Subgroups — C₅×D₃×#535 #14480359

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 960 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×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5715	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#127	C₂	1	2	yes	maximal, complemented
8	C₅×#5674	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#124	C₂	1	2	yes	maximal, complemented
10	C₅×#5607	C₂	1	4	yes	maximal, complemented
11	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
12	C₅×#5592	C₂	1	4	yes	maximal, complemented
13	C₅×D₃×#120	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	C₂×C₅×#535	—	3	1	no	maximal, Hall
17	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₅×#67	C₂²	1	2	yes	complemented
21	C₅×D₃×#41	—	2	8	no	—
22	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#237	C₂²	1	2	yes	complemented
26	C₂×C₅×D₃×D₄	—	2	8	no	—
27	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
28	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
29	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
30	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
31	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
32	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
34	C₂×C₅×#235	C₂²	1	2	yes	complemented
35	C₂×C₅×#235	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
39	C₃×C₅×#127	C₂²	1	2	yes	complemented
40	C₃×C₅×#124	C₂²	1	2	yes	complemented
41	C₃×C₅×#121	C₂²	1	4	yes	complemented
42	C₃×C₅×#120	C₂²	1	4	yes	complemented
43	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	C₅×#953	C₂²	1	4	yes	complemented
45	C₅×#947	C₂²	1	2	yes	complemented
46	C₅×#940	C₂²	1	2	yes	complemented
47	C₅×#940	C₂²	1	8	yes	complemented
48	C₅×#940	C₂²	1	2	yes	complemented
49	C₅×#939	C₂²	1	8	yes	complemented
50	C₅×#938	C₂²	1	4	yes	complemented
51	C₅×#937	C₂²	1	8	yes	complemented
52	C₅×#937	C₂²	1	4	yes	complemented
53	C₅×#936	C₂²	1	2	yes	complemented
54	C₅×#930	C₂²	1	4	yes	complemented
55	C₅×#926	C₂²	1	1	yes	characteristic, complemented
56	C₅×#895	C₂²	1	4	yes	complemented
57	C₅×#892	C₂²	1	2	yes	complemented
58	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₅×#885	C₂²	1	8	yes	complemented
60	C₅×#884	C₂²	1	8	yes	complemented
61	C₅×#882	C₂²	1	8	yes	complemented
62	C₅×#882	C₂²	1	4	yes	complemented
63	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
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	D₃×#535	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂³×C₅×D₄	—	3	1	no	—
73	C₅×#535	—	3	1	no	—
74	C₅×#535	—	3	1	no	—
75	C₅×#535	—	3	2	no	—
76	C₅×#535	—	3	2	no	—
77	C₅×#535	—	3	4	no	—
78	C₅×#535	—	3	4	no	—
79	C₅×#535	—	3	1	no	—
80	C₅×#535	D₃	1	1	yes	characteristic, direct product factor
81	C₂×C₅×#127	—	3	2	no	—
82	C₂×C₅×#124	—	3	2	no	—
83	C₂×C₅×#121	—	3	4	no	—
84	C₂×C₅×#120	—	3	4	no	—
85	C₂×C₅×#117	—	3	1	no	—
86	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
87	C₂³×C₅×D₃	—	2	8	no	—
88	C₂³×C₅×D₃	—	4	8	no	—
89	C₂³×C₅×D₃	C₂³	1	4	yes	—
90	C₂³×C₅×D₃	C₂³	1	2	yes	—
91	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
92	C₂³×C₅×D₃	C₂³	1	2	yes	—
93	C₂³×C₅×D₃	C₂³	1	4	yes	—
94	C₃×C₅×#41	—	2	4	no	—
95	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
96	C₂×C₃×C₅×D₄	—	2	4	no	—
97	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
98	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
99	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
100	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
101	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
104	C₂×C₅×#67	—	2	8	no	—
105	C₂×C₅×#67	C₂³	1	2	yes	—
106	C₂×C₅×#67	C₂³	1	4	yes	—
107	C₂×C₅×#67	C₂³	1	4	yes	—
108	C₂×C₅×#67	C₂³	1	2	yes	—
109	C₂×C₅×#67	C₂³	1	2	yes	complemented
110	C₂×C₅×#67	C₂³	1	8	yes	complemented
111	C₂×C₅×#67	C₂³	1	8	yes	complemented
112	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₂²×C₅×Dic₃	C₂³	1	2	yes	complemented
114	C₅×#239	—	2	4	no	—
115	C₅×D₃×Q₈	—	2	4	no	—
116	C₅×#237	—	2	8	no	—
117	C₅×#237	—	2	4	no	—
118	C₅×D₃×D₄	—	2	8	no	—
119	C₅×D₃×D₄	—	2	8	no	—
120	C₅×D₃×D₄	—	2	8	no	—
121	C₅×D₃×D₄	—	2	4	no	—
122	C₅×D₃×D₄	—	2	8	no	—
123	C₅×D₃×D₄	—	2	8	no	—
124	C₅×D₃×D₄	—	4	16	no	—
125	C₅×#235	—	2	4	no	—
126	C₅×#235	—	2	8	no	—
127	C₂×C₅×D₁₂	—	2	4	no	—
128	C₂×C₅×D₁₂	C₂³	1	2	yes	—
129	C₂×C₅×D₁₂	C₂³	1	2	yes	—
130	C₂×C₅×D₁₂	C₂³	1	2	yes	—
131	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic, complemented
132	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
133	C₂×C₄×C₅×D₃	—	2	8	no	—
134	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
135	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
136	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
137	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×C₅×D₃	C₂³	1	2	yes	complemented
142	C₂×C₄×C₅×D₃	C₂³	1	2	yes	complemented
143	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic, complemented
144	C₂×C₅×Dic₆	C₂³	1	2	yes	complemented
145	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
148	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
149	C₅×#217	C₂³	1	2	yes	—
150	C₅×#217	C₂³	1	8	yes	complemented
151	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
153	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
154	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
155	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
156	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
157	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
158	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
160	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
161	#5830	C₂×C₅	1	1	yes	characteristic, complemented
162	#5805	C₂×C₅	1	1	yes	characteristic, complemented
163	#5715	C₂×C₅	1	2	yes	complemented
164	D₃×#127	C₂×C₅	1	2	yes	complemented
165	#5674	C₂×C₅	1	2	yes	complemented
166	D₃×#124	C₂×C₅	1	2	yes	complemented
167	#5607	C₂×C₅	1	4	yes	complemented
168	D₃×#121	C₂×C₅	1	4	yes	complemented
169	#5592	C₂×C₅	1	4	yes	complemented
170	D₃×#120	C₂×C₅	1	4	yes	complemented
171	#5525	C₂×C₅	1	1	yes	characteristic, complemented
172	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
173	C₂⁵×C₅	—	3	2	no	—
174	C₂×C₅×#41	—	3	1	no	—
175	C₂×C₅×#41	—	3	2	no	—
176	C₂×C₅×#41	—	3	1	no	—
177	C₂×C₅×#41	—	3	1	no	—
178	C₂×C₅×#41	—	3	2	no	—
179	C₂×C₅×#41	—	6	8	no	—
180	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂²×C₅×Q₈	—	3	1	no	—
182	C₂²×C₅×D₄	—	3	2	no	—
183	C₂²×C₅×D₄	—	3	2	no	—
184	C₂²×C₅×D₄	—	3	2	no	—
185	C₂²×C₅×D₄	—	3	2	no	—
186	C₂²×C₅×D₄	—	3	2	no	—
187	C₂²×C₅×D₄	—	3	2	no	—
188	C₂²×C₅×D₄	—	3	1	no	—
189	C₂²×C₅×D₄	—	3	8	no	—
190	C₂²×C₅×D₄	—	3	1	no	—
191	C₂²×C₅×D₄	—	6	8	no	—
192	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
193	C₂³×C₄×C₅	—	3	1	no	—
194	C₂³×C₄×C₅	—	3	2	no	—
195	C₅×#127	—	3	2	no	—
196	C₅×#127	—	3	8	no	—
197	C₅×#127	—	3	2	no	—
198	C₅×#127	—	3	2	no	—
199	C₅×#127	C₂×D₃	1	2	yes	complemented
200	C₅×#124	—	3	2	no	—
201	C₅×#124	—	3	2	no	—
202	C₅×#124	—	3	8	no	—
203	C₅×#124	—	3	2	no	—
204	C₅×#124	C₂×D₃	1	2	yes	complemented
205	C₅×#121	—	3	4	no	—
206	C₅×#121	—	3	8	no	—
207	C₅×#121	—	3	4	no	—
208	C₅×#121	—	3	4	no	—
209	C₅×#121	—	3	8	no	—
210	C₅×#121	C₂×D₃	1	4	yes	complemented
211	C₅×#120	—	3	4	no	—
212	C₅×#120	—	3	4	no	—
213	C₅×#120	—	3	8	no	—
214	C₅×#120	—	3	4	no	—
215	C₅×#120	—	3	8	no	—
216	C₅×#120	C₂×D₃	1	4	yes	complemented
217	C₅×#117	—	3	1	no	—
218	C₅×#117	—	3	2	no	—
219	C₅×#117	—	3	2	no	—
220	C₅×#117	—	3	2	no	—
221	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
222	C₂×C₅×C₄⋊C₄	—	3	2	no	—
223	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
224	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
225	C₂×C₄²×C₅	—	3	2	no	—
226	C₂×#535	—	3	1	no	Sylow
227	C₂³×C₃×C₅	—	2	4	no	—
228	C₂³×C₃×C₅	—	4	4	no	—
229	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
231	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
232	C₂²×C₅×D₃	—	2	4	no	—
233	C₂²×C₅×D₃	—	2	4	no	—
234	C₂²×C₅×D₃	—	2	4	no	—
235	C₂²×C₅×D₃	—	2	8	no	—
236	C₂²×C₅×D₃	—	2	8	no	—
237	C₂²×C₅×D₃	—	2	8	no	—
238	C₂²×C₅×D₃	—	2	16	no	—
239	C₂²×C₅×D₃	—	4	8	no	—
240	C₂²×C₅×D₃	—	4	4	no	—
241	C₂²×C₅×D₃	—	4	32	no	—
242	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
243	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
244	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
245	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
247	C₃×C₅×Q₈	—	2	2	no	—
248	C₃×C₅×D₄	—	2	4	no	—
249	C₃×C₅×D₄	—	2	4	no	—
250	C₃×C₅×D₄	—	2	4	no	—
251	C₃×C₅×D₄	—	2	2	no	—
252	C₃×C₅×D₄	—	4	8	no	—
253	C₂×C₃×C₄×C₅	—	2	4	no	—
254	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
255	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
256	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
257	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₅×#67	—	2	4	no	—
260	C₅×#67	—	2	4	no	—
261	C₅×#67	—	2	4	no	—
262	C₅×#67	—	2	8	no	—
263	C₅×#67	—	2	8	no	—
264	C₅×#67	—	4	8	no	—
265	C₅×#67	—	4	8	no	—
266	C₂×C₅×Dic₃	—	2	4	no	—
267	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	complemented
268	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
269	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
270	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
272	C₅×D₁₂	—	2	4	no	—
273	C₅×D₁₂	—	2	4	no	—
274	C₅×D₁₂	—	2	4	no	—
275	C₅×D₁₂	—	2	2	no	—
276	C₅×D₁₂	—	4	8	no	—
277	C₄×C₅×D₃	—	2	4	no	—
278	C₄×C₅×D₃	—	2	8	no	—
279	C₄×C₅×D₃	—	2	4	no	—
280	C₄×C₅×D₃	—	2	4	no	—
281	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
282	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
283	C₄×C₅×D₃	C₂×D₄	1	4	yes	complemented
284	C₄×C₅×D₃	C₂×D₄	1	4	yes	complemented
285	C₅×Dic₆	—	2	2	no	—
286	C₅×Dic₆	—	2	4	no	—
287	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
288	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₂²×#67	C₂²×C₅	1	2	yes	complemented
291	D₃×#41	—	2	8	no	—
292	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂×#237	C₂²×C₅	1	2	yes	complemented
296	C₂×D₃×D₄	—	2	8	no	—
297	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
298	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
299	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
300	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
301	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
302	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
304	C₂×#235	C₂²×C₅	1	2	yes	complemented
305	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
307	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
308	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
309	C₃×#127	C₂²×C₅	1	2	yes	complemented
310	C₃×#124	C₂²×C₅	1	2	yes	complemented
311	C₃×#121	C₂²×C₅	1	4	yes	complemented
312	C₃×#120	C₂²×C₅	1	4	yes	complemented
313	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
314	#953	C₂²×C₅	1	4	yes	complemented
315	#947	C₂²×C₅	1	2	yes	complemented
316	#940	C₂²×C₅	1	2	yes	complemented
317	#940	C₂²×C₅	1	8	yes	complemented
318	#940	C₂²×C₅	1	2	yes	complemented
319	#939	C₂²×C₅	1	8	yes	complemented
320	#938	C₂²×C₅	1	4	yes	complemented
321	#937	C₂²×C₅	1	8	yes	complemented
322	#937	C₂²×C₅	1	4	yes	complemented
323	#936	C₂²×C₅	1	2	yes	complemented
324	#930	C₂²×C₅	1	4	yes	complemented
325	#926	C₂²×C₅	1	1	yes	characteristic, complemented
326	#895	C₂²×C₅	1	4	yes	complemented
327	#892	C₂²×C₅	1	2	yes	complemented
328	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
329	#885	C₂²×C₅	1	8	yes	complemented
330	#884	C₂²×C₅	1	8	yes	complemented
331	#882	C₂²×C₅	1	8	yes	complemented
332	#882	C₂²×C₅	1	4	yes	complemented
333	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
334	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
335	#877	C₂²×C₅	1	2	yes	complemented
336	#875	C₂²×C₅	1	2	yes	complemented
337	#874	C₂²×C₅	1	2	yes	complemented
338	#872	C₂²×C₅	1	2	yes	complemented
339	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
340	C₂⁴×C₅	—	3	1	no	—
341	C₂⁴×C₅	—	3	4	no	—
342	C₂⁴×C₅	—	3	2	no	—
343	C₂⁴×C₅	—	3	4	no	—
344	C₂⁴×C₅	—	3	2	no	—
345	C₂⁴×C₅	—	6	8	no	—
346	C₂⁴×C₅	—	12	8	no	—
347	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
348	C₅×#41	—	2	4	no	—
349	C₅×#41	—	6	8	no	—
350	C₅×#41	—	6	8	no	—
351	C₅×#41	—	6	4	no	—
352	C₅×#41	—	6	4	no	—
353	C₅×#41	—	6	4	no	—
354	C₂×C₅×Q₈	—	3	2	no	—
355	C₂×C₅×Q₈	—	3	1	no	—
356	C₂×C₅×Q₈	—	6	4	no	—
357	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
358	C₂×C₅×D₄	—	2	4	no	—
359	C₂×C₅×D₄	—	3	2	no	—
360	C₂×C₅×D₄	—	3	2	no	—
361	C₂×C₅×D₄	—	3	4	no	—
362	C₂×C₅×D₄	—	3	4	no	—
363	C₂×C₅×D₄	—	3	2	no	—
364	C₂×C₅×D₄	—	3	8	no	—
365	C₂×C₅×D₄	—	3	8	no	—
366	C₂×C₅×D₄	—	3	2	no	—
367	C₂×C₅×D₄	—	3	2	no	—
368	C₂×C₅×D₄	—	3	2	no	—
369	C₂×C₅×D₄	—	3	1	no	—
370	C₂×C₅×D₄	—	3	8	no	—
371	C₂×C₅×D₄	—	6	8	no	—
372	C₂×C₅×D₄	—	6	8	no	—
373	C₂×C₅×D₄	—	6	8	no	—
374	C₂×C₅×D₄	—	6	8	no	—
375	C₂×C₅×D₄	—	6	4	no	—
376	C₂×C₅×D₄	—	6	8	no	—
377	C₂×C₅×D₄	—	6	8	no	—
378	C₂×C₅×D₄	—	6	4	no	—
379	C₂×C₅×D₄	—	12	16	no	—
380	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
381	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
382	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
383	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic, complemented
384	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
385	C₂²×C₄×C₅	—	3	1	no	—
386	C₂²×C₄×C₅	—	3	8	no	—
387	C₂²×C₄×C₅	—	3	1	no	—
388	C₂²×C₄×C₅	—	3	1	no	—
389	C₂²×C₄×C₅	—	3	1	no	—
390	C₂²×C₄×C₅	—	3	1	no	—
391	C₂²×C₄×C₅	—	3	2	no	—
392	C₂²×C₄×C₅	—	3	4	no	—
393	C₂²×C₄×C₅	—	3	2	no	—
394	C₂²×C₄×C₅	—	3	2	no	—
395	C₂²×C₄×C₅	—	3	2	no	—
396	C₂²×C₄×C₅	—	6	8	no	—
397	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
398	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	complemented
399	C₅×C₄⋊C₄	—	3	4	no	—
400	C₅×C₄⋊C₄	—	3	2	no	—
401	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
402	C₅×C₂²⋊C₄	—	3	2	no	—
403	C₅×C₂²⋊C₄	—	3	8	no	—
404	C₅×C₂²⋊C₄	—	3	4	no	—
405	C₅×C₂²⋊C₄	—	3	8	no	—
406	C₅×C₂²⋊C₄	—	3	8	no	—
407	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
408	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
409	C₄²×C₅	—	3	4	no	—
410	C₄²×C₅	—	3	2	no	—
411	C₄²×C₅	C₂²×D₃	1	2	yes	complemented
412	C₂²×#41	—	3	1	no	—
413	C₂³×D₄	—	3	1	no	—
414	#535	—	3	1	no	—
415	#535	—	3	1	no	—
416	#535	—	3	2	no	—
417	#535	—	3	2	no	—
418	#535	—	3	4	no	—
419	#535	—	3	4	no	—
420	#535	—	3	1	no	—
421	#535	C₅×D₃	1	1	yes	characteristic, direct product factor
422	C₂×#127	—	3	2	no	—
423	C₂×#124	—	3	2	no	—
424	C₂×#121	—	3	4	no	—
425	C₂×#120	—	3	4	no	—
426	C₂×#117	—	3	1	no	—
427	C₂²×C₃×C₅	—	2	2	no	—
428	C₂²×C₃×C₅	—	2	2	no	—
429	C₂²×C₃×C₅	—	2	4	no	—
430	C₂²×C₃×C₅	—	2	4	no	—
431	C₂²×C₃×C₅	—	2	8	no	—
432	C₂²×C₃×C₅	—	4	8	no	—
433	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
434	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
435	C₂×C₅×D₃	—	2	2	no	—
436	C₂×C₅×D₃	—	2	8	no	—
437	C₂×C₅×D₃	—	2	2	no	—
438	C₂×C₅×D₃	—	2	4	no	—
439	C₂×C₅×D₃	—	2	4	no	—
440	C₂×C₅×D₃	—	2	8	no	—
441	C₂×C₅×D₃	—	4	16	no	—
442	C₂×C₅×D₃	—	4	8	no	—
443	C₂×C₅×D₃	—	4	8	no	—
444	C₂×C₅×D₃	—	4	16	no	—
445	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
446	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
447	C₂×C₅×D₃	H(5,𝔽₂)	1	4	yes	—
448	C₃×C₄×C₅	—	2	2	no	—
449	C₃×C₄×C₅	—	2	4	no	—
450	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
451	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
452	C₅×Dic₃	—	2	2	no	—
453	C₅×Dic₃	—	2	4	no	—
454	C₅×Dic₃	C₂²×D₄	1	2	yes	—
455	C₅×Dic₃	C₂²×D₄	1	2	yes	—
456	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
457	C₂³×D₃	—	2	8	no	—
458	C₂³×D₃	—	4	8	no	—
459	C₂³×D₃	C₂³×C₅	1	4	yes	—
460	C₂³×D₃	C₂³×C₅	1	2	yes	—
461	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
462	C₂³×D₃	C₂³×C₅	1	2	yes	—
463	C₂³×D₃	C₂³×C₅	1	4	yes	—
464	C₃×#41	—	2	4	no	—
465	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic, complemented
466	C₂×C₃×D₄	—	2	4	no	—
467	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
468	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
469	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
470	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic, complemented
471	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
472	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	complemented
474	C₂×#67	—	2	8	no	—
475	C₂×#67	C₂³×C₅	1	2	yes	—
476	C₂×#67	C₂³×C₅	1	4	yes	—
477	C₂×#67	C₂³×C₅	1	4	yes	—
478	C₂×#67	C₂³×C₅	1	2	yes	—
479	C₂×#67	C₂³×C₅	1	2	yes	complemented
480	C₂×#67	C₂³×C₅	1	8	yes	complemented
481	C₂×#67	C₂³×C₅	1	8	yes	complemented
482	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
483	C₂²×Dic₃	C₂³×C₅	1	2	yes	complemented
484	#239	—	2	4	no	—
485	D₃×Q₈	—	2	4	no	—
486	#237	—	2	8	no	—
487	#237	—	2	4	no	—
488	D₃×D₄	—	2	8	no	—
489	D₃×D₄	—	2	8	no	—
490	D₃×D₄	—	2	8	no	—
491	D₃×D₄	—	2	4	no	—
492	D₃×D₄	—	2	8	no	—
493	D₃×D₄	—	2	8	no	—
494	D₃×D₄	—	4	16	no	—
495	#235	—	2	4	no	—
496	#235	—	2	8	no	—
497	C₂×D₁₂	—	2	4	no	—
498	C₂×D₁₂	C₂³×C₅	1	2	yes	—
499	C₂×D₁₂	C₂³×C₅	1	2	yes	—
500	C₂×D₁₂	C₂³×C₅	1	2	yes	—
501	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic, complemented
502	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
503	C₂×C₄×D₃	—	2	8	no	—
504	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
505	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
506	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
507	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
508	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
509	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
510	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
511	C₂×C₄×D₃	C₂³×C₅	1	2	yes	complemented
512	C₂×C₄×D₃	C₂³×C₅	1	2	yes	complemented
513	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic, complemented
514	C₂×Dic₆	C₂³×C₅	1	2	yes	complemented
515	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
516	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
517	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
518	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
519	#217	C₂³×C₅	1	2	yes	—
520	#217	C₂³×C₅	1	8	yes	complemented
521	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
523	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
524	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
525	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
526	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
527	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
528	C₂³×C₅	—	2	4	no	—
529	C₂³×C₅	—	3	1	no	—
530	C₂³×C₅	—	3	4	no	—
531	C₂³×C₅	—	3	1	no	—
532	C₂³×C₅	—	3	4	no	—
533	C₂³×C₅	—	3	2	no	—
534	C₂³×C₅	—	4	4	no	—
535	C₂³×C₅	—	6	4	no	—
536	C₂³×C₅	—	6	4	no	—
537	C₂³×C₅	—	6	8	no	—
538	C₂³×C₅	—	6	8	no	—
539	C₂³×C₅	—	6	8	no	—
540	C₂³×C₅	—	6	16	no	—
541	C₂³×C₅	—	6	4	no	—
542	C₂³×C₅	—	12	4	no	—
543	C₂³×C₅	—	12	8	no	—
544	C₂³×C₅	—	12	32	no	—
545	C₂³×C₅	C₂³×D₃	1	4	yes	—
546	C₂³×C₅	C₂³×D₃	1	2	yes	—
547	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
548	C₅×Q₈	—	2	2	no	—
549	C₅×Q₈	—	6	4	no	—
550	C₅×Q₈	—	6	2	no	—
551	C₅×D₄	—	2	4	no	—
552	C₅×D₄	—	2	4	no	—
553	C₅×D₄	—	2	4	no	—
554	C₅×D₄	—	2	2	no	—
555	C₅×D₄	—	4	8	no	—
556	C₅×D₄	—	6	4	no	—
557	C₅×D₄	—	6	8	no	—
558	C₅×D₄	—	6	8	no	—
559	C₅×D₄	—	6	4	no	—
560	C₅×D₄	—	6	4	no	—
561	C₅×D₄	—	6	4	no	—
562	C₅×D₄	—	6	4	no	—
563	C₅×D₄	—	6	4	no	—
564	C₅×D₄	—	6	2	no	—
565	C₅×D₄	—	12	8	no	—
566	C₅×D₄	—	12	8	no	—
567	C₅×D₄	—	12	8	no	—
568	C₂×C₄×C₅	—	2	4	no	—
569	C₂×C₄×C₅	—	3	4	no	—
570	C₂×C₄×C₅	—	3	1	no	—
571	C₂×C₄×C₅	—	3	1	no	—
572	C₂×C₄×C₅	—	3	4	no	—
573	C₂×C₄×C₅	—	3	4	no	—
574	C₂×C₄×C₅	—	3	4	no	—
575	C₂×C₄×C₅	—	3	4	no	—
576	C₂×C₄×C₅	—	3	4	no	—
577	C₂×C₄×C₅	—	3	2	no	—
578	C₂×C₄×C₅	—	6	4	no	—
579	C₂×C₄×C₅	—	6	4	no	—
580	C₂×C₄×C₅	—	6	8	no	—
581	C₂×C₄×C₅	—	6	4	no	—
582	C₂×C₄×C₅	—	6	4	no	—
583	C₂×C₄×C₅	D₃×D₄	1	4	yes	complemented
584	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
585	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
586	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
587	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
588	C₂⁵	—	3	2	no	—
589	C₂×#41	—	3	1	no	—
590	C₂×#41	—	3	2	no	—
591	C₂×#41	—	3	1	no	—
592	C₂×#41	—	3	1	no	—
593	C₂×#41	—	3	2	no	—
594	C₂×#41	—	6	8	no	—
595	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
596	C₂²×Q₈	—	3	1	no	—
597	C₂²×D₄	—	3	2	no	—
598	C₂²×D₄	—	3	2	no	—
599	C₂²×D₄	—	3	2	no	—
600	C₂²×D₄	—	3	2	no	—
601	C₂²×D₄	—	3	2	no	—
602	C₂²×D₄	—	3	2	no	—
603	C₂²×D₄	—	3	1	no	—
604	C₂²×D₄	—	3	8	no	—
605	C₂²×D₄	—	3	1	no	—
606	C₂²×D₄	—	6	8	no	—
607	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
608	C₂³×C₄	—	3	1	no	—
609	C₂³×C₄	—	3	2	no	—
610	#127	—	3	2	no	—
611	#127	—	3	8	no	—
612	#127	—	3	2	no	—
613	#127	—	3	2	no	—
614	#127	C₂×C₅×D₃	1	2	yes	complemented
615	#124	—	3	2	no	—
616	#124	—	3	2	no	—
617	#124	—	3	8	no	—
618	#124	—	3	2	no	—
619	#124	C₂×C₅×D₃	1	2	yes	complemented
620	#121	—	3	4	no	—
621	#121	—	3	8	no	—
622	#121	—	3	4	no	—
623	#121	—	3	4	no	—
624	#121	—	3	8	no	—
625	#121	C₂×C₅×D₃	1	4	yes	complemented
626	#120	—	3	4	no	—
627	#120	—	3	4	no	—
628	#120	—	3	8	no	—
629	#120	—	3	4	no	—
630	#120	—	3	8	no	—
631	#120	C₂×C₅×D₃	1	4	yes	complemented
632	#117	—	3	1	no	—
633	#117	—	3	2	no	—
634	#117	—	3	2	no	—
635	#117	—	3	2	no	—
636	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
637	C₂×C₄⋊C₄	—	3	2	no	—
638	C₂×C₂²⋊C₄	—	3	2	no	—
639	C₂×C₂²⋊C₄	—	3	8	no	—
640	C₂×C₄²	—	3	2	no	—
641	C₂×C₃×C₅	—	2	2	no	—
642	C₂×C₃×C₅	—	4	4	no	—
643	C₂×C₃×C₅	—	4	2	no	—
644	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
645	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
646	C₅×D₃	—	2	2	no	—
647	C₅×D₃	—	4	2	no	—
648	C₅×D₃	—	4	4	no	—
649	C₅×D₃	#535	1	4	yes	direct product factor
650	C₂³×C₃	—	2	4	no	—
651	C₂³×C₃	—	4	4	no	—
652	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
653	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
654	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
655	C₂²×D₃	—	2	4	no	—
656	C₂²×D₃	—	2	4	no	—
657	C₂²×D₃	—	2	4	no	—
658	C₂²×D₃	—	2	8	no	—
659	C₂²×D₃	—	2	8	no	—
660	C₂²×D₃	—	2	8	no	—
661	C₂²×D₃	—	2	16	no	—
662	C₂²×D₃	—	4	8	no	—
663	C₂²×D₃	—	4	4	no	—
664	C₂²×D₃	—	4	32	no	—
665	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
666	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
667	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
668	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
669	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
670	C₃×Q₈	—	2	2	no	—
671	C₃×D₄	—	2	4	no	—
672	C₃×D₄	—	2	4	no	—
673	C₃×D₄	—	2	4	no	—
674	C₃×D₄	—	2	2	no	—
675	C₃×D₄	—	4	8	no	—
676	C₂×C₃×C₄	—	2	4	no	—
677	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
678	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
679	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
680	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
681	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
682	#67	—	2	4	no	—
683	#67	—	2	4	no	—
684	#67	—	2	4	no	—
685	#67	—	2	8	no	—
686	#67	—	2	8	no	—
687	#67	—	4	8	no	—
688	#67	—	4	8	no	—
689	C₂×Dic₃	—	2	4	no	—
690	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	complemented
691	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
692	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
693	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
694	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
695	D₁₂	—	2	4	no	—
696	D₁₂	—	2	4	no	—
697	D₁₂	—	2	4	no	—
698	D₁₂	—	2	2	no	—
699	D₁₂	—	4	8	no	—
700	C₄×D₃	—	2	4	no	—
701	C₄×D₃	—	2	8	no	—
702	C₄×D₃	—	2	4	no	—
703	C₄×D₃	—	2	4	no	—
704	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
705	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
706	C₄×D₃	C₂×C₅×D₄	1	4	yes	complemented
707	C₄×D₃	C₂×C₅×D₄	1	4	yes	complemented
708	Dic₆	—	2	2	no	—
709	Dic₆	—	2	4	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	2	no	—
712	C₂²×C₅	—	2	4	no	—
713	C₂²×C₅	—	2	4	no	—
714	C₂²×C₅	—	2	8	no	—
715	C₂²×C₅	—	3	2	no	—
716	C₂²×C₅	—	3	4	no	—
717	C₂²×C₅	—	3	2	no	—
718	C₂²×C₅	—	4	8	no	—
719	C₂²×C₅	—	6	8	no	—
720	C₂²×C₅	—	6	2	no	—
721	C₂²×C₅	—	6	2	no	—
722	C₂²×C₅	—	6	4	no	—
723	C₂²×C₅	—	6	4	no	—
724	C₂²×C₅	—	6	8	no	—
725	C₂²×C₅	—	12	8	no	—
726	C₂²×C₅	—	12	8	no	—
727	C₂²×C₅	—	12	16	no	—
728	C₂²×C₅	—	12	16	no	—
729	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
730	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
731	C₄×C₅	—	2	2	no	—
732	C₄×C₅	—	2	4	no	—
733	C₄×C₅	—	3	2	no	—
734	C₄×C₅	—	3	2	no	—
735	C₄×C₅	—	6	2	no	—
736	C₄×C₅	—	6	4	no	—
737	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
738	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
739	C₂⁴	—	3	1	no	—
740	C₂⁴	—	3	4	no	—
741	C₂⁴	—	3	2	no	—
742	C₂⁴	—	3	4	no	—
743	C₂⁴	—	3	2	no	—
744	C₂⁴	—	6	8	no	—
745	C₂⁴	—	12	8	no	—
746	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
747	#41	—	2	4	no	—
748	#41	—	6	8	no	—
749	#41	—	6	8	no	—
750	#41	—	6	4	no	—
751	#41	—	6	4	no	—
752	#41	—	6	4	no	—
753	C₂×Q₈	—	3	2	no	—
754	C₂×Q₈	—	3	1	no	—
755	C₂×Q₈	—	6	4	no	—
756	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	3	2	no	—
759	C₂×D₄	—	3	2	no	—
760	C₂×D₄	—	3	4	no	—
761	C₂×D₄	—	3	4	no	—
762	C₂×D₄	—	3	2	no	—
763	C₂×D₄	—	3	8	no	—
764	C₂×D₄	—	3	8	no	—
765	C₂×D₄	—	3	2	no	—
766	C₂×D₄	—	3	2	no	—
767	C₂×D₄	—	3	2	no	—
768	C₂×D₄	—	3	1	no	—
769	C₂×D₄	—	3	8	no	—
770	C₂×D₄	—	6	8	no	—
771	C₂×D₄	—	6	8	no	—
772	C₂×D₄	—	6	8	no	—
773	C₂×D₄	—	6	8	no	—
774	C₂×D₄	—	6	4	no	—
775	C₂×D₄	—	6	8	no	—
776	C₂×D₄	—	6	8	no	—
777	C₂×D₄	—	6	4	no	—
778	C₂×D₄	—	12	16	no	—
779	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
780	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
781	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
782	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
783	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
784	C₂²×C₄	—	3	1	no	—
785	C₂²×C₄	—	3	8	no	—
786	C₂²×C₄	—	3	1	no	—
787	C₂²×C₄	—	3	1	no	—
788	C₂²×C₄	—	3	1	no	—
789	C₂²×C₄	—	3	1	no	—
790	C₂²×C₄	—	3	2	no	—
791	C₂²×C₄	—	3	4	no	—
792	C₂²×C₄	—	3	2	no	—
793	C₂²×C₄	—	3	2	no	—
794	C₂²×C₄	—	3	2	no	—
795	C₂²×C₄	—	6	8	no	—
796	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
797	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	complemented
798	C₄⋊C₄	—	3	4	no	—
799	C₄⋊C₄	—	3	2	no	—
800	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
801	C₂²⋊C₄	—	3	2	no	—
802	C₂²⋊C₄	—	3	8	no	—
803	C₂²⋊C₄	—	3	4	no	—
804	C₂²⋊C₄	—	3	8	no	—
805	C₂²⋊C₄	—	3	8	no	—
806	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
807	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
808	C₄²	—	3	4	no	—
809	C₄²	—	3	2	no	—
810	C₄²	C₂²×C₅×D₃	1	2	yes	complemented
811	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	4	no	—
815	C₂²×C₃	—	2	4	no	—
816	C₂²×C₃	—	2	8	no	—
817	C₂²×C₃	—	4	8	no	—
818	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
819	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
820	C₂×D₃	—	2	2	no	—
821	C₂×D₃	—	2	8	no	—
822	C₂×D₃	—	2	2	no	—
823	C₂×D₃	—	2	4	no	—
824	C₂×D₃	—	2	4	no	—
825	C₂×D₃	—	2	8	no	—
826	C₂×D₃	—	4	16	no	—
827	C₂×D₃	—	4	8	no	—
828	C₂×D₃	—	4	8	no	—
829	C₂×D₃	—	4	16	no	—
830	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
831	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
832	C₂×D₃	C₅×H(5,𝔽₂)	1	4	yes	—
833	C₃×C₄	—	2	2	no	—
834	C₃×C₄	—	2	4	no	—
835	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
836	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
837	Dic₃	—	2	2	no	—
838	Dic₃	—	2	4	no	—
839	Dic₃	C₂²×C₅×D₄	1	2	yes	—
840	Dic₃	C₂²×C₅×D₄	1	2	yes	—
841	C₂×C₅	—	2	2	no	—
842	C₂×C₅	—	3	4	no	—
843	C₂×C₅	—	4	4	no	—
844	C₂×C₅	—	4	2	no	—
845	C₂×C₅	—	6	2	no	—
846	C₂×C₅	—	12	4	no	—
847	C₂×C₅	—	12	2	no	—
848	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
849	C₂×C₅	D₃×H(5,𝔽₂)	1	2	yes	—
850	C₂³	—	2	4	no	—
851	C₂³	—	3	1	no	—
852	C₂³	—	3	4	no	—
853	C₂³	—	3	1	no	—
854	C₂³	—	3	4	no	—
855	C₂³	—	3	2	no	—
856	C₂³	—	4	4	no	—
857	C₂³	—	6	4	no	—
858	C₂³	—	6	4	no	—
859	C₂³	—	6	8	no	—
860	C₂³	—	6	8	no	—
861	C₂³	—	6	8	no	—
862	C₂³	—	6	16	no	—
863	C₂³	—	6	4	no	—
864	C₂³	—	12	4	no	—
865	C₂³	—	12	8	no	—
866	C₂³	—	12	32	no	—
867	C₂³	C₂³×C₅×D₃	1	4	yes	—
868	C₂³	C₂³×C₅×D₃	1	2	yes	—
869	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
870	Q₈	—	2	2	no	—
871	Q₈	—	6	4	no	—
872	Q₈	—	6	2	no	—
873	D₄	—	2	4	no	—
874	D₄	—	2	4	no	—
875	D₄	—	2	4	no	—
876	D₄	—	2	2	no	—
877	D₄	—	4	8	no	—
878	D₄	—	6	4	no	—
879	D₄	—	6	8	no	—
880	D₄	—	6	8	no	—
881	D₄	—	6	4	no	—
882	D₄	—	6	4	no	—
883	D₄	—	6	4	no	—
884	D₄	—	6	4	no	—
885	D₄	—	6	4	no	—
886	D₄	—	6	2	no	—
887	D₄	—	12	8	no	—
888	D₄	—	12	8	no	—
889	D₄	—	12	8	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	3	4	no	—
892	C₂×C₄	—	3	1	no	—
893	C₂×C₄	—	3	1	no	—
894	C₂×C₄	—	3	4	no	—
895	C₂×C₄	—	3	4	no	—
896	C₂×C₄	—	3	4	no	—
897	C₂×C₄	—	3	4	no	—
898	C₂×C₄	—	3	4	no	—
899	C₂×C₄	—	3	2	no	—
900	C₂×C₄	—	6	4	no	—
901	C₂×C₄	—	6	4	no	—
902	C₂×C₄	—	6	8	no	—
903	C₂×C₄	—	6	4	no	—
904	C₂×C₄	—	6	4	no	—
905	C₂×C₄	C₅×D₃×D₄	1	4	yes	complemented
906	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
907	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
908	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
909	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
910	C₂×C₃	—	2	2	no	—
911	C₂×C₃	—	4	4	no	—
912	C₂×C₃	—	4	2	no	—
913	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
914	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
915	D₃	—	2	2	no	—
916	D₃	—	4	4	no	—
917	D₃	—	4	2	no	—
918	D₃	C₅×#535	1	4	yes	direct product factor
919	C₅	D₃×#535	1	1	yes	characteristic, direct product factor, Sylow
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	4	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	3	2	no	—
926	C₂²	—	3	4	no	—
927	C₂²	—	3	2	no	—
928	C₂²	—	4	8	no	—
929	C₂²	—	6	8	no	—
930	C₂²	—	6	2	no	—
931	C₂²	—	6	2	no	—
932	C₂²	—	6	4	no	—
933	C₂²	—	6	4	no	—
934	C₂²	—	6	8	no	—
935	C₂²	—	12	8	no	—
936	C₂²	—	12	16	no	—
937	C₂²	—	12	8	no	—
938	C₂²	—	12	16	no	—
939	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
940	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
941	C₄	—	2	2	no	—
942	C₄	—	2	4	no	—
943	C₄	—	3	2	no	—
944	C₄	—	3	2	no	—
945	C₄	—	6	2	no	—
946	C₄	—	6	4	no	—
947	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
948	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
949	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
950	C₂	—	2	2	no	—
951	C₂	—	3	4	no	—
952	C₂	—	4	4	no	—
953	C₂	—	4	2	no	—
954	C₂	—	6	2	no	—
955	C₂	—	12	4	no	—
956	C₂	—	12	2	no	—
957	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
958	C₂	C₅×D₃×H(5,𝔽₂)	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×#535	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#535	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#535

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×D₃×D₄	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₅×#5830	C₂	semidirect
5. C₅×#5805	C₂	semidirect
6. C₅×#5715	C₂	semidirect
7. C₅×D₃×#127	C₂	semidirect
8. C₅×#5674	C₂	semidirect
9. C₅×D₃×#124	C₂	semidirect
10. C₅×#5607	C₂	semidirect
11. C₅×D₃×#121	C₂	semidirect
12. C₅×#5592	C₂	semidirect
13. C₅×D₃×#120	C₂	semidirect
14. C₅×#5525	C₂	semidirect
15. C₅×D₃×#117	C₂	semidirect
18. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂²×C₅×#67	C₂²	semidirect
22. C₂×C₅×#239	C₂²	semidirect
23. C₂×C₅×D₃×Q₈	C₂²	semidirect
24. C₂×C₅×#237	C₂²	semidirect
25. C₂×C₅×#237	C₂²	semidirect
30. C₂×C₅×D₃×D₄	C₂²	semidirect
31. C₂×C₅×D₃×D₄	C₂²	semidirect
32. C₂×C₅×D₃×D₄	C₂²	semidirect
33. C₂×C₅×D₃×D₄	C₂²	semidirect
34. C₂×C₅×#235	C₂²	semidirect
35. C₂×C₅×#235	C₂²	semidirect
36. C₂²×C₅×D₁₂	C₂²	semidirect
38. C₂²×C₄×C₅×D₃	C₂²	semidirect
39. C₃×C₅×#127	C₂²	semidirect
40. C₃×C₅×#124	C₂²	semidirect
41. C₃×C₅×#121	C₂²	semidirect
42. C₃×C₅×#120	C₂²	semidirect
43. C₃×C₅×#117	C₂²	semidirect
44. C₅×#953	C₂²	semidirect
45. C₅×#947	C₂²	semidirect
46. C₅×#940	C₂²	semidirect
47. C₅×#940	C₂²	semidirect
48. C₅×#940	C₂²	semidirect
49. C₅×#939	C₂²	semidirect
50. C₅×#938	C₂²	semidirect
51. C₅×#937	C₂²	semidirect
52. C₅×#937	C₂²	semidirect
53. C₅×#936	C₂²	semidirect
54. C₅×#930	C₂²	semidirect
55. C₅×#926	C₂²	semidirect
56. C₅×#895	C₂²	semidirect
57. C₅×#892	C₂²	semidirect
58. C₅×D₃×C₄⋊C₄	C₂²	semidirect
59. C₅×#885	C₂²	semidirect
60. C₅×#884	C₂²	semidirect
61. C₅×#882	C₂²	semidirect
62. C₅×#882	C₂²	semidirect
64. C₅×D₃×C₂²⋊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. D₃×#535	C₅	direct (N × H)
80. C₅×#535	D₃	direct (N × H)
95. C₂×C₃×C₅×Q₈	C₂³	semidirect
100. C₂×C₃×C₅×D₄	C₂³	semidirect
101. C₂×C₃×C₅×D₄	C₂³	semidirect
103. C₂²×C₃×C₄×C₅	C₂³	semidirect
109. C₂×C₅×#67	C₂³	semidirect
110. C₂×C₅×#67	C₂³	semidirect
111. C₂×C₅×#67	C₂³	semidirect
113. C₂²×C₅×Dic₃	C₂³	semidirect
131. C₂×C₅×D₁₂	C₂³	semidirect
132. C₂×C₅×D₁₂	C₂³	semidirect
134. C₂×C₄×C₅×D₃	D₄	semidirect
141. C₂×C₄×C₅×D₃	C₂³	semidirect
142. C₂×C₄×C₅×D₃	C₂³	semidirect
143. C₂×C₅×Dic₆	C₂³	semidirect
144. C₂×C₅×Dic₆	C₂³	semidirect
145. C₃×C₅×C₄⋊C₄	C₂³	semidirect
147. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
148. C₃×C₄²×C₅	C₂³	semidirect
150. C₅×#217	C₂³	semidirect
152. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
153. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
154. C₅×C₄⋊Dic₃	C₂³	semidirect
155. C₅×Dic₃⋊C₄	C₂³	semidirect
156. C₄×C₅×Dic₃	C₂³	semidirect
157. C₄×C₅×Dic₃	C₂³	semidirect
158. C₂×D₃×#41	C₂×C₅	semidirect
159. C₂²×D₃×D₄	C₂×C₅	semidirect
160. C₃×#535	C₂×C₅	semidirect
161. #5830	C₂×C₅	semidirect
162. #5805	C₂×C₅	semidirect
163. #5715	C₂×C₅	semidirect
164. D₃×#127	C₂×C₅	semidirect
165. #5674	C₂×C₅	semidirect
166. D₃×#124	C₂×C₅	semidirect
167. #5607	C₂×C₅	semidirect
168. D₃×#121	C₂×C₅	semidirect
169. #5592	C₂×C₅	semidirect
170. D₃×#120	C₂×C₅	semidirect
171. #5525	C₂×C₅	semidirect
172. D₃×#117	C₂×C₅	semidirect
180. C₂×C₅×#41	C₂×D₃	semidirect
192. C₂²×C₅×D₄	C₂×D₃	semidirect
199. C₅×#127	C₂×D₃	semidirect
204. C₅×#124	C₂×D₃	semidirect
210. C₅×#121	C₂×D₃	semidirect
216. C₅×#120	C₂×D₃	semidirect
221. C₅×#117	C₂×D₃	semidirect
254. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
267. C₂×C₅×Dic₃	C₂×D₄	semidirect
283. C₄×C₅×D₃	C₂×D₄	semidirect
284. C₄×C₅×D₃	C₂×D₄	semidirect
288. C₂×C₃×#41	C₂²×C₅	semidirect
289. C₂²×C₃×D₄	C₂²×C₅	semidirect
290. C₂²×#67	C₂²×C₅	semidirect
292. C₂×#239	C₂²×C₅	semidirect
293. C₂×D₃×Q₈	C₂²×C₅	semidirect
294. C₂×#237	C₂²×C₅	semidirect
295. C₂×#237	C₂²×C₅	semidirect
300. C₂×D₃×D₄	C₂²×C₅	semidirect
301. C₂×D₃×D₄	C₂²×C₅	semidirect
302. C₂×D₃×D₄	C₂²×C₅	semidirect
303. C₂×D₃×D₄	C₂²×C₅	semidirect
304. C₂×#235	C₂²×C₅	semidirect
305. C₂×#235	C₂²×C₅	semidirect
306. C₂²×D₁₂	C₂²×C₅	semidirect
308. C₂²×C₄×D₃	C₂²×C₅	semidirect
309. C₃×#127	C₂²×C₅	semidirect
310. C₃×#124	C₂²×C₅	semidirect
311. C₃×#121	C₂²×C₅	semidirect
312. C₃×#120	C₂²×C₅	semidirect
313. C₃×#117	C₂²×C₅	semidirect
314. #953	C₂²×C₅	semidirect
315. #947	C₂²×C₅	semidirect
316. #940	C₂²×C₅	semidirect
317. #940	C₂²×C₅	semidirect
318. #940	C₂²×C₅	semidirect
319. #939	C₂²×C₅	semidirect
320. #938	C₂²×C₅	semidirect
321. #937	C₂²×C₅	semidirect
322. #937	C₂²×C₅	semidirect
323. #936	C₂²×C₅	semidirect
324. #930	C₂²×C₅	semidirect
325. #926	C₂²×C₅	semidirect
326. #895	C₂²×C₅	semidirect
327. #892	C₂²×C₅	semidirect
328. D₃×C₄⋊C₄	C₂²×C₅	semidirect
329. #885	C₂²×C₅	semidirect
330. #884	C₂²×C₅	semidirect
331. #882	C₂²×C₅	semidirect
332. #882	C₂²×C₅	semidirect
334. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
335. #877	C₂²×C₅	semidirect
336. #875	C₂²×C₅	semidirect
337. #874	C₂²×C₅	semidirect
338. #872	C₂²×C₅	semidirect
339. C₄²×D₃	C₂²×C₅	semidirect
357. C₂×C₅×Q₈	C₂²×D₃	semidirect
383. C₂×C₅×D₄	C₂²×D₃	semidirect
384. C₂×C₅×D₄	C₂²×D₃	semidirect
398. C₂²×C₄×C₅	C₂²×D₃	semidirect
401. C₅×C₄⋊C₄	C₂²×D₃	semidirect
408. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
411. C₄²×C₅	C₂²×D₃	semidirect
421. #535	C₅×D₃	direct (N × H)
465. C₂×C₃×Q₈	C₂³×C₅	semidirect
470. C₂×C₃×D₄	C₂³×C₅	semidirect
471. C₂×C₃×D₄	C₂³×C₅	semidirect
473. C₂²×C₃×C₄	C₂³×C₅	semidirect
479. C₂×#67	C₂³×C₅	semidirect
480. C₂×#67	C₂³×C₅	semidirect
481. C₂×#67	C₂³×C₅	semidirect
483. C₂²×Dic₃	C₂³×C₅	semidirect
501. C₂×D₁₂	C₂³×C₅	semidirect
502. C₂×D₁₂	C₂³×C₅	semidirect
504. C₂×C₄×D₃	C₅×D₄	semidirect
511. C₂×C₄×D₃	C₂³×C₅	semidirect
512. C₂×C₄×D₃	C₂³×C₅	semidirect
513. C₂×Dic₆	C₂³×C₅	semidirect
514. C₂×Dic₆	C₂³×C₅	semidirect
515. C₃×C₄⋊C₄	C₂³×C₅	semidirect
517. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
518. C₃×C₄²	C₂³×C₅	semidirect
520. #217	C₂³×C₅	semidirect
522. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
523. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
524. C₄⋊Dic₃	C₂³×C₅	semidirect
525. Dic₃⋊C₄	C₂³×C₅	semidirect
526. C₄×Dic₃	C₂³×C₅	semidirect
527. C₄×Dic₃	C₂³×C₅	semidirect
583. C₂×C₄×C₅	D₃×D₄	semidirect
595. C₂×#41	C₂×C₅×D₃	semidirect
607. C₂²×D₄	C₂×C₅×D₃	semidirect
614. #127	C₂×C₅×D₃	semidirect
619. #124	C₂×C₅×D₃	semidirect
625. #121	C₂×C₅×D₃	semidirect
631. #120	C₂×C₅×D₃	semidirect
636. #117	C₂×C₅×D₃	semidirect
649. C₅×D₃	#535	direct (N × H)
677. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
690. C₂×Dic₃	C₂×C₅×D₄	semidirect
706. C₄×D₃	C₂×C₅×D₄	semidirect
707. C₄×D₃	C₂×C₅×D₄	semidirect
756. C₂×Q₈	C₂²×C₅×D₃	semidirect
782. C₂×D₄	C₂²×C₅×D₃	semidirect
783. C₂×D₄	C₂²×C₅×D₃	semidirect
797. C₂²×C₄	C₂²×C₅×D₃	semidirect
800. C₄⋊C₄	C₂²×C₅×D₃	semidirect
807. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
810. C₄²	C₂²×C₅×D₃	semidirect
811. C₃×C₅	C₂×#535	semidirect
905. C₂×C₄	C₅×D₃×D₄	semidirect
918. D₃	C₅×#535	direct (N × H)
919. C₅	D₃×#535	direct (N × H)
949. C₃	C₂×C₅×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₂²×C₅×D₃×D₄	2
C₃×C₅×#535	2
C₅×#5830	2
C₅×#5805	2
C₅×#5715	2
C₅×D₃×#127	2
C₅×#5674	2
C₅×D₃×#124	2
C₅×#5607	2
C₅×D₃×#121	2
C₅×#5592	2
C₅×D₃×#120	2
C₅×#5525	2
C₅×D₃×#117	2
C₂×C₅×#535	3
D₃×#535	5

Subgroups — C5×D3×#535 #14480359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#535 #14480359