Subgroups — C₃×C₅×#3536 #14276570

Order 1920.

2268 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#562	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#546	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#543	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3536	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₅×#41	C₂²	1	4	yes	complemented
19	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
20	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
23	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#126	C₂²	1	4	yes	complemented
26	C₃×C₅×#125	C₂²	1	4	yes	complemented
27	C₃×C₅×#124	C₂²	1	4	yes	complemented
28	C₃×C₅×#124	C₂²	1	2	yes	complemented
29	C₃×C₅×#124	C₂²	1	4	yes	complemented
30	C₃×C₅×#123	C₂²	1	2	yes	complemented
31	C₃×C₅×#123	C₂²	1	4	yes	complemented
32	C₃×C₅×#123	C₂²	1	4	yes	complemented
33	C₃×C₅×#123	C₂²	1	4	yes	complemented
34	C₃×C₅×#123	C₂²	1	4	yes	complemented
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
39	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
48	C₃×C₅×#121	C₂²	1	2	yes	—
49	C₃×C₅×#121	C₂²	1	2	yes	—
50	C₃×C₅×#121	C₂²	1	2	yes	—
51	C₃×C₅×#121	C₂²	1	2	yes	—
52	C₃×C₅×#121	C₂²	1	1	yes	characteristic
53	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#121	C₂²	1	4	yes	complemented
55	C₃×C₅×#121	C₂²	1	2	yes	complemented
56	C₃×C₅×#121	C₂²	1	4	yes	complemented
57	C₃×C₅×#121	C₂²	1	4	yes	complemented
58	C₃×C₅×#121	C₂²	1	4	yes	complemented
59	C₃×C₅×#121	C₂²	1	4	yes	complemented
60	C₃×C₅×#120	C₂²	1	2	yes	—
61	C₃×C₅×#120	C₂²	1	4	yes	—
62	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
63	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
64	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
65	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
66	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
67	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
68	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
71	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
74	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
76	C₃×#3536	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#562	C₂×C₃	1	4	yes	complemented
78	C₅×#554	C₂×C₃	1	2	yes	complemented
79	C₅×#548	C₂×C₃	1	2	yes	complemented
80	C₅×#547	C₂×C₃	1	2	yes	complemented
81	C₅×#546	C₂×C₃	1	4	yes	complemented
82	C₅×#546	C₂×C₃	1	2	yes	complemented
83	C₅×#543	C₂×C₃	1	2	yes	complemented
84	C₅×#542	C₂×C₃	1	2	yes	complemented
85	C₅×#539	C₂×C₃	1	2	yes	complemented
86	C₅×#538	C₂×C₃	1	2	yes	complemented
87	C₅×#537	C₂×C₃	1	2	yes	complemented
88	C₅×#537	C₂×C₃	1	2	yes	complemented
89	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
93	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
94	C₃×C₅×#41	—	4	2	no	—
95	C₃×C₅×#41	—	4	8	no	—
96	C₃×C₅×#41	—	4	4	no	—
97	C₂×C₃×C₅×Q₈	—	4	2	no	—
98	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
99	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
100	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
102	C₂×C₃×C₅×D₄	—	4	2	no	—
103	C₂×C₃×C₅×D₄	—	4	4	no	—
104	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
106	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
107	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
108	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
109	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
110	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
111	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
112	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
113	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₄×C₅	—	4	2	no	—
115	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
116	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
118	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
122	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
123	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
124	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
125	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
126	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
127	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₄²×C₅	C₂³	1	2	yes	—
157	C₃×C₄²×C₅	C₂³	1	4	yes	—
158	C₃×#562	C₂×C₅	1	4	yes	complemented
159	C₃×#554	C₂×C₅	1	2	yes	complemented
160	C₃×#548	C₂×C₅	1	2	yes	complemented
161	C₃×#547	C₂×C₅	1	2	yes	complemented
162	C₃×#546	C₂×C₅	1	4	yes	complemented
163	C₃×#546	C₂×C₅	1	2	yes	complemented
164	C₃×#543	C₂×C₅	1	2	yes	complemented
165	C₃×#542	C₂×C₅	1	2	yes	complemented
166	C₃×#539	C₂×C₅	1	2	yes	complemented
167	C₃×#538	C₂×C₅	1	2	yes	complemented
168	C₃×#537	C₂×C₅	1	2	yes	complemented
169	C₃×#537	C₂×C₅	1	2	yes	complemented
170	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
173	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂×C₅×#41	C₂²×C₃	1	4	yes	complemented
175	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
176	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
178	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
179	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
181	C₅×#126	C₂²×C₃	1	4	yes	complemented
182	C₅×#125	C₂²×C₃	1	4	yes	complemented
183	C₅×#124	C₂²×C₃	1	4	yes	complemented
184	C₅×#124	C₂²×C₃	1	2	yes	complemented
185	C₅×#124	C₂²×C₃	1	4	yes	complemented
186	C₅×#123	C₂²×C₃	1	2	yes	complemented
187	C₅×#123	C₂²×C₃	1	4	yes	complemented
188	C₅×#123	C₂²×C₃	1	4	yes	complemented
189	C₅×#123	C₂²×C₃	1	4	yes	complemented
190	C₅×#123	C₂²×C₃	1	4	yes	complemented
191	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
192	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
193	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
196	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
197	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
199	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
200	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
201	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
202	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
203	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
204	C₅×#121	C₂²×C₃	1	2	yes	—
205	C₅×#121	C₂²×C₃	1	2	yes	—
206	C₅×#121	C₂²×C₃	1	2	yes	—
207	C₅×#121	C₂²×C₃	1	2	yes	—
208	C₅×#121	C₂²×C₃	1	1	yes	characteristic
209	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₅×#121	C₂²×C₃	1	4	yes	complemented
211	C₅×#121	C₂²×C₃	1	2	yes	complemented
212	C₅×#121	C₂²×C₃	1	4	yes	complemented
213	C₅×#121	C₂²×C₃	1	4	yes	complemented
214	C₅×#121	C₂²×C₃	1	4	yes	complemented
215	C₅×#121	C₂²×C₃	1	4	yes	complemented
216	C₅×#120	C₂²×C₃	1	2	yes	—
217	C₅×#120	C₂²×C₃	1	4	yes	—
218	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
219	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
220	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
221	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
222	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
223	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
224	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
225	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
226	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
227	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
229	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
230	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
231	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
232	#3536	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
233	C₂³×C₃×C₅	—	2	2	no	—
234	C₂³×C₃×C₅	—	2	2	no	—
235	C₂³×C₃×C₅	—	2	4	no	—
236	C₂³×C₃×C₅	—	4	1	no	—
237	C₂³×C₃×C₅	—	4	2	no	—
238	C₂³×C₃×C₅	—	4	2	no	—
239	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
240	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
241	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
242	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
243	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
244	C₃×C₅×Q₈	—	2	4	no	—
245	C₃×C₅×Q₈	—	4	2	no	—
246	C₃×C₅×Q₈	—	4	1	no	—
247	C₃×C₅×Q₈	—	4	4	no	—
248	C₃×C₅×D₄	—	2	8	no	—
249	C₃×C₅×D₄	—	2	4	no	—
250	C₃×C₅×D₄	—	2	4	no	—
251	C₃×C₅×D₄	—	2	4	no	—
252	C₃×C₅×D₄	—	4	2	no	—
253	C₃×C₅×D₄	—	4	4	no	—
254	C₃×C₅×D₄	—	4	2	no	—
255	C₃×C₅×D₄	—	4	1	no	—
256	C₃×C₅×D₄	—	4	4	no	—
257	C₃×C₅×D₄	—	4	4	no	—
258	C₂×C₃×C₄×C₅	—	2	4	no	—
259	C₂×C₃×C₄×C₅	—	2	2	no	—
260	C₂×C₃×C₄×C₅	—	2	2	no	—
261	C₂×C₃×C₄×C₅	—	2	2	no	—
262	C₂×C₃×C₄×C₅	—	2	4	no	—
263	C₂×C₃×C₄×C₅	—	4	1	no	—
264	C₂×C₃×C₄×C₅	—	4	1	no	—
265	C₂×C₃×C₄×C₅	—	4	1	no	—
266	C₂×C₃×C₄×C₅	—	4	2	no	—
267	C₂×C₃×C₄×C₅	—	4	2	no	—
268	C₂×C₃×C₄×C₅	—	4	4	no	—
269	C₂×C₃×C₄×C₅	—	4	4	no	—
270	C₂×C₃×C₄×C₅	—	4	4	no	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
274	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
275	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
278	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×C₃×#41	C₂²×C₅	1	4	yes	complemented
283	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
284	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
286	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
287	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
288	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
289	C₃×#126	C₂²×C₅	1	4	yes	complemented
290	C₃×#125	C₂²×C₅	1	4	yes	complemented
291	C₃×#124	C₂²×C₅	1	4	yes	complemented
292	C₃×#124	C₂²×C₅	1	4	yes	complemented
293	C₃×#124	C₂²×C₅	1	2	yes	complemented
294	C₃×#123	C₂²×C₅	1	2	yes	complemented
295	C₃×#123	C₂²×C₅	1	4	yes	complemented
296	C₃×#123	C₂²×C₅	1	4	yes	complemented
297	C₃×#123	C₂²×C₅	1	4	yes	complemented
298	C₃×#123	C₂²×C₅	1	4	yes	complemented
299	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
300	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
301	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
302	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
303	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
304	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
305	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
306	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
307	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
308	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
310	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
311	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
312	C₃×#121	C₂²×C₅	1	2	yes	—
313	C₃×#121	C₂²×C₅	1	2	yes	—
314	C₃×#121	C₂²×C₅	1	2	yes	—
315	C₃×#121	C₂²×C₅	1	2	yes	—
316	C₃×#121	C₂²×C₅	1	1	yes	characteristic
317	C₃×#121	C₂²×C₅	1	4	yes	complemented
318	C₃×#121	C₂²×C₅	1	4	yes	complemented
319	C₃×#121	C₂²×C₅	1	4	yes	complemented
320	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₃×#121	C₂²×C₅	1	4	yes	complemented
322	C₃×#121	C₂²×C₅	1	2	yes	complemented
323	C₃×#121	C₂²×C₅	1	4	yes	complemented
324	C₃×#120	C₂²×C₅	1	2	yes	—
325	C₃×#120	C₂²×C₅	1	4	yes	—
326	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
327	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
328	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
329	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
330	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
331	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
332	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
333	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
334	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
335	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
336	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
337	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
338	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
339	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
340	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
341	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
342	C₅×#41	—	4	2	no	—
343	C₅×#41	—	4	8	no	—
344	C₅×#41	—	4	4	no	—
345	C₂×C₅×Q₈	—	4	2	no	—
346	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
347	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
348	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
349	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
350	C₂×C₅×D₄	—	4	2	no	—
351	C₂×C₅×D₄	—	4	4	no	—
352	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
353	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
354	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
355	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
356	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
357	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
358	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
359	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
360	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
361	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
362	C₂²×C₄×C₅	—	4	2	no	—
363	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
364	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
366	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
369	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
370	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
371	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
372	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
373	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
375	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
376	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
377	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
380	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
381	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
382	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
384	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
385	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
387	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
388	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
390	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
392	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
393	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
394	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
395	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
396	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
397	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
398	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
399	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
400	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
401	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
402	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
403	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
404	C₄²×C₅	C₂³×C₃	1	2	yes	—
405	C₄²×C₅	C₂³×C₃	1	4	yes	—
406	#562	C₂×C₃×C₅	1	4	yes	complemented
407	#554	C₂×C₃×C₅	1	2	yes	complemented
408	#548	C₂×C₃×C₅	1	2	yes	complemented
409	#547	C₂×C₃×C₅	1	2	yes	complemented
410	#546	C₂×C₃×C₅	1	4	yes	complemented
411	#546	C₂×C₃×C₅	1	2	yes	complemented
412	#543	C₂×C₃×C₅	1	2	yes	complemented
413	#542	C₂×C₃×C₅	1	2	yes	complemented
414	#539	C₂×C₃×C₅	1	2	yes	complemented
415	#538	C₂×C₃×C₅	1	2	yes	complemented
416	#537	C₂×C₃×C₅	1	2	yes	complemented
417	#537	C₂×C₃×C₅	1	2	yes	complemented
418	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
419	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
420	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
421	C₂²×C₃×C₅	—	2	1	no	—
422	C₂²×C₃×C₅	—	2	1	no	—
423	C₂²×C₃×C₅	—	2	1	no	—
424	C₂²×C₃×C₅	—	2	1	no	—
425	C₂²×C₃×C₅	—	2	1	no	—
426	C₂²×C₃×C₅	—	2	2	no	—
427	C₂²×C₃×C₅	—	2	2	no	—
428	C₂²×C₃×C₅	—	2	4	no	—
429	C₂²×C₃×C₅	—	2	4	no	—
430	C₂²×C₃×C₅	—	2	1	no	—
431	C₂²×C₃×C₅	—	2	2	no	—
432	C₂²×C₃×C₅	—	2	1	no	—
433	C₂²×C₃×C₅	—	2	4	no	—
434	C₂²×C₃×C₅	—	4	4	no	—
435	C₂²×C₃×C₅	—	8	4	no	—
436	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
437	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
438	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
439	C₃×C₄×C₅	—	2	1	no	—
440	C₃×C₄×C₅	—	2	4	no	—
441	C₃×C₄×C₅	—	2	1	no	—
442	C₃×C₄×C₅	—	2	2	no	—
443	C₃×C₄×C₅	—	2	1	no	—
444	C₃×C₄×C₅	—	2	4	no	—
445	C₃×C₄×C₅	—	2	2	no	—
446	C₃×C₄×C₅	—	2	4	no	—
447	C₃×C₄×C₅	—	2	2	no	—
448	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
449	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
450	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
451	C₃×#41	—	4	2	no	—
452	C₃×#41	—	4	8	no	—
453	C₃×#41	—	4	4	no	—
454	C₂×C₃×Q₈	—	4	2	no	—
455	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
456	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
457	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
458	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
459	C₂×C₃×D₄	—	4	2	no	—
460	C₂×C₃×D₄	—	4	4	no	—
461	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
462	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
463	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
464	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
465	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
466	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
467	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
468	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
469	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
470	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
471	C₂²×C₃×C₄	—	4	2	no	—
472	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
473	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
475	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
477	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
479	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
480	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
481	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
482	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
484	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
485	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
486	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
487	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
488	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
489	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
490	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
491	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
492	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
493	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
494	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
495	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
496	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
497	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
498	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
504	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
505	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
506	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
507	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
508	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
509	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
510	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
511	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
512	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
513	C₃×C₄²	C₂³×C₅	1	2	yes	—
514	C₃×C₄²	C₂³×C₅	1	4	yes	—
515	C₂³×C₅	—	2	2	no	—
516	C₂³×C₅	—	2	2	no	—
517	C₂³×C₅	—	2	4	no	—
518	C₂³×C₅	—	4	1	no	—
519	C₂³×C₅	—	4	2	no	—
520	C₂³×C₅	—	4	2	no	—
521	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
522	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
523	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
524	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
525	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
526	C₅×Q₈	—	2	4	no	—
527	C₅×Q₈	—	4	2	no	—
528	C₅×Q₈	—	4	1	no	—
529	C₅×Q₈	—	4	4	no	—
530	C₅×D₄	—	2	8	no	—
531	C₅×D₄	—	2	4	no	—
532	C₅×D₄	—	2	4	no	—
533	C₅×D₄	—	2	4	no	—
534	C₅×D₄	—	4	2	no	—
535	C₅×D₄	—	4	4	no	—
536	C₅×D₄	—	4	2	no	—
537	C₅×D₄	—	4	1	no	—
538	C₅×D₄	—	4	4	no	—
539	C₅×D₄	—	4	4	no	—
540	C₂×C₄×C₅	—	2	4	no	—
541	C₂×C₄×C₅	—	2	2	no	—
542	C₂×C₄×C₅	—	2	2	no	—
543	C₂×C₄×C₅	—	2	2	no	—
544	C₂×C₄×C₅	—	2	4	no	—
545	C₂×C₄×C₅	—	4	1	no	—
546	C₂×C₄×C₅	—	4	1	no	—
547	C₂×C₄×C₅	—	4	1	no	—
548	C₂×C₄×C₅	—	4	2	no	—
549	C₂×C₄×C₅	—	4	2	no	—
550	C₂×C₄×C₅	—	4	4	no	—
551	C₂×C₄×C₅	—	4	4	no	—
552	C₂×C₄×C₅	—	4	4	no	—
553	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
554	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
555	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
556	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
557	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
558	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
559	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
560	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
561	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
562	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
563	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
564	C₂×#41	C₂²×C₃×C₅	1	4	yes	complemented
565	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
566	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
567	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
568	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
569	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
570	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
571	#126	C₂²×C₃×C₅	1	4	yes	complemented
572	#125	C₂²×C₃×C₅	1	4	yes	complemented
573	#124	C₂²×C₃×C₅	1	4	yes	complemented
574	#124	C₂²×C₃×C₅	1	2	yes	complemented
575	#124	C₂²×C₃×C₅	1	4	yes	complemented
576	#123	C₂²×C₃×C₅	1	2	yes	complemented
577	#123	C₂²×C₃×C₅	1	4	yes	complemented
578	#123	C₂²×C₃×C₅	1	4	yes	complemented
579	#123	C₂²×C₃×C₅	1	4	yes	complemented
580	#123	C₂²×C₃×C₅	1	4	yes	complemented
581	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
582	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
583	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
585	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
586	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
587	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
588	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
589	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
590	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
591	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
592	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
593	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
594	#121	C₂²×C₃×C₅	1	2	yes	—
595	#121	C₂²×C₃×C₅	1	2	yes	—
596	#121	C₂²×C₃×C₅	1	2	yes	—
597	#121	C₂²×C₃×C₅	1	2	yes	—
598	#121	C₂²×C₃×C₅	1	1	yes	characteristic
599	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
600	#121	C₂²×C₃×C₅	1	4	yes	complemented
601	#121	C₂²×C₃×C₅	1	2	yes	complemented
602	#121	C₂²×C₃×C₅	1	4	yes	complemented
603	#121	C₂²×C₃×C₅	1	4	yes	complemented
604	#121	C₂²×C₃×C₅	1	4	yes	complemented
605	#121	C₂²×C₃×C₅	1	4	yes	complemented
606	#120	C₂²×C₃×C₅	1	2	yes	—
607	#120	C₂²×C₃×C₅	1	4	yes	—
608	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
609	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
610	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
611	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
612	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
613	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
614	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
615	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
617	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
618	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
619	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
622	C₂×C₃×C₅	—	2	2	no	—
623	C₂×C₃×C₅	—	2	2	no	—
624	C₂×C₃×C₅	—	4	2	no	—
625	C₂×C₃×C₅	—	4	1	no	—
626	C₂×C₃×C₅	—	4	4	no	—
627	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
630	C₂³×C₃	—	2	2	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	2	4	no	—
633	C₂³×C₃	—	4	1	no	—
634	C₂³×C₃	—	4	2	no	—
635	C₂³×C₃	—	4	2	no	—
636	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
637	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
638	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
639	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
640	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
641	C₃×Q₈	—	2	4	no	—
642	C₃×Q₈	—	4	2	no	—
643	C₃×Q₈	—	4	1	no	—
644	C₃×Q₈	—	4	4	no	—
645	C₃×D₄	—	2	8	no	—
646	C₃×D₄	—	2	4	no	—
647	C₃×D₄	—	2	4	no	—
648	C₃×D₄	—	2	4	no	—
649	C₃×D₄	—	4	2	no	—
650	C₃×D₄	—	4	4	no	—
651	C₃×D₄	—	4	2	no	—
652	C₃×D₄	—	4	1	no	—
653	C₃×D₄	—	4	4	no	—
654	C₃×D₄	—	4	4	no	—
655	C₂×C₃×C₄	—	2	4	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	4	no	—
660	C₂×C₃×C₄	—	4	1	no	—
661	C₂×C₃×C₄	—	4	1	no	—
662	C₂×C₃×C₄	—	4	1	no	—
663	C₂×C₃×C₄	—	4	2	no	—
664	C₂×C₃×C₄	—	4	2	no	—
665	C₂×C₃×C₄	—	4	4	no	—
666	C₂×C₃×C₄	—	4	4	no	—
667	C₂×C₃×C₄	—	4	4	no	—
668	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
669	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
670	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
671	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
672	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
673	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
674	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
675	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
676	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
677	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
678	C₂²×C₅	—	2	1	no	—
679	C₂²×C₅	—	2	1	no	—
680	C₂²×C₅	—	2	1	no	—
681	C₂²×C₅	—	2	1	no	—
682	C₂²×C₅	—	2	1	no	—
683	C₂²×C₅	—	2	2	no	—
684	C₂²×C₅	—	2	2	no	—
685	C₂²×C₅	—	2	4	no	—
686	C₂²×C₅	—	2	4	no	—
687	C₂²×C₅	—	2	1	no	—
688	C₂²×C₅	—	2	2	no	—
689	C₂²×C₅	—	2	1	no	—
690	C₂²×C₅	—	2	4	no	—
691	C₂²×C₅	—	4	4	no	—
692	C₂²×C₅	—	8	4	no	—
693	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
694	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
695	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
696	C₄×C₅	—	2	1	no	—
697	C₄×C₅	—	2	4	no	—
698	C₄×C₅	—	2	1	no	—
699	C₄×C₅	—	2	2	no	—
700	C₄×C₅	—	2	1	no	—
701	C₄×C₅	—	2	4	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	4	no	—
704	C₄×C₅	—	2	2	no	—
705	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
706	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
707	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
708	#41	—	4	2	no	—
709	#41	—	4	8	no	—
710	#41	—	4	4	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
713	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
714	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
715	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
719	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
720	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
721	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
722	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
723	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
724	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
725	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
726	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
727	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
730	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
731	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
732	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
733	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
734	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
735	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
736	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
737	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
738	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
739	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
740	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
741	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
742	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
743	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
744	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
745	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
746	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
747	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
748	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
749	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
750	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
751	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
752	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
753	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
754	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
755	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
756	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
757	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
758	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
759	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
760	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
761	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
762	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
763	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
764	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
765	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
766	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
767	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
768	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
769	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
770	C₄²	C₂³×C₃×C₅	1	2	yes	—
771	C₄²	C₂³×C₃×C₅	1	4	yes	—
772	C₃×C₅	#3536	1	1	yes	characteristic, direct product factor, Hall
773	C₂²×C₃	—	2	1	no	—
774	C₂²×C₃	—	2	1	no	—
775	C₂²×C₃	—	2	1	no	—
776	C₂²×C₃	—	2	1	no	—
777	C₂²×C₃	—	2	1	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	4	no	—
781	C₂²×C₃	—	2	4	no	—
782	C₂²×C₃	—	2	1	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	2	4	no	—
786	C₂²×C₃	—	4	4	no	—
787	C₂²×C₃	—	8	4	no	—
788	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
789	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
790	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
791	C₃×C₄	—	2	1	no	—
792	C₃×C₄	—	2	4	no	—
793	C₃×C₄	—	2	1	no	—
794	C₃×C₄	—	2	2	no	—
795	C₃×C₄	—	2	1	no	—
796	C₃×C₄	—	2	4	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	4	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
801	C₂×C₅	—	2	2	no	—
802	C₂×C₅	—	2	2	no	—
803	C₂×C₅	—	4	1	no	—
804	C₂×C₅	—	4	4	no	—
805	C₂×C₅	—	4	2	no	—
806	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
808	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	4	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	2	no	—
814	C₂³	—	4	2	no	—
815	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
816	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
817	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
818	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
819	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	4	no	—
824	D₄	—	2	8	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
848	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
849	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
850	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
851	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
852	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
853	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
854	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
855	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
856	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
857	C₂×C₃	—	2	2	no	—
858	C₂×C₃	—	2	2	no	—
859	C₂×C₃	—	4	1	no	—
860	C₂×C₃	—	4	4	no	—
861	C₂×C₃	—	4	2	no	—
862	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
865	C₅	C₃×#3536	1	1	yes	characteristic, direct product factor, Sylow
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	4	4	no	—
880	C₂²	—	8	4	no	—
881	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
882	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
883	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
894	C₃	C₅×#3536	1	1	yes	characteristic, direct product factor, Sylow
895	C₂	—	2	2	no	—
896	C₂	—	2	2	no	—
897	C₂	—	4	1	no	—
898	C₂	—	4	4	no	—
899	C₂	—	4	2	no	—
900	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#562	C₂	semidirect
2. C₃×C₅×#554	C₂	semidirect
3. C₃×C₅×#548	C₂	semidirect
4. C₃×C₅×#547	C₂	semidirect
5. C₃×C₅×#546	C₂	semidirect
6. C₃×C₅×#546	C₂	semidirect
7. C₃×C₅×#543	C₂	semidirect
8. C₃×C₅×#542	C₂	semidirect
9. C₃×C₅×#539	C₂	semidirect
10. C₃×C₅×#538	C₂	semidirect
11. C₃×C₅×#537	C₂	semidirect
12. C₃×C₅×#537	C₂	semidirect
13. C₃×C₅×#525	C₂	semidirect
14. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
15. C₂×C₃×C₅×#121	C₂	semidirect
16. C₅×#3536	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₂×C₃×C₅×#41	C₂²	semidirect
20. C₂²×C₃×C₅×Q₈	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#126	C₂²	semidirect
26. C₃×C₅×#125	C₂²	semidirect
27. C₃×C₅×#124	C₂²	semidirect
28. C₃×C₅×#124	C₂²	semidirect
29. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₅×#123	C₂²	semidirect
31. C₃×C₅×#123	C₂²	semidirect
32. C₃×C₅×#123	C₂²	semidirect
33. C₃×C₅×#123	C₂²	semidirect
34. C₃×C₅×#123	C₂²	semidirect
39. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
41. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
43. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
53. C₃×C₅×#121	C₂²	semidirect
54. C₃×C₅×#121	C₂²	semidirect
55. C₃×C₅×#121	C₂²	semidirect
56. C₃×C₅×#121	C₂²	semidirect
57. C₃×C₅×#121	C₂²	semidirect
58. C₃×C₅×#121	C₂²	semidirect
59. C₃×C₅×#121	C₂²	semidirect
62. C₃×C₄×C₅×Q₈	C₂²	semidirect
65. C₃×C₄×C₅×D₄	C₂²	semidirect
66. C₃×C₄×C₅×D₄	C₂²	semidirect
67. C₃×C₄×C₅×D₄	C₂²	semidirect
68. C₃×C₅×#117	C₂²	semidirect
70. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
71. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
72. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
76. C₃×#3536	C₅	direct (N × H)
77. C₅×#562	C₂×C₃	semidirect
78. C₅×#554	C₂×C₃	semidirect
79. C₅×#548	C₂×C₃	semidirect
80. C₅×#547	C₂×C₃	semidirect
81. C₅×#546	C₂×C₃	semidirect
82. C₅×#546	C₂×C₃	semidirect
83. C₅×#543	C₂×C₃	semidirect
84. C₅×#542	C₂×C₃	semidirect
85. C₅×#539	C₂×C₃	semidirect
86. C₅×#538	C₂×C₃	semidirect
87. C₅×#537	C₂×C₃	semidirect
88. C₅×#537	C₂×C₃	semidirect
89. C₅×#525	C₂×C₃	semidirect
90. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
91. C₂×C₅×#121	C₂×C₃	semidirect
158. C₃×#562	C₂×C₅	semidirect
159. C₃×#554	C₂×C₅	semidirect
160. C₃×#548	C₂×C₅	semidirect
161. C₃×#547	C₂×C₅	semidirect
162. C₃×#546	C₂×C₅	semidirect
163. C₃×#546	C₂×C₅	semidirect
164. C₃×#543	C₂×C₅	semidirect
165. C₃×#542	C₂×C₅	semidirect
166. C₃×#539	C₂×C₅	semidirect
167. C₃×#538	C₂×C₅	semidirect
168. C₃×#537	C₂×C₅	semidirect
169. C₃×#537	C₂×C₅	semidirect
170. C₃×#525	C₂×C₅	semidirect
171. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
172. C₂×C₃×#121	C₂×C₅	semidirect
173. C₂×C₅×#41	C₂²×C₃	semidirect
174. C₂×C₅×#41	C₂²×C₃	semidirect
175. C₂×C₅×#41	C₂²×C₃	semidirect
176. C₂²×C₅×Q₈	C₂²×C₃	semidirect
180. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
181. C₅×#126	C₂²×C₃	semidirect
182. C₅×#125	C₂²×C₃	semidirect
183. C₅×#124	C₂²×C₃	semidirect
184. C₅×#124	C₂²×C₃	semidirect
185. C₅×#124	C₂²×C₃	semidirect
186. C₅×#123	C₂²×C₃	semidirect
187. C₅×#123	C₂²×C₃	semidirect
188. C₅×#123	C₂²×C₃	semidirect
189. C₅×#123	C₂²×C₃	semidirect
190. C₅×#123	C₂²×C₃	semidirect
195. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
197. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
198. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
200. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
201. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
202. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
203. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
209. C₅×#121	C₂²×C₃	semidirect
210. C₅×#121	C₂²×C₃	semidirect
211. C₅×#121	C₂²×C₃	semidirect
212. C₅×#121	C₂²×C₃	semidirect
213. C₅×#121	C₂²×C₃	semidirect
214. C₅×#121	C₂²×C₃	semidirect
215. C₅×#121	C₂²×C₃	semidirect
218. C₄×C₅×Q₈	C₂²×C₃	semidirect
221. C₄×C₅×D₄	C₂²×C₃	semidirect
222. C₄×C₅×D₄	C₂²×C₃	semidirect
223. C₄×C₅×D₄	C₂²×C₃	semidirect
224. C₅×#117	C₂²×C₃	semidirect
226. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
227. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
228. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
232. #3536	C₃×C₅	direct (N × H)
281. C₂×C₃×#41	C₂²×C₅	semidirect
282. C₂×C₃×#41	C₂²×C₅	semidirect
283. C₂×C₃×#41	C₂²×C₅	semidirect
284. C₂²×C₃×Q₈	C₂²×C₅	semidirect
288. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
289. C₃×#126	C₂²×C₅	semidirect
290. C₃×#125	C₂²×C₅	semidirect
291. C₃×#124	C₂²×C₅	semidirect
292. C₃×#124	C₂²×C₅	semidirect
293. C₃×#124	C₂²×C₅	semidirect
294. C₃×#123	C₂²×C₅	semidirect
295. C₃×#123	C₂²×C₅	semidirect
296. C₃×#123	C₂²×C₅	semidirect
297. C₃×#123	C₂²×C₅	semidirect
298. C₃×#123	C₂²×C₅	semidirect
303. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
304. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
305. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
306. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
307. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
308. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
309. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
310. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
311. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
317. C₃×#121	C₂²×C₅	semidirect
318. C₃×#121	C₂²×C₅	semidirect
319. C₃×#121	C₂²×C₅	semidirect
320. C₃×#121	C₂²×C₅	semidirect
321. C₃×#121	C₂²×C₅	semidirect
322. C₃×#121	C₂²×C₅	semidirect
323. C₃×#121	C₂²×C₅	semidirect
326. C₃×C₄×Q₈	C₂²×C₅	semidirect
329. C₃×C₄×D₄	C₂²×C₅	semidirect
330. C₃×C₄×D₄	C₂²×C₅	semidirect
331. C₃×C₄×D₄	C₂²×C₅	semidirect
332. C₃×#117	C₂²×C₅	semidirect
334. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
335. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
336. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
406. #562	C₂×C₃×C₅	semidirect
407. #554	C₂×C₃×C₅	semidirect
408. #548	C₂×C₃×C₅	semidirect
409. #547	C₂×C₃×C₅	semidirect
410. #546	C₂×C₃×C₅	semidirect
411. #546	C₂×C₃×C₅	semidirect
412. #543	C₂×C₃×C₅	semidirect
413. #542	C₂×C₃×C₅	semidirect
414. #539	C₂×C₃×C₅	semidirect
415. #538	C₂×C₃×C₅	semidirect
416. #537	C₂×C₃×C₅	semidirect
417. #537	C₂×C₃×C₅	semidirect
418. #525	C₂×C₃×C₅	semidirect
419. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
420. C₂×#121	C₂×C₃×C₅	semidirect
563. C₂×#41	C₂²×C₃×C₅	semidirect
564. C₂×#41	C₂²×C₃×C₅	semidirect
565. C₂×#41	C₂²×C₃×C₅	semidirect
566. C₂²×Q₈	C₂²×C₃×C₅	semidirect
570. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
571. #126	C₂²×C₃×C₅	semidirect
572. #125	C₂²×C₃×C₅	semidirect
573. #124	C₂²×C₃×C₅	semidirect
574. #124	C₂²×C₃×C₅	semidirect
575. #124	C₂²×C₃×C₅	semidirect
576. #123	C₂²×C₃×C₅	semidirect
577. #123	C₂²×C₃×C₅	semidirect
578. #123	C₂²×C₃×C₅	semidirect
579. #123	C₂²×C₃×C₅	semidirect
580. #123	C₂²×C₃×C₅	semidirect
585. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
586. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
587. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
588. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
589. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
590. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
591. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
592. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
593. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
599. #121	C₂²×C₃×C₅	semidirect
600. #121	C₂²×C₃×C₅	semidirect
601. #121	C₂²×C₃×C₅	semidirect
602. #121	C₂²×C₃×C₅	semidirect
603. #121	C₂²×C₃×C₅	semidirect
604. #121	C₂²×C₃×C₅	semidirect
605. #121	C₂²×C₃×C₅	semidirect
608. C₄×Q₈	C₂²×C₃×C₅	semidirect
611. C₄×D₄	C₂²×C₃×C₅	semidirect
612. C₄×D₄	C₂²×C₃×C₅	semidirect
613. C₄×D₄	C₂²×C₃×C₅	semidirect
614. #117	C₂²×C₃×C₅	semidirect
616. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
617. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
618. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
772. C₃×C₅	#3536	direct (N × H)
865. C₅	C₃×#3536	direct (N × H)
894. C₃	C₅×#3536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#562	2
C₃×C₅×#554	2
C₃×C₅×#548	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#543	2
C₃×C₅×#542	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#121	2
C₅×#3536	3
C₃×#3536	5

Subgroups — C3×C5×#3536 #14276570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3536 #14276570