Subgroups — C₅×#86427 #14481505

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5710	C₂	1	2	yes	maximal, complemented
3	C₅×#5706	C₂	1	2	yes	maximal, complemented
4	C₅×#5696	C₂	1	2	yes	maximal, complemented
5	C₅×#5691	C₂	1	2	yes	maximal, complemented
6	C₅×#5665	C₂	1	2	yes	maximal, complemented
7	C₅×#5663	C₂	1	2	yes	maximal, complemented
8	C₅×#5656	C₂	1	2	yes	maximal, complemented
9	C₅×#5649	C₂	1	2	yes	maximal, complemented
10	C₅×#5644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5640	C₂	1	2	yes	maximal, complemented
12	C₅×#5624	C₂	1	2	yes	maximal, complemented
13	C₅×#5622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5596	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5560	C₂	1	2	yes	maximal, complemented
17	C₄×C₅×#237	C₂	1	2	yes	maximal, complemented
18	C₅×#5515	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3455	—	3	1	no	maximal, Hall
21	C₂×C₅×#237	C₂²	1	2	yes	—
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₃×C₅×#126	C₂²	1	2	yes	complemented
24	C₃×C₅×#125	C₂²	1	2	yes	complemented
25	C₃×C₅×#123	C₂²	1	2	yes	—
26	C₃×C₅×#123	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₃×C₅×#121	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×#947	C₂²	1	2	yes	—
33	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
34	C₅×#944	C₂²	1	1	yes	characteristic, complemented
35	C₅×#940	C₂²	1	1	yes	characteristic, complemented
36	C₅×#939	C₂²	1	2	yes	—
37	C₅×#939	C₂²	1	2	yes	—
38	C₅×#937	C₂²	1	2	yes	—
39	C₅×D₄×Dic₃	C₂²	1	2	yes	—
40	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₅×#930	C₂²	1	2	yes	—
42	C₅×#930	C₂²	1	1	yes	characteristic
43	C₅×#929	C₂²	1	2	yes	—
44	C₅×#929	C₂²	1	2	yes	—
45	C₄×C₅×#67	C₂²	1	2	yes	—
46	C₄×C₅×#67	C₂²	1	2	yes	complemented
47	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
50	C₅×#924	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
54	C₅×#898	C₂²	1	2	yes	—
55	C₅×#898	C₂²	1	2	yes	—
56	C₅×#898	C₂²	1	2	yes	—
57	C₅×#898	C₂²	1	2	yes	complemented
58	C₅×#898	C₂²	1	2	yes	complemented
59	C₅×#897	C₂²	1	2	yes	complemented
60	C₅×#896	C₂²	1	2	yes	—
61	C₅×#896	C₂²	1	2	yes	—
62	C₅×#896	C₂²	1	2	yes	complemented
63	C₅×#895	C₂²	1	2	yes	—
64	C₅×#894	C₂²	1	2	yes	—
65	C₅×#894	C₂²	1	2	yes	—
66	C₅×#894	C₂²	1	2	yes	complemented
67	C₅×#893	C₂²	1	2	yes	—
68	C₅×#893	C₂²	1	2	yes	—
69	C₅×#893	C₂²	1	1	yes	characteristic, complemented
70	C₅×#892	C₂²	1	2	yes	—
71	C₅×#892	C₂²	1	2	yes	—
72	C₅×#892	C₂²	1	2	yes	—
73	C₅×#892	C₂²	1	2	yes	—
74	C₅×#892	C₂²	1	2	yes	complemented
75	C₅×#890	C₂²	1	2	yes	complemented
76	C₅×#889	C₂²	1	2	yes	complemented
77	C₅×#889	C₂²	1	2	yes	complemented
78	C₅×#889	C₂²	1	2	yes	complemented
79	C₅×#888	C₂²	1	1	yes	characteristic, complemented
80	C₅×#888	C₂²	1	1	yes	characteristic, complemented
81	C₅×#887	C₂²	1	2	yes	complemented
82	C₅×#887	C₂²	1	2	yes	complemented
83	C₅×#887	C₂²	1	1	yes	characteristic, complemented
84	C₅×#886	C₂²	1	2	yes	—
85	C₅×#886	C₂²	1	2	yes	complemented
86	C₅×#885	C₂²	1	2	yes	—
87	C₅×#885	C₂²	1	2	yes	—
88	C₅×#885	C₂²	1	2	yes	complemented
89	C₅×#884	C₂²	1	2	yes	—
90	C₅×#884	C₂²	1	2	yes	—
91	C₅×#884	C₂²	1	2	yes	—
92	C₅×#883	C₂²	1	2	yes	complemented
93	C₅×#882	C₂²	1	2	yes	—
94	C₅×#67⋊C₄	C₂²	1	2	yes	—
95	C₅×#67⋊C₄	C₂²	1	2	yes	—
96	C₅×#67⋊C₄	C₂²	1	2	yes	—
97	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
98	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
99	C₅×#879	C₂²	1	2	yes	complemented
100	C₅×#878	C₂²	1	2	yes	—
101	C₅×#878	C₂²	1	2	yes	complemented
102	C₅×#877	C₂²	1	2	yes	—
103	C₅×#877	C₂²	1	2	yes	complemented
104	C₅×#876	C₂²	1	2	yes	—
105	C₅×#875	C₂²	1	2	yes	—
106	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
107	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
108	#86427	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#542	—	3	2	no	—
110	C₅×#542	—	3	2	no	—
111	C₅×#541	—	3	2	no	—
112	C₅×#540	—	3	2	no	—
113	C₅×#539	—	3	2	no	—
114	C₅×#539	—	3	1	no	—
115	C₅×#539	D₃	1	1	yes	characteristic, complemented
116	C₅×#538	—	3	1	no	—
117	C₅×#538	—	3	1	no	—
118	C₅×#538	—	3	2	no	—
119	C₅×#533	—	3	1	no	—
120	C₅×#532	—	3	1	no	—
121	C₅×#529	—	3	2	no	—
122	C₅×#529	—	3	2	no	—
123	C₅×#529	—	3	2	no	—
124	C₅×#529	—	3	2	no	—
125	C₅×#525	—	3	2	no	—
126	C₄×C₅×#41	—	3	2	no	—
127	C₂×C₅×#117	—	3	1	no	—
128	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
131	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
133	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
136	C₂×C₅×#67	C₂³	1	2	yes	—
137	C₂×C₅×#67	C₂³	1	2	yes	—
138	C₂×C₅×#67	C₂³	1	2	yes	—
139	C₂×C₅×#67	C₂³	1	2	yes	—
140	C₂×C₅×#67	C₂³	1	2	yes	—
141	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
142	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
143	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
144	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
145	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
146	C₅×#237	—	2	8	no	—
147	C₂×C₅×D₁₂	C₂³	1	2	yes	—
148	C₂×C₅×D₁₂	C₂³	1	2	yes	—
149	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
150	C₂×C₄×C₅×D₃	—	2	4	no	—
151	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
152	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
153	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
154	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
155	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
156	C₂×C₅×Dic₆	C₂³	1	2	yes	—
157	C₂×C₅×Dic₆	C₂³	1	2	yes	—
158	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
159	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₃×C₄²×C₅	C₂³	1	2	yes	—
173	C₅×#217	C₂³	1	2	yes	—
174	C₅×#217	C₂³	1	2	yes	—
175	C₅×#217	C₂³	1	2	yes	—
176	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
177	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
178	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
179	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
180	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
181	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
182	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
183	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
184	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
185	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
186	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
187	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
188	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
189	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
190	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
191	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
192	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
193	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
194	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
195	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
196	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
197	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
198	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
199	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
200	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
201	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
202	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
203	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
204	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
205	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
206	C₄×C₅×Dic₃	C₂³	1	2	yes	—
207	C₄×C₅×Dic₃	C₂³	1	2	yes	—
208	C₄×C₅×Dic₃	C₂³	1	2	yes	—
209	C₄×C₅×Dic₃	C₂³	1	2	yes	—
210	C₄×C₅×Dic₃	C₂³	1	2	yes	—
211	C₄×C₅×Dic₃	C₂³	1	2	yes	—
212	C₄×C₅×Dic₃	C₂³	1	2	yes	—
213	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
214	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
215	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
216	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
217	C₃×#539	C₂×C₅	1	1	yes	characteristic, complemented
218	#5710	C₂×C₅	1	2	yes	complemented
219	#5706	C₂×C₅	1	2	yes	complemented
220	#5696	C₂×C₅	1	2	yes	complemented
221	#5691	C₂×C₅	1	2	yes	complemented
222	#5665	C₂×C₅	1	2	yes	complemented
223	#5663	C₂×C₅	1	2	yes	complemented
224	#5656	C₂×C₅	1	2	yes	complemented
225	#5649	C₂×C₅	1	2	yes	complemented
226	#5644	C₂×C₅	1	1	yes	characteristic, complemented
227	#5640	C₂×C₅	1	2	yes	complemented
228	#5624	C₂×C₅	1	2	yes	complemented
229	#5622	C₂×C₅	1	1	yes	characteristic, complemented
230	#5617	C₂×C₅	1	1	yes	characteristic, complemented
231	#5596	C₂×C₅	1	1	yes	characteristic, complemented
232	#5560	C₂×C₅	1	2	yes	complemented
233	C₄×#237	C₂×C₅	1	2	yes	complemented
234	#5515	C₂×C₅	1	1	yes	characteristic, complemented
235	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
236	C₂×C₅×#41	—	3	2	no	—
237	C₂³×C₄×C₅	—	3	1	no	—
238	C₅×C₄⋊Q₈	—	3	1	no	—
239	C₅×C₄⋊Q₈	—	3	1	no	—
240	C₅×C₄⋊Q₈	—	3	1	no	—
241	C₅×#127	—	3	1	no	—
242	C₅×#126	—	3	2	no	—
243	C₅×#126	—	3	2	no	—
244	C₅×#126	—	3	2	no	—
245	C₅×#126	—	3	2	no	—
246	C₅×#126	—	3	2	no	—
247	C₅×#126	—	3	2	no	—
248	C₅×#126	—	3	2	no	—
249	C₅×#126	C₂×D₃	1	2	yes	complemented
250	C₅×#125	—	3	2	no	—
251	C₅×#125	—	3	2	no	—
252	C₅×#125	—	3	2	no	—
253	C₅×#125	—	3	2	no	—
254	C₅×#125	C₂×D₃	1	2	yes	complemented
255	C₅×#124	—	3	2	no	—
256	C₅×#124	—	3	2	no	—
257	C₅×#124	—	3	2	no	—
258	C₅×#124	—	3	2	no	—
259	C₅×#124	—	3	2	no	—
260	C₅×#123	—	3	2	no	—
261	C₅×#123	—	3	2	no	—
262	C₅×#123	—	3	2	no	—
263	C₅×#123	—	3	2	no	—
264	C₅×#123	—	3	2	no	—
265	C₅×#123	—	3	2	no	—
266	C₅×#123	—	3	2	no	—
267	C₅×#123	—	3	2	no	—
268	C₅×#123	C₂×D₃	1	2	yes	—
269	C₅×#123	C₂×D₃	1	2	yes	complemented
270	C₅×C₂²⋊Q₈	—	3	1	no	—
271	C₅×C₂²⋊Q₈	—	3	2	no	—
272	C₅×C₂²⋊Q₈	—	3	2	no	—
273	C₅×C₂²⋊Q₈	—	3	2	no	—
274	C₅×C₂²⋊Q₈	—	3	2	no	—
275	C₅×C₂²⋊Q₈	—	3	2	no	—
276	C₅×C₂²⋊Q₈	—	3	2	no	—
277	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
278	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
279	C₅×#121	—	3	2	no	—
280	C₅×#121	—	3	2	no	—
281	C₅×#121	—	3	2	no	—
282	C₅×#121	—	3	1	no	—
283	C₅×#121	—	3	2	no	—
284	C₅×#121	—	3	2	no	—
285	C₅×#121	—	3	2	no	—
286	C₅×#121	—	3	2	no	—
287	C₅×#121	C₂×D₃	1	1	yes	characteristic
288	C₅×#120	—	3	2	no	—
289	C₅×#120	—	3	2	no	—
290	C₄×C₅×Q₈	—	3	1	no	—
291	C₄×C₅×Q₈	—	3	2	no	—
292	C₄×C₅×Q₈	—	3	1	no	—
293	C₄×C₅×Q₈	—	3	2	no	—
294	C₄×C₅×Q₈	—	3	2	no	—
295	C₄×C₅×D₄	—	3	2	no	—
296	C₄×C₅×D₄	—	3	1	no	—
297	C₄×C₅×D₄	—	3	2	no	—
298	C₄×C₅×D₄	—	3	2	no	—
299	C₄×C₅×D₄	—	3	2	no	—
300	C₄×C₅×D₄	—	3	2	no	—
301	C₄×C₅×D₄	—	3	1	no	—
302	C₄×C₅×D₄	—	3	2	no	—
303	C₄×C₅×D₄	—	3	2	no	—
304	C₄×C₅×D₄	—	3	2	no	—
305	C₄×C₅×D₄	—	3	2	no	—
306	C₄×C₅×D₄	—	3	2	no	—
307	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
308	C₅×#117	—	3	2	no	—
309	C₅×#117	—	3	2	no	—
310	C₅×#117	—	3	2	no	—
311	C₅×#117	—	3	2	no	—
312	C₅×#117	—	3	2	no	—
313	C₅×#117	—	3	2	no	—
314	C₅×#117	—	3	2	no	—
315	C₂×C₅×C₄⋊C₄	—	3	1	no	—
316	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
317	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
318	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
319	C₂×C₄²×C₅	—	3	1	no	—
320	C₂×C₄²×C₅	—	3	1	no	—
321	C₂×C₄²×C₅	—	3	2	no	—
322	C₂×C₄²×C₅	—	3	2	no	—
323	#3455	—	3	1	no	Sylow
324	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
325	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
326	C₂²×C₅×D₃	—	2	2	no	—
327	C₂²×C₅×D₃	—	4	1	no	—
328	C₂²×C₅×D₃	—	4	1	no	—
329	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
330	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
331	C₃×C₅×Q₈	—	4	1	no	—
332	C₃×C₅×D₄	—	2	4	no	—
333	C₃×C₅×D₄	—	4	1	no	—
334	C₂×C₃×C₄×C₅	—	2	2	no	—
335	C₂×C₃×C₄×C₅	—	4	1	no	—
336	C₂×C₃×C₄×C₅	—	4	1	no	—
337	C₂×C₃×C₄×C₅	—	4	2	no	—
338	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
339	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
340	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
342	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
343	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
344	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
345	C₅×#67	—	2	4	no	—
346	C₅×#67	—	2	4	no	—
347	C₅×#67	—	4	2	no	—
348	C₅×#67	—	4	2	no	—
349	C₅×#67	—	4	2	no	—
350	C₂×C₅×Dic₃	—	2	4	no	—
351	C₂×C₅×Dic₃	—	4	1	no	—
352	C₂×C₅×Dic₃	—	4	2	no	—
353	C₂×C₅×Dic₃	—	4	1	no	—
354	C₂×C₅×Dic₃	#41	1	4	yes	—
355	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
356	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
357	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
358	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
360	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
363	C₅×D₁₂	—	4	2	no	—
364	C₅×D₁₂	—	4	1	no	—
365	C₅×D₁₂	—	4	2	no	—
366	C₄×C₅×D₃	—	2	4	no	—
367	C₄×C₅×D₃	—	2	4	no	—
368	C₄×C₅×D₃	—	2	4	no	—
369	C₄×C₅×D₃	—	4	2	no	—
370	C₄×C₅×D₃	—	4	2	no	—
371	C₅×Dic₆	—	2	4	no	—
372	C₅×Dic₆	—	4	2	no	—
373	C₅×Dic₆	—	4	1	no	—
374	C₂×#237	C₂²×C₅	1	2	yes	—
375	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
376	C₃×#126	C₂²×C₅	1	2	yes	complemented
377	C₃×#125	C₂²×C₅	1	2	yes	complemented
378	C₃×#123	C₂²×C₅	1	2	yes	—
379	C₃×#123	C₂²×C₅	1	2	yes	complemented
380	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
382	C₃×#121	C₂²×C₅	1	1	yes	characteristic
383	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
384	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
385	#947	C₂²×C₅	1	2	yes	—
386	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
387	#944	C₂²×C₅	1	1	yes	characteristic, complemented
388	#940	C₂²×C₅	1	1	yes	characteristic, complemented
389	#939	C₂²×C₅	1	2	yes	—
390	#939	C₂²×C₅	1	2	yes	—
391	#937	C₂²×C₅	1	2	yes	—
392	D₄×Dic₃	C₂²×C₅	1	2	yes	—
393	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
394	#930	C₂²×C₅	1	1	yes	characteristic
395	#930	C₂²×C₅	1	2	yes	—
396	#929	C₂²×C₅	1	2	yes	—
397	#929	C₂²×C₅	1	2	yes	—
398	C₄×#67	C₂²×C₅	1	2	yes	—
399	C₄×#67	C₂²×C₅	1	2	yes	complemented
400	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
401	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
402	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
403	#924	C₂²×C₅	1	1	yes	characteristic
404	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
405	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
406	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
407	#898	C₂²×C₅	1	2	yes	—
408	#898	C₂²×C₅	1	2	yes	—
409	#898	C₂²×C₅	1	2	yes	—
410	#898	C₂²×C₅	1	2	yes	complemented
411	#898	C₂²×C₅	1	2	yes	complemented
412	#897	C₂²×C₅	1	2	yes	complemented
413	#896	C₂²×C₅	1	2	yes	—
414	#896	C₂²×C₅	1	2	yes	—
415	#896	C₂²×C₅	1	2	yes	complemented
416	#895	C₂²×C₅	1	2	yes	—
417	#894	C₂²×C₅	1	2	yes	—
418	#894	C₂²×C₅	1	2	yes	—
419	#894	C₂²×C₅	1	2	yes	complemented
420	#893	C₂²×C₅	1	2	yes	—
421	#893	C₂²×C₅	1	2	yes	—
422	#893	C₂²×C₅	1	1	yes	characteristic, complemented
423	#892	C₂²×C₅	1	2	yes	—
424	#892	C₂²×C₅	1	2	yes	—
425	#892	C₂²×C₅	1	2	yes	—
426	#892	C₂²×C₅	1	2	yes	—
427	#892	C₂²×C₅	1	2	yes	complemented
428	#890	C₂²×C₅	1	2	yes	complemented
429	#889	C₂²×C₅	1	2	yes	complemented
430	#889	C₂²×C₅	1	2	yes	complemented
431	#889	C₂²×C₅	1	2	yes	complemented
432	#888	C₂²×C₅	1	1	yes	characteristic, complemented
433	#888	C₂²×C₅	1	1	yes	characteristic, complemented
434	#887	C₂²×C₅	1	2	yes	complemented
435	#887	C₂²×C₅	1	2	yes	complemented
436	#887	C₂²×C₅	1	1	yes	characteristic, complemented
437	#886	C₂²×C₅	1	2	yes	—
438	#886	C₂²×C₅	1	2	yes	complemented
439	#885	C₂²×C₅	1	2	yes	—
440	#885	C₂²×C₅	1	2	yes	—
441	#885	C₂²×C₅	1	2	yes	complemented
442	#884	C₂²×C₅	1	2	yes	—
443	#884	C₂²×C₅	1	2	yes	—
444	#884	C₂²×C₅	1	2	yes	—
445	#883	C₂²×C₅	1	2	yes	complemented
446	#882	C₂²×C₅	1	2	yes	—
447	#67⋊C₄	C₂²×C₅	1	2	yes	—
448	#67⋊C₄	C₂²×C₅	1	2	yes	—
449	#67⋊C₄	C₂²×C₅	1	2	yes	—
450	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
451	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
452	#879	C₂²×C₅	1	2	yes	complemented
453	#878	C₂²×C₅	1	2	yes	—
454	#878	C₂²×C₅	1	2	yes	complemented
455	#877	C₂²×C₅	1	2	yes	—
456	#877	C₂²×C₅	1	2	yes	complemented
457	#876	C₂²×C₅	1	2	yes	—
458	#875	C₂²×C₅	1	2	yes	—
459	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
460	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
461	C₂⁴×C₅	—	3	1	no	—
462	C₅×#41	—	6	8	no	—
463	C₂×C₅×Q₈	—	3	2	no	—
464	C₂×C₅×Q₈	—	3	2	no	—
465	C₂×C₅×Q₈	—	3	1	no	—
466	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
467	C₂×C₅×D₄	—	3	2	no	—
468	C₂×C₅×D₄	—	3	2	no	—
469	C₂×C₅×D₄	—	3	2	no	—
470	C₂×C₅×D₄	—	3	2	no	—
471	C₂×C₅×D₄	—	3	2	no	—
472	C₂×C₅×D₄	—	3	2	no	—
473	C₂×C₅×D₄	—	3	2	no	—
474	C₂×C₅×D₄	—	3	1	no	—
475	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
476	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
477	C₂²×C₄×C₅	—	3	1	no	—
478	C₂²×C₄×C₅	—	3	2	no	—
479	C₂²×C₄×C₅	—	3	1	no	—
480	C₂²×C₄×C₅	—	3	1	no	—
481	C₂²×C₄×C₅	—	3	2	no	—
482	C₂²×C₄×C₅	—	3	2	no	—
483	C₂²×C₄×C₅	—	3	2	no	—
484	C₂²×C₄×C₅	—	3	2	no	—
485	C₂²×C₄×C₅	—	3	2	no	—
486	C₂²×C₄×C₅	—	3	2	no	—
487	C₂²×C₄×C₅	—	6	4	no	—
488	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
489	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
490	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
491	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
492	C₅×C₄⋊C₄	—	3	2	no	—
493	C₅×C₄⋊C₄	—	3	2	no	—
494	C₅×C₄⋊C₄	—	3	2	no	—
495	C₅×C₄⋊C₄	—	3	2	no	—
496	C₅×C₄⋊C₄	—	3	2	no	—
497	C₅×C₄⋊C₄	—	3	2	no	—
498	C₅×C₄⋊C₄	—	3	2	no	—
499	C₅×C₄⋊C₄	—	3	2	no	—
500	C₅×C₄⋊C₄	—	3	1	no	—
501	C₅×C₄⋊C₄	—	3	2	no	—
502	C₅×C₄⋊C₄	—	3	2	no	—
503	C₅×C₄⋊C₄	—	3	2	no	—
504	C₅×C₄⋊C₄	—	3	2	no	—
505	C₅×C₄⋊C₄	—	3	2	no	—
506	C₅×C₄⋊C₄	—	3	2	no	—
507	C₅×C₄⋊C₄	—	3	1	no	—
508	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
509	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
510	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
511	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
512	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
513	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
514	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
515	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
516	C₅×C₂²⋊C₄	—	3	2	no	—
517	C₅×C₂²⋊C₄	—	3	2	no	—
518	C₅×C₂²⋊C₄	—	3	2	no	—
519	C₅×C₂²⋊C₄	—	3	2	no	—
520	C₅×C₂²⋊C₄	—	3	2	no	—
521	C₅×C₂²⋊C₄	—	3	2	no	—
522	C₅×C₂²⋊C₄	—	3	2	no	—
523	C₅×C₂²⋊C₄	—	3	2	no	—
524	C₅×C₂²⋊C₄	—	3	2	no	—
525	C₅×C₂²⋊C₄	—	3	2	no	—
526	C₅×C₂²⋊C₄	—	3	2	no	—
527	C₅×C₂²⋊C₄	—	3	2	no	—
528	C₅×C₂²⋊C₄	—	3	2	no	—
529	C₅×C₂²⋊C₄	—	3	2	no	—
530	C₅×C₂²⋊C₄	—	3	2	no	—
531	C₅×C₂²⋊C₄	—	3	2	no	—
532	C₅×C₂²⋊C₄	—	3	2	no	—
533	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
534	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
535	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
536	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
537	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
538	C₄²×C₅	—	3	2	no	—
539	C₄²×C₅	—	3	1	no	—
540	C₄²×C₅	—	3	2	no	—
541	C₄²×C₅	—	3	2	no	—
542	C₄²×C₅	—	3	1	no	—
543	C₄²×C₅	—	3	2	no	—
544	C₄²×C₅	—	3	1	no	—
545	C₄²×C₅	—	3	1	no	—
546	C₄²×C₅	—	3	2	no	—
547	C₄²×C₅	—	3	2	no	—
548	C₄²×C₅	—	3	2	no	—
549	C₄²×C₅	C₂²×D₃	1	2	yes	—
550	#542	—	3	2	no	—
551	#542	—	3	2	no	—
552	#541	—	3	2	no	—
553	#540	—	3	2	no	—
554	#539	—	3	2	no	—
555	#539	—	3	1	no	—
556	#539	C₅×D₃	1	1	yes	characteristic, complemented
557	#538	—	3	1	no	—
558	#538	—	3	1	no	—
559	#538	—	3	2	no	—
560	#533	—	3	1	no	—
561	#532	—	3	1	no	—
562	#529	—	3	2	no	—
563	#529	—	3	2	no	—
564	#529	—	3	2	no	—
565	#529	—	3	2	no	—
566	#525	—	3	2	no	—
567	C₄×#41	—	3	2	no	—
568	C₂×#117	—	3	1	no	—
569	C₂²×C₃×C₅	—	2	1	no	—
570	C₂²×C₃×C₅	—	2	1	no	—
571	C₂²×C₃×C₅	—	2	2	no	—
572	C₂²×C₃×C₅	—	2	2	no	—
573	C₂²×C₃×C₅	—	2	2	no	—
574	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
575	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
576	C₂×C₅×D₃	—	2	2	no	—
577	C₂×C₅×D₃	—	2	2	no	—
578	C₂×C₅×D₃	—	2	2	no	—
579	C₂×C₅×D₃	—	2	2	no	—
580	C₂×C₅×D₃	—	2	2	no	—
581	C₂×C₅×D₃	—	2	2	no	—
582	C₂×C₅×D₃	—	4	4	no	—
583	C₃×C₄×C₅	—	2	2	no	—
584	C₃×C₄×C₅	—	2	2	no	—
585	C₃×C₄×C₅	—	2	2	no	—
586	C₃×C₄×C₅	—	2	1	no	—
587	C₃×C₄×C₅	—	2	2	no	—
588	C₃×C₄×C₅	—	2	1	no	—
589	C₃×C₄×C₅	—	2	2	no	—
590	C₅×Dic₃	—	2	2	no	—
591	C₅×Dic₃	—	2	1	no	—
592	C₅×Dic₃	—	2	2	no	—
593	C₅×Dic₃	—	2	2	no	—
594	C₅×Dic₃	—	2	2	no	—
595	C₅×Dic₃	—	2	1	no	—
596	C₅×Dic₃	C₂×#41	1	2	yes	—
597	C₅×Dic₃	C₂×#41	1	2	yes	—
598	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
600	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
601	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
602	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
603	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
606	C₂×#67	C₂³×C₅	1	2	yes	—
607	C₂×#67	C₂³×C₅	1	2	yes	—
608	C₂×#67	C₂³×C₅	1	2	yes	—
609	C₂×#67	C₂³×C₅	1	2	yes	—
610	C₂×#67	C₂³×C₅	1	2	yes	—
611	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
612	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
613	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
614	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
615	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
616	#237	—	2	8	no	—
617	C₂×D₁₂	C₂³×C₅	1	2	yes	—
618	C₂×D₁₂	C₂³×C₅	1	2	yes	—
619	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
620	C₂×C₄×D₃	—	2	4	no	—
621	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
622	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
623	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
624	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
625	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
626	C₂×Dic₆	C₂³×C₅	1	2	yes	—
627	C₂×Dic₆	C₂³×C₅	1	2	yes	—
628	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
629	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
630	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
631	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
632	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
633	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
634	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
635	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
636	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
637	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
638	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
639	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
640	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
641	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
642	C₃×C₄²	C₂³×C₅	1	2	yes	—
643	#217	C₂³×C₅	1	2	yes	—
644	#217	C₂³×C₅	1	2	yes	—
645	#217	C₂³×C₅	1	2	yes	—
646	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
647	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
648	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
649	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
650	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
651	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
652	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
653	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
654	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
655	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
656	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
657	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
658	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
659	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
660	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
661	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
662	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
663	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
664	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
665	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
666	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
667	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
668	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
669	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
670	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
671	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
672	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
673	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
674	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
675	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
676	C₄×Dic₃	C₂³×C₅	1	2	yes	—
677	C₄×Dic₃	C₂³×C₅	1	2	yes	—
678	C₄×Dic₃	C₂³×C₅	1	2	yes	—
679	C₄×Dic₃	C₂³×C₅	1	2	yes	—
680	C₄×Dic₃	C₂³×C₅	1	2	yes	—
681	C₄×Dic₃	C₂³×C₅	1	2	yes	—
682	C₄×Dic₃	C₂³×C₅	1	2	yes	—
683	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
684	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
685	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
686	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
687	C₂³×C₅	—	3	2	no	—
688	C₂³×C₅	—	3	2	no	—
689	C₂³×C₅	—	6	2	no	—
690	C₂³×C₅	—	12	1	no	—
691	C₂³×C₅	—	12	1	no	—
692	C₂³×C₅	C₂³×D₃	1	2	yes	—
693	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
694	C₅×Q₈	—	4	1	no	—
695	C₅×Q₈	—	6	4	no	—
696	C₅×Q₈	—	12	1	no	—
697	C₅×Q₈	—	12	2	no	—
698	C₅×D₄	—	2	4	no	—
699	C₅×D₄	—	4	1	no	—
700	C₅×D₄	—	6	4	no	—
701	C₅×D₄	—	6	4	no	—
702	C₅×D₄	—	12	1	no	—
703	C₅×D₄	—	12	2	no	—
704	C₅×D₄	—	12	2	no	—
705	C₅×D₄	—	12	2	no	—
706	C₅×D₄	—	12	2	no	—
707	C₅×D₄	—	12	2	no	—
708	C₂×C₄×C₅	—	2	2	no	—
709	C₂×C₄×C₅	—	3	4	no	—
710	C₂×C₄×C₅	—	3	1	no	—
711	C₂×C₄×C₅	—	3	1	no	—
712	C₂×C₄×C₅	—	3	2	no	—
713	C₂×C₄×C₅	—	3	1	no	—
714	C₂×C₄×C₅	—	3	2	no	—
715	C₂×C₄×C₅	—	3	2	no	—
716	C₂×C₄×C₅	—	3	2	no	—
717	C₂×C₄×C₅	—	3	1	no	—
718	C₂×C₄×C₅	—	4	1	no	—
719	C₂×C₄×C₅	—	4	2	no	—
720	C₂×C₄×C₅	—	4	1	no	—
721	C₂×C₄×C₅	—	6	4	no	—
722	C₂×C₄×C₅	—	6	4	no	—
723	C₂×C₄×C₅	—	6	4	no	—
724	C₂×C₄×C₅	—	6	4	no	—
725	C₂×C₄×C₅	—	12	2	no	—
726	C₂×C₄×C₅	—	12	2	no	—
727	C₂×C₄×C₅	—	12	1	no	—
728	C₂×C₄×C₅	—	12	2	no	—
729	C₂×C₄×C₅	—	12	1	no	—
730	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
731	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
732	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
733	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
734	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
735	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
736	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
737	C₂×#41	—	3	2	no	—
738	C₂³×C₄	—	3	1	no	—
739	C₄⋊Q₈	—	3	1	no	—
740	C₄⋊Q₈	—	3	1	no	—
741	C₄⋊Q₈	—	3	1	no	—
742	#127	—	3	1	no	—
743	#126	—	3	2	no	—
744	#126	—	3	2	no	—
745	#126	—	3	2	no	—
746	#126	—	3	2	no	—
747	#126	—	3	2	no	—
748	#126	—	3	2	no	—
749	#126	—	3	2	no	—
750	#126	C₂×C₅×D₃	1	2	yes	complemented
751	#125	—	3	2	no	—
752	#125	—	3	2	no	—
753	#125	—	3	2	no	—
754	#125	—	3	2	no	—
755	#125	C₂×C₅×D₃	1	2	yes	complemented
756	#124	—	3	2	no	—
757	#124	—	3	2	no	—
758	#124	—	3	2	no	—
759	#124	—	3	2	no	—
760	#124	—	3	2	no	—
761	#123	—	3	2	no	—
762	#123	—	3	2	no	—
763	#123	—	3	2	no	—
764	#123	—	3	2	no	—
765	#123	—	3	2	no	—
766	#123	—	3	2	no	—
767	#123	—	3	2	no	—
768	#123	—	3	2	no	—
769	#123	C₂×C₅×D₃	1	2	yes	—
770	#123	C₂×C₅×D₃	1	2	yes	complemented
771	C₂²⋊Q₈	—	3	1	no	—
772	C₂²⋊Q₈	—	3	2	no	—
773	C₂²⋊Q₈	—	3	2	no	—
774	C₂²⋊Q₈	—	3	2	no	—
775	C₂²⋊Q₈	—	3	2	no	—
776	C₂²⋊Q₈	—	3	2	no	—
777	C₂²⋊Q₈	—	3	2	no	—
778	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
780	#121	—	3	2	no	—
781	#121	—	3	2	no	—
782	#121	—	3	2	no	—
783	#121	—	3	1	no	—
784	#121	—	3	2	no	—
785	#121	—	3	2	no	—
786	#121	—	3	2	no	—
787	#121	—	3	2	no	—
788	#121	C₂×C₅×D₃	1	1	yes	characteristic
789	#120	—	3	2	no	—
790	#120	—	3	2	no	—
791	C₄×Q₈	—	3	1	no	—
792	C₄×Q₈	—	3	2	no	—
793	C₄×Q₈	—	3	1	no	—
794	C₄×Q₈	—	3	2	no	—
795	C₄×Q₈	—	3	2	no	—
796	C₄×D₄	—	3	2	no	—
797	C₄×D₄	—	3	1	no	—
798	C₄×D₄	—	3	2	no	—
799	C₄×D₄	—	3	2	no	—
800	C₄×D₄	—	3	2	no	—
801	C₄×D₄	—	3	2	no	—
802	C₄×D₄	—	3	1	no	—
803	C₄×D₄	—	3	2	no	—
804	C₄×D₄	—	3	2	no	—
805	C₄×D₄	—	3	2	no	—
806	C₄×D₄	—	3	2	no	—
807	C₄×D₄	—	3	2	no	—
808	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
809	#117	—	3	2	no	—
810	#117	—	3	2	no	—
811	#117	—	3	2	no	—
812	#117	—	3	2	no	—
813	#117	—	3	2	no	—
814	#117	—	3	2	no	—
815	#117	—	3	2	no	—
816	C₂×C₄⋊C₄	—	3	1	no	—
817	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	—	3	1	no	—
819	C₂×C₂²⋊C₄	—	3	1	no	—
820	C₂×C₄²	—	3	1	no	—
821	C₂×C₄²	—	3	1	no	—
822	C₂×C₄²	—	3	2	no	—
823	C₂×C₄²	—	3	2	no	—
824	C₂×C₃×C₅	—	2	2	no	—
825	C₂×C₃×C₅	—	4	2	no	—
826	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
827	C₂×C₃×C₅	#585	1	1	yes	characteristic
828	C₂×C₃×C₅	#585	1	1	yes	characteristic
829	C₅×D₃	—	4	2	no	—
830	C₅×D₃	—	4	2	no	—
831	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
832	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
833	C₂²×D₃	—	2	2	no	—
834	C₂²×D₃	—	4	1	no	—
835	C₂²×D₃	—	4	1	no	—
836	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
837	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
838	C₃×Q₈	—	4	1	no	—
839	C₃×D₄	—	2	4	no	—
840	C₃×D₄	—	4	1	no	—
841	C₂×C₃×C₄	—	2	2	no	—
842	C₂×C₃×C₄	—	4	1	no	—
843	C₂×C₃×C₄	—	4	1	no	—
844	C₂×C₃×C₄	—	4	2	no	—
845	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
846	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
847	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
848	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
849	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
850	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
851	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
852	#67	—	2	4	no	—
853	#67	—	2	4	no	—
854	#67	—	4	2	no	—
855	#67	—	4	2	no	—
856	#67	—	4	2	no	—
857	C₂×Dic₃	—	2	4	no	—
858	C₂×Dic₃	—	4	1	no	—
859	C₂×Dic₃	—	4	2	no	—
860	C₂×Dic₃	—	4	1	no	—
861	C₂×Dic₃	C₅×#41	1	4	yes	—
862	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
863	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
864	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
865	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
866	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
867	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
868	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
869	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
870	D₁₂	—	4	2	no	—
871	D₁₂	—	4	1	no	—
872	D₁₂	—	4	2	no	—
873	C₄×D₃	—	2	4	no	—
874	C₄×D₃	—	2	4	no	—
875	C₄×D₃	—	2	4	no	—
876	C₄×D₃	—	4	2	no	—
877	C₄×D₃	—	4	2	no	—
878	Dic₆	—	2	4	no	—
879	Dic₆	—	4	2	no	—
880	Dic₆	—	4	1	no	—
881	C₂²×C₅	—	2	1	no	—
882	C₂²×C₅	—	2	1	no	—
883	C₂²×C₅	—	2	2	no	—
884	C₂²×C₅	—	2	2	no	—
885	C₂²×C₅	—	2	2	no	—
886	C₂²×C₅	—	6	2	no	—
887	C₂²×C₅	—	6	2	no	—
888	C₂²×C₅	—	6	2	no	—
889	C₂²×C₅	—	6	2	no	—
890	C₂²×C₅	—	6	2	no	—
891	C₂²×C₅	—	6	2	no	—
892	C₂²×C₅	—	12	4	no	—
893	C₂²×C₅	D₃×#41	1	2	yes	—
894	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
895	C₄×C₅	—	2	2	no	—
896	C₄×C₅	—	2	2	no	—
897	C₄×C₅	—	2	2	no	—
898	C₄×C₅	—	2	1	no	—
899	C₄×C₅	—	2	2	no	—
900	C₄×C₅	—	2	1	no	—
901	C₄×C₅	—	2	2	no	—
902	C₄×C₅	—	3	2	no	—
903	C₄×C₅	—	3	2	no	—
904	C₄×C₅	—	6	2	no	—
905	C₄×C₅	—	6	2	no	—
906	C₄×C₅	—	6	2	no	—
907	C₄×C₅	—	6	1	no	—
908	C₄×C₅	—	6	2	no	—
909	C₄×C₅	—	6	1	no	—
910	C₂⁴	—	3	1	no	—
911	#41	—	6	8	no	—
912	C₂×Q₈	—	3	2	no	—
913	C₂×Q₈	—	3	2	no	—
914	C₂×Q₈	—	3	1	no	—
915	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
916	C₂×D₄	—	3	2	no	—
917	C₂×D₄	—	3	2	no	—
918	C₂×D₄	—	3	2	no	—
919	C₂×D₄	—	3	2	no	—
920	C₂×D₄	—	3	2	no	—
921	C₂×D₄	—	3	2	no	—
922	C₂×D₄	—	3	2	no	—
923	C₂×D₄	—	3	1	no	—
924	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
925	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
926	C₂²×C₄	—	3	1	no	—
927	C₂²×C₄	—	3	2	no	—
928	C₂²×C₄	—	3	1	no	—
929	C₂²×C₄	—	3	1	no	—
930	C₂²×C₄	—	3	2	no	—
931	C₂²×C₄	—	3	2	no	—
932	C₂²×C₄	—	3	2	no	—
933	C₂²×C₄	—	3	2	no	—
934	C₂²×C₄	—	3	2	no	—
935	C₂²×C₄	—	3	2	no	—
936	C₂²×C₄	—	6	4	no	—
937	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
938	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
940	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
941	C₄⋊C₄	—	3	2	no	—
942	C₄⋊C₄	—	3	2	no	—
943	C₄⋊C₄	—	3	2	no	—
944	C₄⋊C₄	—	3	2	no	—
945	C₄⋊C₄	—	3	2	no	—
946	C₄⋊C₄	—	3	2	no	—
947	C₄⋊C₄	—	3	2	no	—
948	C₄⋊C₄	—	3	2	no	—
949	C₄⋊C₄	—	3	1	no	—
950	C₄⋊C₄	—	3	2	no	—
951	C₄⋊C₄	—	3	2	no	—
952	C₄⋊C₄	—	3	2	no	—
953	C₄⋊C₄	—	3	2	no	—
954	C₄⋊C₄	—	3	2	no	—
955	C₄⋊C₄	—	3	2	no	—
956	C₄⋊C₄	—	3	1	no	—
957	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
958	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
959	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
960	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
962	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
963	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
964	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
965	C₂²⋊C₄	—	3	2	no	—
966	C₂²⋊C₄	—	3	2	no	—
967	C₂²⋊C₄	—	3	2	no	—
968	C₂²⋊C₄	—	3	2	no	—
969	C₂²⋊C₄	—	3	2	no	—
970	C₂²⋊C₄	—	3	2	no	—
971	C₂²⋊C₄	—	3	2	no	—
972	C₂²⋊C₄	—	3	2	no	—
973	C₂²⋊C₄	—	3	2	no	—
974	C₂²⋊C₄	—	3	2	no	—
975	C₂²⋊C₄	—	3	2	no	—
976	C₂²⋊C₄	—	3	2	no	—
977	C₂²⋊C₄	—	3	2	no	—
978	C₂²⋊C₄	—	3	2	no	—
979	C₂²⋊C₄	—	3	2	no	—
980	C₂²⋊C₄	—	3	2	no	—
981	C₂²⋊C₄	—	3	2	no	—
982	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
983	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
984	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
985	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
986	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
987	C₄²	—	3	2	no	—
988	C₄²	—	3	1	no	—
989	C₄²	—	3	2	no	—
990	C₄²	—	3	2	no	—
991	C₄²	—	3	1	no	—
992	C₄²	—	3	2	no	—
993	C₄²	—	3	1	no	—
994	C₄²	—	3	1	no	—
995	C₄²	—	3	2	no	—
996	C₄²	—	3	2	no	—
997	C₄²	—	3	2	no	—
998	C₄²	C₂²×C₅×D₃	1	2	yes	—
999	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
1000	C₂²×C₃	—	2	1	no	—
1001	C₂²×C₃	—	2	1	no	—
1002	C₂²×C₃	—	2	2	no	—
1003	C₂²×C₃	—	2	2	no	—
1004	C₂²×C₃	—	2	2	no	—
1005	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
1006	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1007	C₂×D₃	—	2	2	no	—
1008	C₂×D₃	—	2	2	no	—
1009	C₂×D₃	—	2	2	no	—
1010	C₂×D₃	—	2	2	no	—
1011	C₂×D₃	—	2	2	no	—
1012	C₂×D₃	—	2	2	no	—
1013	C₂×D₃	—	4	4	no	—
1014	C₃×C₄	—	2	2	no	—
1015	C₃×C₄	—	2	2	no	—
1016	C₃×C₄	—	2	2	no	—
1017	C₃×C₄	—	2	1	no	—
1018	C₃×C₄	—	2	2	no	—
1019	C₃×C₄	—	2	1	no	—
1020	C₃×C₄	—	2	2	no	—
1021	Dic₃	—	2	2	no	—
1022	Dic₃	—	2	1	no	—
1023	Dic₃	—	2	2	no	—
1024	Dic₃	—	2	2	no	—
1025	Dic₃	—	2	2	no	—
1026	Dic₃	—	2	1	no	—
1027	Dic₃	C₂×C₅×#41	1	2	yes	—
1028	Dic₃	C₂×C₅×#41	1	2	yes	—
1029	C₂×C₅	—	2	2	no	—
1030	C₂×C₅	—	4	2	no	—
1031	C₂×C₅	—	12	2	no	—
1032	C₂×C₅	—	12	2	no	—
1033	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1034	C₂×C₅	#5966	1	1	yes	characteristic
1035	C₂×C₅	#5968	1	1	yes	characteristic
1036	C₂³	—	3	2	no	—
1037	C₂³	—	3	2	no	—
1038	C₂³	—	6	2	no	—
1039	C₂³	—	12	1	no	—
1040	C₂³	—	12	1	no	—
1041	C₂³	C₂³×C₅×D₃	1	2	yes	—
1042	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1043	Q₈	—	4	1	no	—
1044	Q₈	—	6	4	no	—
1045	Q₈	—	12	1	no	—
1046	Q₈	—	12	2	no	—
1047	D₄	—	2	4	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	6	4	no	—
1050	D₄	—	6	4	no	—
1051	D₄	—	12	1	no	—
1052	D₄	—	12	2	no	—
1053	D₄	—	12	2	no	—
1054	D₄	—	12	2	no	—
1055	D₄	—	12	2	no	—
1056	D₄	—	12	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	3	4	no	—
1059	C₂×C₄	—	3	1	no	—
1060	C₂×C₄	—	3	1	no	—
1061	C₂×C₄	—	3	2	no	—
1062	C₂×C₄	—	3	1	no	—
1063	C₂×C₄	—	3	2	no	—
1064	C₂×C₄	—	3	2	no	—
1065	C₂×C₄	—	3	2	no	—
1066	C₂×C₄	—	3	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	6	4	no	—
1071	C₂×C₄	—	6	4	no	—
1072	C₂×C₄	—	6	4	no	—
1073	C₂×C₄	—	6	4	no	—
1074	C₂×C₄	—	12	2	no	—
1075	C₂×C₄	—	12	2	no	—
1076	C₂×C₄	—	12	1	no	—
1077	C₂×C₄	—	12	2	no	—
1078	C₂×C₄	—	12	1	no	—
1079	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1080	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1081	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1082	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1083	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1084	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1085	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1086	C₂×C₃	—	2	2	no	—
1087	C₂×C₃	—	4	2	no	—
1088	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1089	C₂×C₃	C₅×#585	1	1	yes	characteristic
1090	C₂×C₃	C₅×#585	1	1	yes	characteristic
1091	D₃	—	4	2	no	—
1092	D₃	—	4	2	no	—
1093	C₅	#86427	1	1	yes	characteristic, direct product factor, Sylow
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	6	2	no	—
1100	C₂²	—	6	2	no	—
1101	C₂²	—	6	2	no	—
1102	C₂²	—	6	2	no	—
1103	C₂²	—	6	2	no	—
1104	C₂²	—	6	2	no	—
1105	C₂²	—	12	4	no	—
1106	C₂²	C₅×D₃×#41	1	2	yes	—
1107	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	3	2	no	—
1116	C₄	—	3	2	no	—
1117	C₄	—	6	2	no	—
1118	C₄	—	6	2	no	—
1119	C₄	—	6	2	no	—
1120	C₄	—	6	1	no	—
1121	C₄	—	6	2	no	—
1122	C₄	—	6	1	no	—
1123	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
1124	C₂	—	2	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	12	2	no	—
1127	C₂	—	12	2	no	—
1128	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1129	C₂	C₅×#5966	1	1	yes	characteristic
1130	C₂	C₅×#5968	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×#539	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#539	D₃
hypocenter	C₃	C₅×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#539

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#539	C₂	semidirect
2. C₅×#5710	C₂	semidirect
3. C₅×#5706	C₂	semidirect
4. C₅×#5696	C₂	semidirect
5. C₅×#5691	C₂	semidirect
6. C₅×#5665	C₂	semidirect
7. C₅×#5663	C₂	semidirect
8. C₅×#5656	C₂	semidirect
9. C₅×#5649	C₂	semidirect
10. C₅×#5644	C₂	semidirect
11. C₅×#5640	C₂	semidirect
12. C₅×#5624	C₂	semidirect
13. C₅×#5622	C₂	semidirect
14. C₅×#5617	C₂	semidirect
15. C₅×#5596	C₂	semidirect
16. C₅×#5560	C₂	semidirect
17. C₄×C₅×#237	C₂	semidirect
18. C₅×#5515	C₂	semidirect
19. C₂×C₅×#892	C₂	semidirect
23. C₃×C₅×#126	C₂²	semidirect
24. C₃×C₅×#125	C₂²	semidirect
26. C₃×C₅×#123	C₂²	semidirect
28. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₅×Q₈×Dic₃	C₂²	semidirect
34. C₅×#944	C₂²	semidirect
35. C₅×#940	C₂²	semidirect
40. C₅×D₄×Dic₃	C₂²	semidirect
46. C₄×C₅×#67	C₂²	semidirect
53. C₂×C₄×C₅×Dic₃	C₂²	semidirect
57. C₅×#898	C₂²	semidirect
58. C₅×#898	C₂²	semidirect
59. C₅×#897	C₂²	semidirect
62. C₅×#896	C₂²	semidirect
66. C₅×#894	C₂²	semidirect
69. C₅×#893	C₂²	semidirect
74. C₅×#892	C₂²	semidirect
75. C₅×#890	C₂²	semidirect
76. C₅×#889	C₂²	semidirect
77. C₅×#889	C₂²	semidirect
78. C₅×#889	C₂²	semidirect
79. C₅×#888	C₂²	semidirect
80. C₅×#888	C₂²	semidirect
81. C₅×#887	C₂²	semidirect
82. C₅×#887	C₂²	semidirect
83. C₅×#887	C₂²	semidirect
85. C₅×#886	C₂²	semidirect
88. C₅×#885	C₂²	semidirect
92. C₅×#883	C₂²	semidirect
97. C₅×#67⋊C₄	C₂²	semidirect
98. C₅×#67⋊C₄	C₂²	semidirect
99. C₅×#879	C₂²	semidirect
101. C₅×#878	C₂²	semidirect
103. C₅×#877	C₂²	semidirect
106. C₄²×C₅×D₃	C₂²	semidirect
107. C₄×C₅×Dic₆	C₂²	semidirect
108. #86427	C₅	direct (N × H)
115. C₅×#539	D₃	semidirect
217. C₃×#539	C₂×C₅	semidirect
218. #5710	C₂×C₅	semidirect
219. #5706	C₂×C₅	semidirect
220. #5696	C₂×C₅	semidirect
221. #5691	C₂×C₅	semidirect
222. #5665	C₂×C₅	semidirect
223. #5663	C₂×C₅	semidirect
224. #5656	C₂×C₅	semidirect
225. #5649	C₂×C₅	semidirect
226. #5644	C₂×C₅	semidirect
227. #5640	C₂×C₅	semidirect
228. #5624	C₂×C₅	semidirect
229. #5622	C₂×C₅	semidirect
230. #5617	C₂×C₅	semidirect
231. #5596	C₂×C₅	semidirect
232. #5560	C₂×C₅	semidirect
233. C₄×#237	C₂×C₅	semidirect
234. #5515	C₂×C₅	semidirect
235. C₂×#892	C₂×C₅	semidirect
249. C₅×#126	C₂×D₃	semidirect
254. C₅×#125	C₂×D₃	semidirect
269. C₅×#123	C₂×D₃	semidirect
278. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
376. C₃×#126	C₂²×C₅	semidirect
377. C₃×#125	C₂²×C₅	semidirect
379. C₃×#123	C₂²×C₅	semidirect
381. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
386. Q₈×Dic₃	C₂²×C₅	semidirect
387. #944	C₂²×C₅	semidirect
388. #940	C₂²×C₅	semidirect
393. D₄×Dic₃	C₂²×C₅	semidirect
399. C₄×#67	C₂²×C₅	semidirect
406. C₂×C₄×Dic₃	C₂²×C₅	semidirect
410. #898	C₂²×C₅	semidirect
411. #898	C₂²×C₅	semidirect
412. #897	C₂²×C₅	semidirect
415. #896	C₂²×C₅	semidirect
419. #894	C₂²×C₅	semidirect
422. #893	C₂²×C₅	semidirect
427. #892	C₂²×C₅	semidirect
428. #890	C₂²×C₅	semidirect
429. #889	C₂²×C₅	semidirect
430. #889	C₂²×C₅	semidirect
431. #889	C₂²×C₅	semidirect
432. #888	C₂²×C₅	semidirect
433. #888	C₂²×C₅	semidirect
434. #887	C₂²×C₅	semidirect
435. #887	C₂²×C₅	semidirect
436. #887	C₂²×C₅	semidirect
438. #886	C₂²×C₅	semidirect
441. #885	C₂²×C₅	semidirect
445. #883	C₂²×C₅	semidirect
450. #67⋊C₄	C₂²×C₅	semidirect
451. #67⋊C₄	C₂²×C₅	semidirect
452. #879	C₂²×C₅	semidirect
454. #878	C₂²×C₅	semidirect
456. #877	C₂²×C₅	semidirect
459. C₄²×D₃	C₂²×C₅	semidirect
460. C₄×Dic₆	C₂²×C₅	semidirect
556. #539	C₅×D₃	semidirect
750. #126	C₂×C₅×D₃	semidirect
755. #125	C₂×C₅×D₃	semidirect
770. #123	C₂×C₅×D₃	semidirect
779. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
999. C₃×C₅	#3455	semidirect
1093. C₅	#86427	direct (N × H)
1123. C₃	C₅×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#539	2
C₅×#5710	2
C₅×#5706	2
C₅×#5696	2
C₅×#5691	2
C₅×#5665	2
C₅×#5663	2
C₅×#5656	2
C₅×#5649	2
C₅×#5644	2
C₅×#5640	2
C₅×#5624	2
C₅×#5622	2
C₅×#5617	2
C₅×#5596	2
C₅×#5560	2
C₄×C₅×#237	2
C₅×#5515	2
C₂×C₅×#892	2
C₅×#3455	3
#86427	5

Subgroups — C5×#86427 #14481505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86427 #14481505