Subgroups — C₅×#86338 #14480647

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 908 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, complemented
2	C₂²×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5816	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5725	C₂	1	2	yes	maximal, complemented
7	C₅×#5724	C₂	1	2	yes	maximal, complemented
8	C₅×#5674	C₂	1	2	yes	maximal, complemented
9	C₅×#5668	C₂	1	2	yes	maximal, complemented
10	C₅×#5656	C₂	1	4	yes	maximal, complemented
11	C₅×#5653	C₂	1	4	yes	maximal, complemented
12	C₅×#5629	C₂	1	4	yes	maximal, complemented
13	C₅×#5627	C₂	1	4	yes	maximal, complemented
14	C₅×#5525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3449	—	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	—	2	8	no	—
21	C₂×C₅×#239	C₂²	1	2	yes	—
22	C₂×C₅×#239	C₂²	1	2	yes	—
23	C₂×C₅×#239	C₂²	1	2	yes	complemented
24	C₂×C₅×#239	C₂²	1	2	yes	complemented
25	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#237	C₂²	1	2	yes	—
28	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
30	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#235	C₂²	1	1	yes	characteristic
32	C₂×C₅×#235	C₂²	1	2	yes	complemented
33	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
34	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
37	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	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×#947	C₂²	1	2	yes	complemented
45	C₅×#946	C₂²	1	4	yes	complemented
46	C₅×#944	C₂²	1	2	yes	complemented
47	C₅×#940	C₂²	1	2	yes	complemented
48	C₅×#937	C₂²	1	4	yes	complemented
49	C₅×#930	C₂²	1	4	yes	complemented
50	C₅×#929	C₂²	1	4	yes	complemented
51	C₅×#926	C₂²	1	1	yes	characteristic, complemented
52	C₅×#896	C₂²	1	8	yes	complemented
53	C₅×#895	C₂²	1	8	yes	complemented
54	C₅×#895	C₂²	1	4	yes	complemented
55	C₅×#894	C₂²	1	8	yes	complemented
56	C₅×#893	C₂²	1	8	yes	complemented
57	C₅×#892	C₂²	1	2	yes	complemented
58	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₅×#884	C₂²	1	8	yes	complemented
60	C₅×#884	C₂²	1	8	yes	complemented
61	C₅×#882	C₂²	1	4	yes	complemented
62	C₅×#882	C₂²	1	8	yes	complemented
63	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
64	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₅×#877	C₂²	1	2	yes	complemented
66	C₅×#875	C₂²	1	2	yes	complemented
67	C₅×#874	C₂²	1	2	yes	complemented
68	C₅×#872	C₂²	1	2	yes	complemented
69	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
70	#86338	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂²×C₅×#41	—	3	1	no	—
73	C₅×#537	—	3	4	no	—
74	C₅×#536	—	3	1	no	—
75	C₅×#536	—	3	2	no	—
76	C₅×#536	D₃	1	1	yes	characteristic, complemented
77	C₅×#535	—	3	1	no	—
78	C₅×#535	—	3	2	no	—
79	C₅×#535	—	3	1	no	—
80	C₅×#534	—	3	4	no	—
81	C₅×#532	—	3	2	no	—
82	C₅×#532	—	3	2	no	—
83	C₅×#525	—	3	4	no	—
84	C₅×#525	—	3	4	no	—
85	C₂×C₅×#117	—	3	1	no	—
86	C₂³×C₅×D₃	C₂³	1	2	yes	—
87	C₂³×C₅×D₃	C₂³	1	2	yes	—
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₃×C₅×#41	—	2	4	no	—
90	C₂×C₃×C₅×Q₈	—	2	4	no	—
91	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
92	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
93	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
95	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
97	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₅×#67	C₂³	1	2	yes	—
100	C₂×C₅×#67	C₂³	1	2	yes	—
101	C₂×C₅×#67	C₂³	1	2	yes	—
102	C₂×C₅×#67	C₂³	1	8	yes	—
103	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
104	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₅×#239	—	2	8	no	—
106	C₅×#239	—	2	8	no	—
107	C₅×#239	—	2	8	no	—
108	C₅×#239	—	2	8	no	—
109	C₅×#239	—	2	4	no	—
110	C₅×D₃×Q₈	—	2	4	no	—
111	C₅×#237	—	2	8	no	—
112	C₅×#237	—	2	4	no	—
113	C₅×D₃×D₄	—	2	8	no	—
114	C₅×D₃×D₄	—	2	4	no	—
115	C₅×#235	—	2	4	no	—
116	C₅×#235	—	2	8	no	—
117	C₂×C₅×D₁₂	—	2	8	no	—
118	C₂×C₅×D₁₂	—	2	4	no	—
119	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
120	C₂×C₅×D₁₂	C₂³	1	2	yes	—
121	C₂×C₅×D₁₂	C₂³	1	4	yes	—
122	C₂×C₅×D₁₂	C₂³	1	4	yes	—
123	C₂×C₅×D₁₂	C₂³	1	2	yes	—
124	C₂×C₅×D₁₂	C₂³	1	2	yes	—
125	C₂×C₅×D₁₂	C₂³	1	8	yes	—
126	C₂×C₄×C₅×D₃	—	2	8	no	—
127	C₂×C₄×C₅×D₃	—	2	8	no	—
128	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
129	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
130	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
131	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
132	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
133	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
134	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
135	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
139	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
140	C₂×C₅×Dic₆	C₂³	1	2	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
145	C₃×C₄²×C₅	C₂³	1	2	yes	—
146	C₅×#217	C₂³	1	2	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
149	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
150	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
151	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
152	C₅×Dic₃⋊C₄	C₂³	1	4	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, complemented
157	C₂²×#239	C₂×C₅	1	1	yes	characteristic, complemented
158	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
159	#5830	C₂×C₅	1	1	yes	characteristic, complemented
160	#5816	C₂×C₅	1	1	yes	characteristic, complemented
161	#5725	C₂×C₅	1	2	yes	complemented
162	#5724	C₂×C₅	1	2	yes	complemented
163	#5674	C₂×C₅	1	2	yes	complemented
164	#5668	C₂×C₅	1	2	yes	complemented
165	#5656	C₂×C₅	1	4	yes	complemented
166	#5653	C₂×C₅	1	4	yes	complemented
167	#5629	C₂×C₅	1	4	yes	complemented
168	#5627	C₂×C₅	1	4	yes	complemented
169	#5525	C₂×C₅	1	1	yes	characteristic, complemented
170	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₅×#41	—	3	2	no	—
172	C₂×C₅×#41	—	3	1	no	—
173	C₂×C₅×#41	—	3	2	no	—
174	C₂×C₅×#41	—	3	2	no	—
175	C₂×C₅×#41	—	3	2	no	—
176	C₂×C₅×#41	—	3	2	no	—
177	C₂×C₅×#41	—	3	1	no	—
178	C₂×C₅×#41	—	3	1	no	—
179	C₂×C₅×#41	—	3	2	no	—
180	C₂×C₅×#41	—	6	8	no	—
181	C₂×C₅×#41	—	6	8	no	—
182	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
183	C₂²×C₅×Q₈	—	3	1	no	—
184	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
185	C₂²×C₅×D₄	—	3	2	no	—
186	C₂²×C₅×D₄	—	3	1	no	—
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	C₂×D₃	1	2	yes	complemented
194	C₅×#127	—	3	2	no	—
195	C₅×#127	—	3	2	no	—
196	C₅×#124	—	3	2	no	—
197	C₅×#124	—	3	2	no	—
198	C₅×#124	—	3	2	no	—
199	C₅×#124	C₂×D₃	1	2	yes	complemented
200	C₅×#123	—	3	4	no	—
201	C₅×#123	—	3	8	no	—
202	C₅×#123	C₂×D₃	1	4	yes	complemented
203	C₅×C₂²⋊Q₈	—	3	4	no	—
204	C₅×C₂²⋊Q₈	—	3	8	no	—
205	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
206	C₅×#121	—	3	4	no	—
207	C₅×#121	—	3	4	no	—
208	C₅×#121	—	3	8	no	—
209	C₅×#121	—	3	8	no	—
210	C₅×#121	—	3	8	no	—
211	C₅×#120	—	3	4	no	—
212	C₅×#120	—	3	8	no	—
213	C₅×#120	—	3	4	no	—
214	C₄×C₅×D₄	—	3	8	no	—
215	C₄×C₅×D₄	—	3	8	no	—
216	C₅×#117	—	3	1	no	—
217	C₅×#117	—	3	2	no	—
218	C₅×#117	—	3	2	no	—
219	C₅×#117	—	3	2	no	—
220	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
221	C₂×C₅×C₄⋊C₄	—	3	2	no	—
222	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
223	C₂×C₄²×C₅	—	3	2	no	—
224	#3449	—	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	—	4	2	no	—
230	C₂²×C₅×D₃	—	4	4	no	—
231	C₂²×C₅×D₃	—	4	4	no	—
232	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
233	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
234	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
235	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
237	C₃×C₅×Q₈	—	2	2	no	—
238	C₃×C₅×Q₈	—	2	4	no	—
239	C₃×C₅×Q₈	—	2	4	no	—
240	C₃×C₅×D₄	—	2	4	no	—
241	C₃×C₅×D₄	—	2	2	no	—
242	C₂×C₃×C₄×C₅	—	2	4	no	—
243	C₂×C₃×C₄×C₅	—	2	4	no	—
244	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
247	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
250	C₅×#67	—	2	4	no	—
251	C₅×#67	—	2	4	no	—
252	C₅×#67	—	2	4	no	—
253	C₅×#67	—	4	8	no	—
254	C₂×C₅×Dic₃	—	2	4	no	—
255	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
257	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
258	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
260	C₅×D₁₂	—	2	8	no	—
261	C₅×D₁₂	—	2	8	no	—
262	C₅×D₁₂	—	2	4	no	—
263	C₅×D₁₂	—	2	4	no	—
264	C₅×D₁₂	—	2	4	no	—
265	C₅×D₁₂	—	2	2	no	—
266	C₅×D₁₂	—	4	8	no	—
267	C₄×C₅×D₃	—	2	4	no	—
268	C₄×C₅×D₃	—	2	4	no	—
269	C₄×C₅×D₃	—	2	4	no	—
270	C₄×C₅×D₃	—	2	8	no	—
271	C₄×C₅×D₃	—	2	8	no	—
272	C₄×C₅×D₃	—	4	4	no	—
273	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
274	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
275	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
276	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
277	C₅×Dic₆	—	2	2	no	—
278	C₅×Dic₆	—	2	4	no	—
279	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
280	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	D₃×#41	—	2	8	no	—
282	C₂×#239	—	2	8	no	—
283	C₂×#239	C₂²×C₅	1	2	yes	—
284	C₂×#239	C₂²×C₅	1	2	yes	—
285	C₂×#239	C₂²×C₅	1	2	yes	complemented
286	C₂×#239	C₂²×C₅	1	2	yes	complemented
287	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₂×#237	C₂²×C₅	1	2	yes	—
290	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
292	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×#235	C₂²×C₅	1	1	yes	characteristic
294	C₂×#235	C₂²×C₅	1	2	yes	complemented
295	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
296	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
298	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
299	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
300	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
301	C₃×#124	C₂²×C₅	1	2	yes	complemented
302	C₃×#123	C₂²×C₅	1	4	yes	complemented
303	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
304	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
305	#947	C₂²×C₅	1	2	yes	complemented
306	#947	C₂²×C₅	1	2	yes	complemented
307	#946	C₂²×C₅	1	4	yes	complemented
308	#944	C₂²×C₅	1	2	yes	complemented
309	#940	C₂²×C₅	1	2	yes	complemented
310	#937	C₂²×C₅	1	4	yes	complemented
311	#930	C₂²×C₅	1	4	yes	complemented
312	#929	C₂²×C₅	1	4	yes	complemented
313	#926	C₂²×C₅	1	1	yes	characteristic, complemented
314	#896	C₂²×C₅	1	8	yes	complemented
315	#895	C₂²×C₅	1	8	yes	complemented
316	#895	C₂²×C₅	1	4	yes	complemented
317	#894	C₂²×C₅	1	8	yes	complemented
318	#893	C₂²×C₅	1	8	yes	complemented
319	#892	C₂²×C₅	1	2	yes	complemented
320	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
321	#884	C₂²×C₅	1	8	yes	complemented
322	#884	C₂²×C₅	1	8	yes	complemented
323	#882	C₂²×C₅	1	4	yes	complemented
324	#882	C₂²×C₅	1	8	yes	complemented
325	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
326	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
327	#877	C₂²×C₅	1	2	yes	complemented
328	#875	C₂²×C₅	1	2	yes	complemented
329	#874	C₂²×C₅	1	2	yes	complemented
330	#872	C₂²×C₅	1	2	yes	complemented
331	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
332	C₂⁴×C₅	—	3	1	no	—
333	C₂⁴×C₅	—	3	2	no	—
334	C₂⁴×C₅	—	3	2	no	—
335	C₅×#41	—	2	4	no	—
336	C₅×#41	—	6	8	no	—
337	C₅×#41	—	6	8	no	—
338	C₅×#41	—	6	4	no	—
339	C₅×#41	—	6	8	no	—
340	C₅×#41	—	6	8	no	—
341	C₅×#41	—	6	8	no	—
342	C₅×#41	—	6	8	no	—
343	C₅×#41	—	6	4	no	—
344	C₅×#41	—	6	4	no	—
345	C₂×C₅×Q₈	—	2	4	no	—
346	C₂×C₅×Q₈	—	3	2	no	—
347	C₂×C₅×Q₈	—	3	1	no	—
348	C₂×C₅×Q₈	—	6	4	no	—
349	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
350	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
351	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
352	C₂×C₅×D₄	—	3	2	no	—
353	C₂×C₅×D₄	—	3	2	no	—
354	C₂×C₅×D₄	—	3	2	no	—
355	C₂×C₅×D₄	—	3	8	no	—
356	C₂×C₅×D₄	—	3	4	no	—
357	C₂×C₅×D₄	—	3	2	no	—
358	C₂×C₅×D₄	—	3	4	no	—
359	C₂×C₅×D₄	—	3	2	no	—
360	C₂×C₅×D₄	—	3	1	no	—
361	C₂×C₅×D₄	—	3	2	no	—
362	C₂×C₅×D₄	—	3	8	no	—
363	C₂×C₅×D₄	—	6	8	no	—
364	C₂×C₅×D₄	—	6	4	no	—
365	C₂×C₅×D₄	—	6	8	no	—
366	C₂×C₅×D₄	—	6	4	no	—
367	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
368	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
369	C₂²×C₄×C₅	—	3	1	no	—
370	C₂²×C₄×C₅	—	3	8	no	—
371	C₂²×C₄×C₅	—	3	1	no	—
372	C₂²×C₄×C₅	—	3	1	no	—
373	C₂²×C₄×C₅	—	3	1	no	—
374	C₂²×C₄×C₅	—	3	1	no	—
375	C₂²×C₄×C₅	—	3	2	no	—
376	C₂²×C₄×C₅	—	3	2	no	—
377	C₂²×C₄×C₅	—	3	4	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	4	no	—
382	C₂²×C₄×C₅	—	6	8	no	—
383	C₂²×C₄×C₅	—	6	8	no	—
384	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
385	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
386	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
387	C₅×C₄⋊C₄	—	3	4	no	—
388	C₅×C₄⋊C₄	—	3	2	no	—
389	C₅×C₄⋊C₄	—	3	8	no	—
390	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
391	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
392	C₅×C₂²⋊C₄	—	3	2	no	—
393	C₅×C₂²⋊C₄	—	3	4	no	—
394	C₅×C₂²⋊C₄	—	3	8	no	—
395	C₅×C₂²⋊C₄	—	3	8	no	—
396	C₅×C₂²⋊C₄	—	3	8	no	—
397	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
398	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
399	C₄²×C₅	—	3	4	no	—
400	C₄²×C₅	—	3	2	no	—
401	C₄²×C₅	C₂²×D₃	1	2	yes	—
402	C₂²×#41	—	3	1	no	—
403	C₂²×#41	—	3	1	no	—
404	#537	—	3	4	no	—
405	#536	—	3	1	no	—
406	#536	—	3	2	no	—
407	#536	C₅×D₃	1	1	yes	characteristic, complemented
408	#535	—	3	1	no	—
409	#535	—	3	2	no	—
410	#535	—	3	1	no	—
411	#534	—	3	4	no	—
412	#532	—	3	2	no	—
413	#532	—	3	2	no	—
414	#525	—	3	4	no	—
415	#525	—	3	4	no	—
416	C₂×#117	—	3	1	no	—
417	C₂²×C₃×C₅	—	2	2	no	—
418	C₂²×C₃×C₅	—	2	2	no	—
419	C₂²×C₃×C₅	—	2	4	no	—
420	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
421	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	2	2	no	—
424	C₂×C₅×D₃	—	2	4	no	—
425	C₂×C₅×D₃	—	2	2	no	—
426	C₂×C₅×D₃	—	2	4	no	—
427	C₂×C₅×D₃	—	2	8	no	—
428	C₂×C₅×D₃	—	4	4	no	—
429	C₂×C₅×D₃	—	4	8	no	—
430	C₂×C₅×D₃	—	4	8	no	—
431	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
432	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	4	no	—
435	C₃×C₄×C₅	—	2	4	no	—
436	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
437	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
438	C₅×Dic₃	—	2	2	no	—
439	C₅×Dic₃	—	2	4	no	—
440	C₅×Dic₃	C₂²×D₄	1	2	yes	—
441	C₅×Dic₃	C₂²×D₄	1	2	yes	—
442	C₂³×D₃	C₂³×C₅	1	2	yes	—
443	C₂³×D₃	C₂³×C₅	1	2	yes	—
444	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
445	C₃×#41	—	2	4	no	—
446	C₂×C₃×Q₈	—	2	4	no	—
447	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
448	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
449	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
451	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
453	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
454	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
455	C₂×#67	C₂³×C₅	1	2	yes	—
456	C₂×#67	C₂³×C₅	1	2	yes	—
457	C₂×#67	C₂³×C₅	1	2	yes	—
458	C₂×#67	C₂³×C₅	1	8	yes	—
459	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
460	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
461	#239	—	2	8	no	—
462	#239	—	2	8	no	—
463	#239	—	2	8	no	—
464	#239	—	2	8	no	—
465	#239	—	2	4	no	—
466	D₃×Q₈	—	2	4	no	—
467	#237	—	2	8	no	—
468	#237	—	2	4	no	—
469	D₃×D₄	—	2	8	no	—
470	D₃×D₄	—	2	4	no	—
471	#235	—	2	4	no	—
472	#235	—	2	8	no	—
473	C₂×D₁₂	—	2	8	no	—
474	C₂×D₁₂	—	2	4	no	—
475	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
476	C₂×D₁₂	C₂³×C₅	1	2	yes	—
477	C₂×D₁₂	C₂³×C₅	1	4	yes	—
478	C₂×D₁₂	C₂³×C₅	1	4	yes	—
479	C₂×D₁₂	C₂³×C₅	1	2	yes	—
480	C₂×D₁₂	C₂³×C₅	1	2	yes	—
481	C₂×D₁₂	C₂³×C₅	1	8	yes	—
482	C₂×C₄×D₃	—	2	8	no	—
483	C₂×C₄×D₃	—	2	8	no	—
484	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
485	C₂×C₄×D₃	C₂³×C₅	1	4	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	2	yes	—
490	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
491	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
493	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
494	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
495	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
496	C₂×Dic₆	C₂³×C₅	1	2	yes	—
497	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
498	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
501	C₃×C₄²	C₂³×C₅	1	2	yes	—
502	#217	C₂³×C₅	1	2	yes	—
503	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
504	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
505	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
506	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
507	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
508	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
509	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
510	C₄×Dic₃	C₂³×C₅	1	2	yes	—
511	C₄×Dic₃	C₂³×C₅	1	4	yes	—
512	C₂³×C₅	—	3	1	no	—
513	C₂³×C₅	—	3	1	no	—
514	C₂³×C₅	—	3	4	no	—
515	C₂³×C₅	—	3	2	no	—
516	C₂³×C₅	—	3	4	no	—
517	C₂³×C₅	—	6	4	no	—
518	C₂³×C₅	—	6	4	no	—
519	C₂³×C₅	—	12	2	no	—
520	C₂³×C₅	—	12	4	no	—
521	C₂³×C₅	—	12	4	no	—
522	C₂³×C₅	C₂³×D₃	1	2	yes	—
523	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
524	C₅×Q₈	—	2	4	no	—
525	C₅×Q₈	—	2	4	no	—
526	C₅×Q₈	—	2	2	no	—
527	C₅×Q₈	—	6	4	no	—
528	C₅×Q₈	—	6	2	no	—
529	C₅×D₄	—	2	4	no	—
530	C₅×D₄	—	2	2	no	—
531	C₅×D₄	—	6	4	no	—
532	C₅×D₄	—	6	8	no	—
533	C₅×D₄	—	6	8	no	—
534	C₅×D₄	—	6	4	no	—
535	C₅×D₄	—	6	4	no	—
536	C₅×D₄	—	6	4	no	—
537	C₅×D₄	—	6	4	no	—
538	C₅×D₄	—	6	4	no	—
539	C₅×D₄	—	6	2	no	—
540	C₅×D₄	—	12	8	no	—
541	C₅×D₄	—	12	8	no	—
542	C₂×C₄×C₅	—	2	4	no	—
543	C₂×C₄×C₅	—	2	4	no	—
544	C₂×C₄×C₅	—	3	4	no	—
545	C₂×C₄×C₅	—	3	1	no	—
546	C₂×C₄×C₅	—	3	1	no	—
547	C₂×C₄×C₅	—	3	4	no	—
548	C₂×C₄×C₅	—	3	4	no	—
549	C₂×C₄×C₅	—	3	4	no	—
550	C₂×C₄×C₅	—	3	4	no	—
551	C₂×C₄×C₅	—	3	4	no	—
552	C₂×C₄×C₅	—	3	2	no	—
553	C₂×C₄×C₅	—	6	4	no	—
554	C₂×C₄×C₅	—	6	8	no	—
555	C₂×C₄×C₅	—	6	8	no	—
556	C₂×C₄×C₅	—	6	4	no	—
557	C₂×C₄×C₅	—	6	4	no	—
558	C₂×C₄×C₅	—	6	4	no	—
559	C₂×C₄×C₅	—	12	4	no	—
560	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
561	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
562	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
563	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
564	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
565	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
566	C₂×#41	—	3	2	no	—
567	C₂×#41	—	3	1	no	—
568	C₂×#41	—	3	2	no	—
569	C₂×#41	—	3	2	no	—
570	C₂×#41	—	3	2	no	—
571	C₂×#41	—	3	2	no	—
572	C₂×#41	—	3	1	no	—
573	C₂×#41	—	3	1	no	—
574	C₂×#41	—	3	2	no	—
575	C₂×#41	—	6	8	no	—
576	C₂×#41	—	6	8	no	—
577	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
578	C₂²×Q₈	—	3	1	no	—
579	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
580	C₂²×D₄	—	3	2	no	—
581	C₂²×D₄	—	3	1	no	—
582	C₂²×D₄	—	3	2	no	—
583	C₂²×D₄	—	3	1	no	—
584	C₂³×C₄	—	3	1	no	—
585	C₂³×C₄	—	3	2	no	—
586	C₂³×C₄	—	3	2	no	—
587	C₄⋊Q₈	—	3	2	no	—
588	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
589	#127	—	3	2	no	—
590	#127	—	3	2	no	—
591	#124	—	3	2	no	—
592	#124	—	3	2	no	—
593	#124	—	3	2	no	—
594	#124	C₂×C₅×D₃	1	2	yes	complemented
595	#123	—	3	4	no	—
596	#123	—	3	8	no	—
597	#123	C₂×C₅×D₃	1	4	yes	complemented
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	—	3	8	no	—
600	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
601	#121	—	3	4	no	—
602	#121	—	3	4	no	—
603	#121	—	3	8	no	—
604	#121	—	3	8	no	—
605	#121	—	3	8	no	—
606	#120	—	3	4	no	—
607	#120	—	3	8	no	—
608	#120	—	3	4	no	—
609	C₄×D₄	—	3	8	no	—
610	C₄×D₄	—	3	8	no	—
611	#117	—	3	1	no	—
612	#117	—	3	2	no	—
613	#117	—	3	2	no	—
614	#117	—	3	2	no	—
615	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
616	C₂×C₄⋊C₄	—	3	2	no	—
617	C₂×C₂²⋊C₄	—	3	2	no	—
618	C₂×C₄²	—	3	2	no	—
619	C₂×C₃×C₅	—	2	2	no	—
620	C₂×C₃×C₅	—	4	2	no	—
621	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
622	C₂×C₃×C₅	#585	1	2	yes	—
623	C₅×D₃	—	2	2	no	—
624	C₅×D₃	—	2	2	no	—
625	C₅×D₃	—	4	4	no	—
626	C₅×D₃	—	4	2	no	—
627	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
628	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
629	C₂²×D₃	—	2	4	no	—
630	C₂²×D₃	—	2	4	no	—
631	C₂²×D₃	—	4	2	no	—
632	C₂²×D₃	—	4	4	no	—
633	C₂²×D₃	—	4	4	no	—
634	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
635	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
636	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
637	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
638	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
639	C₃×Q₈	—	2	2	no	—
640	C₃×Q₈	—	2	4	no	—
641	C₃×Q₈	—	2	4	no	—
642	C₃×D₄	—	2	4	no	—
643	C₃×D₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	4	no	—
645	C₂×C₃×C₄	—	2	4	no	—
646	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
647	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
648	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
649	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
650	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
651	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
652	#67	—	2	4	no	—
653	#67	—	2	4	no	—
654	#67	—	2	4	no	—
655	#67	—	4	8	no	—
656	C₂×Dic₃	—	2	4	no	—
657	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
658	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
659	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
660	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
661	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
662	D₁₂	—	2	8	no	—
663	D₁₂	—	2	8	no	—
664	D₁₂	—	2	4	no	—
665	D₁₂	—	2	4	no	—
666	D₁₂	—	2	4	no	—
667	D₁₂	—	2	2	no	—
668	D₁₂	—	4	8	no	—
669	C₄×D₃	—	2	4	no	—
670	C₄×D₃	—	2	4	no	—
671	C₄×D₃	—	2	4	no	—
672	C₄×D₃	—	2	8	no	—
673	C₄×D₃	—	2	8	no	—
674	C₄×D₃	—	4	4	no	—
675	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
676	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
677	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
678	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
679	Dic₆	—	2	2	no	—
680	Dic₆	—	2	4	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	2	4	no	—
684	C₂²×C₅	—	3	2	no	—
685	C₂²×C₅	—	3	2	no	—
686	C₂²×C₅	—	6	2	no	—
687	C₂²×C₅	—	6	2	no	—
688	C₂²×C₅	—	6	4	no	—
689	C₂²×C₅	—	6	2	no	—
690	C₂²×C₅	—	6	4	no	—
691	C₂²×C₅	—	6	8	no	—
692	C₂²×C₅	—	12	4	no	—
693	C₂²×C₅	—	12	8	no	—
694	C₂²×C₅	—	12	8	no	—
695	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
696	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	4	no	—
699	C₄×C₅	—	2	4	no	—
700	C₄×C₅	—	3	2	no	—
701	C₄×C₅	—	3	2	no	—
702	C₄×C₅	—	6	2	no	—
703	C₄×C₅	—	6	4	no	—
704	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
705	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
706	C₂⁴	—	3	1	no	—
707	C₂⁴	—	3	2	no	—
708	C₂⁴	—	3	2	no	—
709	#41	—	2	4	no	—
710	#41	—	6	8	no	—
711	#41	—	6	8	no	—
712	#41	—	6	4	no	—
713	#41	—	6	8	no	—
714	#41	—	6	8	no	—
715	#41	—	6	8	no	—
716	#41	—	6	8	no	—
717	#41	—	6	4	no	—
718	#41	—	6	4	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	3	2	no	—
721	C₂×Q₈	—	3	1	no	—
722	C₂×Q₈	—	6	4	no	—
723	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
724	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
725	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
726	C₂×D₄	—	3	2	no	—
727	C₂×D₄	—	3	2	no	—
728	C₂×D₄	—	3	2	no	—
729	C₂×D₄	—	3	8	no	—
730	C₂×D₄	—	3	4	no	—
731	C₂×D₄	—	3	2	no	—
732	C₂×D₄	—	3	4	no	—
733	C₂×D₄	—	3	2	no	—
734	C₂×D₄	—	3	1	no	—
735	C₂×D₄	—	3	2	no	—
736	C₂×D₄	—	3	8	no	—
737	C₂×D₄	—	6	8	no	—
738	C₂×D₄	—	6	4	no	—
739	C₂×D₄	—	6	8	no	—
740	C₂×D₄	—	6	4	no	—
741	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
742	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
743	C₂²×C₄	—	3	1	no	—
744	C₂²×C₄	—	3	8	no	—
745	C₂²×C₄	—	3	1	no	—
746	C₂²×C₄	—	3	1	no	—
747	C₂²×C₄	—	3	1	no	—
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	3	2	no	—
750	C₂²×C₄	—	3	2	no	—
751	C₂²×C₄	—	3	4	no	—
752	C₂²×C₄	—	3	4	no	—
753	C₂²×C₄	—	3	2	no	—
754	C₂²×C₄	—	3	2	no	—
755	C₂²×C₄	—	3	4	no	—
756	C₂²×C₄	—	6	8	no	—
757	C₂²×C₄	—	6	8	no	—
758	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
759	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
760	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
761	C₄⋊C₄	—	3	4	no	—
762	C₄⋊C₄	—	3	2	no	—
763	C₄⋊C₄	—	3	8	no	—
764	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
765	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
766	C₂²⋊C₄	—	3	2	no	—
767	C₂²⋊C₄	—	3	4	no	—
768	C₂²⋊C₄	—	3	8	no	—
769	C₂²⋊C₄	—	3	8	no	—
770	C₂²⋊C₄	—	3	8	no	—
771	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
772	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
773	C₄²	—	3	4	no	—
774	C₄²	—	3	2	no	—
775	C₄²	C₂²×C₅×D₃	1	2	yes	—
776	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	4	no	—
780	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
781	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
782	C₂×D₃	—	2	2	no	—
783	C₂×D₃	—	2	2	no	—
784	C₂×D₃	—	2	4	no	—
785	C₂×D₃	—	2	2	no	—
786	C₂×D₃	—	2	4	no	—
787	C₂×D₃	—	2	8	no	—
788	C₂×D₃	—	4	4	no	—
789	C₂×D₃	—	4	8	no	—
790	C₂×D₃	—	4	8	no	—
791	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
792	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	4	no	—
795	C₃×C₄	—	2	4	no	—
796	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
797	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
798	Dic₃	—	2	2	no	—
799	Dic₃	—	2	4	no	—
800	Dic₃	C₂²×C₅×D₄	1	2	yes	—
801	Dic₃	C₂²×C₅×D₄	1	2	yes	—
802	C₂×C₅	—	2	2	no	—
803	C₂×C₅	—	4	2	no	—
804	C₂×C₅	—	6	2	no	—
805	C₂×C₅	—	6	2	no	—
806	C₂×C₅	—	12	4	no	—
807	C₂×C₅	—	12	2	no	—
808	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
809	C₂×C₅	#5968	1	2	yes	—
810	C₂³	—	3	1	no	—
811	C₂³	—	3	1	no	—
812	C₂³	—	3	4	no	—
813	C₂³	—	3	2	no	—
814	C₂³	—	3	4	no	—
815	C₂³	—	6	4	no	—
816	C₂³	—	6	4	no	—
817	C₂³	—	12	2	no	—
818	C₂³	—	12	4	no	—
819	C₂³	—	12	4	no	—
820	C₂³	C₂³×C₅×D₃	1	2	yes	—
821	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
822	Q₈	—	2	4	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	6	4	no	—
826	Q₈	—	6	2	no	—
827	D₄	—	2	4	no	—
828	D₄	—	2	2	no	—
829	D₄	—	6	4	no	—
830	D₄	—	6	8	no	—
831	D₄	—	6	8	no	—
832	D₄	—	6	4	no	—
833	D₄	—	6	4	no	—
834	D₄	—	6	4	no	—
835	D₄	—	6	4	no	—
836	D₄	—	6	2	no	—
837	D₄	—	6	4	no	—
838	D₄	—	12	8	no	—
839	D₄	—	12	8	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	3	4	no	—
843	C₂×C₄	—	3	1	no	—
844	C₂×C₄	—	3	1	no	—
845	C₂×C₄	—	3	4	no	—
846	C₂×C₄	—	3	4	no	—
847	C₂×C₄	—	3	4	no	—
848	C₂×C₄	—	3	4	no	—
849	C₂×C₄	—	3	4	no	—
850	C₂×C₄	—	3	2	no	—
851	C₂×C₄	—	6	4	no	—
852	C₂×C₄	—	6	8	no	—
853	C₂×C₄	—	6	8	no	—
854	C₂×C₄	—	6	4	no	—
855	C₂×C₄	—	6	4	no	—
856	C₂×C₄	—	6	4	no	—
857	C₂×C₄	—	12	4	no	—
858	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
859	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
860	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
861	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
862	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
863	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
864	C₂×C₃	—	2	2	no	—
865	C₂×C₃	—	4	2	no	—
866	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
867	C₂×C₃	C₅×#585	1	2	yes	—
868	D₃	—	2	2	no	—
869	D₃	—	2	2	no	—
870	D₃	—	4	4	no	—
871	D₃	—	4	2	no	—
872	C₅	#86338	1	1	yes	characteristic, direct product factor, Sylow
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	3	2	no	—
877	C₂²	—	3	2	no	—
878	C₂²	—	6	2	no	—
879	C₂²	—	6	2	no	—
880	C₂²	—	6	4	no	—
881	C₂²	—	6	2	no	—
882	C₂²	—	6	4	no	—
883	C₂²	—	6	8	no	—
884	C₂²	—	12	4	no	—
885	C₂²	—	12	8	no	—
886	C₂²	—	12	8	no	—
887	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
888	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	3	2	no	—
893	C₄	—	3	2	no	—
894	C₄	—	6	2	no	—
895	C₄	—	6	4	no	—
896	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
897	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
898	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
899	C₂	—	2	2	no	—
900	C₂	—	4	2	no	—
901	C₂	—	6	2	no	—
902	C₂	—	6	2	no	—
903	C₂	—	12	4	no	—
904	C₂	—	12	2	no	—
905	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
906	C₂	C₅×#5968	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
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₅×#3449
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
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₂²×C₅×#239	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₅×#5830	C₂	semidirect
5. C₅×#5816	C₂	semidirect
6. C₅×#5725	C₂	semidirect
7. C₅×#5724	C₂	semidirect
8. C₅×#5674	C₂	semidirect
9. C₅×#5668	C₂	semidirect
10. C₅×#5656	C₂	semidirect
11. C₅×#5653	C₂	semidirect
12. C₅×#5629	C₂	semidirect
13. C₅×#5627	C₂	semidirect
14. C₅×#5525	C₂	semidirect
15. C₅×D₃×#117	C₂	semidirect
18. C₂²×C₃×C₅×Q₈	C₂²	semidirect
23. C₂×C₅×#239	C₂²	semidirect
24. C₂×C₅×#239	C₂²	semidirect
25. C₂×C₅×#239	C₂²	semidirect
26. C₂×C₅×D₃×Q₈	C₂²	semidirect
28. C₂×C₅×#237	C₂²	semidirect
30. C₂×C₅×D₃×D₄	C₂²	semidirect
32. C₂×C₅×#235	C₂²	semidirect
34. C₂²×C₅×D₁₂	C₂²	semidirect
36. C₂²×C₄×C₅×D₃	C₂²	semidirect
37. C₂²×C₄×C₅×D₃	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×#947	C₂²	semidirect
45. C₅×#946	C₂²	semidirect
46. C₅×#944	C₂²	semidirect
47. C₅×#940	C₂²	semidirect
48. C₅×#937	C₂²	semidirect
49. C₅×#930	C₂²	semidirect
50. C₅×#929	C₂²	semidirect
51. C₅×#926	C₂²	semidirect
52. C₅×#896	C₂²	semidirect
53. C₅×#895	C₂²	semidirect
54. C₅×#895	C₂²	semidirect
55. C₅×#894	C₂²	semidirect
56. C₅×#893	C₂²	semidirect
57. C₅×#892	C₂²	semidirect
58. C₅×D₃×C₄⋊C₄	C₂²	semidirect
59. C₅×#884	C₂²	semidirect
60. C₅×#884	C₂²	semidirect
61. C₅×#882	C₂²	semidirect
62. C₅×#882	C₂²	semidirect
63. C₅×#67⋊C₄	C₂²	semidirect
65. C₅×#877	C₂²	semidirect
66. C₅×#875	C₂²	semidirect
67. C₅×#874	C₂²	semidirect
68. C₅×#872	C₂²	semidirect
69. C₄²×C₅×D₃	C₂²	semidirect
70. #86338	C₅	direct (N × H)
76. C₅×#536	D₃	semidirect
128. C₂×C₄×C₅×D₃	D₄	semidirect
156. C₂×D₃×#41	C₂×C₅	semidirect
157. C₂²×#239	C₂×C₅	semidirect
158. C₃×#536	C₂×C₅	semidirect
159. #5830	C₂×C₅	semidirect
160. #5816	C₂×C₅	semidirect
161. #5725	C₂×C₅	semidirect
162. #5724	C₂×C₅	semidirect
163. #5674	C₂×C₅	semidirect
164. #5668	C₂×C₅	semidirect
165. #5656	C₂×C₅	semidirect
166. #5653	C₂×C₅	semidirect
167. #5629	C₂×C₅	semidirect
168. #5627	C₂×C₅	semidirect
169. #5525	C₂×C₅	semidirect
170. D₃×#117	C₂×C₅	semidirect
184. C₂²×C₅×Q₈	C₂×D₃	semidirect
193. C₅×C₄⋊Q₈	C₂×D₃	semidirect
199. C₅×#124	C₂×D₃	semidirect
202. C₅×#123	C₂×D₃	semidirect
205. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
220. C₅×#117	C₂×D₃	semidirect
280. C₂²×C₃×Q₈	C₂²×C₅	semidirect
285. C₂×#239	C₂²×C₅	semidirect
286. C₂×#239	C₂²×C₅	semidirect
287. C₂×#239	C₂²×C₅	semidirect
288. C₂×D₃×Q₈	C₂²×C₅	semidirect
290. C₂×#237	C₂²×C₅	semidirect
292. C₂×D₃×D₄	C₂²×C₅	semidirect
294. C₂×#235	C₂²×C₅	semidirect
296. C₂²×D₁₂	C₂²×C₅	semidirect
298. C₂²×C₄×D₃	C₂²×C₅	semidirect
299. C₂²×C₄×D₃	C₂²×C₅	semidirect
300. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
301. C₃×#124	C₂²×C₅	semidirect
302. C₃×#123	C₂²×C₅	semidirect
303. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
304. C₃×#117	C₂²×C₅	semidirect
305. #947	C₂²×C₅	semidirect
306. #947	C₂²×C₅	semidirect
307. #946	C₂²×C₅	semidirect
308. #944	C₂²×C₅	semidirect
309. #940	C₂²×C₅	semidirect
310. #937	C₂²×C₅	semidirect
311. #930	C₂²×C₅	semidirect
312. #929	C₂²×C₅	semidirect
313. #926	C₂²×C₅	semidirect
314. #896	C₂²×C₅	semidirect
315. #895	C₂²×C₅	semidirect
316. #895	C₂²×C₅	semidirect
317. #894	C₂²×C₅	semidirect
318. #893	C₂²×C₅	semidirect
319. #892	C₂²×C₅	semidirect
320. D₃×C₄⋊C₄	C₂²×C₅	semidirect
321. #884	C₂²×C₅	semidirect
322. #884	C₂²×C₅	semidirect
323. #882	C₂²×C₅	semidirect
324. #882	C₂²×C₅	semidirect
325. #67⋊C₄	C₂²×C₅	semidirect
327. #877	C₂²×C₅	semidirect
328. #875	C₂²×C₅	semidirect
329. #874	C₂²×C₅	semidirect
330. #872	C₂²×C₅	semidirect
331. C₄²×D₃	C₂²×C₅	semidirect
407. #536	C₅×D₃	semidirect
484. C₂×C₄×D₃	C₅×D₄	semidirect
579. C₂²×Q₈	C₂×C₅×D₃	semidirect
588. C₄⋊Q₈	C₂×C₅×D₃	semidirect
594. #124	C₂×C₅×D₃	semidirect
597. #123	C₂×C₅×D₃	semidirect
600. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
615. #117	C₂×C₅×D₃	semidirect
776. C₃×C₅	#3449	semidirect
872. C₅	#86338	direct (N × H)
898. C₃	C₅×#3449	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×#239	2
C₃×C₅×#536	2
C₅×#5830	2
C₅×#5816	2
C₅×#5725	2
C₅×#5724	2
C₅×#5674	2
C₅×#5668	2
C₅×#5656	2
C₅×#5653	2
C₅×#5629	2
C₅×#5627	2
C₅×#5525	2
C₅×D₃×#117	2
C₅×#3449	3
#86338	5

Subgroups — C5×#86338 #14480647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86338 #14480647