Subgroups — C₅×#86019 #14481511

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5791	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5665	C₂	1	4	yes	maximal, complemented
7	C₅×#5643	C₂	1	2	yes	maximal, complemented
8	C₅×#5625	C₂	1	2	yes	maximal, complemented
9	C₅×#5619	C₂	1	2	yes	maximal, complemented
10	C₅×#5603	C₂	1	2	yes	maximal, complemented
11	C₅×#5593	C₂	1	4	yes	maximal, complemented
12	C₅×#5557	C₂	1	4	yes	maximal, complemented
13	C₅×#5538	C₂	1	4	yes	maximal, complemented
14	C₅×#5522	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5517	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3455	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#235	C₂²	1	1	yes	characteristic
20	C₃×C₅×#123	C₂²	1	2	yes	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₅×#121	C₂²	1	2	yes	—
23	C₃×C₅×#120	C₂²	1	2	yes	—
24	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₅×#953	C₂²	1	2	yes	—
27	C₂×C₅×#217	C₂²	1	2	yes	—
28	C₅×#947	C₂²	1	1	yes	characteristic, complemented
29	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
30	C₅×#944	C₂²	1	1	yes	characteristic, complemented
31	C₅×#940	C₂²	1	1	yes	characteristic, complemented
32	C₅×#939	C₂²	1	4	yes	—
33	C₅×#939	C₂²	1	4	yes	—
34	C₅×#938	C₂²	1	4	yes	—
35	C₅×#936	C₂²	1	4	yes	—
36	C₅×#936	C₂²	1	1	yes	characteristic, complemented
37	C₅×#935	C₂²	1	4	yes	—
38	C₅×D₄×Dic₃	C₂²	1	4	yes	—
39	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
40	C₅×#930	C₂²	1	2	yes	—
41	C₅×#929	C₂²	1	2	yes	—
42	C₄×C₅×#67	C₂²	1	4	yes	—
43	C₄×C₅×#67	C₂²	1	4	yes	complemented
44	C₅×#926	C₂²	1	1	yes	characteristic
45	C₅×#926	C₂²	1	2	yes	—
46	C₅×#926	C₂²	1	2	yes	—
47	C₅×#926	C₂²	1	2	yes	—
48	C₅×#926	C₂²	1	2	yes	—
49	C₅×#926	C₂²	1	2	yes	complemented
50	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
51	C₅×#924	C₂²	1	2	yes	—
52	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
55	C₅×#898	C₂²	1	4	yes	complemented
56	C₅×#897	C₂²	1	4	yes	complemented
57	C₅×#893	C₂²	1	2	yes	complemented
58	C₅×#890	C₂²	1	4	yes	complemented
59	C₅×#890	C₂²	1	2	yes	complemented
60	C₅×#889	C₂²	1	4	yes	complemented
61	C₅×#888	C₂²	1	2	yes	complemented
62	C₅×#887	C₂²	1	2	yes	complemented
63	C₅×#886	C₂²	1	4	yes	complemented
64	C₅×#885	C₂²	1	4	yes	—
65	C₅×#883	C₂²	1	4	yes	—
66	C₅×#883	C₂²	1	4	yes	complemented
67	C₅×#67⋊C₄	C₂²	1	4	yes	—
68	C₅×#879	C₂²	1	4	yes	—
69	C₅×#879	C₂²	1	4	yes	—
70	C₅×#879	C₂²	1	4	yes	complemented
71	C₅×#878	C₂²	1	4	yes	—
72	C₅×#878	C₂²	1	4	yes	complemented
73	C₅×#872	C₂²	1	2	yes	complemented
74	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
75	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
76	#86019	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#542	—	3	2	no	—
78	C₅×#542	—	3	2	no	—
79	C₅×#541	—	3	2	no	—
80	C₅×#540	—	3	2	no	—
81	C₅×#539	—	3	4	no	—
82	C₅×#538	—	3	4	no	—
83	C₅×#533	—	3	1	no	—
84	C₅×#532	—	3	1	no	—
85	C₅×#529	—	3	4	no	—
86	C₅×#529	—	3	4	no	—
87	C₅×#525	—	3	1	no	—
88	C₅×#525	D₃	1	1	yes	characteristic, complemented
89	C₄×C₅×#41	—	3	1	no	—
90	C₄×C₅×#41	—	3	1	no	—
91	C₂×C₅×#117	—	3	1	no	—
92	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₅×#41	—	2	4	no	—
94	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
98	C₂²×C₃×C₄×C₅	—	2	4	no	—
99	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
100	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
101	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₅×#67	C₂³	1	2	yes	—
105	C₂×C₅×#67	C₂³	1	4	yes	—
106	C₂×C₅×#67	C₂³	1	4	yes	—
107	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
108	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
109	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
110	C₅×#235	—	2	4	no	—
111	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
112	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
113	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
114	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
115	C₂×C₅×Dic₆	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃×C₄²×C₅	C₂³	1	2	yes	—
122	C₅×#217	C₂³	1	2	yes	—
123	C₅×#217	C₂³	1	4	yes	—
124	C₅×#217	C₂³	1	4	yes	—
125	C₅×#217	C₂³	1	2	yes	—
126	C₅×#217	C₂³	1	2	yes	—
127	C₅×#217	C₂³	1	4	yes	—
128	C₅×#217	C₂³	1	2	yes	—
129	C₅×#217	C₂³	1	2	yes	—
130	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
131	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
132	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
134	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
135	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
136	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
137	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
138	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
139	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
140	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
141	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₄×C₅×Dic₃	C₂³	1	2	yes	—
146	C₄×C₅×Dic₃	C₂³	1	2	yes	—
147	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
148	C₄×C₅×Dic₃	C₂³	1	4	yes	—
149	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
150	C₄×C₅×Dic₃	C₂³	1	4	yes	—
151	C₄×C₅×Dic₃	C₂³	1	2	yes	—
152	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
153	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
154	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
155	#5832	C₂×C₅	1	1	yes	characteristic, complemented
156	Dic₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
157	#5791	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
159	#5665	C₂×C₅	1	4	yes	complemented
160	#5643	C₂×C₅	1	2	yes	complemented
161	#5625	C₂×C₅	1	2	yes	complemented
162	#5619	C₂×C₅	1	2	yes	complemented
163	#5603	C₂×C₅	1	2	yes	complemented
164	#5593	C₂×C₅	1	4	yes	complemented
165	#5557	C₂×C₅	1	4	yes	complemented
166	#5538	C₂×C₅	1	4	yes	complemented
167	#5522	C₂×C₅	1	1	yes	characteristic, complemented
168	#5517	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂×C₅×#41	—	3	1	no	—
170	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
171	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
172	C₅×C₄⋊Q₈	—	3	1	no	—
173	C₅×C₄⋊Q₈	—	3	2	no	—
174	C₅×#127	—	3	1	no	—
175	C₅×#126	—	3	4	no	—
176	C₅×#126	—	3	4	no	—
177	C₅×#126	—	3	4	no	—
178	C₅×#126	—	3	4	no	—
179	C₅×#125	—	3	4	no	—
180	C₅×#125	—	3	4	no	—
181	C₅×#125	—	3	2	no	—
182	C₅×#124	—	3	1	no	—
183	C₅×#124	—	3	4	no	—
184	C₅×#124	—	3	1	no	—
185	C₅×#124	—	3	4	no	—
186	C₅×#123	—	3	4	no	—
187	C₅×#123	—	3	2	no	—
188	C₅×#123	—	3	4	no	—
189	C₅×#123	—	3	4	no	—
190	C₅×#123	—	3	4	no	—
191	C₅×#123	C₂×D₃	1	2	yes	—
192	C₅×C₂²⋊Q₈	—	3	2	no	—
193	C₅×C₂²⋊Q₈	—	3	4	no	—
194	C₅×C₂²⋊Q₈	—	3	4	no	—
195	C₅×C₂²⋊Q₈	—	3	4	no	—
196	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
197	C₅×#121	—	3	4	no	—
198	C₅×#121	—	3	4	no	—
199	C₅×#121	—	3	4	no	—
200	C₅×#121	—	3	2	no	—
201	C₅×#121	C₂×D₃	1	2	yes	—
202	C₅×#120	—	3	2	no	—
203	C₅×#120	C₂×D₃	1	2	yes	—
204	C₄×C₅×Q₈	—	3	2	no	—
205	C₄×C₅×Q₈	—	3	2	no	—
206	C₄×C₅×Q₈	—	3	4	no	—
207	C₄×C₅×D₄	—	3	4	no	—
208	C₄×C₅×D₄	—	3	2	no	—
209	C₄×C₅×D₄	—	3	4	no	—
210	C₄×C₅×D₄	—	3	4	no	—
211	C₄×C₅×D₄	—	3	2	no	—
212	C₄×C₅×D₄	—	3	4	no	—
213	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
214	C₅×#117	—	3	2	no	—
215	C₅×#117	—	3	2	no	—
216	C₅×#117	—	3	2	no	—
217	C₅×#117	—	3	2	no	—
218	C₅×#117	—	3	1	no	—
219	C₅×#117	—	3	2	no	—
220	C₅×#117	—	3	2	no	—
221	C₅×#117	C₂×D₃	1	1	yes	characteristic
222	C₂×C₅×C₄⋊C₄	—	3	2	no	—
223	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
224	C₂×C₄²×C₅	—	3	1	no	—
225	C₂×C₄²×C₅	—	3	1	no	—
226	C₂×C₄²×C₅	—	3	2	no	—
227	C₂×C₄²×C₅	—	3	2	no	—
228	#3455	—	3	1	no	Sylow
229	C₂³×C₃×C₅	—	2	2	no	—
230	C₂³×C₃×C₅	—	4	2	no	—
231	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
232	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
233	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
234	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
235	C₃×C₅×Q₈	—	2	2	no	—
236	C₃×C₅×D₄	—	2	4	no	—
237	C₃×C₅×D₄	—	2	2	no	—
238	C₃×C₅×D₄	—	4	4	no	—
239	C₂×C₃×C₄×C₅	—	2	2	no	—
240	C₂×C₃×C₄×C₅	—	2	4	no	—
241	C₂×C₃×C₄×C₅	—	2	4	no	—
242	C₂×C₃×C₄×C₅	—	2	4	no	—
243	C₂×C₃×C₄×C₅	#41	1	4	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₅×#67	—	2	4	no	—
250	C₅×#67	—	4	4	no	—
251	C₅×#67	—	4	4	no	—
252	C₂×C₅×Dic₃	—	4	2	no	—
253	C₂×C₅×Dic₃	—	4	4	no	—
254	C₂×C₅×Dic₃	—	4	2	no	—
255	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
257	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
258	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
259	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
260	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
261	C₅×D₁₂	—	2	2	no	—
262	C₄×C₅×D₃	—	2	4	no	—
263	C₄×C₅×D₃	—	4	4	no	—
264	C₅×Dic₆	—	2	2	no	—
265	C₅×Dic₆	—	4	4	no	—
266	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×#235	C₂²×C₅	1	1	yes	characteristic
269	C₃×#123	C₂²×C₅	1	2	yes	—
270	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
271	C₃×#121	C₂²×C₅	1	2	yes	—
272	C₃×#120	C₂²×C₅	1	2	yes	—
273	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
274	C₃×#117	C₂²×C₅	1	1	yes	characteristic
275	#953	C₂²×C₅	1	2	yes	—
276	C₂×#217	C₂²×C₅	1	2	yes	—
277	#947	C₂²×C₅	1	1	yes	characteristic, complemented
278	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
279	#944	C₂²×C₅	1	1	yes	characteristic, complemented
280	#940	C₂²×C₅	1	1	yes	characteristic, complemented
281	#939	C₂²×C₅	1	4	yes	—
282	#939	C₂²×C₅	1	4	yes	—
283	#938	C₂²×C₅	1	4	yes	—
284	#936	C₂²×C₅	1	4	yes	—
285	#936	C₂²×C₅	1	1	yes	characteristic, complemented
286	#935	C₂²×C₅	1	4	yes	—
287	D₄×Dic₃	C₂²×C₅	1	4	yes	—
288	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
289	#930	C₂²×C₅	1	2	yes	—
290	#929	C₂²×C₅	1	2	yes	—
291	C₄×#67	C₂²×C₅	1	4	yes	—
292	C₄×#67	C₂²×C₅	1	4	yes	complemented
293	#926	C₂²×C₅	1	2	yes	—
294	#926	C₂²×C₅	1	1	yes	characteristic
295	#926	C₂²×C₅	1	2	yes	—
296	#926	C₂²×C₅	1	2	yes	—
297	#926	C₂²×C₅	1	2	yes	—
298	#926	C₂²×C₅	1	2	yes	complemented
299	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
300	#924	C₂²×C₅	1	2	yes	—
301	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
302	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
304	#898	C₂²×C₅	1	4	yes	complemented
305	#897	C₂²×C₅	1	4	yes	complemented
306	#893	C₂²×C₅	1	2	yes	complemented
307	#890	C₂²×C₅	1	4	yes	complemented
308	#890	C₂²×C₅	1	2	yes	complemented
309	#889	C₂²×C₅	1	4	yes	complemented
310	#888	C₂²×C₅	1	2	yes	complemented
311	#887	C₂²×C₅	1	2	yes	complemented
312	#886	C₂²×C₅	1	4	yes	complemented
313	#885	C₂²×C₅	1	4	yes	—
314	#883	C₂²×C₅	1	4	yes	—
315	#883	C₂²×C₅	1	4	yes	complemented
316	#67⋊C₄	C₂²×C₅	1	4	yes	—
317	#879	C₂²×C₅	1	4	yes	—
318	#879	C₂²×C₅	1	4	yes	—
319	#879	C₂²×C₅	1	4	yes	complemented
320	#878	C₂²×C₅	1	4	yes	—
321	#878	C₂²×C₅	1	4	yes	complemented
322	#872	C₂²×C₅	1	2	yes	complemented
323	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
324	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
325	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
326	C₅×#41	—	2	4	no	—
327	C₅×#41	—	6	4	no	—
328	C₂×C₅×Q₈	—	3	1	no	—
329	C₂×C₅×Q₈	—	3	4	no	—
330	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×D₄	—	3	2	no	—
332	C₂×C₅×D₄	—	3	4	no	—
333	C₂×C₅×D₄	—	3	4	no	—
334	C₂×C₅×D₄	—	3	1	no	—
335	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
336	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
337	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
338	C₂²×C₄×C₅	—	2	4	no	—
339	C₂²×C₄×C₅	—	3	2	no	—
340	C₂²×C₄×C₅	—	3	2	no	—
341	C₂²×C₄×C₅	—	3	4	no	—
342	C₂²×C₄×C₅	—	3	2	no	—
343	C₂²×C₄×C₅	—	3	4	no	—
344	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
345	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
346	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
347	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
348	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
349	C₅×C₄⋊C₄	—	3	2	no	—
350	C₅×C₄⋊C₄	—	3	2	no	—
351	C₅×C₄⋊C₄	—	3	2	no	—
352	C₅×C₄⋊C₄	—	3	2	no	—
353	C₅×C₄⋊C₄	—	3	2	no	—
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	—	3	4	no	—
356	C₅×C₄⋊C₄	—	3	4	no	—
357	C₅×C₄⋊C₄	—	3	4	no	—
358	C₅×C₄⋊C₄	—	3	4	no	—
359	C₅×C₄⋊C₄	—	3	4	no	—
360	C₅×C₄⋊C₄	—	3	4	no	—
361	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
362	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
363	C₅×C₂²⋊C₄	—	3	2	no	—
364	C₅×C₂²⋊C₄	—	3	2	no	—
365	C₅×C₂²⋊C₄	—	3	2	no	—
366	C₅×C₂²⋊C₄	—	3	2	no	—
367	C₅×C₂²⋊C₄	—	3	2	no	—
368	C₅×C₂²⋊C₄	—	3	4	no	—
369	C₅×C₂²⋊C₄	—	3	4	no	—
370	C₅×C₂²⋊C₄	—	3	4	no	—
371	C₅×C₂²⋊C₄	—	3	4	no	—
372	C₅×C₂²⋊C₄	—	3	4	no	—
373	C₅×C₂²⋊C₄	—	3	4	no	—
374	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
375	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
376	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
377	C₄²×C₅	—	3	2	no	—
378	C₄²×C₅	—	3	1	no	—
379	C₄²×C₅	—	3	1	no	—
380	C₄²×C₅	—	3	4	no	—
381	C₄²×C₅	—	3	4	no	—
382	C₄²×C₅	—	3	1	no	—
383	C₄²×C₅	—	3	1	no	—
384	C₄²×C₅	—	3	2	no	—
385	C₄²×C₅	—	3	2	no	—
386	C₄²×C₅	C₂²×D₃	1	2	yes	—
387	#542	—	3	2	no	—
388	#542	—	3	2	no	—
389	#541	—	3	2	no	—
390	#540	—	3	2	no	—
391	#539	—	3	4	no	—
392	#538	—	3	4	no	—
393	#533	—	3	1	no	—
394	#532	—	3	1	no	—
395	#529	—	3	4	no	—
396	#529	—	3	4	no	—
397	#525	—	3	1	no	—
398	#525	C₅×D₃	1	1	yes	characteristic, complemented
399	C₄×#41	—	3	1	no	—
400	C₄×#41	—	3	1	no	—
401	C₂×#117	—	3	1	no	—
402	C₂²×C₃×C₅	—	2	2	no	—
403	C₂²×C₃×C₅	—	2	2	no	—
404	C₂²×C₃×C₅	—	2	2	no	—
405	C₂²×C₃×C₅	—	2	4	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	4	4	no	—
409	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
410	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
411	C₂×C₅×D₃	—	2	2	no	—
412	C₂×C₅×D₃	—	2	4	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	2	no	—
415	C₃×C₄×C₅	—	2	4	no	—
416	C₃×C₄×C₅	C₂×#41	1	2	yes	—
417	C₃×C₄×C₅	C₂×#41	1	2	yes	—
418	C₅×Dic₃	—	2	2	no	—
419	C₅×Dic₃	—	2	2	no	—
420	C₅×Dic₃	—	2	4	no	—
421	C₅×Dic₃	—	2	2	no	—
422	C₅×Dic₃	—	2	2	no	—
423	C₅×Dic₃	—	2	2	no	—
424	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
425	C₃×#41	—	2	4	no	—
426	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
428	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
430	C₂²×C₃×C₄	—	2	4	no	—
431	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
432	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
433	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
435	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×#67	C₂³×C₅	1	2	yes	—
437	C₂×#67	C₂³×C₅	1	4	yes	—
438	C₂×#67	C₂³×C₅	1	4	yes	—
439	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
440	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
441	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
442	#235	—	2	4	no	—
443	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
445	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
446	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
447	C₂×Dic₆	C₂³×C₅	1	4	yes	—
448	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
449	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
450	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
451	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
452	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
453	C₃×C₄²	C₂³×C₅	1	2	yes	—
454	#217	C₂³×C₅	1	2	yes	—
455	#217	C₂³×C₅	1	4	yes	—
456	#217	C₂³×C₅	1	4	yes	—
457	#217	C₂³×C₅	1	2	yes	—
458	#217	C₂³×C₅	1	2	yes	—
459	#217	C₂³×C₅	1	4	yes	—
460	#217	C₂³×C₅	1	2	yes	—
461	#217	C₂³×C₅	1	2	yes	—
462	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
463	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
464	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
465	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
466	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
467	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
468	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
469	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
470	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
471	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
472	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
473	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
474	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
475	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
476	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
477	C₄×Dic₃	C₂³×C₅	1	2	yes	—
478	C₄×Dic₃	C₂³×C₅	1	2	yes	—
479	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
480	C₄×Dic₃	C₂³×C₅	1	4	yes	—
481	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
482	C₄×Dic₃	C₂³×C₅	1	4	yes	—
483	C₄×Dic₃	C₂³×C₅	1	2	yes	—
484	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
485	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
486	C₂³×C₅	—	2	2	no	—
487	C₂³×C₅	—	3	2	no	—
488	C₂³×C₅	—	4	2	no	—
489	C₂³×C₅	C₂³×D₃	1	2	yes	—
490	C₂³×C₅	C₂³×D₃	1	2	yes	—
491	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
492	C₅×Q₈	—	2	2	no	—
493	C₅×Q₈	—	6	2	no	—
494	C₅×Q₈	—	12	4	no	—
495	C₅×D₄	—	2	4	no	—
496	C₅×D₄	—	2	2	no	—
497	C₅×D₄	—	4	4	no	—
498	C₅×D₄	—	6	4	no	—
499	C₅×D₄	—	6	2	no	—
500	C₅×D₄	—	12	4	no	—
501	C₅×D₄	—	12	4	no	—
502	C₂×C₄×C₅	—	2	2	no	—
503	C₂×C₄×C₅	—	2	4	no	—
504	C₂×C₄×C₅	—	2	4	no	—
505	C₂×C₄×C₅	—	2	4	no	—
506	C₂×C₄×C₅	—	3	2	no	—
507	C₂×C₄×C₅	—	3	2	no	—
508	C₂×C₄×C₅	—	3	2	no	—
509	C₂×C₄×C₅	—	3	2	no	—
510	C₂×C₄×C₅	—	3	4	no	—
511	C₂×C₄×C₅	—	3	2	no	—
512	C₂×C₄×C₅	—	6	4	no	—
513	C₂×C₄×C₅	—	12	4	no	—
514	C₂×C₄×C₅	—	12	2	no	—
515	C₂×C₄×C₅	—	12	4	no	—
516	C₂×C₄×C₅	—	12	2	no	—
517	C₂×C₄×C₅	#237	1	4	yes	—
518	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
519	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
520	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
521	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
522	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
523	C₂×#41	—	3	1	no	—
524	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
525	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
526	C₄⋊Q₈	—	3	1	no	—
527	C₄⋊Q₈	—	3	2	no	—
528	#127	—	3	1	no	—
529	#126	—	3	4	no	—
530	#126	—	3	4	no	—
531	#126	—	3	4	no	—
532	#126	—	3	4	no	—
533	#125	—	3	4	no	—
534	#125	—	3	4	no	—
535	#125	—	3	2	no	—
536	#124	—	3	1	no	—
537	#124	—	3	4	no	—
538	#124	—	3	1	no	—
539	#124	—	3	4	no	—
540	#123	—	3	4	no	—
541	#123	—	3	2	no	—
542	#123	—	3	4	no	—
543	#123	—	3	4	no	—
544	#123	—	3	4	no	—
545	#123	C₂×C₅×D₃	1	2	yes	—
546	C₂²⋊Q₈	—	3	2	no	—
547	C₂²⋊Q₈	—	3	4	no	—
548	C₂²⋊Q₈	—	3	4	no	—
549	C₂²⋊Q₈	—	3	4	no	—
550	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
551	#121	—	3	4	no	—
552	#121	—	3	4	no	—
553	#121	—	3	4	no	—
554	#121	—	3	2	no	—
555	#121	C₂×C₅×D₃	1	2	yes	—
556	#120	—	3	2	no	—
557	#120	C₂×C₅×D₃	1	2	yes	—
558	C₄×Q₈	—	3	2	no	—
559	C₄×Q₈	—	3	2	no	—
560	C₄×Q₈	—	3	4	no	—
561	C₄×D₄	—	3	4	no	—
562	C₄×D₄	—	3	2	no	—
563	C₄×D₄	—	3	4	no	—
564	C₄×D₄	—	3	4	no	—
565	C₄×D₄	—	3	2	no	—
566	C₄×D₄	—	3	4	no	—
567	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
568	#117	—	3	2	no	—
569	#117	—	3	2	no	—
570	#117	—	3	2	no	—
571	#117	—	3	2	no	—
572	#117	—	3	1	no	—
573	#117	—	3	2	no	—
574	#117	—	3	2	no	—
575	#117	C₂×C₅×D₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	—	3	2	no	—
577	C₂×C₂²⋊C₄	—	3	2	no	—
578	C₂×C₄²	—	3	1	no	—
579	C₂×C₄²	—	3	1	no	—
580	C₂×C₄²	—	3	2	no	—
581	C₂×C₄²	—	3	2	no	—
582	C₂×C₃×C₅	—	2	2	no	—
583	C₂×C₃×C₅	—	4	2	no	—
584	C₂×C₃×C₅	—	4	2	no	—
585	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
586	C₂×C₃×C₅	#585	1	2	yes	—
587	C₅×D₃	—	4	2	no	—
588	C₂³×C₃	—	2	2	no	—
589	C₂³×C₃	—	4	2	no	—
590	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
591	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
592	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
593	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
594	C₃×Q₈	—	2	2	no	—
595	C₃×D₄	—	2	4	no	—
596	C₃×D₄	—	2	2	no	—
597	C₃×D₄	—	4	4	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	4	no	—
600	C₂×C₃×C₄	—	2	4	no	—
601	C₂×C₃×C₄	—	2	4	no	—
602	C₂×C₃×C₄	C₅×#41	1	4	yes	—
603	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
604	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
605	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
606	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
607	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	#67	—	2	4	no	—
609	#67	—	4	4	no	—
610	#67	—	4	4	no	—
611	C₂×Dic₃	—	4	2	no	—
612	C₂×Dic₃	—	4	4	no	—
613	C₂×Dic₃	—	4	2	no	—
614	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
615	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
616	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
617	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
618	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
619	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
620	D₁₂	—	2	2	no	—
621	C₄×D₃	—	2	4	no	—
622	C₄×D₃	—	4	4	no	—
623	Dic₆	—	2	2	no	—
624	Dic₆	—	4	4	no	—
625	C₂²×C₅	—	2	2	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	—	2	2	no	—
628	C₂²×C₅	—	2	4	no	—
629	C₂²×C₅	—	2	2	no	—
630	C₂²×C₅	—	2	2	no	—
631	C₂²×C₅	—	4	4	no	—
632	C₂²×C₅	—	6	2	no	—
633	C₂²×C₅	—	6	4	no	—
634	C₂²×C₅	C₂×#237	1	2	yes	—
635	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	4	no	—
639	C₄×C₅	—	6	2	no	—
640	C₄×C₅	—	6	2	no	—
641	C₄×C₅	—	6	2	no	—
642	C₄×C₅	—	6	2	no	—
643	C₄×C₅	—	6	4	no	—
644	C₄×C₅	—	6	2	no	—
645	C₄×C₅	C₂×#237	1	2	yes	—
646	C₄×C₅	C₂×#237	1	2	yes	—
647	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
648	#41	—	2	4	no	—
649	#41	—	6	4	no	—
650	C₂×Q₈	—	3	1	no	—
651	C₂×Q₈	—	3	4	no	—
652	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
653	C₂×D₄	—	3	2	no	—
654	C₂×D₄	—	3	4	no	—
655	C₂×D₄	—	3	4	no	—
656	C₂×D₄	—	3	1	no	—
657	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
658	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
659	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	3	2	no	—
662	C₂²×C₄	—	3	2	no	—
663	C₂²×C₄	—	3	4	no	—
664	C₂²×C₄	—	3	2	no	—
665	C₂²×C₄	—	3	4	no	—
666	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
667	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
668	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
669	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
670	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
671	C₄⋊C₄	—	3	2	no	—
672	C₄⋊C₄	—	3	2	no	—
673	C₄⋊C₄	—	3	2	no	—
674	C₄⋊C₄	—	3	2	no	—
675	C₄⋊C₄	—	3	2	no	—
676	C₄⋊C₄	—	3	4	no	—
677	C₄⋊C₄	—	3	4	no	—
678	C₄⋊C₄	—	3	4	no	—
679	C₄⋊C₄	—	3	4	no	—
680	C₄⋊C₄	—	3	4	no	—
681	C₄⋊C₄	—	3	4	no	—
682	C₄⋊C₄	—	3	4	no	—
683	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
684	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
685	C₂²⋊C₄	—	3	2	no	—
686	C₂²⋊C₄	—	3	2	no	—
687	C₂²⋊C₄	—	3	2	no	—
688	C₂²⋊C₄	—	3	2	no	—
689	C₂²⋊C₄	—	3	2	no	—
690	C₂²⋊C₄	—	3	4	no	—
691	C₂²⋊C₄	—	3	4	no	—
692	C₂²⋊C₄	—	3	4	no	—
693	C₂²⋊C₄	—	3	4	no	—
694	C₂²⋊C₄	—	3	4	no	—
695	C₂²⋊C₄	—	3	4	no	—
696	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
697	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
698	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
699	C₄²	—	3	1	no	—
700	C₄²	—	3	1	no	—
701	C₄²	—	3	2	no	—
702	C₄²	—	3	2	no	—
703	C₄²	—	3	2	no	—
704	C₄²	—	3	1	no	—
705	C₄²	—	3	1	no	—
706	C₄²	—	3	4	no	—
707	C₄²	—	3	4	no	—
708	C₄²	C₂²×C₅×D₃	1	2	yes	—
709	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	—	2	2	no	—
712	C₂²×C₃	—	2	2	no	—
713	C₂²×C₃	—	2	4	no	—
714	C₂²×C₃	—	2	2	no	—
715	C₂²×C₃	—	2	2	no	—
716	C₂²×C₃	—	4	4	no	—
717	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
718	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
719	C₂×D₃	—	2	2	no	—
720	C₂×D₃	—	2	4	no	—
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	4	no	—
724	C₃×C₄	C₂×C₅×#41	1	2	yes	—
725	C₃×C₄	C₂×C₅×#41	1	2	yes	—
726	Dic₃	—	2	2	no	—
727	Dic₃	—	2	2	no	—
728	Dic₃	—	2	4	no	—
729	Dic₃	—	2	2	no	—
730	Dic₃	—	2	2	no	—
731	Dic₃	—	2	2	no	—
732	C₂×C₅	—	2	2	no	—
733	C₂×C₅	—	4	2	no	—
734	C₂×C₅	—	4	2	no	—
735	C₂×C₅	—	12	2	no	—
736	C₂×C₅	C₂²×#237	1	1	yes	characteristic
737	C₂×C₅	#5964	1	2	yes	—
738	C₂³	—	2	2	no	—
739	C₂³	—	3	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	C₂³×C₅×D₃	1	2	yes	—
742	C₂³	C₂³×C₅×D₃	1	2	yes	—
743	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	6	2	no	—
746	Q₈	—	12	4	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	2	no	—
749	D₄	—	4	4	no	—
750	D₄	—	6	4	no	—
751	D₄	—	6	2	no	—
752	D₄	—	12	4	no	—
753	D₄	—	12	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	3	2	no	—
759	C₂×C₄	—	3	2	no	—
760	C₂×C₄	—	3	2	no	—
761	C₂×C₄	—	3	2	no	—
762	C₂×C₄	—	3	4	no	—
763	C₂×C₄	—	3	2	no	—
764	C₂×C₄	—	6	4	no	—
765	C₂×C₄	—	12	4	no	—
766	C₂×C₄	—	12	2	no	—
767	C₂×C₄	—	12	4	no	—
768	C₂×C₄	—	12	2	no	—
769	C₂×C₄	C₅×#237	1	4	yes	—
770	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
771	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
772	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
773	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
775	C₂×C₃	—	2	2	no	—
776	C₂×C₃	—	4	2	no	—
777	C₂×C₃	—	4	2	no	—
778	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
779	C₂×C₃	C₅×#585	1	2	yes	—
780	D₃	—	4	2	no	—
781	C₅	#86019	1	1	yes	characteristic, direct product factor, Sylow
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	6	2	no	—
790	C₂²	—	6	4	no	—
791	C₂²	C₂×C₅×#237	1	2	yes	—
792	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	4	no	—
796	C₄	—	6	2	no	—
797	C₄	—	6	2	no	—
798	C₄	—	6	2	no	—
799	C₄	—	6	2	no	—
800	C₄	—	6	4	no	—
801	C₄	—	6	2	no	—
802	C₄	C₂×C₅×#237	1	2	yes	—
803	C₄	C₂×C₅×#237	1	2	yes	—
804	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
805	C₂	—	2	2	no	—
806	C₂	—	4	2	no	—
807	C₂	—	4	2	no	—
808	C₂	—	12	2	no	—
809	C₂	C₂²×C₅×#237	1	1	yes	characteristic
810	C₂	C₅×#5964	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#525	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#525	D₃
hypocenter	C₃	C₅×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#525

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#525	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₅×Dic₃×#41	C₂	semidirect
4. C₅×#5791	C₂	semidirect
5. C₂×C₅×#926	C₂	semidirect
6. C₅×#5665	C₂	semidirect
7. C₅×#5643	C₂	semidirect
8. C₅×#5625	C₂	semidirect
9. C₅×#5619	C₂	semidirect
10. C₅×#5603	C₂	semidirect
11. C₅×#5593	C₂	semidirect
12. C₅×#5557	C₂	semidirect
13. C₅×#5538	C₂	semidirect
14. C₅×#5522	C₂	semidirect
15. C₅×#5517	C₂	semidirect
28. C₅×#947	C₂²	semidirect
29. C₅×Q₈×Dic₃	C₂²	semidirect
30. C₅×#944	C₂²	semidirect
31. C₅×#940	C₂²	semidirect
36. C₅×#936	C₂²	semidirect
39. C₅×D₄×Dic₃	C₂²	semidirect
43. C₄×C₅×#67	C₂²	semidirect
49. C₅×#926	C₂²	semidirect
54. C₂×C₄×C₅×Dic₃	C₂²	semidirect
55. C₅×#898	C₂²	semidirect
56. C₅×#897	C₂²	semidirect
57. C₅×#893	C₂²	semidirect
58. C₅×#890	C₂²	semidirect
59. C₅×#890	C₂²	semidirect
60. C₅×#889	C₂²	semidirect
61. C₅×#888	C₂²	semidirect
62. C₅×#887	C₂²	semidirect
63. C₅×#886	C₂²	semidirect
66. C₅×#883	C₂²	semidirect
70. C₅×#879	C₂²	semidirect
72. C₅×#878	C₂²	semidirect
73. C₅×#872	C₂²	semidirect
74. C₄²×C₅×D₃	C₂²	semidirect
75. C₄×C₅×Dic₆	C₂²	semidirect
76. #86019	C₅	direct (N × H)
88. C₅×#525	D₃	semidirect
154. C₃×#525	C₂×C₅	semidirect
155. #5832	C₂×C₅	semidirect
156. Dic₃×#41	C₂×C₅	semidirect
157. #5791	C₂×C₅	semidirect
158. C₂×#926	C₂×C₅	semidirect
159. #5665	C₂×C₅	semidirect
160. #5643	C₂×C₅	semidirect
161. #5625	C₂×C₅	semidirect
162. #5619	C₂×C₅	semidirect
163. #5603	C₂×C₅	semidirect
164. #5593	C₂×C₅	semidirect
165. #5557	C₂×C₅	semidirect
166. #5538	C₂×C₅	semidirect
167. #5522	C₂×C₅	semidirect
168. #5517	C₂×C₅	semidirect
277. #947	C₂²×C₅	semidirect
278. Q₈×Dic₃	C₂²×C₅	semidirect
279. #944	C₂²×C₅	semidirect
280. #940	C₂²×C₅	semidirect
285. #936	C₂²×C₅	semidirect
288. D₄×Dic₃	C₂²×C₅	semidirect
292. C₄×#67	C₂²×C₅	semidirect
298. #926	C₂²×C₅	semidirect
303. C₂×C₄×Dic₃	C₂²×C₅	semidirect
304. #898	C₂²×C₅	semidirect
305. #897	C₂²×C₅	semidirect
306. #893	C₂²×C₅	semidirect
307. #890	C₂²×C₅	semidirect
308. #890	C₂²×C₅	semidirect
309. #889	C₂²×C₅	semidirect
310. #888	C₂²×C₅	semidirect
311. #887	C₂²×C₅	semidirect
312. #886	C₂²×C₅	semidirect
315. #883	C₂²×C₅	semidirect
319. #879	C₂²×C₅	semidirect
321. #878	C₂²×C₅	semidirect
322. #872	C₂²×C₅	semidirect
323. C₄²×D₃	C₂²×C₅	semidirect
324. C₄×Dic₆	C₂²×C₅	semidirect
398. #525	C₅×D₃	semidirect
709. C₃×C₅	#3455	semidirect
781. C₅	#86019	direct (N × H)
804. 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×#525	2
C₅×#5832	2
C₅×Dic₃×#41	2
C₅×#5791	2
C₂×C₅×#926	2
C₅×#5665	2
C₅×#5643	2
C₅×#5625	2
C₅×#5619	2
C₅×#5603	2
C₅×#5593	2
C₅×#5557	2
C₅×#5538	2
C₅×#5522	2
C₅×#5517	2
C₅×#3455	3
#86019	5

Subgroups — C5×#86019 #14481511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86019 #14481511