Subgroups — C₅×D₃×#536 #14480458

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5825	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5816	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5724	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₅×#5675	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#124	C₂	1	2	yes	maximal, complemented
10	C₅×D₃×#123	C₂	1	4	yes	maximal, complemented
11	C₅×#5648	C₂	1	4	yes	maximal, complemented
12	C₅×#5628	C₂	1	4	yes	maximal, complemented
13	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₅×#5526	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#536	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₅×D₃×#41	—	2	8	no	—
20	C₂×C₅×#239	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×Q₈	—	2	8	no	—
22	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
23	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
24	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
26	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
27	C₂×C₅×#237	C₂²	1	2	yes	—
28	C₂×C₅×#237	C₂²	1	1	yes	characteristic
29	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
30	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×#235	C₂²	1	1	yes	characteristic
32	C₂×C₅×#235	C₂²	1	2	yes	—
33	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
34	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
35	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₂²×C₅×Dic₆	C₂²	1	2	yes	complemented
37	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₃×C₅×#124	C₂²	1	2	yes	complemented
40	C₃×C₅×#123	C₂²	1	4	yes	complemented
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₅×#947	C₂²	1	2	yes	complemented
44	C₅×#946	C₂²	1	4	yes	complemented
45	C₅×#944	C₂²	1	2	yes	complemented
46	C₅×#944	C₂²	1	2	yes	complemented
47	C₅×#936	C₂²	1	2	yes	complemented
48	C₅×#935	C₂²	1	4	yes	complemented
49	C₅×#929	C₂²	1	4	yes	complemented
50	C₅×#926	C₂²	1	1	yes	characteristic, complemented
51	C₅×#924	C₂²	1	4	yes	complemented
52	C₅×#897	C₂²	1	4	yes	complemented
53	C₅×#896	C₂²	1	8	yes	complemented
54	C₅×#894	C₂²	1	8	yes	complemented
55	C₅×#892	C₂²	1	2	yes	complemented
56	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	—
57	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₅×#888	C₂²	1	8	yes	complemented
59	C₅×#886	C₂²	1	4	yes	complemented
60	C₅×#885	C₂²	1	8	yes	complemented
61	C₅×#883	C₂²	1	8	yes	complemented
62	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	—
64	C₅×#878	C₂²	1	8	yes	complemented
65	C₅×#877	C₂²	1	2	yes	complemented
66	C₅×#875	C₂²	1	2	yes	complemented
67	C₅×#872	C₂²	1	2	yes	complemented
68	C₄²×C₅×D₃	C₂²	1	2	yes	—
69	C₅×#869	C₂²	1	2	yes	complemented
70	D₃×#536	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂³×C₅×Q₈	—	3	1	no	—
73	C₅×#536	—	3	1	no	—
74	C₅×#536	—	3	1	no	—
75	C₅×#536	—	3	2	no	—
76	C₅×#536	—	3	2	no	—
77	C₅×#536	—	3	4	no	—
78	C₅×#536	—	3	4	no	—
79	C₅×#536	—	3	1	no	—
80	C₅×#536	D₃	1	1	yes	characteristic, direct product factor
81	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
82	C₂×C₅×#124	—	3	2	no	—
83	C₂×C₅×#123	—	3	4	no	—
84	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
85	C₂×C₅×#117	—	3	1	no	—
86	C₂³×C₅×D₃	C₂³	1	2	yes	—
87	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₃×C₅×#41	—	2	4	no	—
89	C₂×C₃×C₅×Q₈	—	2	4	no	—
90	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
92	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
93	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
94	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
96	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₅×#67	C₂³	1	2	yes	—
99	C₂×C₅×#67	C₂³	1	2	yes	—
100	C₂×C₅×#67	C₂³	1	2	yes	—
101	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
102	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
103	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₅×#239	—	2	4	no	—
105	C₅×D₃×Q₈	—	2	8	no	—
106	C₅×D₃×Q₈	—	2	8	no	—
107	C₅×D₃×Q₈	—	2	8	no	—
108	C₅×D₃×Q₈	—	2	8	no	—
109	C₅×D₃×Q₈	—	2	4	no	—
110	C₅×#237	—	2	8	no	—
111	C₅×#237	—	2	4	no	—
112	C₅×D₃×D₄	—	2	8	no	—
113	C₅×D₃×D₄	—	2	4	no	—
114	C₅×#235	—	2	4	no	—
115	C₅×#235	—	2	8	no	—
116	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
117	C₂×C₅×D₁₂	C₂³	1	2	yes	—
118	C₂×C₄×C₅×D₃	—	2	8	no	—
119	C₂×C₄×C₅×D₃	—	2	8	no	—
120	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
121	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
122	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
124	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
125	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
126	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
127	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
128	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
129	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
130	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
131	C₂×C₅×Dic₆	—	2	4	no	—
132	C₂×C₅×Dic₆	—	2	8	no	—
133	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
134	C₂×C₅×Dic₆	C₂³	1	2	yes	—
135	C₂×C₅×Dic₆	C₂³	1	4	yes	—
136	C₂×C₅×Dic₆	C₂³	1	4	yes	—
137	C₂×C₅×Dic₆	C₂³	1	2	yes	—
138	C₂×C₅×Dic₆	C₂³	1	2	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
143	C₃×C₄²×C₅	C₂³	1	2	yes	—
144	C₅×#217	C₂³	1	2	yes	—
145	C₅×#217	C₂³	1	8	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
149	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
150	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
151	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
152	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
153	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
154	C₄×C₅×Dic₃	C₂³	1	2	yes	—
155	C₄×C₅×Dic₃	C₂³	1	4	yes	—
156	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic
157	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
158	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
159	#5825	C₂×C₅	1	1	yes	characteristic, complemented
160	#5816	C₂×C₅	1	1	yes	characteristic, complemented
161	#5724	C₂×C₅	1	2	yes	complemented
162	D₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
163	#5675	C₂×C₅	1	2	yes	complemented
164	D₃×#124	C₂×C₅	1	2	yes	complemented
165	D₃×#123	C₂×C₅	1	4	yes	complemented
166	#5648	C₂×C₅	1	4	yes	complemented
167	#5628	C₂×C₅	1	4	yes	complemented
168	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
169	#5526	C₂×C₅	1	1	yes	characteristic, complemented
170	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₅×#41	—	3	1	no	—
172	C₂×C₅×#41	—	3	2	no	—
173	C₂×C₅×#41	—	3	1	no	—
174	C₂×C₅×#41	—	3	2	no	—
175	C₂×C₅×#41	—	3	1	no	—
176	C₂×C₅×#41	—	6	8	no	—
177	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
178	C₂²×C₅×Q₈	—	3	2	no	—
179	C₂²×C₅×Q₈	—	3	2	no	—
180	C₂²×C₅×Q₈	—	3	1	no	—
181	C₂²×C₅×Q₈	—	3	2	no	—
182	C₂²×C₅×Q₈	—	3	2	no	—
183	C₂²×C₅×Q₈	—	3	2	no	—
184	C₂²×C₅×Q₈	—	3	1	no	—
185	C₂²×C₅×Q₈	—	6	8	no	—
186	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
187	C₂²×C₅×D₄	—	3	2	no	—
188	C₂²×C₅×D₄	—	3	1	no	—
189	C₂³×C₄×C₅	—	3	1	no	—
190	C₂³×C₄×C₅	—	3	2	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	8	no	—
195	C₅×C₄⋊Q₈	—	3	2	no	—
196	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
197	C₅×#124	—	3	2	no	—
198	C₅×#124	—	3	2	no	—
199	C₅×#124	—	3	8	no	—
200	C₅×#124	—	3	2	no	—
201	C₅×#124	C₂×D₃	1	2	yes	complemented
202	C₅×#123	—	3	4	no	—
203	C₅×#123	—	3	4	no	—
204	C₅×#123	—	3	8	no	—
205	C₅×#123	—	3	8	no	—
206	C₅×#123	—	3	4	no	—
207	C₅×#123	C₂×D₃	1	4	yes	complemented
208	C₅×C₂²⋊Q₈	—	3	4	no	—
209	C₅×C₂²⋊Q₈	—	3	4	no	—
210	C₅×C₂²⋊Q₈	—	3	8	no	—
211	C₅×C₂²⋊Q₈	—	3	4	no	—
212	C₅×C₂²⋊Q₈	—	3	8	no	—
213	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
214	C₅×#117	—	3	1	no	—
215	C₅×#117	—	3	2	no	—
216	C₅×#117	—	3	2	no	—
217	C₅×#117	—	3	2	no	—
218	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
219	C₂×C₅×C₄⋊C₄	—	3	2	no	—
220	C₂×C₅×C₄⋊C₄	—	3	8	no	—
221	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
222	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
223	C₂×C₄²×C₅	—	3	2	no	—
224	C₂×#536	—	3	1	no	Sylow
225	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
226	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₅×D₃	—	2	4	no	—
228	C₂²×C₅×D₃	—	2	4	no	—
229	C₂²×C₅×D₃	—	2	8	no	—
230	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
231	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
232	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
234	C₃×C₅×Q₈	—	2	4	no	—
235	C₃×C₅×Q₈	—	2	4	no	—
236	C₃×C₅×Q₈	—	2	2	no	—
237	C₃×C₅×D₄	—	2	4	no	—
238	C₃×C₅×D₄	—	2	2	no	—
239	C₂×C₃×C₄×C₅	—	2	4	no	—
240	C₂×C₃×C₄×C₅	—	2	4	no	—
241	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₅×#67	—	2	4	no	—
248	C₅×#67	—	2	4	no	—
249	C₅×#67	—	2	4	no	—
250	C₂×C₅×Dic₃	—	2	4	no	—
251	C₂×C₅×Dic₃	—	2	4	no	—
252	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
253	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
254	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
255	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
258	C₅×D₁₂	—	2	4	no	—
259	C₅×D₁₂	—	2	2	no	—
260	C₄×C₅×D₃	—	2	4	no	—
261	C₄×C₅×D₃	—	2	8	no	—
262	C₄×C₅×D₃	—	2	8	no	—
263	C₄×C₅×D₃	—	2	8	no	—
264	C₄×C₅×D₃	—	2	4	no	—
265	C₄×C₅×D₃	—	2	4	no	—
266	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
267	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
268	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
269	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
270	C₅×Dic₆	—	2	4	no	—
271	C₅×Dic₆	—	2	4	no	—
272	C₅×Dic₆	—	2	2	no	—
273	C₅×Dic₆	—	2	8	no	—
274	C₅×Dic₆	—	2	8	no	—
275	C₅×Dic₆	—	2	4	no	—
276	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
277	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	D₃×#41	—	2	8	no	—
279	C₂×#239	C₂²×C₅	1	1	yes	characteristic
280	C₂×D₃×Q₈	—	2	8	no	—
281	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
282	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
283	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
284	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
285	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
286	C₂×#237	C₂²×C₅	1	2	yes	—
287	C₂×#237	C₂²×C₅	1	1	yes	characteristic
288	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
289	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×#235	C₂²×C₅	1	1	yes	characteristic
291	C₂×#235	C₂²×C₅	1	2	yes	—
292	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
293	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
294	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
295	C₂²×Dic₆	C₂²×C₅	1	2	yes	complemented
296	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
298	C₃×#124	C₂²×C₅	1	2	yes	complemented
299	C₃×#123	C₂²×C₅	1	4	yes	complemented
300	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
301	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
302	#947	C₂²×C₅	1	2	yes	complemented
303	#946	C₂²×C₅	1	4	yes	complemented
304	#944	C₂²×C₅	1	2	yes	complemented
305	#944	C₂²×C₅	1	2	yes	complemented
306	#936	C₂²×C₅	1	2	yes	complemented
307	#935	C₂²×C₅	1	4	yes	complemented
308	#929	C₂²×C₅	1	4	yes	complemented
309	#926	C₂²×C₅	1	1	yes	characteristic, complemented
310	#924	C₂²×C₅	1	4	yes	complemented
311	#897	C₂²×C₅	1	4	yes	complemented
312	#896	C₂²×C₅	1	8	yes	complemented
313	#894	C₂²×C₅	1	8	yes	complemented
314	#892	C₂²×C₅	1	2	yes	complemented
315	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
316	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
317	#888	C₂²×C₅	1	8	yes	complemented
318	#886	C₂²×C₅	1	4	yes	complemented
319	#885	C₂²×C₅	1	8	yes	complemented
320	#883	C₂²×C₅	1	8	yes	complemented
321	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
322	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
323	#878	C₂²×C₅	1	8	yes	complemented
324	#877	C₂²×C₅	1	2	yes	complemented
325	#875	C₂²×C₅	1	2	yes	complemented
326	#872	C₂²×C₅	1	2	yes	complemented
327	C₄²×D₃	C₂²×C₅	1	2	yes	—
328	#869	C₂²×C₅	1	2	yes	complemented
329	C₂⁴×C₅	—	3	1	no	—
330	C₂⁴×C₅	—	3	2	no	—
331	C₅×#41	—	2	4	no	—
332	C₅×#41	—	6	8	no	—
333	C₅×#41	—	6	8	no	—
334	C₅×#41	—	6	4	no	—
335	C₅×#41	—	6	4	no	—
336	C₅×#41	—	6	4	no	—
337	C₂×C₅×Q₈	—	2	4	no	—
338	C₂×C₅×Q₈	—	3	4	no	—
339	C₂×C₅×Q₈	—	3	2	no	—
340	C₂×C₅×Q₈	—	3	4	no	—
341	C₂×C₅×Q₈	—	3	2	no	—
342	C₂×C₅×Q₈	—	3	2	no	—
343	C₂×C₅×Q₈	—	3	1	no	—
344	C₂×C₅×Q₈	—	6	8	no	—
345	C₂×C₅×Q₈	—	6	8	no	—
346	C₂×C₅×Q₈	—	6	8	no	—
347	C₂×C₅×Q₈	—	6	8	no	—
348	C₂×C₅×Q₈	—	6	8	no	—
349	C₂×C₅×Q₈	—	6	4	no	—
350	C₂×C₅×Q₈	—	6	4	no	—
351	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
352	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
353	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
354	C₂×C₅×D₄	—	3	2	no	—
355	C₂×C₅×D₄	—	3	2	no	—
356	C₂×C₅×D₄	—	3	2	no	—
357	C₂×C₅×D₄	—	3	2	no	—
358	C₂×C₅×D₄	—	3	1	no	—
359	C₂×C₅×D₄	—	6	4	no	—
360	C₂×C₅×D₄	—	6	8	no	—
361	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
362	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
363	C₂²×C₄×C₅	—	3	1	no	—
364	C₂²×C₄×C₅	—	3	8	no	—
365	C₂²×C₄×C₅	—	3	1	no	—
366	C₂²×C₄×C₅	—	3	1	no	—
367	C₂²×C₄×C₅	—	3	1	no	—
368	C₂²×C₄×C₅	—	3	1	no	—
369	C₂²×C₄×C₅	—	3	2	no	—
370	C₂²×C₄×C₅	—	3	2	no	—
371	C₂²×C₄×C₅	—	3	4	no	—
372	C₂²×C₄×C₅	—	3	4	no	—
373	C₂²×C₄×C₅	—	3	2	no	—
374	C₂²×C₄×C₅	—	3	2	no	—
375	C₂²×C₄×C₅	—	3	2	no	—
376	C₂²×C₄×C₅	—	3	4	no	—
377	C₂²×C₄×C₅	—	6	8	no	—
378	C₂²×C₄×C₅	—	6	8	no	—
379	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
380	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
381	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
382	C₅×C₄⋊C₄	—	3	4	no	—
383	C₅×C₄⋊C₄	—	3	2	no	—
384	C₅×C₄⋊C₄	—	3	8	no	—
385	C₅×C₄⋊C₄	—	3	8	no	—
386	C₅×C₄⋊C₄	—	3	8	no	—
387	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
388	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
389	C₅×C₂²⋊C₄	—	3	2	no	—
390	C₅×C₂²⋊C₄	—	3	8	no	—
391	C₅×C₂²⋊C₄	—	3	4	no	—
392	C₅×C₂²⋊C₄	—	3	8	no	—
393	C₅×C₂²⋊C₄	—	3	8	no	—
394	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
395	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
396	C₄²×C₅	—	3	4	no	—
397	C₄²×C₅	—	3	2	no	—
398	C₄²×C₅	C₂²×D₃	1	2	yes	—
399	C₂²×#41	—	3	1	no	—
400	C₂³×Q₈	—	3	1	no	—
401	#536	—	3	1	no	—
402	#536	—	3	1	no	—
403	#536	—	3	2	no	—
404	#536	—	3	2	no	—
405	#536	—	3	4	no	—
406	#536	—	3	4	no	—
407	#536	—	3	1	no	—
408	#536	C₅×D₃	1	1	yes	characteristic, direct product factor
409	C₂×C₄⋊Q₈	—	3	2	no	—
410	C₂×#124	—	3	2	no	—
411	C₂×#123	—	3	4	no	—
412	C₂×C₂²⋊Q₈	—	3	4	no	—
413	C₂×#117	—	3	1	no	—
414	C₂²×C₃×C₅	—	2	2	no	—
415	C₂²×C₃×C₅	—	2	2	no	—
416	C₂²×C₃×C₅	—	2	4	no	—
417	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
418	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
419	C₂×C₅×D₃	—	2	2	no	—
420	C₂×C₅×D₃	—	2	8	no	—
421	C₂×C₅×D₃	—	2	2	no	—
422	C₂×C₅×D₃	—	2	4	no	—
423	C₂×C₅×D₃	—	4	8	no	—
424	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
425	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
426	C₂×C₅×D₃	2₋¹⁺⁴	1	4	yes	—
427	C₃×C₄×C₅	—	2	4	no	—
428	C₃×C₄×C₅	—	2	2	no	—
429	C₃×C₄×C₅	—	2	4	no	—
430	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
431	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
432	C₅×Dic₃	—	2	4	no	—
433	C₅×Dic₃	—	2	2	no	—
434	C₅×Dic₃	—	2	4	no	—
435	C₅×Dic₃	C₂²×D₄	1	2	yes	—
436	C₅×Dic₃	C₂²×D₄	1	2	yes	—
437	C₂³×D₃	C₂³×C₅	1	2	yes	—
438	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
439	C₃×#41	—	2	4	no	—
440	C₂×C₃×Q₈	—	2	4	no	—
441	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
443	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
444	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
445	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
446	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
447	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
448	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
449	C₂×#67	C₂³×C₅	1	2	yes	—
450	C₂×#67	C₂³×C₅	1	2	yes	—
451	C₂×#67	C₂³×C₅	1	2	yes	—
452	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
453	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
454	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
455	#239	—	2	4	no	—
456	D₃×Q₈	—	2	8	no	—
457	D₃×Q₈	—	2	8	no	—
458	D₃×Q₈	—	2	8	no	—
459	D₃×Q₈	—	2	8	no	—
460	D₃×Q₈	—	2	4	no	—
461	#237	—	2	8	no	—
462	#237	—	2	4	no	—
463	D₃×D₄	—	2	8	no	—
464	D₃×D₄	—	2	4	no	—
465	#235	—	2	4	no	—
466	#235	—	2	8	no	—
467	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
468	C₂×D₁₂	C₂³×C₅	1	2	yes	—
469	C₂×C₄×D₃	—	2	8	no	—
470	C₂×C₄×D₃	—	2	8	no	—
471	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
472	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
473	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
474	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
475	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
476	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
477	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
478	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
480	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
482	C₂×Dic₆	—	2	4	no	—
483	C₂×Dic₆	—	2	8	no	—
484	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
485	C₂×Dic₆	C₂³×C₅	1	2	yes	—
486	C₂×Dic₆	C₂³×C₅	1	4	yes	—
487	C₂×Dic₆	C₂³×C₅	1	4	yes	—
488	C₂×Dic₆	C₂³×C₅	1	2	yes	—
489	C₂×Dic₆	C₂³×C₅	1	2	yes	—
490	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
491	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
492	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
493	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
494	C₃×C₄²	C₂³×C₅	1	2	yes	—
495	#217	C₂³×C₅	1	2	yes	—
496	#217	C₂³×C₅	1	8	yes	—
497	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
498	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
499	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
500	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
501	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
502	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
503	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
504	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
505	C₄×Dic₃	C₂³×C₅	1	2	yes	—
506	C₄×Dic₃	C₂³×C₅	1	4	yes	—
507	C₂³×C₅	—	3	1	no	—
508	C₂³×C₅	—	3	4	no	—
509	C₂³×C₅	—	3	1	no	—
510	C₂³×C₅	—	3	2	no	—
511	C₂³×C₅	—	6	4	no	—
512	C₂³×C₅	—	6	4	no	—
513	C₂³×C₅	—	6	8	no	—
514	C₂³×C₅	C₂³×D₃	1	2	yes	—
515	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
516	C₅×Q₈	—	2	4	no	—
517	C₅×Q₈	—	2	4	no	—
518	C₅×Q₈	—	2	2	no	—
519	C₅×Q₈	—	6	8	no	—
520	C₅×Q₈	—	6	8	no	—
521	C₅×Q₈	—	6	4	no	—
522	C₅×Q₈	—	6	4	no	—
523	C₅×Q₈	—	6	4	no	—
524	C₅×Q₈	—	6	2	no	—
525	C₅×D₄	—	2	4	no	—
526	C₅×D₄	—	2	2	no	—
527	C₅×D₄	—	6	4	no	—
528	C₅×D₄	—	6	4	no	—
529	C₅×D₄	—	6	4	no	—
530	C₅×D₄	—	6	4	no	—
531	C₅×D₄	—	6	2	no	—
532	C₂×C₄×C₅	—	2	4	no	—
533	C₂×C₄×C₅	—	2	4	no	—
534	C₂×C₄×C₅	—	3	4	no	—
535	C₂×C₄×C₅	—	3	1	no	—
536	C₂×C₄×C₅	—	3	1	no	—
537	C₂×C₄×C₅	—	3	4	no	—
538	C₂×C₄×C₅	—	3	4	no	—
539	C₂×C₄×C₅	—	3	4	no	—
540	C₂×C₄×C₅	—	3	4	no	—
541	C₂×C₄×C₅	—	3	4	no	—
542	C₂×C₄×C₅	—	3	4	no	—
543	C₂×C₄×C₅	—	3	2	no	—
544	C₂×C₄×C₅	—	6	4	no	—
545	C₂×C₄×C₅	—	6	8	no	—
546	C₂×C₄×C₅	—	6	4	no	—
547	C₂×C₄×C₅	—	6	8	no	—
548	C₂×C₄×C₅	—	6	8	no	—
549	C₂×C₄×C₅	—	6	4	no	—
550	C₂×C₄×C₅	—	6	4	no	—
551	C₂×C₄×C₅	—	6	4	no	—
552	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
553	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
554	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
555	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
556	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
557	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
558	C₂×#41	—	3	1	no	—
559	C₂×#41	—	3	2	no	—
560	C₂×#41	—	3	1	no	—
561	C₂×#41	—	3	2	no	—
562	C₂×#41	—	3	1	no	—
563	C₂×#41	—	6	8	no	—
564	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
565	C₂²×Q₈	—	3	2	no	—
566	C₂²×Q₈	—	3	2	no	—
567	C₂²×Q₈	—	3	1	no	—
568	C₂²×Q₈	—	3	2	no	—
569	C₂²×Q₈	—	3	2	no	—
570	C₂²×Q₈	—	3	2	no	—
571	C₂²×Q₈	—	3	1	no	—
572	C₂²×Q₈	—	6	8	no	—
573	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
574	C₂²×D₄	—	3	2	no	—
575	C₂²×D₄	—	3	1	no	—
576	C₂³×C₄	—	3	1	no	—
577	C₂³×C₄	—	3	2	no	—
578	C₂³×C₄	—	3	2	no	—
579	C₄⋊Q₈	—	3	2	no	—
580	C₄⋊Q₈	—	3	2	no	—
581	C₄⋊Q₈	—	3	8	no	—
582	C₄⋊Q₈	—	3	2	no	—
583	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
584	#124	—	3	2	no	—
585	#124	—	3	2	no	—
586	#124	—	3	8	no	—
587	#124	—	3	2	no	—
588	#124	C₂×C₅×D₃	1	2	yes	complemented
589	#123	—	3	4	no	—
590	#123	—	3	4	no	—
591	#123	—	3	8	no	—
592	#123	—	3	8	no	—
593	#123	—	3	4	no	—
594	#123	C₂×C₅×D₃	1	4	yes	complemented
595	C₂²⋊Q₈	—	3	4	no	—
596	C₂²⋊Q₈	—	3	4	no	—
597	C₂²⋊Q₈	—	3	8	no	—
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	—	3	8	no	—
600	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
601	#117	—	3	1	no	—
602	#117	—	3	2	no	—
603	#117	—	3	2	no	—
604	#117	—	3	2	no	—
605	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
606	C₂×C₄⋊C₄	—	3	2	no	—
607	C₂×C₄⋊C₄	—	3	8	no	—
608	C₂×C₂²⋊C₄	—	3	2	no	—
609	C₂×C₂²⋊C₄	—	3	8	no	—
610	C₂×C₄²	—	3	2	no	—
611	C₂×C₃×C₅	—	2	2	no	—
612	C₂×C₃×C₅	—	4	2	no	—
613	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
614	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
615	C₅×D₃	—	2	2	no	—
616	C₅×D₃	—	4	2	no	—
617	C₅×D₃	#536	1	4	yes	direct product factor
618	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
619	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
620	C₂²×D₃	—	2	4	no	—
621	C₂²×D₃	—	2	4	no	—
622	C₂²×D₃	—	2	8	no	—
623	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
624	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
625	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
626	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
627	C₃×Q₈	—	2	4	no	—
628	C₃×Q₈	—	2	4	no	—
629	C₃×Q₈	—	2	2	no	—
630	C₃×D₄	—	2	4	no	—
631	C₃×D₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	4	no	—
633	C₂×C₃×C₄	—	2	4	no	—
634	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
635	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
636	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
637	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
638	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
639	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
640	#67	—	2	4	no	—
641	#67	—	2	4	no	—
642	#67	—	2	4	no	—
643	C₂×Dic₃	—	2	4	no	—
644	C₂×Dic₃	—	2	4	no	—
645	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
646	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
647	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
648	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
649	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
650	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
651	D₁₂	—	2	4	no	—
652	D₁₂	—	2	2	no	—
653	C₄×D₃	—	2	4	no	—
654	C₄×D₃	—	2	8	no	—
655	C₄×D₃	—	2	8	no	—
656	C₄×D₃	—	2	8	no	—
657	C₄×D₃	—	2	4	no	—
658	C₄×D₃	—	2	4	no	—
659	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
660	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
661	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
662	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
663	Dic₆	—	2	4	no	—
664	Dic₆	—	2	4	no	—
665	Dic₆	—	2	2	no	—
666	Dic₆	—	2	8	no	—
667	Dic₆	—	2	8	no	—
668	Dic₆	—	2	4	no	—
669	C₂²×C₅	—	2	2	no	—
670	C₂²×C₅	—	2	2	no	—
671	C₂²×C₅	—	2	4	no	—
672	C₂²×C₅	—	3	2	no	—
673	C₂²×C₅	—	3	4	no	—
674	C₂²×C₅	—	3	2	no	—
675	C₂²×C₅	—	6	8	no	—
676	C₂²×C₅	—	6	2	no	—
677	C₂²×C₅	—	6	2	no	—
678	C₂²×C₅	—	6	4	no	—
679	C₂²×C₅	—	12	8	no	—
680	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
681	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	2	4	no	—
684	C₄×C₅	—	2	4	no	—
685	C₄×C₅	—	3	2	no	—
686	C₄×C₅	—	3	2	no	—
687	C₄×C₅	—	6	2	no	—
688	C₄×C₅	—	6	4	no	—
689	C₄×C₅	—	6	4	no	—
690	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
691	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
692	C₂⁴	—	3	1	no	—
693	C₂⁴	—	3	2	no	—
694	#41	—	2	4	no	—
695	#41	—	6	8	no	—
696	#41	—	6	8	no	—
697	#41	—	6	4	no	—
698	#41	—	6	4	no	—
699	#41	—	6	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	3	4	no	—
702	C₂×Q₈	—	3	2	no	—
703	C₂×Q₈	—	3	4	no	—
704	C₂×Q₈	—	3	2	no	—
705	C₂×Q₈	—	3	2	no	—
706	C₂×Q₈	—	3	1	no	—
707	C₂×Q₈	—	6	8	no	—
708	C₂×Q₈	—	6	8	no	—
709	C₂×Q₈	—	6	8	no	—
710	C₂×Q₈	—	6	8	no	—
711	C₂×Q₈	—	6	8	no	—
712	C₂×Q₈	—	6	4	no	—
713	C₂×Q₈	—	6	4	no	—
714	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
715	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
716	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
717	C₂×D₄	—	3	2	no	—
718	C₂×D₄	—	3	2	no	—
719	C₂×D₄	—	3	2	no	—
720	C₂×D₄	—	3	2	no	—
721	C₂×D₄	—	3	1	no	—
722	C₂×D₄	—	6	4	no	—
723	C₂×D₄	—	6	8	no	—
724	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
725	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
726	C₂²×C₄	—	3	1	no	—
727	C₂²×C₄	—	3	8	no	—
728	C₂²×C₄	—	3	1	no	—
729	C₂²×C₄	—	3	1	no	—
730	C₂²×C₄	—	3	1	no	—
731	C₂²×C₄	—	3	1	no	—
732	C₂²×C₄	—	3	2	no	—
733	C₂²×C₄	—	3	2	no	—
734	C₂²×C₄	—	3	4	no	—
735	C₂²×C₄	—	3	4	no	—
736	C₂²×C₄	—	3	2	no	—
737	C₂²×C₄	—	3	2	no	—
738	C₂²×C₄	—	3	2	no	—
739	C₂²×C₄	—	3	4	no	—
740	C₂²×C₄	—	6	8	no	—
741	C₂²×C₄	—	6	8	no	—
742	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
743	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
744	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
745	C₄⋊C₄	—	3	4	no	—
746	C₄⋊C₄	—	3	2	no	—
747	C₄⋊C₄	—	3	8	no	—
748	C₄⋊C₄	—	3	8	no	—
749	C₄⋊C₄	—	3	8	no	—
750	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
751	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
752	C₂²⋊C₄	—	3	2	no	—
753	C₂²⋊C₄	—	3	8	no	—
754	C₂²⋊C₄	—	3	4	no	—
755	C₂²⋊C₄	—	3	8	no	—
756	C₂²⋊C₄	—	3	8	no	—
757	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
758	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
759	C₄²	—	3	4	no	—
760	C₄²	—	3	2	no	—
761	C₄²	C₂²×C₅×D₃	1	2	yes	—
762	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
763	C₂²×C₃	—	2	2	no	—
764	C₂²×C₃	—	2	2	no	—
765	C₂²×C₃	—	2	4	no	—
766	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
767	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
768	C₂×D₃	—	2	2	no	—
769	C₂×D₃	—	2	8	no	—
770	C₂×D₃	—	2	2	no	—
771	C₂×D₃	—	2	4	no	—
772	C₂×D₃	—	4	8	no	—
773	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
774	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
775	C₂×D₃	C₅×2₋¹⁺⁴	1	4	yes	—
776	C₃×C₄	—	2	4	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	4	no	—
779	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
780	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
781	Dic₃	—	2	4	no	—
782	Dic₃	—	2	2	no	—
783	Dic₃	—	2	4	no	—
784	Dic₃	C₂²×C₅×D₄	1	2	yes	—
785	Dic₃	C₂²×C₅×D₄	1	2	yes	—
786	C₂×C₅	—	2	2	no	—
787	C₂×C₅	—	3	4	no	—
788	C₂×C₅	—	4	2	no	—
789	C₂×C₅	—	6	2	no	—
790	C₂×C₅	—	12	2	no	—
791	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
792	C₂×C₅	D₃×2₋¹⁺⁴	1	2	yes	—
793	C₂³	—	3	1	no	—
794	C₂³	—	3	4	no	—
795	C₂³	—	3	1	no	—
796	C₂³	—	3	2	no	—
797	C₂³	—	6	4	no	—
798	C₂³	—	6	4	no	—
799	C₂³	—	6	8	no	—
800	C₂³	C₂³×C₅×D₃	1	2	yes	—
801	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
802	Q₈	—	2	4	no	—
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	6	8	no	—
806	Q₈	—	6	8	no	—
807	Q₈	—	6	4	no	—
808	Q₈	—	6	4	no	—
809	Q₈	—	6	4	no	—
810	Q₈	—	6	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	6	4	no	—
814	D₄	—	6	4	no	—
815	D₄	—	6	4	no	—
816	D₄	—	6	4	no	—
817	D₄	—	6	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	3	4	no	—
821	C₂×C₄	—	3	1	no	—
822	C₂×C₄	—	3	1	no	—
823	C₂×C₄	—	3	4	no	—
824	C₂×C₄	—	3	4	no	—
825	C₂×C₄	—	3	4	no	—
826	C₂×C₄	—	3	4	no	—
827	C₂×C₄	—	3	4	no	—
828	C₂×C₄	—	3	4	no	—
829	C₂×C₄	—	3	2	no	—
830	C₂×C₄	—	6	4	no	—
831	C₂×C₄	—	6	4	no	—
832	C₂×C₄	—	6	8	no	—
833	C₂×C₄	—	6	8	no	—
834	C₂×C₄	—	6	8	no	—
835	C₂×C₄	—	6	4	no	—
836	C₂×C₄	—	6	4	no	—
837	C₂×C₄	—	6	4	no	—
838	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
839	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
840	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
841	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
842	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
843	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
844	C₂×C₃	—	2	2	no	—
845	C₂×C₃	—	4	2	no	—
846	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
847	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
848	D₃	—	2	2	no	—
849	D₃	—	4	2	no	—
850	D₃	C₅×#536	1	4	yes	direct product factor
851	C₅	D₃×#536	1	1	yes	characteristic, direct product factor, Sylow
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	3	2	no	—
856	C₂²	—	3	4	no	—
857	C₂²	—	3	2	no	—
858	C₂²	—	6	8	no	—
859	C₂²	—	6	2	no	—
860	C₂²	—	6	2	no	—
861	C₂²	—	6	4	no	—
862	C₂²	—	12	8	no	—
863	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
864	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	4	no	—
868	C₄	—	3	2	no	—
869	C₄	—	3	2	no	—
870	C₄	—	6	2	no	—
871	C₄	—	6	4	no	—
872	C₄	—	6	4	no	—
873	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
874	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
875	C₃	C₂×C₅×#536	1	1	yes	characteristic, complemented, Sylow
876	C₂	—	2	2	no	—
877	C₂	—	3	4	no	—
878	C₂	—	4	2	no	—
879	C₂	—	6	2	no	—
880	C₂	—	12	2	no	—
881	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
882	C₂	C₅×D₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#536	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×#41	C₂
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₂×C₅×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#536

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×D₃×Q₈	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₅×#5825	C₂	semidirect
5. C₅×#5816	C₂	semidirect
6. C₅×#5724	C₂	semidirect
7. C₅×D₃×C₄⋊Q₈	C₂	semidirect
8. C₅×#5675	C₂	semidirect
9. C₅×D₃×#124	C₂	semidirect
10. C₅×D₃×#123	C₂	semidirect
11. C₅×#5648	C₂	semidirect
12. C₅×#5628	C₂	semidirect
13. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
14. C₅×#5526	C₂	semidirect
15. C₅×D₃×#117	C₂	semidirect
18. C₂²×C₃×C₅×Q₈	C₂²	semidirect
25. C₂×C₅×D₃×Q₈	C₂²	semidirect
26. C₂×C₅×D₃×Q₈	C₂²	semidirect
36. C₂²×C₅×Dic₆	C₂²	semidirect
37. C₂²×C₅×Dic₆	C₂²	semidirect
38. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
39. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₅×#117	C₂²	semidirect
43. C₅×#947	C₂²	semidirect
44. C₅×#946	C₂²	semidirect
45. C₅×#944	C₂²	semidirect
46. C₅×#944	C₂²	semidirect
47. C₅×#936	C₂²	semidirect
48. C₅×#935	C₂²	semidirect
49. C₅×#929	C₂²	semidirect
50. C₅×#926	C₂²	semidirect
51. C₅×#924	C₂²	semidirect
52. C₅×#897	C₂²	semidirect
53. C₅×#896	C₂²	semidirect
54. C₅×#894	C₂²	semidirect
55. C₅×#892	C₂²	semidirect
58. C₅×#888	C₂²	semidirect
59. C₅×#886	C₂²	semidirect
60. C₅×#885	C₂²	semidirect
61. C₅×#883	C₂²	semidirect
64. C₅×#878	C₂²	semidirect
65. C₅×#877	C₂²	semidirect
66. C₅×#875	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
69. C₅×#869	C₂²	semidirect
70. D₃×#536	C₅	direct (N × H)
80. C₅×#536	D₃	direct (N × H)
157. C₂²×D₃×Q₈	C₂×C₅	semidirect
158. C₃×#536	C₂×C₅	semidirect
159. #5825	C₂×C₅	semidirect
160. #5816	C₂×C₅	semidirect
161. #5724	C₂×C₅	semidirect
162. D₃×C₄⋊Q₈	C₂×C₅	semidirect
163. #5675	C₂×C₅	semidirect
164. D₃×#124	C₂×C₅	semidirect
165. D₃×#123	C₂×C₅	semidirect
166. #5648	C₂×C₅	semidirect
167. #5628	C₂×C₅	semidirect
168. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
169. #5526	C₂×C₅	semidirect
170. D₃×#117	C₂×C₅	semidirect
186. C₂²×C₅×Q₈	C₂×D₃	semidirect
196. C₅×C₄⋊Q₈	C₂×D₃	semidirect
201. C₅×#124	C₂×D₃	semidirect
207. C₅×#123	C₂×D₃	semidirect
213. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
218. C₅×#117	C₂×D₃	semidirect
277. C₂²×C₃×Q₈	C₂²×C₅	semidirect
284. C₂×D₃×Q₈	C₂²×C₅	semidirect
285. C₂×D₃×Q₈	C₂²×C₅	semidirect
295. C₂²×Dic₆	C₂²×C₅	semidirect
296. C₂²×Dic₆	C₂²×C₅	semidirect
297. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
298. C₃×#124	C₂²×C₅	semidirect
299. C₃×#123	C₂²×C₅	semidirect
300. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
301. C₃×#117	C₂²×C₅	semidirect
302. #947	C₂²×C₅	semidirect
303. #946	C₂²×C₅	semidirect
304. #944	C₂²×C₅	semidirect
305. #944	C₂²×C₅	semidirect
306. #936	C₂²×C₅	semidirect
307. #935	C₂²×C₅	semidirect
308. #929	C₂²×C₅	semidirect
309. #926	C₂²×C₅	semidirect
310. #924	C₂²×C₅	semidirect
311. #897	C₂²×C₅	semidirect
312. #896	C₂²×C₅	semidirect
313. #894	C₂²×C₅	semidirect
314. #892	C₂²×C₅	semidirect
317. #888	C₂²×C₅	semidirect
318. #886	C₂²×C₅	semidirect
319. #885	C₂²×C₅	semidirect
320. #883	C₂²×C₅	semidirect
323. #878	C₂²×C₅	semidirect
324. #877	C₂²×C₅	semidirect
325. #875	C₂²×C₅	semidirect
326. #872	C₂²×C₅	semidirect
328. #869	C₂²×C₅	semidirect
408. #536	C₅×D₃	direct (N × H)
573. C₂²×Q₈	C₂×C₅×D₃	semidirect
583. C₄⋊Q₈	C₂×C₅×D₃	semidirect
588. #124	C₂×C₅×D₃	semidirect
594. #123	C₂×C₅×D₃	semidirect
600. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
605. #117	C₂×C₅×D₃	semidirect
617. C₅×D₃	#536	direct (N × H)
762. C₃×C₅	C₂×#536	semidirect
850. D₃	C₅×#536	direct (N × H)
851. C₅	D₃×#536	direct (N × H)
875. C₃	C₂×C₅×#536	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×D₃×#41	2
C₂²×C₅×D₃×Q₈	2
C₃×C₅×#536	2
C₅×#5825	2
C₅×#5816	2
C₅×#5724	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5675	2
C₅×D₃×#124	2
C₅×D₃×#123	2
C₅×#5648	2
C₅×#5628	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5526	2
C₅×D₃×#117	2
C₂×C₅×#536	3
D₃×#536	5

Subgroups — C5×D3×#536 #14480458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#536 #14480458