Subgroups — C₃×C₅×#3520 #14276554

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#551	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
12	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#520	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3520	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
20	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×#126	C₂²	1	2	yes	complemented
28	C₃×C₅×#126	C₂²	1	4	yes	complemented
29	C₃×C₅×#126	C₂²	1	4	yes	complemented
30	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#125	C₂²	1	2	yes	complemented
32	C₃×C₅×#125	C₂²	1	4	yes	complemented
33	C₃×C₅×#124	C₂²	1	2	yes	—
34	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#124	C₂²	1	4	yes	complemented
36	C₃×C₅×#123	C₂²	1	2	yes	—
37	C₃×C₅×#123	C₂²	1	4	yes	—
38	C₃×C₅×#123	C₂²	1	4	yes	complemented
39	C₃×C₅×#123	C₂²	1	4	yes	complemented
40	C₃×C₅×#123	C₂²	1	4	yes	complemented
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
50	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
51	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
52	C₃×C₅×#121	C₂²	1	1	yes	characteristic
53	C₃×C₅×#121	C₂²	1	4	yes	—
54	C₃×C₅×#121	C₂²	1	2	yes	—
55	C₃×C₅×#121	C₂²	1	2	yes	complemented
56	C₃×C₅×#120	C₂²	1	4	yes	—
57	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
58	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
59	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
61	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
62	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
63	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
64	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
65	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
66	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
67	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
68	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
69	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
70	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
71	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
72	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
73	C₃×C₅×#117	C₂²	1	2	yes	—
74	C₃×C₅×#117	C₂²	1	2	yes	complemented
75	C₃×C₅×#117	C₂²	1	4	yes	complemented
76	C₃×C₅×#117	C₂²	1	2	yes	complemented
77	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
79	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
84	C₃×#3520	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
86	C₅×#554	C₂×C₃	1	2	yes	complemented
87	C₅×#552	C₂×C₃	1	2	yes	complemented
88	C₅×#551	C₂×C₃	1	4	yes	complemented
89	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#548	C₂×C₃	1	2	yes	complemented
91	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
92	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
93	C₅×#546	C₂×C₃	1	2	yes	complemented
94	C₅×#542	C₂×C₃	1	2	yes	complemented
95	C₅×#539	C₂×C₃	1	4	yes	complemented
96	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
97	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
98	C₅×#525	C₂×C₃	1	2	yes	complemented
99	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
100	C₅×#520	C₂×C₃	1	2	yes	complemented
101	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
103	C₃×C₅×#41	—	2	8	no	—
104	C₃×C₅×#41	—	4	4	no	—
105	C₂×C₃×C₅×Q₈	—	4	4	no	—
106	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
109	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
110	C₂×C₃×C₅×D₄	—	2	4	no	—
111	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
112	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
113	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
115	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
117	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄×C₅	—	4	4	no	—
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	1	yes	characteristic
122	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
123	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
124	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
125	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
126	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
127	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
128	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
129	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
130	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
147	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
149	C₃×C₅×C₄⋊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	2	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
166	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
169	C₃×C₄²×C₅	C₂³	1	4	yes	—
170	C₃×C₄²×C₅	C₂³	1	4	yes	—
171	C₃×C₄²×C₅	C₂³	1	2	yes	—
172	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
173	C₃×#554	C₂×C₅	1	2	yes	complemented
174	C₃×#552	C₂×C₅	1	2	yes	complemented
175	C₃×#551	C₂×C₅	1	4	yes	complemented
176	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
177	C₃×#548	C₂×C₅	1	2	yes	complemented
178	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
179	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
180	C₃×#546	C₂×C₅	1	2	yes	complemented
181	C₃×#542	C₂×C₅	1	2	yes	complemented
182	C₃×#539	C₂×C₅	1	4	yes	complemented
183	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
184	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
185	C₃×#525	C₂×C₅	1	2	yes	complemented
186	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
187	C₃×#520	C₂×C₅	1	2	yes	complemented
188	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
189	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
190	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
191	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
192	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
193	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
194	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
197	C₅×#126	C₂²×C₃	1	2	yes	complemented
198	C₅×#126	C₂²×C₃	1	4	yes	complemented
199	C₅×#126	C₂²×C₃	1	4	yes	complemented
200	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₅×#125	C₂²×C₃	1	2	yes	complemented
202	C₅×#125	C₂²×C₃	1	4	yes	complemented
203	C₅×#124	C₂²×C₃	1	2	yes	—
204	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₅×#124	C₂²×C₃	1	4	yes	complemented
206	C₅×#123	C₂²×C₃	1	2	yes	—
207	C₅×#123	C₂²×C₃	1	4	yes	—
208	C₅×#123	C₂²×C₃	1	4	yes	complemented
209	C₅×#123	C₂²×C₃	1	4	yes	complemented
210	C₅×#123	C₂²×C₃	1	4	yes	complemented
211	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
212	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
213	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
214	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
215	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
216	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
217	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
218	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
219	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
220	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
221	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
222	C₅×#121	C₂²×C₃	1	1	yes	characteristic
223	C₅×#121	C₂²×C₃	1	4	yes	—
224	C₅×#121	C₂²×C₃	1	2	yes	—
225	C₅×#121	C₂²×C₃	1	2	yes	complemented
226	C₅×#120	C₂²×C₃	1	4	yes	—
227	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
228	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
229	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
230	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
231	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
232	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
233	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
234	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
235	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
236	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
237	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
238	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
239	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
240	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
241	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
242	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₅×#117	C₂²×C₃	1	2	yes	—
244	C₅×#117	C₂²×C₃	1	2	yes	complemented
245	C₅×#117	C₂²×C₃	1	4	yes	complemented
246	C₅×#117	C₂²×C₃	1	2	yes	complemented
247	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
248	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
249	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
250	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
251	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
252	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
253	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
254	#3520	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³×C₃×C₅	—	2	4	no	—
256	C₂³×C₃×C₅	—	2	4	no	—
257	C₂³×C₃×C₅	—	4	2	no	—
258	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
259	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
260	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
261	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
262	C₃×C₅×Q₈	—	2	4	no	—
263	C₃×C₅×Q₈	—	2	2	no	—
264	C₃×C₅×Q₈	—	2	4	no	—
265	C₃×C₅×Q₈	—	4	4	no	—
266	C₃×C₅×D₄	—	2	4	no	—
267	C₃×C₅×D₄	—	2	8	no	—
268	C₃×C₅×D₄	—	2	4	no	—
269	C₃×C₅×D₄	—	2	2	no	—
270	C₃×C₅×D₄	—	2	2	no	—
271	C₃×C₅×D₄	—	4	4	no	—
272	C₃×C₅×D₄	#41	1	4	yes	complemented
273	C₂×C₃×C₄×C₅	—	2	8	no	—
274	C₂×C₃×C₄×C₅	—	2	2	no	—
275	C₂×C₃×C₄×C₅	—	2	2	no	—
276	C₂×C₃×C₄×C₅	—	2	4	no	—
277	C₂×C₃×C₄×C₅	—	2	2	no	—
278	C₂×C₃×C₄×C₅	—	2	4	no	—
279	C₂×C₃×C₄×C₅	—	2	4	no	—
280	C₂×C₃×C₄×C₅	—	4	2	no	—
281	C₂×C₃×C₄×C₅	—	4	2	no	—
282	C₂×C₃×C₄×C₅	—	4	2	no	—
283	C₂×C₃×C₄×C₅	—	4	4	no	—
284	C₂×C₃×C₄×C₅	—	4	4	no	—
285	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
287	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
289	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
294	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
295	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
296	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
299	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
300	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	complemented
301	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
302	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
303	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
306	C₃×#126	C₂²×C₅	1	2	yes	complemented
307	C₃×#126	C₂²×C₅	1	4	yes	complemented
308	C₃×#126	C₂²×C₅	1	4	yes	complemented
309	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₃×#125	C₂²×C₅	1	2	yes	complemented
311	C₃×#125	C₂²×C₅	1	4	yes	complemented
312	C₃×#124	C₂²×C₅	1	2	yes	—
313	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₃×#124	C₂²×C₅	1	4	yes	complemented
315	C₃×#123	C₂²×C₅	1	2	yes	—
316	C₃×#123	C₂²×C₅	1	4	yes	—
317	C₃×#123	C₂²×C₅	1	4	yes	complemented
318	C₃×#123	C₂²×C₅	1	4	yes	complemented
319	C₃×#123	C₂²×C₅	1	4	yes	complemented
320	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
321	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
322	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
323	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
324	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
325	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
326	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
327	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
328	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
329	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
330	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
331	C₃×#121	C₂²×C₅	1	1	yes	characteristic
332	C₃×#121	C₂²×C₅	1	4	yes	—
333	C₃×#121	C₂²×C₅	1	2	yes	—
334	C₃×#121	C₂²×C₅	1	2	yes	complemented
335	C₃×#120	C₂²×C₅	1	4	yes	—
336	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
337	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
338	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
339	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
340	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
341	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
342	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
343	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
344	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
345	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
346	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
347	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
348	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
349	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
350	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
351	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
352	C₃×#117	C₂²×C₅	1	2	yes	—
353	C₃×#117	C₂²×C₅	1	2	yes	complemented
354	C₃×#117	C₂²×C₅	1	4	yes	complemented
355	C₃×#117	C₂²×C₅	1	2	yes	complemented
356	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
357	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
358	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
359	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
360	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
361	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
362	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
363	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
364	C₅×#41	—	2	8	no	—
365	C₅×#41	—	4	4	no	—
366	C₂×C₅×Q₈	—	4	4	no	—
367	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
368	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
369	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
370	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
371	C₂×C₅×D₄	—	2	4	no	—
372	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
373	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
374	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
375	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
376	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
378	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
379	C₂²×C₄×C₅	—	4	4	no	—
380	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
381	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
382	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
383	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
384	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
385	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
386	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
387	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
388	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
389	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
390	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
391	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
392	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
393	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
395	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
397	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
398	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
402	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
403	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
408	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
410	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
412	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
413	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
414	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
416	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
418	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
419	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
420	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
423	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
424	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
427	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
428	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
429	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
430	C₄²×C₅	C₂³×C₃	1	4	yes	—
431	C₄²×C₅	C₂³×C₃	1	4	yes	—
432	C₄²×C₅	C₂³×C₃	1	2	yes	—
433	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
434	#554	C₂×C₃×C₅	1	2	yes	complemented
435	#552	C₂×C₃×C₅	1	2	yes	complemented
436	#551	C₂×C₃×C₅	1	4	yes	complemented
437	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
438	#548	C₂×C₃×C₅	1	2	yes	complemented
439	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
440	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
441	#546	C₂×C₃×C₅	1	2	yes	complemented
442	#542	C₂×C₃×C₅	1	2	yes	complemented
443	#539	C₂×C₃×C₅	1	4	yes	complemented
444	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
445	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
446	#525	C₂×C₃×C₅	1	2	yes	complemented
447	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
448	#520	C₂×C₃×C₅	1	2	yes	complemented
449	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
450	C₂²×C₃×C₅	—	2	1	no	—
451	C₂²×C₃×C₅	—	2	2	no	—
452	C₂²×C₃×C₅	—	2	1	no	—
453	C₂²×C₃×C₅	—	2	2	no	—
454	C₂²×C₃×C₅	—	2	2	no	—
455	C₂²×C₃×C₅	—	2	2	no	—
456	C₂²×C₃×C₅	—	2	2	no	—
457	C₂²×C₃×C₅	—	2	2	no	—
458	C₂²×C₃×C₅	—	2	2	no	—
459	C₂²×C₃×C₅	—	2	2	no	—
460	C₂²×C₃×C₅	—	4	8	no	—
461	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
462	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
463	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
464	C₃×C₄×C₅	—	2	2	no	—
465	C₃×C₄×C₅	—	2	1	no	—
466	C₃×C₄×C₅	—	2	4	no	—
467	C₃×C₄×C₅	—	2	1	no	—
468	C₃×C₄×C₅	—	2	2	no	—
469	C₃×C₄×C₅	—	2	2	no	—
470	C₃×C₄×C₅	—	2	4	no	—
471	C₃×C₄×C₅	—	2	2	no	—
472	C₃×C₄×C₅	—	2	1	no	—
473	C₃×C₄×C₅	—	2	1	no	—
474	C₃×C₄×C₅	—	2	2	no	—
475	C₃×C₄×C₅	C₂×#41	1	2	yes	—
476	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
477	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
478	C₃×#41	—	2	8	no	—
479	C₃×#41	—	4	4	no	—
480	C₂×C₃×Q₈	—	4	4	no	—
481	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
482	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
484	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
485	C₂×C₃×D₄	—	2	4	no	—
486	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
487	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
488	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
489	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
490	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
491	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
492	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
493	C₂²×C₃×C₄	—	4	4	no	—
494	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
497	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
498	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
499	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
500	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
501	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
502	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
503	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
504	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
505	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
506	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
507	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
508	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
509	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
510	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
511	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
512	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
513	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
514	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
515	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
516	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
517	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
518	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
519	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
520	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
521	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
522	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
523	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
524	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
525	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
526	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
527	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
528	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
529	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
530	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
531	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
532	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
533	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
534	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
535	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
536	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
537	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
538	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
539	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
540	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
541	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
542	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
543	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
544	C₃×C₄²	C₂³×C₅	1	4	yes	—
545	C₃×C₄²	C₂³×C₅	1	4	yes	—
546	C₃×C₄²	C₂³×C₅	1	2	yes	—
547	C₂³×C₅	—	2	4	no	—
548	C₂³×C₅	—	2	4	no	—
549	C₂³×C₅	—	4	2	no	—
550	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
551	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
552	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
553	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
554	C₅×Q₈	—	2	4	no	—
555	C₅×Q₈	—	2	2	no	—
556	C₅×Q₈	—	2	4	no	—
557	C₅×Q₈	—	4	4	no	—
558	C₅×D₄	—	2	4	no	—
559	C₅×D₄	—	2	8	no	—
560	C₅×D₄	—	2	4	no	—
561	C₅×D₄	—	2	2	no	—
562	C₅×D₄	—	2	2	no	—
563	C₅×D₄	—	4	4	no	—
564	C₅×D₄	C₃×#41	1	4	yes	complemented
565	C₂×C₄×C₅	—	2	8	no	—
566	C₂×C₄×C₅	—	2	2	no	—
567	C₂×C₄×C₅	—	2	2	no	—
568	C₂×C₄×C₅	—	2	4	no	—
569	C₂×C₄×C₅	—	2	2	no	—
570	C₂×C₄×C₅	—	2	4	no	—
571	C₂×C₄×C₅	—	2	4	no	—
572	C₂×C₄×C₅	—	4	2	no	—
573	C₂×C₄×C₅	—	4	2	no	—
574	C₂×C₄×C₅	—	4	2	no	—
575	C₂×C₄×C₅	—	4	4	no	—
576	C₂×C₄×C₅	—	4	4	no	—
577	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
578	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
579	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
580	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
581	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
582	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
583	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
584	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
585	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
586	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
587	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
588	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
589	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
590	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
591	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
592	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
593	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
594	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
595	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
596	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
597	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
598	#126	C₂²×C₃×C₅	1	2	yes	complemented
599	#126	C₂²×C₃×C₅	1	4	yes	complemented
600	#126	C₂²×C₃×C₅	1	4	yes	complemented
601	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
602	#125	C₂²×C₃×C₅	1	2	yes	complemented
603	#125	C₂²×C₃×C₅	1	4	yes	complemented
604	#124	C₂²×C₃×C₅	1	2	yes	—
605	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
606	#124	C₂²×C₃×C₅	1	4	yes	complemented
607	#123	C₂²×C₃×C₅	1	2	yes	—
608	#123	C₂²×C₃×C₅	1	4	yes	—
609	#123	C₂²×C₃×C₅	1	4	yes	complemented
610	#123	C₂²×C₃×C₅	1	4	yes	complemented
611	#123	C₂²×C₃×C₅	1	4	yes	complemented
612	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
614	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
615	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
616	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
617	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
618	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
619	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
620	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
621	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
622	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
623	#121	C₂²×C₃×C₅	1	1	yes	characteristic
624	#121	C₂²×C₃×C₅	1	4	yes	—
625	#121	C₂²×C₃×C₅	1	2	yes	—
626	#121	C₂²×C₃×C₅	1	2	yes	complemented
627	#120	C₂²×C₃×C₅	1	4	yes	—
628	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
629	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
630	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
631	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
632	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
633	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
634	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
635	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
636	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
637	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
638	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
639	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
640	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
641	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
642	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
643	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
644	#117	C₂²×C₃×C₅	1	2	yes	—
645	#117	C₂²×C₃×C₅	1	2	yes	complemented
646	#117	C₂²×C₃×C₅	1	4	yes	complemented
647	#117	C₂²×C₃×C₅	1	2	yes	complemented
648	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
650	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
651	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
652	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
654	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
655	C₂×C₃×C₅	—	2	2	no	—
656	C₂×C₃×C₅	—	2	4	no	—
657	C₂×C₃×C₅	—	4	2	no	—
658	C₂×C₃×C₅	—	4	2	no	—
659	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
660	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
662	C₂³×C₃	—	2	4	no	—
663	C₂³×C₃	—	2	4	no	—
664	C₂³×C₃	—	4	2	no	—
665	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
666	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
667	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
668	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
669	C₃×Q₈	—	2	4	no	—
670	C₃×Q₈	—	2	2	no	—
671	C₃×Q₈	—	2	4	no	—
672	C₃×Q₈	—	4	4	no	—
673	C₃×D₄	—	2	4	no	—
674	C₃×D₄	—	2	8	no	—
675	C₃×D₄	—	2	4	no	—
676	C₃×D₄	—	2	2	no	—
677	C₃×D₄	—	2	2	no	—
678	C₃×D₄	—	4	4	no	—
679	C₃×D₄	C₅×#41	1	4	yes	complemented
680	C₂×C₃×C₄	—	2	8	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	4	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	4	no	—
686	C₂×C₃×C₄	—	2	4	no	—
687	C₂×C₃×C₄	—	4	2	no	—
688	C₂×C₃×C₄	—	4	2	no	—
689	C₂×C₃×C₄	—	4	2	no	—
690	C₂×C₃×C₄	—	4	4	no	—
691	C₂×C₃×C₄	—	4	4	no	—
692	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
693	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
694	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
695	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
696	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
697	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
698	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
699	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
700	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
701	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
702	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
703	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
705	C₂²×C₅	—	2	1	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	1	no	—
708	C₂²×C₅	—	2	2	no	—
709	C₂²×C₅	—	2	2	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	2	no	—
712	C₂²×C₅	—	2	2	no	—
713	C₂²×C₅	—	2	2	no	—
714	C₂²×C₅	—	2	2	no	—
715	C₂²×C₅	—	4	8	no	—
716	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
717	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
718	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
719	C₄×C₅	—	2	2	no	—
720	C₄×C₅	—	2	1	no	—
721	C₄×C₅	—	2	4	no	—
722	C₄×C₅	—	2	1	no	—
723	C₄×C₅	—	2	2	no	—
724	C₄×C₅	—	2	2	no	—
725	C₄×C₅	—	2	4	no	—
726	C₄×C₅	—	2	2	no	—
727	C₄×C₅	—	2	1	no	—
728	C₄×C₅	—	2	1	no	—
729	C₄×C₅	—	2	2	no	—
730	C₄×C₅	C₂×C₃×#41	1	2	yes	—
731	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
732	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
733	#41	—	2	8	no	—
734	#41	—	4	4	no	—
735	C₂×Q₈	—	4	4	no	—
736	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
737	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
738	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
739	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
742	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
743	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
744	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
745	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
746	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
747	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
750	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
751	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
752	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
753	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
754	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
755	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
756	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
757	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
758	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
759	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
760	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
761	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
762	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
763	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
764	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
765	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
766	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
767	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
768	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
769	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
770	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
771	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
772	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
773	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
774	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
775	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
776	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
777	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
778	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
779	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
780	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
781	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
782	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
783	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
784	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
785	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
786	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
787	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
788	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
789	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
790	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
791	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
792	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
793	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
794	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
795	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
796	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
797	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
798	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
799	C₄²	C₂³×C₃×C₅	1	4	yes	—
800	C₄²	C₂³×C₃×C₅	1	4	yes	—
801	C₄²	C₂³×C₃×C₅	1	2	yes	—
802	C₃×C₅	#3520	1	1	yes	characteristic, direct product factor, Hall
803	C₂²×C₃	—	2	1	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	1	no	—
806	C₂²×C₃	—	2	2	no	—
807	C₂²×C₃	—	2	2	no	—
808	C₂²×C₃	—	2	2	no	—
809	C₂²×C₃	—	2	2	no	—
810	C₂²×C₃	—	2	2	no	—
811	C₂²×C₃	—	2	2	no	—
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	4	8	no	—
814	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
815	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
816	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
817	C₃×C₄	—	2	2	no	—
818	C₃×C₄	—	2	1	no	—
819	C₃×C₄	—	2	4	no	—
820	C₃×C₄	—	2	1	no	—
821	C₃×C₄	—	2	2	no	—
822	C₃×C₄	—	2	2	no	—
823	C₃×C₄	—	2	4	no	—
824	C₃×C₄	—	2	2	no	—
825	C₃×C₄	—	2	1	no	—
826	C₃×C₄	—	2	1	no	—
827	C₃×C₄	—	2	2	no	—
828	C₃×C₄	C₂×C₅×#41	1	2	yes	—
829	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
830	C₂×C₅	—	2	2	no	—
831	C₂×C₅	—	2	4	no	—
832	C₂×C₅	—	4	2	no	—
833	C₂×C₅	—	4	2	no	—
834	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
835	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂³	—	2	4	no	—
838	C₂³	—	2	4	no	—
839	C₂³	—	4	2	no	—
840	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
841	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
842	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
843	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
844	Q₈	—	2	4	no	—
845	Q₈	—	2	2	no	—
846	Q₈	—	2	4	no	—
847	Q₈	—	4	4	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	8	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	2	no	—
853	D₄	—	4	4	no	—
854	D₄	C₃×C₅×#41	1	4	yes	complemented
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
868	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
869	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
870	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
871	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
872	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
873	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
874	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
875	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
876	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
877	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
878	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
879	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
880	C₂×C₃	—	2	2	no	—
881	C₂×C₃	—	2	4	no	—
882	C₂×C₃	—	4	2	no	—
883	C₂×C₃	—	4	2	no	—
884	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
885	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
887	C₅	C₃×#3520	1	1	yes	characteristic, direct product factor, Sylow
888	C₂²	—	2	1	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	8	no	—
899	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
900	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
901	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	4	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	1	no	—
911	C₄	—	2	1	no	—
912	C₄	—	2	2	no	—
913	C₄	C₂×C₃×C₅×#41	1	2	yes	—
914	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
915	C₃	C₅×#3520	1	1	yes	characteristic, direct product factor, Sylow
916	C₂	—	2	2	no	—
917	C₂	—	2	4	no	—
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	C₂²×C₃×C₅×#41	1	1	yes	characteristic
921	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
922	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×#556	C₂	semidirect
2. C₃×C₅×#554	C₂	semidirect
3. C₃×C₅×#552	C₂	semidirect
4. C₃×C₅×#551	C₂	semidirect
5. C₃×C₅×D₄×Q₈	C₂	semidirect
6. C₃×C₅×#548	C₂	semidirect
7. C₃×C₅×#547	C₂	semidirect
8. C₃×C₅×#547	C₂	semidirect
9. C₃×C₅×#546	C₂	semidirect
10. C₃×C₅×#542	C₂	semidirect
11. C₃×C₅×#539	C₂	semidirect
12. C₃×C₅×#533	C₂	semidirect
13. C₃×C₅×#529	C₂	semidirect
14. C₃×C₅×#525	C₂	semidirect
15. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
16. C₃×C₅×#520	C₂	semidirect
17. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
18. C₅×#3520	C₃	direct (N × H)
20. C₂×C₃×C₅×#41	C₂²	semidirect
21. C₂²×C₃×C₅×Q₈	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
26. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₃×C₅×#126	C₂²	semidirect
28. C₃×C₅×#126	C₂²	semidirect
29. C₃×C₅×#126	C₂²	semidirect
30. C₃×C₅×#125	C₂²	semidirect
31. C₃×C₅×#125	C₂²	semidirect
32. C₃×C₅×#125	C₂²	semidirect
34. C₃×C₅×#124	C₂²	semidirect
35. C₃×C₅×#124	C₂²	semidirect
38. C₃×C₅×#123	C₂²	semidirect
39. C₃×C₅×#123	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
45. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
50. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
51. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
55. C₃×C₅×#121	C₂²	semidirect
57. C₃×C₄×C₅×Q₈	C₂²	semidirect
58. C₃×C₄×C₅×Q₈	C₂²	semidirect
59. C₃×C₄×C₅×Q₈	C₂²	semidirect
60. C₃×C₄×C₅×Q₈	C₂²	semidirect
70. C₃×C₄×C₅×D₄	C₂²	semidirect
71. C₃×C₄×C₅×D₄	C₂²	semidirect
72. C₃×C₄×C₅×D₄	C₂²	semidirect
74. C₃×C₅×#117	C₂²	semidirect
75. C₃×C₅×#117	C₂²	semidirect
76. C₃×C₅×#117	C₂²	semidirect
78. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
80. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
84. C₃×#3520	C₅	direct (N × H)
85. C₅×#556	C₂×C₃	semidirect
86. C₅×#554	C₂×C₃	semidirect
87. C₅×#552	C₂×C₃	semidirect
88. C₅×#551	C₂×C₃	semidirect
89. C₅×D₄×Q₈	C₂×C₃	semidirect
90. C₅×#548	C₂×C₃	semidirect
91. C₅×#547	C₂×C₃	semidirect
92. C₅×#547	C₂×C₃	semidirect
93. C₅×#546	C₂×C₃	semidirect
94. C₅×#542	C₂×C₃	semidirect
95. C₅×#539	C₂×C₃	semidirect
96. C₅×#533	C₂×C₃	semidirect
97. C₅×#529	C₂×C₃	semidirect
98. C₅×#525	C₂×C₃	semidirect
99. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
100. C₅×#520	C₂×C₃	semidirect
101. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
172. C₃×#556	C₂×C₅	semidirect
173. C₃×#554	C₂×C₅	semidirect
174. C₃×#552	C₂×C₅	semidirect
175. C₃×#551	C₂×C₅	semidirect
176. C₃×D₄×Q₈	C₂×C₅	semidirect
177. C₃×#548	C₂×C₅	semidirect
178. C₃×#547	C₂×C₅	semidirect
179. C₃×#547	C₂×C₅	semidirect
180. C₃×#546	C₂×C₅	semidirect
181. C₃×#542	C₂×C₅	semidirect
182. C₃×#539	C₂×C₅	semidirect
183. C₃×#533	C₂×C₅	semidirect
184. C₃×#529	C₂×C₅	semidirect
185. C₃×#525	C₂×C₅	semidirect
186. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
187. C₃×#520	C₂×C₅	semidirect
188. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
190. C₂×C₅×#41	C₂²×C₃	semidirect
191. C₂²×C₅×Q₈	C₂²×C₃	semidirect
194. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
195. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
196. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
197. C₅×#126	C₂²×C₃	semidirect
198. C₅×#126	C₂²×C₃	semidirect
199. C₅×#126	C₂²×C₃	semidirect
200. C₅×#125	C₂²×C₃	semidirect
201. C₅×#125	C₂²×C₃	semidirect
202. C₅×#125	C₂²×C₃	semidirect
204. C₅×#124	C₂²×C₃	semidirect
205. C₅×#124	C₂²×C₃	semidirect
208. C₅×#123	C₂²×C₃	semidirect
209. C₅×#123	C₂²×C₃	semidirect
210. C₅×#123	C₂²×C₃	semidirect
215. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
216. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
217. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
218. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
219. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
220. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
221. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
225. C₅×#121	C₂²×C₃	semidirect
227. C₄×C₅×Q₈	C₂²×C₃	semidirect
228. C₄×C₅×Q₈	C₂²×C₃	semidirect
229. C₄×C₅×Q₈	C₂²×C₃	semidirect
230. C₄×C₅×Q₈	C₂²×C₃	semidirect
240. C₄×C₅×D₄	C₂²×C₃	semidirect
241. C₄×C₅×D₄	C₂²×C₃	semidirect
242. C₄×C₅×D₄	C₂²×C₃	semidirect
244. C₅×#117	C₂²×C₃	semidirect
245. C₅×#117	C₂²×C₃	semidirect
246. C₅×#117	C₂²×C₃	semidirect
248. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
249. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
250. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
254. #3520	C₃×C₅	direct (N × H)
272. C₃×C₅×D₄	#41	semidirect
299. C₂×C₃×#41	C₂²×C₅	semidirect
300. C₂²×C₃×Q₈	C₂²×C₅	semidirect
303. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
304. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
305. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
306. C₃×#126	C₂²×C₅	semidirect
307. C₃×#126	C₂²×C₅	semidirect
308. C₃×#126	C₂²×C₅	semidirect
309. C₃×#125	C₂²×C₅	semidirect
310. C₃×#125	C₂²×C₅	semidirect
311. C₃×#125	C₂²×C₅	semidirect
313. C₃×#124	C₂²×C₅	semidirect
314. C₃×#124	C₂²×C₅	semidirect
317. C₃×#123	C₂²×C₅	semidirect
318. C₃×#123	C₂²×C₅	semidirect
319. C₃×#123	C₂²×C₅	semidirect
324. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
325. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
326. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
327. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
328. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
329. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
330. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
334. C₃×#121	C₂²×C₅	semidirect
336. C₃×C₄×Q₈	C₂²×C₅	semidirect
337. C₃×C₄×Q₈	C₂²×C₅	semidirect
338. C₃×C₄×Q₈	C₂²×C₅	semidirect
339. C₃×C₄×Q₈	C₂²×C₅	semidirect
349. C₃×C₄×D₄	C₂²×C₅	semidirect
350. C₃×C₄×D₄	C₂²×C₅	semidirect
351. C₃×C₄×D₄	C₂²×C₅	semidirect
353. C₃×#117	C₂²×C₅	semidirect
354. C₃×#117	C₂²×C₅	semidirect
355. C₃×#117	C₂²×C₅	semidirect
357. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
358. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
359. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
433. #556	C₂×C₃×C₅	semidirect
434. #554	C₂×C₃×C₅	semidirect
435. #552	C₂×C₃×C₅	semidirect
436. #551	C₂×C₃×C₅	semidirect
437. D₄×Q₈	C₂×C₃×C₅	semidirect
438. #548	C₂×C₃×C₅	semidirect
439. #547	C₂×C₃×C₅	semidirect
440. #547	C₂×C₃×C₅	semidirect
441. #546	C₂×C₃×C₅	semidirect
442. #542	C₂×C₃×C₅	semidirect
443. #539	C₂×C₃×C₅	semidirect
444. #533	C₂×C₃×C₅	semidirect
445. #529	C₂×C₃×C₅	semidirect
446. #525	C₂×C₃×C₅	semidirect
447. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
448. #520	C₂×C₃×C₅	semidirect
449. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
564. C₅×D₄	C₃×#41	semidirect
591. C₂×#41	C₂²×C₃×C₅	semidirect
592. C₂²×Q₈	C₂²×C₃×C₅	semidirect
595. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
596. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
597. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
598. #126	C₂²×C₃×C₅	semidirect
599. #126	C₂²×C₃×C₅	semidirect
600. #126	C₂²×C₃×C₅	semidirect
601. #125	C₂²×C₃×C₅	semidirect
602. #125	C₂²×C₃×C₅	semidirect
603. #125	C₂²×C₃×C₅	semidirect
605. #124	C₂²×C₃×C₅	semidirect
606. #124	C₂²×C₃×C₅	semidirect
609. #123	C₂²×C₃×C₅	semidirect
610. #123	C₂²×C₃×C₅	semidirect
611. #123	C₂²×C₃×C₅	semidirect
616. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
617. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
618. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
619. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
620. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
621. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
622. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
626. #121	C₂²×C₃×C₅	semidirect
628. C₄×Q₈	C₂²×C₃×C₅	semidirect
629. C₄×Q₈	C₂²×C₃×C₅	semidirect
630. C₄×Q₈	C₂²×C₃×C₅	semidirect
631. C₄×Q₈	C₂²×C₃×C₅	semidirect
641. C₄×D₄	C₂²×C₃×C₅	semidirect
642. C₄×D₄	C₂²×C₃×C₅	semidirect
643. C₄×D₄	C₂²×C₃×C₅	semidirect
645. #117	C₂²×C₃×C₅	semidirect
646. #117	C₂²×C₃×C₅	semidirect
647. #117	C₂²×C₃×C₅	semidirect
649. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
650. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
651. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
679. C₃×D₄	C₅×#41	semidirect
802. C₃×C₅	#3520	direct (N × H)
854. D₄	C₃×C₅×#41	semidirect
887. C₅	C₃×#3520	direct (N × H)
915. C₃	C₅×#3520	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×#556	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#548	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#542	2
C₃×C₅×#539	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₃×C₅×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#520	2
C₂×C₃×C₄×C₅×D₄	2
C₅×#3520	3
C₃×#3520	5

Subgroups — C3×C5×#3520 #14276554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3520 #14276554