Subgroups — C₃×C₅×#3558 #14276592

Order 1920.

2320 conjugacy classes of subgroups.

The subgroup lattice has 880 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	2	yes	maximal, complemented
2	C₃×C₅×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#559	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#546	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×D₄²	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#538	C₂	1	4	yes	maximal, complemented
11	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#534	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3558	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
22	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#127	C₂²	1	2	yes	—
25	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#126	C₂²	1	2	yes	complemented
27	C₃×C₅×#126	C₂²	1	4	yes	complemented
28	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#124	C₂²	1	2	yes	complemented
30	C₃×C₅×#124	C₂²	1	2	yes	complemented
31	C₃×C₅×#124	C₂²	1	2	yes	complemented
32	C₃×C₅×#124	C₂²	1	2	yes	complemented
33	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#124	C₂²	1	2	yes	complemented
35	C₃×C₅×#124	C₂²	1	2	yes	complemented
36	C₃×C₅×#124	C₂²	1	4	yes	complemented
37	C₃×C₅×#124	C₂²	1	4	yes	complemented
38	C₃×C₅×#124	C₂²	1	4	yes	complemented
39	C₃×C₅×#123	C₂²	1	2	yes	complemented
40	C₃×C₅×#123	C₂²	1	4	yes	complemented
41	C₃×C₅×#123	C₂²	1	4	yes	complemented
42	C₃×C₅×#123	C₂²	1	4	yes	complemented
43	C₃×C₅×#123	C₂²	1	4	yes	complemented
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
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	4	yes	complemented
48	C₃×C₅×#121	C₂²	1	1	yes	characteristic
49	C₃×C₅×#121	C₂²	1	2	yes	—
50	C₃×C₅×#121	C₂²	1	2	yes	complemented
51	C₃×C₅×#121	C₂²	1	2	yes	complemented
52	C₃×C₅×#121	C₂²	1	4	yes	complemented
53	C₃×C₅×#121	C₂²	1	4	yes	complemented
54	C₃×C₅×#121	C₂²	1	4	yes	complemented
55	C₃×C₅×#121	C₂²	1	4	yes	complemented
56	C₃×C₅×#121	C₂²	1	4	yes	complemented
57	C₃×C₅×#120	C₂²	1	4	yes	complemented
58	C₃×C₅×#120	C₂²	1	4	yes	complemented
59	C₃×C₅×#120	C₂²	1	4	yes	complemented
60	C₃×C₅×#120	C₂²	1	4	yes	complemented
61	C₃×C₅×#120	C₂²	1	4	yes	complemented
62	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
64	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
65	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
67	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
68	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
69	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
70	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
71	C₃×C₅×#117	C₂²	1	2	yes	complemented
72	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
74	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
75	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
76	C₃×#3558	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#562	C₂×C₃	1	2	yes	complemented
78	C₅×H(3,𝔽₄)	C₂×C₃	1	2	yes	complemented
79	C₅×#559	C₂×C₃	1	2	yes	complemented
80	C₅×#548	C₂×C₃	1	2	yes	complemented
81	C₅×#546	C₂×C₃	1	2	yes	complemented
82	C₅×#546	C₂×C₃	1	4	yes	complemented
83	C₅×D₄²	C₂×C₃	1	2	yes	complemented
84	C₅×#542	C₂×C₃	1	2	yes	complemented
85	C₅×#538	C₂×C₃	1	2	yes	complemented
86	C₅×#538	C₂×C₃	1	4	yes	complemented
87	C₅×#535	C₂×C₃	1	2	yes	complemented
88	C₅×#534	C₂×C₃	1	2	yes	complemented
89	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
93	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
94	C₃×C₅×#41	—	4	4	no	—
95	C₃×C₅×#41	—	4	4	no	—
96	C₂×C₃×C₅×Q₈	—	4	2	no	—
97	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
98	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
100	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
101	C₂×C₃×C₅×D₄	—	4	2	no	—
102	C₂×C₃×C₅×D₄	—	4	4	no	—
103	C₂×C₃×C₅×D₄	—	4	8	no	—
104	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
106	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
107	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
108	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
110	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
111	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
112	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
113	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
114	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
115	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
116	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	4	yes	—
123	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
124	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
125	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
150	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
152	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
153	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
155	C₃×C₄²×C₅	C₂³	1	2	yes	—
156	C₃×C₄²×C₅	C₂³	1	4	yes	—
157	C₃×#562	C₂×C₅	1	2	yes	complemented
158	C₃×H(3,𝔽₄)	C₂×C₅	1	2	yes	complemented
159	C₃×#559	C₂×C₅	1	2	yes	complemented
160	C₃×#548	C₂×C₅	1	2	yes	complemented
161	C₃×#546	C₂×C₅	1	2	yes	complemented
162	C₃×#546	C₂×C₅	1	4	yes	complemented
163	C₃×D₄²	C₂×C₅	1	2	yes	complemented
164	C₃×#542	C₂×C₅	1	2	yes	complemented
165	C₃×#538	C₂×C₅	1	2	yes	complemented
166	C₃×#538	C₂×C₅	1	4	yes	complemented
167	C₃×#535	C₂×C₅	1	2	yes	complemented
168	C₃×#534	C₂×C₅	1	2	yes	complemented
169	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
170	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
173	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
174	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
176	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
177	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
178	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×#127	C₂²×C₃	1	2	yes	—
180	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₅×#126	C₂²×C₃	1	2	yes	complemented
182	C₅×#126	C₂²×C₃	1	4	yes	complemented
183	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×#124	C₂²×C₃	1	2	yes	complemented
185	C₅×#124	C₂²×C₃	1	2	yes	complemented
186	C₅×#124	C₂²×C₃	1	2	yes	complemented
187	C₅×#124	C₂²×C₃	1	2	yes	complemented
188	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₅×#124	C₂²×C₃	1	2	yes	complemented
190	C₅×#124	C₂²×C₃	1	2	yes	complemented
191	C₅×#124	C₂²×C₃	1	4	yes	complemented
192	C₅×#124	C₂²×C₃	1	4	yes	complemented
193	C₅×#124	C₂²×C₃	1	4	yes	complemented
194	C₅×#123	C₂²×C₃	1	2	yes	complemented
195	C₅×#123	C₂²×C₃	1	4	yes	complemented
196	C₅×#123	C₂²×C₃	1	4	yes	complemented
197	C₅×#123	C₂²×C₃	1	4	yes	complemented
198	C₅×#123	C₂²×C₃	1	4	yes	complemented
199	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
201	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
202	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
203	C₅×#121	C₂²×C₃	1	1	yes	characteristic
204	C₅×#121	C₂²×C₃	1	2	yes	—
205	C₅×#121	C₂²×C₃	1	2	yes	complemented
206	C₅×#121	C₂²×C₃	1	2	yes	complemented
207	C₅×#121	C₂²×C₃	1	4	yes	complemented
208	C₅×#121	C₂²×C₃	1	4	yes	complemented
209	C₅×#121	C₂²×C₃	1	4	yes	complemented
210	C₅×#121	C₂²×C₃	1	4	yes	complemented
211	C₅×#121	C₂²×C₃	1	4	yes	complemented
212	C₅×#120	C₂²×C₃	1	4	yes	complemented
213	C₅×#120	C₂²×C₃	1	4	yes	complemented
214	C₅×#120	C₂²×C₃	1	4	yes	complemented
215	C₅×#120	C₂²×C₃	1	4	yes	complemented
216	C₅×#120	C₂²×C₃	1	4	yes	complemented
217	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
219	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
220	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
222	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
223	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
224	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
225	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
226	C₅×#117	C₂²×C₃	1	2	yes	complemented
227	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
228	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
229	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
230	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
231	#3558	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³×C₃×C₅	—	2	4	no	—
233	C₂³×C₃×C₅	—	4	2	no	—
234	C₂³×C₃×C₅	—	4	4	no	—
235	C₂³×C₃×C₅	—	4	4	no	—
236	C₂³×C₃×C₅	—	4	2	no	—
237	C₂³×C₃×C₅	—	4	4	no	—
238	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
239	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
240	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
241	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
242	C₃×C₅×Q₈	—	2	4	no	—
243	C₃×C₅×Q₈	—	4	2	no	—
244	C₃×C₅×Q₈	—	4	1	no	—
245	C₃×C₅×Q₈	—	4	2	no	—
246	C₃×C₅×D₄	—	2	4	no	—
247	C₃×C₅×D₄	—	2	8	no	—
248	C₃×C₅×D₄	—	2	4	no	—
249	C₃×C₅×D₄	—	2	4	no	—
250	C₃×C₅×D₄	—	4	4	no	—
251	C₃×C₅×D₄	—	4	2	no	—
252	C₃×C₅×D₄	—	4	4	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	2	no	—
258	C₃×C₅×D₄	—	4	4	no	—
259	C₂×C₃×C₄×C₅	—	2	2	no	—
260	C₂×C₃×C₄×C₅	—	2	2	no	—
261	C₂×C₃×C₄×C₅	—	2	4	no	—
262	C₂×C₃×C₄×C₅	—	4	1	no	—
263	C₂×C₃×C₄×C₅	—	4	4	no	—
264	C₂×C₃×C₄×C₅	—	4	2	no	—
265	C₂×C₃×C₄×C₅	—	4	4	no	—
266	C₂×C₃×C₄×C₅	—	4	4	no	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
276	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
279	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
280	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
282	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
283	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
284	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#127	C₂²×C₅	1	2	yes	—
286	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃×#126	C₂²×C₅	1	2	yes	complemented
288	C₃×#126	C₂²×C₅	1	4	yes	complemented
289	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₃×#124	C₂²×C₅	1	4	yes	complemented
291	C₃×#124	C₂²×C₅	1	2	yes	complemented
292	C₃×#124	C₂²×C₅	1	2	yes	complemented
293	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃×#124	C₂²×C₅	1	2	yes	complemented
295	C₃×#124	C₂²×C₅	1	2	yes	complemented
296	C₃×#124	C₂²×C₅	1	4	yes	complemented
297	C₃×#124	C₂²×C₅	1	4	yes	complemented
298	C₃×#124	C₂²×C₅	1	2	yes	complemented
299	C₃×#124	C₂²×C₅	1	2	yes	complemented
300	C₃×#123	C₂²×C₅	1	4	yes	complemented
301	C₃×#123	C₂²×C₅	1	4	yes	complemented
302	C₃×#123	C₂²×C₅	1	4	yes	complemented
303	C₃×#123	C₂²×C₅	1	2	yes	complemented
304	C₃×#123	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	1	yes	characteristic, complemented
308	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
309	C₃×#121	C₂²×C₅	1	1	yes	characteristic
310	C₃×#121	C₂²×C₅	1	2	yes	—
311	C₃×#121	C₂²×C₅	1	4	yes	complemented
312	C₃×#121	C₂²×C₅	1	4	yes	complemented
313	C₃×#121	C₂²×C₅	1	2	yes	complemented
314	C₃×#121	C₂²×C₅	1	2	yes	complemented
315	C₃×#121	C₂²×C₅	1	4	yes	complemented
316	C₃×#121	C₂²×C₅	1	4	yes	complemented
317	C₃×#121	C₂²×C₅	1	4	yes	complemented
318	C₃×#120	C₂²×C₅	1	4	yes	complemented
319	C₃×#120	C₂²×C₅	1	4	yes	complemented
320	C₃×#120	C₂²×C₅	1	4	yes	complemented
321	C₃×#120	C₂²×C₅	1	4	yes	complemented
322	C₃×#120	C₂²×C₅	1	4	yes	complemented
323	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
325	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
326	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
327	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
328	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
329	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
330	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
331	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
332	C₃×#117	C₂²×C₅	1	2	yes	complemented
333	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
334	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
335	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
336	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
337	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
338	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
339	C₅×#41	—	4	4	no	—
340	C₅×#41	—	4	4	no	—
341	C₂×C₅×Q₈	—	4	2	no	—
342	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
343	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
344	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
345	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
346	C₂×C₅×D₄	—	4	2	no	—
347	C₂×C₅×D₄	—	4	4	no	—
348	C₂×C₅×D₄	—	4	8	no	—
349	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
350	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
351	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
352	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
353	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
357	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
358	C₂×C₅×D₄	C₂³×C₃	1	2	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	4	yes	—
362	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
364	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
365	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
367	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
368	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
369	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
370	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
374	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
375	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
376	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
377	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
378	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
379	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
380	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
381	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
382	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
383	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
384	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
385	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
386	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
387	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
388	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₂²⋊C₄	C₂³×C₃	1	2	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	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
397	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
398	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
399	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
400	C₄²×C₅	C₂³×C₃	1	2	yes	—
401	C₄²×C₅	C₂³×C₃	1	4	yes	—
402	#562	C₂×C₃×C₅	1	2	yes	complemented
403	H(3,𝔽₄)	C₂×C₃×C₅	1	2	yes	complemented
404	#559	C₂×C₃×C₅	1	2	yes	complemented
405	#548	C₂×C₃×C₅	1	2	yes	complemented
406	#546	C₂×C₃×C₅	1	2	yes	complemented
407	#546	C₂×C₃×C₅	1	4	yes	complemented
408	D₄²	C₂×C₃×C₅	1	2	yes	complemented
409	#542	C₂×C₃×C₅	1	2	yes	complemented
410	#538	C₂×C₃×C₅	1	2	yes	complemented
411	#538	C₂×C₃×C₅	1	4	yes	complemented
412	#535	C₂×C₃×C₅	1	2	yes	complemented
413	#534	C₂×C₃×C₅	1	2	yes	complemented
414	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
415	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
416	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
417	C₂²×C₃×C₅	—	2	1	no	—
418	C₂²×C₃×C₅	—	2	1	no	—
419	C₂²×C₃×C₅	—	2	2	no	—
420	C₂²×C₃×C₅	—	2	4	no	—
421	C₂²×C₃×C₅	—	2	4	no	—
422	C₂²×C₃×C₅	—	2	4	no	—
423	C₂²×C₃×C₅	—	2	2	no	—
424	C₂²×C₃×C₅	—	2	4	no	—
425	C₂²×C₃×C₅	—	2	4	no	—
426	C₂²×C₃×C₅	—	2	2	no	—
427	C₂²×C₃×C₅	—	2	4	no	—
428	C₂²×C₃×C₅	—	8	4	no	—
429	C₂²×C₃×C₅	—	8	8	no	—
430	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
431	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
432	C₃×C₄×C₅	—	2	1	no	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	1	no	—
435	C₃×C₄×C₅	—	2	1	no	—
436	C₃×C₄×C₅	—	2	2	no	—
437	C₃×C₄×C₅	—	2	4	no	—
438	C₃×C₄×C₅	—	2	4	no	—
439	C₃×C₄×C₅	—	2	1	no	—
440	C₃×C₄×C₅	—	2	1	no	—
441	C₃×C₄×C₅	—	2	2	no	—
442	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
443	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
444	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
445	C₃×#41	—	4	4	no	—
446	C₃×#41	—	4	4	no	—
447	C₂×C₃×Q₈	—	4	2	no	—
448	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
449	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
451	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
452	C₂×C₃×D₄	—	4	2	no	—
453	C₂×C₃×D₄	—	4	4	no	—
454	C₂×C₃×D₄	—	4	8	no	—
455	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
456	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
457	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
458	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
459	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
461	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
462	C₂×C₃×D₄	C₂³×C₅	1	4	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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
469	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
471	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
473	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
474	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
475	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
476	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
477	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
478	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
479	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
480	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
481	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
482	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
483	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
484	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
485	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
486	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
487	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
488	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
489	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
490	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
491	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
492	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
493	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
494	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
495	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
496	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
502	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
503	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
504	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
505	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
506	C₃×C₄²	C₂³×C₅	1	2	yes	—
507	C₃×C₄²	C₂³×C₅	1	4	yes	—
508	C₂³×C₅	—	2	4	no	—
509	C₂³×C₅	—	4	2	no	—
510	C₂³×C₅	—	4	4	no	—
511	C₂³×C₅	—	4	4	no	—
512	C₂³×C₅	—	4	2	no	—
513	C₂³×C₅	—	4	4	no	—
514	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
515	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
516	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
517	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
518	C₅×Q₈	—	2	4	no	—
519	C₅×Q₈	—	4	2	no	—
520	C₅×Q₈	—	4	1	no	—
521	C₅×Q₈	—	4	2	no	—
522	C₅×D₄	—	2	4	no	—
523	C₅×D₄	—	2	8	no	—
524	C₅×D₄	—	2	4	no	—
525	C₅×D₄	—	2	4	no	—
526	C₅×D₄	—	4	4	no	—
527	C₅×D₄	—	4	2	no	—
528	C₅×D₄	—	4	4	no	—
529	C₅×D₄	—	4	4	no	—
530	C₅×D₄	—	4	2	no	—
531	C₅×D₄	—	4	1	no	—
532	C₅×D₄	—	4	4	no	—
533	C₅×D₄	—	4	2	no	—
534	C₅×D₄	—	4	4	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	2	4	no	—
538	C₂×C₄×C₅	—	4	1	no	—
539	C₂×C₄×C₅	—	4	4	no	—
540	C₂×C₄×C₅	—	4	2	no	—
541	C₂×C₄×C₅	—	4	4	no	—
542	C₂×C₄×C₅	—	4	4	no	—
543	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
544	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
545	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
546	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
547	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
548	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
549	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
550	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
551	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
552	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
553	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
554	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
555	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
556	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
557	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
558	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
559	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
560	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
561	#127	C₂²×C₃×C₅	1	2	yes	—
562	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
563	#126	C₂²×C₃×C₅	1	2	yes	complemented
564	#126	C₂²×C₃×C₅	1	4	yes	complemented
565	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
566	#124	C₂²×C₃×C₅	1	2	yes	complemented
567	#124	C₂²×C₃×C₅	1	2	yes	complemented
568	#124	C₂²×C₃×C₅	1	2	yes	complemented
569	#124	C₂²×C₃×C₅	1	2	yes	complemented
570	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
571	#124	C₂²×C₃×C₅	1	2	yes	complemented
572	#124	C₂²×C₃×C₅	1	2	yes	complemented
573	#124	C₂²×C₃×C₅	1	4	yes	complemented
574	#124	C₂²×C₃×C₅	1	4	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	1	yes	characteristic, complemented
582	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
583	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
584	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
585	#121	C₂²×C₃×C₅	1	1	yes	characteristic
586	#121	C₂²×C₃×C₅	1	2	yes	—
587	#121	C₂²×C₃×C₅	1	2	yes	complemented
588	#121	C₂²×C₃×C₅	1	2	yes	complemented
589	#121	C₂²×C₃×C₅	1	4	yes	complemented
590	#121	C₂²×C₃×C₅	1	4	yes	complemented
591	#121	C₂²×C₃×C₅	1	4	yes	complemented
592	#121	C₂²×C₃×C₅	1	4	yes	complemented
593	#121	C₂²×C₃×C₅	1	4	yes	complemented
594	#120	C₂²×C₃×C₅	1	4	yes	complemented
595	#120	C₂²×C₃×C₅	1	4	yes	complemented
596	#120	C₂²×C₃×C₅	1	4	yes	complemented
597	#120	C₂²×C₃×C₅	1	4	yes	complemented
598	#120	C₂²×C₃×C₅	1	4	yes	complemented
599	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
600	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
601	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
602	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
603	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
604	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
605	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
606	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
607	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
608	#117	C₂²×C₃×C₅	1	2	yes	complemented
609	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
610	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
611	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
612	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
613	C₂×C₃×C₅	—	2	2	no	—
614	C₂×C₃×C₅	—	4	4	no	—
615	C₂×C₃×C₅	—	4	2	no	—
616	C₂×C₃×C₅	—	4	4	no	—
617	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂×C₃×C₅	#585	1	1	yes	characteristic
620	C₂³×C₃	—	2	4	no	—
621	C₂³×C₃	—	4	2	no	—
622	C₂³×C₃	—	4	4	no	—
623	C₂³×C₃	—	4	4	no	—
624	C₂³×C₃	—	4	2	no	—
625	C₂³×C₃	—	4	4	no	—
626	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
627	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
628	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
629	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
630	C₃×Q₈	—	2	4	no	—
631	C₃×Q₈	—	4	2	no	—
632	C₃×Q₈	—	4	1	no	—
633	C₃×Q₈	—	4	2	no	—
634	C₃×D₄	—	2	4	no	—
635	C₃×D₄	—	2	8	no	—
636	C₃×D₄	—	2	4	no	—
637	C₃×D₄	—	2	4	no	—
638	C₃×D₄	—	4	4	no	—
639	C₃×D₄	—	4	2	no	—
640	C₃×D₄	—	4	4	no	—
641	C₃×D₄	—	4	4	no	—
642	C₃×D₄	—	4	2	no	—
643	C₃×D₄	—	4	1	no	—
644	C₃×D₄	—	4	4	no	—
645	C₃×D₄	—	4	2	no	—
646	C₃×D₄	—	4	4	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	4	no	—
650	C₂×C₃×C₄	—	4	1	no	—
651	C₂×C₃×C₄	—	4	4	no	—
652	C₂×C₃×C₄	—	4	2	no	—
653	C₂×C₃×C₄	—	4	4	no	—
654	C₂×C₃×C₄	—	4	4	no	—
655	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
656	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
657	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
658	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
659	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
660	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
661	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
662	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
663	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
664	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
665	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
666	C₂²×C₅	—	2	1	no	—
667	C₂²×C₅	—	2	1	no	—
668	C₂²×C₅	—	2	2	no	—
669	C₂²×C₅	—	2	4	no	—
670	C₂²×C₅	—	2	4	no	—
671	C₂²×C₅	—	2	4	no	—
672	C₂²×C₅	—	2	2	no	—
673	C₂²×C₅	—	2	4	no	—
674	C₂²×C₅	—	2	4	no	—
675	C₂²×C₅	—	2	2	no	—
676	C₂²×C₅	—	2	4	no	—
677	C₂²×C₅	—	8	4	no	—
678	C₂²×C₅	—	8	8	no	—
679	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
680	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
681	C₄×C₅	—	2	1	no	—
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	2	1	no	—
684	C₄×C₅	—	2	1	no	—
685	C₄×C₅	—	2	2	no	—
686	C₄×C₅	—	2	4	no	—
687	C₄×C₅	—	2	4	no	—
688	C₄×C₅	—	2	1	no	—
689	C₄×C₅	—	2	1	no	—
690	C₄×C₅	—	2	2	no	—
691	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
692	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
693	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
698	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
699	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
700	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	8	no	—
704	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
705	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
706	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
707	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
708	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
709	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
710	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
711	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
712	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
713	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
714	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
715	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
716	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
717	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
718	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
719	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
720	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
721	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
722	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
723	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
724	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
725	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
726	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
727	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
728	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
729	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
730	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
731	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
732	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
733	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
734	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
735	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
736	C₂²⋊C₄	C₂³×C₃×C₅	1	4	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	4	yes	—
740	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
741	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
742	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
743	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
744	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
745	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
746	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
747	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
748	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
749	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
750	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
751	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
752	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
753	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
754	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
755	C₄²	C₂³×C₃×C₅	1	2	yes	—
756	C₄²	C₂³×C₃×C₅	1	4	yes	—
757	C₃×C₅	#3558	1	1	yes	characteristic, direct product factor, Hall
758	C₂²×C₃	—	2	1	no	—
759	C₂²×C₃	—	2	1	no	—
760	C₂²×C₃	—	2	2	no	—
761	C₂²×C₃	—	2	4	no	—
762	C₂²×C₃	—	2	4	no	—
763	C₂²×C₃	—	2	4	no	—
764	C₂²×C₃	—	2	2	no	—
765	C₂²×C₃	—	2	4	no	—
766	C₂²×C₃	—	2	4	no	—
767	C₂²×C₃	—	2	2	no	—
768	C₂²×C₃	—	2	4	no	—
769	C₂²×C₃	—	8	4	no	—
770	C₂²×C₃	—	8	8	no	—
771	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
772	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
773	C₃×C₄	—	2	1	no	—
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	2	1	no	—
776	C₃×C₄	—	2	1	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	4	no	—
779	C₃×C₄	—	2	4	no	—
780	C₃×C₄	—	2	1	no	—
781	C₃×C₄	—	2	1	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
784	C₂×C₅	—	2	2	no	—
785	C₂×C₅	—	4	2	no	—
786	C₂×C₅	—	4	4	no	—
787	C₂×C₅	—	4	4	no	—
788	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
789	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
790	C₂×C₅	C₃×#585	1	1	yes	characteristic
791	C₂³	—	2	4	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
798	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
799	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
800	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
801	Q₈	—	2	4	no	—
802	Q₈	—	4	2	no	—
803	Q₈	—	4	2	no	—
804	Q₈	—	4	1	no	—
805	D₄	—	2	4	no	—
806	D₄	—	2	8	no	—
807	D₄	—	2	4	no	—
808	D₄	—	2	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
827	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
828	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
829	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
830	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
831	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
832	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
833	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
834	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
835	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
836	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
837	C₂×C₃	—	2	2	no	—
838	C₂×C₃	—	4	2	no	—
839	C₂×C₃	—	4	4	no	—
840	C₂×C₃	—	4	4	no	—
841	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
843	C₂×C₃	C₅×#585	1	1	yes	characteristic
844	C₅	C₃×#3558	1	1	yes	characteristic, direct product factor, Sylow
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	8	4	no	—
857	C₂²	—	8	8	no	—
858	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
859	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	4	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
871	C₃	C₅×#3558	1	1	yes	characteristic, direct product factor, Sylow
872	C₂	—	2	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	4	4	no	—
875	C₂	—	4	4	no	—
876	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂	C₃×C₅×#585	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×H(3,𝔽₄)	C₂	semidirect
3. C₃×C₅×#559	C₂	semidirect
4. C₃×C₅×#548	C₂	semidirect
5. C₃×C₅×#546	C₂	semidirect
6. C₃×C₅×#546	C₂	semidirect
7. C₃×C₅×D₄²	C₂	semidirect
8. C₃×C₅×#542	C₂	semidirect
9. C₃×C₅×#538	C₂	semidirect
10. C₃×C₅×#538	C₂	semidirect
11. C₃×C₅×#535	C₂	semidirect
12. C₃×C₅×#534	C₂	semidirect
13. C₃×C₅×#532	C₂	semidirect
14. C₃×C₅×#529	C₂	semidirect
15. C₂×C₃×C₅×#124	C₂	semidirect
16. C₅×#3558	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₂²×C₃×C₅×Q₈	C₂²	semidirect
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₃×C₅×D₄	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#127	C₂²	semidirect
26. C₃×C₅×#126	C₂²	semidirect
27. C₃×C₅×#126	C₂²	semidirect
28. C₃×C₅×#125	C₂²	semidirect
29. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₅×#124	C₂²	semidirect
31. C₃×C₅×#124	C₂²	semidirect
32. C₃×C₅×#124	C₂²	semidirect
33. C₃×C₅×#124	C₂²	semidirect
34. C₃×C₅×#124	C₂²	semidirect
35. C₃×C₅×#124	C₂²	semidirect
36. C₃×C₅×#124	C₂²	semidirect
37. C₃×C₅×#124	C₂²	semidirect
38. C₃×C₅×#124	C₂²	semidirect
39. C₃×C₅×#123	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×#123	C₂²	semidirect
42. C₃×C₅×#123	C₂²	semidirect
43. C₃×C₅×#123	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
50. C₃×C₅×#121	C₂²	semidirect
51. C₃×C₅×#121	C₂²	semidirect
52. C₃×C₅×#121	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×#120	C₂²	semidirect
58. C₃×C₅×#120	C₂²	semidirect
59. C₃×C₅×#120	C₂²	semidirect
60. C₃×C₅×#120	C₂²	semidirect
61. C₃×C₅×#120	C₂²	semidirect
62. C₃×C₄×C₅×Q₈	C₂²	semidirect
63. C₃×C₄×C₅×Q₈	C₂²	semidirect
64. C₃×C₄×C₅×D₄	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×C₄×C₅×D₄	C₂²	semidirect
69. C₃×C₄×C₅×D₄	C₂²	semidirect
70. C₃×C₄×C₅×D₄	C₂²	semidirect
71. C₃×C₅×#117	C₂²	semidirect
72. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
73. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
74. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
75. C₂×C₃×C₄²×C₅	C₂²	semidirect
76. C₃×#3558	C₅	direct (N × H)
77. C₅×#562	C₂×C₃	semidirect
78. C₅×H(3,𝔽₄)	C₂×C₃	semidirect
79. C₅×#559	C₂×C₃	semidirect
80. C₅×#548	C₂×C₃	semidirect
81. C₅×#546	C₂×C₃	semidirect
82. C₅×#546	C₂×C₃	semidirect
83. C₅×D₄²	C₂×C₃	semidirect
84. C₅×#542	C₂×C₃	semidirect
85. C₅×#538	C₂×C₃	semidirect
86. C₅×#538	C₂×C₃	semidirect
87. C₅×#535	C₂×C₃	semidirect
88. C₅×#534	C₂×C₃	semidirect
89. C₅×#532	C₂×C₃	semidirect
90. C₅×#529	C₂×C₃	semidirect
91. C₂×C₅×#124	C₂×C₃	semidirect
157. C₃×#562	C₂×C₅	semidirect
158. C₃×H(3,𝔽₄)	C₂×C₅	semidirect
159. C₃×#559	C₂×C₅	semidirect
160. C₃×#548	C₂×C₅	semidirect
161. C₃×#546	C₂×C₅	semidirect
162. C₃×#546	C₂×C₅	semidirect
163. C₃×D₄²	C₂×C₅	semidirect
164. C₃×#542	C₂×C₅	semidirect
165. C₃×#538	C₂×C₅	semidirect
166. C₃×#538	C₂×C₅	semidirect
167. C₃×#535	C₂×C₅	semidirect
168. C₃×#534	C₂×C₅	semidirect
169. C₃×#532	C₂×C₅	semidirect
170. C₃×#529	C₂×C₅	semidirect
171. C₂×C₃×#124	C₂×C₅	semidirect
172. C₂×C₅×#41	C₂²×C₃	semidirect
173. C₂×C₅×#41	C₂²×C₃	semidirect
174. C₂²×C₅×Q₈	C₂²×C₃	semidirect
176. C₂²×C₅×D₄	C₂²×C₃	semidirect
177. C₂²×C₅×D₄	C₂²×C₃	semidirect
178. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
180. C₅×#127	C₂²×C₃	semidirect
181. C₅×#126	C₂²×C₃	semidirect
182. C₅×#126	C₂²×C₃	semidirect
183. C₅×#125	C₂²×C₃	semidirect
184. C₅×#124	C₂²×C₃	semidirect
185. C₅×#124	C₂²×C₃	semidirect
186. C₅×#124	C₂²×C₃	semidirect
187. C₅×#124	C₂²×C₃	semidirect
188. C₅×#124	C₂²×C₃	semidirect
189. C₅×#124	C₂²×C₃	semidirect
190. C₅×#124	C₂²×C₃	semidirect
191. C₅×#124	C₂²×C₃	semidirect
192. C₅×#124	C₂²×C₃	semidirect
193. C₅×#124	C₂²×C₃	semidirect
194. C₅×#123	C₂²×C₃	semidirect
195. C₅×#123	C₂²×C₃	semidirect
196. C₅×#123	C₂²×C₃	semidirect
197. C₅×#123	C₂²×C₃	semidirect
198. C₅×#123	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
205. C₅×#121	C₂²×C₃	semidirect
206. C₅×#121	C₂²×C₃	semidirect
207. C₅×#121	C₂²×C₃	semidirect
208. C₅×#121	C₂²×C₃	semidirect
209. C₅×#121	C₂²×C₃	semidirect
210. C₅×#121	C₂²×C₃	semidirect
211. C₅×#121	C₂²×C₃	semidirect
212. C₅×#120	C₂²×C₃	semidirect
213. C₅×#120	C₂²×C₃	semidirect
214. C₅×#120	C₂²×C₃	semidirect
215. C₅×#120	C₂²×C₃	semidirect
216. C₅×#120	C₂²×C₃	semidirect
217. C₄×C₅×Q₈	C₂²×C₃	semidirect
218. C₄×C₅×Q₈	C₂²×C₃	semidirect
219. C₄×C₅×D₄	C₂²×C₃	semidirect
220. C₄×C₅×D₄	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. C₄×C₅×D₄	C₂²×C₃	semidirect
225. C₄×C₅×D₄	C₂²×C₃	semidirect
226. C₅×#117	C₂²×C₃	semidirect
227. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
228. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
229. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
230. C₂×C₄²×C₅	C₂²×C₃	semidirect
231. #3558	C₃×C₅	direct (N × H)
278. C₂×C₃×#41	C₂²×C₅	semidirect
279. C₂×C₃×#41	C₂²×C₅	semidirect
280. C₂²×C₃×Q₈	C₂²×C₅	semidirect
282. C₂²×C₃×D₄	C₂²×C₅	semidirect
283. C₂²×C₃×D₄	C₂²×C₅	semidirect
284. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
286. C₃×#127	C₂²×C₅	semidirect
287. C₃×#126	C₂²×C₅	semidirect
288. C₃×#126	C₂²×C₅	semidirect
289. C₃×#125	C₂²×C₅	semidirect
290. C₃×#124	C₂²×C₅	semidirect
291. C₃×#124	C₂²×C₅	semidirect
292. C₃×#124	C₂²×C₅	semidirect
293. C₃×#124	C₂²×C₅	semidirect
294. C₃×#124	C₂²×C₅	semidirect
295. C₃×#124	C₂²×C₅	semidirect
296. C₃×#124	C₂²×C₅	semidirect
297. C₃×#124	C₂²×C₅	semidirect
298. C₃×#124	C₂²×C₅	semidirect
299. C₃×#124	C₂²×C₅	semidirect
300. C₃×#123	C₂²×C₅	semidirect
301. C₃×#123	C₂²×C₅	semidirect
302. C₃×#123	C₂²×C₅	semidirect
303. C₃×#123	C₂²×C₅	semidirect
304. C₃×#123	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
311. C₃×#121	C₂²×C₅	semidirect
312. C₃×#121	C₂²×C₅	semidirect
313. C₃×#121	C₂²×C₅	semidirect
314. C₃×#121	C₂²×C₅	semidirect
315. C₃×#121	C₂²×C₅	semidirect
316. C₃×#121	C₂²×C₅	semidirect
317. C₃×#121	C₂²×C₅	semidirect
318. C₃×#120	C₂²×C₅	semidirect
319. C₃×#120	C₂²×C₅	semidirect
320. C₃×#120	C₂²×C₅	semidirect
321. C₃×#120	C₂²×C₅	semidirect
322. C₃×#120	C₂²×C₅	semidirect
323. C₃×C₄×Q₈	C₂²×C₅	semidirect
324. C₃×C₄×Q₈	C₂²×C₅	semidirect
325. C₃×C₄×D₄	C₂²×C₅	semidirect
326. C₃×C₄×D₄	C₂²×C₅	semidirect
327. C₃×C₄×D₄	C₂²×C₅	semidirect
328. C₃×C₄×D₄	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
333. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
334. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
335. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
336. C₂×C₃×C₄²	C₂²×C₅	semidirect
402. #562	C₂×C₃×C₅	semidirect
403. H(3,𝔽₄)	C₂×C₃×C₅	semidirect
404. #559	C₂×C₃×C₅	semidirect
405. #548	C₂×C₃×C₅	semidirect
406. #546	C₂×C₃×C₅	semidirect
407. #546	C₂×C₃×C₅	semidirect
408. D₄²	C₂×C₃×C₅	semidirect
409. #542	C₂×C₃×C₅	semidirect
410. #538	C₂×C₃×C₅	semidirect
411. #538	C₂×C₃×C₅	semidirect
412. #535	C₂×C₃×C₅	semidirect
413. #534	C₂×C₃×C₅	semidirect
414. #532	C₂×C₃×C₅	semidirect
415. #529	C₂×C₃×C₅	semidirect
416. C₂×#124	C₂×C₃×C₅	semidirect
554. C₂×#41	C₂²×C₃×C₅	semidirect
555. C₂×#41	C₂²×C₃×C₅	semidirect
556. C₂²×Q₈	C₂²×C₃×C₅	semidirect
558. C₂²×D₄	C₂²×C₃×C₅	semidirect
559. C₂²×D₄	C₂²×C₃×C₅	semidirect
560. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
562. #127	C₂²×C₃×C₅	semidirect
563. #126	C₂²×C₃×C₅	semidirect
564. #126	C₂²×C₃×C₅	semidirect
565. #125	C₂²×C₃×C₅	semidirect
566. #124	C₂²×C₃×C₅	semidirect
567. #124	C₂²×C₃×C₅	semidirect
568. #124	C₂²×C₃×C₅	semidirect
569. #124	C₂²×C₃×C₅	semidirect
570. #124	C₂²×C₃×C₅	semidirect
571. #124	C₂²×C₃×C₅	semidirect
572. #124	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
581. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
582. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
583. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
584. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
587. #121	C₂²×C₃×C₅	semidirect
588. #121	C₂²×C₃×C₅	semidirect
589. #121	C₂²×C₃×C₅	semidirect
590. #121	C₂²×C₃×C₅	semidirect
591. #121	C₂²×C₃×C₅	semidirect
592. #121	C₂²×C₃×C₅	semidirect
593. #121	C₂²×C₃×C₅	semidirect
594. #120	C₂²×C₃×C₅	semidirect
595. #120	C₂²×C₃×C₅	semidirect
596. #120	C₂²×C₃×C₅	semidirect
597. #120	C₂²×C₃×C₅	semidirect
598. #120	C₂²×C₃×C₅	semidirect
599. C₄×Q₈	C₂²×C₃×C₅	semidirect
600. C₄×Q₈	C₂²×C₃×C₅	semidirect
601. C₄×D₄	C₂²×C₃×C₅	semidirect
602. C₄×D₄	C₂²×C₃×C₅	semidirect
603. C₄×D₄	C₂²×C₃×C₅	semidirect
604. C₄×D₄	C₂²×C₃×C₅	semidirect
605. C₄×D₄	C₂²×C₃×C₅	semidirect
606. C₄×D₄	C₂²×C₃×C₅	semidirect
607. C₄×D₄	C₂²×C₃×C₅	semidirect
608. #117	C₂²×C₃×C₅	semidirect
609. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
610. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
611. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
612. C₂×C₄²	C₂²×C₃×C₅	semidirect
757. C₃×C₅	#3558	direct (N × H)
844. C₅	C₃×#3558	direct (N × H)
871. C₃	C₅×#3558	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×H(3,𝔽₄)	2
C₃×C₅×#559	2
C₃×C₅×#548	2
C₃×C₅×#546	2
C₃×C₅×D₄²	2
C₃×C₅×#542	2
C₃×C₅×#538	2
C₃×C₅×#535	2
C₃×C₅×#534	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₂×C₃×C₅×#124	2
C₅×#3558	3
C₃×#3558	5

Subgroups — C3×C5×#3558 #14276592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3558 #14276592