#887	C₂²	semidirect
58. C₅×#887	C₂²	semidirect
59. C₅×#887	C₂²	semidirect
60. C₅×#887	C₂²	semidirect
67. C₅×#879	C₂²	semidirect
68. C₅×#879	C₂²	semidirect
69. C₅×#879	C₂²	semidirect
70. C₅×#878	C₂²	semidirect
71. C₅×#877	C₂²	semidirect
72. C₅×#876	C₂²	semidirect
75. C₅×#872	C₂²	semidirect
79. C₅×#869	C₂²	semidirect
80. C₄×C₅×Dic₆	C₂²	semidirect
81. C₄×C₅×Dic₆	C₂²	semidirect
82. C₄×C₅×Dic₆	C₂²	semidirect
83. C₄×C₅×Dic₆	C₂²	semidirect
84. D₃×#556	C₅	direct (N × H)
93. C₅×#556	D₃	direct (N × H)
171. C₃×#556	C₂×C₅	semidirect
172. #5732	C₂×C₅	semidirect
173. D₃×C₄⋊Q₈	C₂×C₅	semidirect
174. D₃×#126	C₂×C₅	semidirect
175. #5702	C₂×C₅	semidirect
177. #5671	C₂×C₅	semidirect
178. #5641	C₂×C₅	semidirect
179. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
180. #5584	C₂×C₅	semidirect
181. C₄×D₃×Q₈	C₂×C₅	semidirect
182. C₄×D₃×Q₈	C₂×C₅	semidirect
183. #5568	C₂×C₅	semidirect
185. #5542	C₂×C₅	semidirect
186. #5533	C₂×C₅	semidirect
187. D₃×#117	C₂×C₅	semidirect
196. C₅×C₄⋊Q₈	C₂×D₃	semidirect
204. C₅×#126	C₂×D₃	semidirect
216. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
227. C₄×C₅×Q₈	C₂×D₃	semidirect
228. C₄×C₅×Q₈	C₂×D₃	semidirect
240. C₅×#117	C₂×D₃	semidirect
298. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
299. C₃×#126	C₂²×C₅	semidirect
301. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
302. C₃×C₄×Q₈	C₂²×C₅	semidirect
303. C₃×C₄×Q₈	C₂²×C₅	semidirect
305. C₃×#117	C₂²×C₅	semidirect
307. #946	C₂²×C₅	semidirect
308. Q₈×Dic₃	C₂²×C₅	semidirect
309. Q₈×Dic₃	C₂²×C₅	semidirect
310. #944	C₂²×C₅	semidirect
314. #926	C₂²×C₅	semidirect
315. #924	C₂²×C₅	semidirect
316. #898	C₂²×C₅	semidirect
317. #898	C₂²×C₅	semidirect
318. #898	C₂²×C₅	semidirect
319. #897	C₂²×C₅	semidirect
320. #896	C₂²×C₅	semidirect
322. #892	C₂²×C₅	semidirect
323. #892	C₂²×C₅	semidirect
330. #888	C₂²×C₅	semidirect
331. #888	C₂²×C₅	semidirect
332. #887	C₂²×C₅	semidirect
333. #887	C₂²×C₅	semidirect
334. #887	C₂²×C₅	semidirect
335. #887	C₂²×C₅	semidirect
342. #879	C₂²×C₅	semidirect
343. #879	C₂²×C₅	semidirect
344. #879	C₂²×C₅	semidirect
345. #878	C₂²×C₅	semidirect
346. #877	C₂²×C₅	semidirect
347. #876	C₂²×C₅	semidirect
350. #872	C₂²×C₅	semidirect
354. #869	C₂²×C₅	semidirect
355. C₄×Dic₆	C₂²×C₅	semidirect
356. C₄×Dic₆	C₂²×C₅	semidirect
357. C₄×Dic₆	C₂²×C₅	semidirect
358. C₄×Dic₆	C₂²×C₅	semidirect
436. #556	C₅×D₃	direct (N × H)
587. C₄⋊Q₈	C₂×C₅×D₃	semidirect
595. #126	C₂×C₅×D₃	semidirect
607. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
618. C₄×Q₈	C₂×C₅×D₃	semidirect
619. C₄×Q₈	C₂×C₅×D₃	semidirect
631. #117	C₂×C₅×D₃	semidirect
649. C₅×D₃	#556	direct (N × H)
784. C₃×C₅	C₂×#556	semidirect
861. D₃	C₅×#556	direct (N × H)
862. C₅	D₃×#556	direct (N × H)
888. C₃	C₂×C₅×#556	semidirect

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
C₅×#5732	2
C₅×D₃×C₄⋊Q₈	2
C₅×D₃×#126	2
C₅×#5702	2
C₅×D₃×#124	2
C₅×#5671	2
C₅×#5641	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5584	2
C₄×C₅×D₃×Q₈	2
C₅×#5568	2
C₄×C₅×D₃×D₄	2
C₅×#5542	2
C₅×#5533	2
C₅×D₃×#117	2
C₂×C₅×#556	3
D₃×#556	5

Subgroups — C5×D3×#556 #14483982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#556 #14483982