Subgroups — C₅×D₃×#554 #14483784

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5690	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#125	C₂	1	2	yes	maximal, complemented
6	C₅×#5636	C₂	1	4	yes	maximal, complemented
7	C₅×#5635	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
9	C₅×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₅×#5579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal
13	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
14	C₅×#5543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5539	C₂	1	2	yes	maximal, complemented
16	C₅×#5511	C₂	1	2	yes	maximal, complemented
17	C₂×C₅×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
18	C₂×C₅×#554	—	3	1	no	maximal, Hall
19	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
21	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
23	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#125	C₂²	1	2	yes	complemented
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₅×#946	C₂²	1	4	yes	complemented
33	C₅×#946	C₂²	1	2	yes	complemented
34	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₅×#944	C₂²	1	2	yes	complemented
36	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₅×D₄×Dic₃	C₂²	1	2	yes	—
38	C₄×C₅×#67	C₂²	1	2	yes	—
39	C₄×C₅×#67	C₂²	1	4	yes	—
40	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
41	C₅×#924	C₂²	1	4	yes	complemented
42	C₅×#924	C₂²	1	2	yes	complemented
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
44	C₅×#897	C₂²	1	4	yes	complemented
45	C₅×#897	C₂²	1	2	yes	complemented
46	C₅×#896	C₂²	1	4	yes	complemented
47	C₅×#896	C₂²	1	4	yes	complemented
48	C₅×#896	C₂²	1	4	yes	complemented
49	C₅×#893	C₂²	1	1	yes	characteristic
50	C₅×#893	C₂²	1	2	yes	—
51	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
53	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
55	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
59	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₅×#890	C₂²	1	2	yes	complemented
62	C₅×#890	C₂²	1	2	yes	complemented
63	C₅×#889	C₂²	1	4	yes	complemented
64	C₅×#889	C₂²	1	4	yes	complemented
65	C₅×#888	C₂²	1	2	yes	complemented
66	C₅×#888	C₂²	1	2	yes	complemented
67	C₅×#887	C₂²	1	1	yes	characteristic, complemented
68	C₅×#887	C₂²	1	2	yes	complemented
69	C₅×#67⋊C₄	C₂²	1	4	yes	—
70	C₅×#67⋊C₄	C₂²	1	2	yes	—
71	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₅×#878	C₂²	1	4	yes	complemented
74	C₅×#878	C₂²	1	4	yes	complemented
75	C₅×#878	C₂²	1	4	yes	complemented
76	C₄×C₅×D₁₂	C₂²	1	2	yes	—
77	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
78	C₄²×C₅×D₃	C₂²	1	2	yes	—
79	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
80	C₅×#870	C₂²	1	2	yes	complemented
81	C₅×#869	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
83	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	D₃×#554	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#554	—	3	1	no	—
86	C₅×#554	—	3	2	no	—
87	C₅×#554	—	3	2	no	—
88	C₅×#554	—	3	4	no	—
89	C₅×#554	—	3	1	no	—
90	C₅×#554	—	3	2	no	—
91	C₅×#554	—	3	1	no	—
92	C₅×#554	—	3	2	no	—
93	C₅×#554	D₃	1	1	yes	characteristic, direct product factor
94	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
95	C₂×C₅×#125	—	3	2	no	—
96	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
97	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
98	C₂×C₄×C₅×Q₈	—	3	1	no	—
99	C₂×C₄×C₅×D₄	—	3	2	no	—
100	C₂×C₄×C₅×D₄	—	3	1	no	—
101	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
102	C₂³×C₅×D₃	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
108	C₂×C₅×#67	C₂³	1	2	yes	—
109	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
110	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
111	C₅×D₃×Q₈	—	2	4	no	—
112	C₅×D₃×Q₈	—	4	4	no	—
113	C₅×D₃×D₄	Q₈	1	8	yes	complemented
114	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
115	C₂×C₄×C₅×D₃	—	2	8	no	—
116	C₂×C₄×C₅×D₃	—	4	8	no	—
117	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
118	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
120	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
121	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
122	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
124	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
125	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
126	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
128	C₂×C₅×Dic₆	C₂³	1	2	yes	—
129	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
130	C₂×C₅×Dic₆	C₂³	1	2	yes	—
131	C₂×C₅×Dic₆	C₂³	1	4	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₃×C₄²×C₅	C₂³	1	2	yes	—
143	C₅×#217	C₂³	1	4	yes	—
144	C₅×#217	C₂³	1	2	yes	—
145	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
150	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
151	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
152	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
153	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
155	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
156	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
157	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
158	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
159	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
160	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
163	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
164	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
166	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
167	C₄×C₅×Dic₃	C₂³	1	2	yes	—
168	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
169	C₄×C₅×Dic₃	C₂³	1	2	yes	—
170	C₄×C₅×Dic₃	C₂³	1	2	yes	—
171	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
172	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
173	#5730	C₂×C₅	1	1	yes	characteristic, complemented
174	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
175	#5690	C₂×C₅	1	2	yes	complemented
176	D₃×#125	C₂×C₅	1	2	yes	complemented
177	#5636	C₂×C₅	1	4	yes	complemented
178	#5635	C₂×C₅	1	2	yes	complemented
179	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
180	D₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
181	#5579	C₂×C₅	1	1	yes	characteristic, complemented
182	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
183	C₄×D₃×D₄	C₂×C₅	1	2	yes	—
184	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
185	#5543	C₂×C₅	1	1	yes	characteristic, complemented
186	#5539	C₂×C₅	1	2	yes	complemented
187	#5511	C₂×C₅	1	2	yes	complemented
188	C₂×D₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
189	C₂²×C₅×Q₈	—	3	1	no	—
190	C₂²×C₅×Q₈	—	3	2	no	—
191	C₂²×C₅×D₄	—	3	1	no	—
192	C₂³×C₄×C₅	—	3	2	no	—
193	C₂³×C₄×C₅	—	3	4	no	—
194	C₅×C₄⋊Q₈	—	3	2	no	—
195	C₅×C₄⋊Q₈	—	3	2	no	—
196	C₅×C₄⋊Q₈	—	3	2	no	—
197	C₅×C₄⋊Q₈	—	3	1	no	—
198	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
199	C₅×#125	—	3	4	no	—
200	C₅×#125	—	3	4	no	—
201	C₅×#125	—	3	2	no	—
202	C₅×#125	—	3	2	no	—
203	C₅×#125	—	3	2	no	—
204	C₅×#125	C₂×D₃	1	2	yes	complemented
205	C₅×C₂²⋊Q₈	—	3	4	no	—
206	C₅×C₂²⋊Q₈	—	3	2	no	—
207	C₅×C₂²⋊Q₈	—	3	4	no	—
208	C₅×C₂²⋊Q₈	—	3	2	no	—
209	C₅×C₂²⋊Q₈	—	3	4	no	—
210	C₅×C₂²⋊Q₈	—	3	4	no	—
211	C₅×C₂²⋊Q₈	—	3	4	no	—
212	C₅×C₂²⋊Q₈	—	3	4	no	—
213	C₅×C₂²⋊Q₈	—	3	2	no	—
214	C₅×C₂²⋊Q₈	—	3	4	no	—
215	C₅×C₂²⋊Q₈	—	3	4	no	—
216	C₅×C₂²⋊Q₈	—	3	4	no	—
217	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
218	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
219	C₄×C₅×Q₈	—	3	1	no	—
220	C₄×C₅×Q₈	—	3	2	no	—
221	C₄×C₅×Q₈	—	3	1	no	—
222	C₄×C₅×Q₈	—	3	1	no	—
223	C₄×C₅×Q₈	—	3	2	no	—
224	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
225	C₄×C₅×D₄	—	3	2	no	—
226	C₄×C₅×D₄	—	3	1	no	—
227	C₄×C₅×D₄	—	3	4	no	—
228	C₄×C₅×D₄	—	3	2	no	—
229	C₄×C₅×D₄	—	3	2	no	—
230	C₄×C₅×D₄	—	3	1	no	—
231	C₄×C₅×D₄	—	3	4	no	—
232	C₄×C₅×D₄	—	3	2	no	—
233	C₄×C₅×D₄	—	3	2	no	—
234	C₄×C₅×D₄	—	3	1	no	—
235	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
236	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
237	C₂×C₅×C₄⋊C₄	—	3	4	no	—
238	C₂×C₅×C₄⋊C₄	—	3	2	no	—
239	C₂×C₅×C₄⋊C₄	—	3	1	no	—
240	C₂×C₅×C₄⋊C₄	—	3	4	no	—
241	C₂×C₅×C₄⋊C₄	—	3	2	no	—
242	C₂×C₅×C₄⋊C₄	—	3	1	no	—
243	C₂×C₅×C₄⋊C₄	—	3	2	no	—
244	C₂×C₅×C₄⋊C₄	—	3	2	no	—
245	C₂×C₅×C₄⋊C₄	—	3	4	no	—
246	C₂×C₅×C₄⋊C₄	—	3	4	no	—
247	C₂×C₅×C₄⋊C₄	—	3	2	no	—
248	C₂×C₅×C₄⋊C₄	—	3	2	no	—
249	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
250	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
251	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
252	C₂×C₄²×C₅	—	3	2	no	—
253	C₂×C₄²×C₅	—	3	1	no	—
254	C₂×#554	—	3	1	no	Sylow
255	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
256	C₂²×C₅×D₃	—	2	4	no	—
257	C₂²×C₅×D₃	—	2	4	no	—
258	C₂²×C₅×D₃	C₂×Q₈	1	8	yes	—
259	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
260	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
261	C₃×C₅×Q₈	—	2	2	no	—
262	C₃×C₅×Q₈	—	4	2	no	—
263	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
264	C₂×C₃×C₄×C₅	—	2	4	no	—
265	C₂×C₃×C₄×C₅	—	4	4	no	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	2	yes	—
270	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₅×#67	C₂×Q₈	1	8	yes	complemented
274	C₂×C₅×Dic₃	—	2	4	no	—
275	C₂×C₅×Dic₃	—	4	4	no	—
276	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
277	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
278	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
280	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
281	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
283	C₅×D₁₂	C₂×Q₈	1	4	yes	complemented
284	C₄×C₅×D₃	—	2	4	no	—
285	C₄×C₅×D₃	—	2	4	no	—
286	C₄×C₅×D₃	—	2	4	no	—
287	C₄×C₅×D₃	—	2	8	no	—
288	C₄×C₅×D₃	—	2	2	no	—
289	C₄×C₅×D₃	—	2	4	no	—
290	C₄×C₅×D₃	—	2	4	no	—
291	C₄×C₅×D₃	—	4	4	no	—
292	C₄×C₅×D₃	—	4	4	no	—
293	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
294	C₄×C₅×D₃	#41	1	4	yes	—
295	C₅×Dic₆	—	2	2	no	—
296	C₅×Dic₆	—	2	4	no	—
297	C₅×Dic₆	—	4	4	no	—
298	C₅×Dic₆	—	4	2	no	—
299	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
300	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
301	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
302	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
303	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
304	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₃×#125	C₂²×C₅	1	2	yes	complemented
306	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
307	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
308	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
310	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
312	#946	C₂²×C₅	1	2	yes	complemented
313	#946	C₂²×C₅	1	4	yes	complemented
314	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
315	#944	C₂²×C₅	1	2	yes	complemented
316	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
317	D₄×Dic₃	C₂²×C₅	1	2	yes	—
318	C₄×#67	C₂²×C₅	1	2	yes	—
319	C₄×#67	C₂²×C₅	1	4	yes	—
320	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
321	#924	C₂²×C₅	1	4	yes	complemented
322	#924	C₂²×C₅	1	2	yes	complemented
323	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
324	#897	C₂²×C₅	1	4	yes	complemented
325	#897	C₂²×C₅	1	2	yes	complemented
326	#896	C₂²×C₅	1	4	yes	complemented
327	#896	C₂²×C₅	1	4	yes	complemented
328	#896	C₂²×C₅	1	4	yes	complemented
329	#893	C₂²×C₅	1	1	yes	characteristic
330	#893	C₂²×C₅	1	2	yes	—
331	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
332	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
333	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
334	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
335	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
336	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
337	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
338	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
339	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
340	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
341	#890	C₂²×C₅	1	2	yes	complemented
342	#890	C₂²×C₅	1	2	yes	complemented
343	#889	C₂²×C₅	1	4	yes	complemented
344	#889	C₂²×C₅	1	4	yes	complemented
345	#888	C₂²×C₅	1	2	yes	complemented
346	#888	C₂²×C₅	1	2	yes	complemented
347	#887	C₂²×C₅	1	2	yes	complemented
348	#887	C₂²×C₅	1	1	yes	characteristic, complemented
349	#67⋊C₄	C₂²×C₅	1	4	yes	—
350	#67⋊C₄	C₂²×C₅	1	2	yes	—
351	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
352	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
353	#878	C₂²×C₅	1	4	yes	complemented
354	#878	C₂²×C₅	1	4	yes	complemented
355	#878	C₂²×C₅	1	4	yes	complemented
356	C₄×D₁₂	C₂²×C₅	1	2	yes	—
357	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
358	C₄²×D₃	C₂²×C₅	1	2	yes	—
359	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
360	#870	C₂²×C₅	1	2	yes	complemented
361	#869	C₂²×C₅	1	1	yes	characteristic, complemented
362	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
363	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
364	C₂⁴×C₅	—	3	2	no	—
365	C₂×C₅×Q₈	—	3	2	no	—
366	C₂×C₅×Q₈	—	3	1	no	—
367	C₂×C₅×Q₈	—	3	4	no	—
368	C₂×C₅×Q₈	—	3	2	no	—
369	C₂×C₅×Q₈	—	6	4	no	—
370	C₂×C₅×Q₈	—	12	4	no	—
371	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
372	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
373	C₂×C₅×D₄	—	3	2	no	—
374	C₂×C₅×D₄	—	3	8	no	—
375	C₂×C₅×D₄	—	3	1	no	—
376	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₄×C₅	—	3	1	no	—
378	C₂²×C₄×C₅	—	3	1	no	—
379	C₂²×C₄×C₅	—	3	2	no	—
380	C₂²×C₄×C₅	—	3	4	no	—
381	C₂²×C₄×C₅	—	3	2	no	—
382	C₂²×C₄×C₅	—	3	1	no	—
383	C₂²×C₄×C₅	—	3	2	no	—
384	C₂²×C₄×C₅	—	3	2	no	—
385	C₂²×C₄×C₅	—	3	4	no	—
386	C₂²×C₄×C₅	—	3	2	no	—
387	C₂²×C₄×C₅	—	3	2	no	—
388	C₂²×C₄×C₅	—	3	4	no	—
389	C₂²×C₄×C₅	—	3	4	no	—
390	C₂²×C₄×C₅	—	6	8	no	—
391	C₂²×C₄×C₅	—	12	8	no	—
392	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
393	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
394	C₅×C₄⋊C₄	—	3	2	no	—
395	C₅×C₄⋊C₄	—	3	1	no	—
396	C₅×C₄⋊C₄	—	3	4	no	—
397	C₅×C₄⋊C₄	—	3	4	no	—
398	C₅×C₄⋊C₄	—	3	4	no	—
399	C₅×C₄⋊C₄	—	3	4	no	—
400	C₅×C₄⋊C₄	—	3	2	no	—
401	C₅×C₄⋊C₄	—	3	2	no	—
402	C₅×C₄⋊C₄	—	3	1	no	—
403	C₅×C₄⋊C₄	—	3	4	no	—
404	C₅×C₄⋊C₄	—	3	2	no	—
405	C₅×C₄⋊C₄	—	3	2	no	—
406	C₅×C₄⋊C₄	—	3	2	no	—
407	C₅×C₄⋊C₄	—	3	2	no	—
408	C₅×C₄⋊C₄	—	3	4	no	—
409	C₅×C₄⋊C₄	—	3	4	no	—
410	C₅×C₄⋊C₄	—	3	4	no	—
411	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
412	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
413	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
414	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
415	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
416	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
417	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
418	C₅×C₂²⋊C₄	—	3	4	no	—
419	C₅×C₂²⋊C₄	—	3	2	no	—
420	C₅×C₂²⋊C₄	—	3	4	no	—
421	C₅×C₂²⋊C₄	—	3	2	no	—
422	C₅×C₂²⋊C₄	—	3	2	no	—
423	C₅×C₂²⋊C₄	—	3	4	no	—
424	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
425	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
426	C₄²×C₅	—	3	2	no	—
427	C₄²×C₅	—	3	2	no	—
428	C₄²×C₅	—	3	2	no	—
429	C₄²×C₅	—	3	1	no	—
430	C₄²×C₅	—	3	1	no	—
431	C₄²×C₅	—	3	1	no	—
432	C₄²×C₅	C₂²×D₃	1	2	yes	—
433	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
434	#554	—	3	1	no	—
435	#554	—	3	2	no	—
436	#554	—	3	2	no	—
437	#554	—	3	4	no	—
438	#554	—	3	1	no	—
439	#554	—	3	2	no	—
440	#554	—	3	1	no	—
441	#554	—	3	2	no	—
442	#554	C₅×D₃	1	1	yes	characteristic, direct product factor
443	C₂×C₄⋊Q₈	—	3	1	no	—
444	C₂×#125	—	3	2	no	—
445	C₂×C₂²⋊Q₈	—	3	4	no	—
446	C₂×C₂²⋊Q₈	—	3	2	no	—
447	C₂×C₄×Q₈	—	3	1	no	—
448	C₂×C₄×D₄	—	3	2	no	—
449	C₂×C₄×D₄	—	3	1	no	—
450	C₂²×C₄⋊C₄	—	3	2	no	—
451	C₂²×C₃×C₅	—	2	2	no	—
452	C₂²×C₃×C₅	—	2	2	no	—
453	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	—
454	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
455	C₂×C₅×D₃	—	2	2	no	—
456	C₂×C₅×D₃	—	2	2	no	—
457	C₂×C₅×D₃	—	2	16	no	—
458	C₂×C₅×D₃	C₂²×Q₈	1	4	yes	—
459	C₂×C₅×D₃	C₂²×Q₈	1	2	yes	—
460	C₂×C₅×D₃	C₂×#41	1	2	yes	—
461	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	2	no	—
464	C₃×C₄×C₅	—	2	1	no	—
465	C₃×C₄×C₅	—	2	4	no	—
466	C₃×C₄×C₅	—	2	2	no	—
467	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
468	C₃×C₄×C₅	C₂×#41	1	2	yes	—
469	C₅×Dic₃	—	2	2	no	—
470	C₅×Dic₃	—	2	2	no	—
471	C₅×Dic₃	—	2	1	no	—
472	C₅×Dic₃	—	2	4	no	—
473	C₅×Dic₃	—	2	2	no	—
474	C₅×Dic₃	C₂²×Q₈	1	2	yes	—
475	C₅×Dic₃	C₂×#41	1	2	yes	—
476	C₂³×D₃	C₂³×C₅	1	2	yes	—
477	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
478	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
479	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
480	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
481	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
482	C₂×#67	C₂³×C₅	1	2	yes	—
483	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
484	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
485	D₃×Q₈	—	2	4	no	—
486	D₃×Q₈	—	4	4	no	—
487	D₃×D₄	C₅×Q₈	1	8	yes	complemented
488	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
489	C₂×C₄×D₃	—	2	8	no	—
490	C₂×C₄×D₃	—	4	8	no	—
491	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
492	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
493	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
494	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
495	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
496	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
497	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
498	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
499	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
500	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
501	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
502	C₂×Dic₆	C₂³×C₅	1	2	yes	—
503	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
504	C₂×Dic₆	C₂³×C₅	1	2	yes	—
505	C₂×Dic₆	C₂³×C₅	1	4	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	2	yes	—
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	4	yes	—
512	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
513	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
514	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
515	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
516	C₃×C₄²	C₂³×C₅	1	2	yes	—
517	#217	C₂³×C₅	1	4	yes	—
518	#217	C₂³×C₅	1	2	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
523	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
524	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
525	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
526	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
527	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
528	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
529	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
530	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
531	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
532	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
533	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
536	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
537	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
538	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
539	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
540	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
541	C₄×Dic₃	C₂³×C₅	1	2	yes	—
542	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
543	C₄×Dic₃	C₂³×C₅	1	2	yes	—
544	C₄×Dic₃	C₂³×C₅	1	2	yes	—
545	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
546	C₂³×C₅	—	3	1	no	—
547	C₂³×C₅	—	3	8	no	—
548	C₂³×C₅	—	3	2	no	—
549	C₂³×C₅	—	6	4	no	—
550	C₂³×C₅	—	6	4	no	—
551	C₂³×C₅	C₂³×D₃	1	2	yes	—
552	C₅×Q₈	—	2	2	no	—
553	C₅×Q₈	—	4	2	no	—
554	C₅×Q₈	—	6	4	no	—
555	C₅×Q₈	—	6	2	no	—
556	C₅×Q₈	—	12	4	no	—
557	C₅×Q₈	—	12	2	no	—
558	C₅×D₄	—	3	8	no	—
559	C₅×D₄	—	3	4	no	—
560	C₅×D₄	D₃×Q₈	1	4	yes	complemented
561	C₂×C₄×C₅	—	2	4	no	—
562	C₂×C₄×C₅	—	3	1	no	—
563	C₂×C₄×C₅	—	3	1	no	—
564	C₂×C₄×C₅	—	3	4	no	—
565	C₂×C₄×C₅	—	3	4	no	—
566	C₂×C₄×C₅	—	3	2	no	—
567	C₂×C₄×C₅	—	3	1	no	—
568	C₂×C₄×C₅	—	3	2	no	—
569	C₂×C₄×C₅	—	3	2	no	—
570	C₂×C₄×C₅	—	3	4	no	—
571	C₂×C₄×C₅	—	4	4	no	—
572	C₂×C₄×C₅	—	6	4	no	—
573	C₂×C₄×C₅	—	6	4	no	—
574	C₂×C₄×C₅	—	6	4	no	—
575	C₂×C₄×C₅	—	6	8	no	—
576	C₂×C₄×C₅	—	6	4	no	—
577	C₂×C₄×C₅	—	6	2	no	—
578	C₂×C₄×C₅	—	6	4	no	—
579	C₂×C₄×C₅	—	6	4	no	—
580	C₂×C₄×C₅	—	12	4	no	—
581	C₂×C₄×C₅	—	12	4	no	—
582	C₂×C₄×C₅	—	12	4	no	—
583	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
584	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
585	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
586	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
587	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
588	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
590	C₂²×Q₈	—	3	1	no	—
591	C₂²×Q₈	—	3	2	no	—
592	C₂²×D₄	—	3	1	no	—
593	C₂³×C₄	—	3	2	no	—
594	C₂³×C₄	—	3	4	no	—
595	C₄⋊Q₈	—	3	2	no	—
596	C₄⋊Q₈	—	3	2	no	—
597	C₄⋊Q₈	—	3	2	no	—
598	C₄⋊Q₈	—	3	1	no	—
599	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
600	#125	—	3	4	no	—
601	#125	—	3	4	no	—
602	#125	—	3	2	no	—
603	#125	—	3	2	no	—
604	#125	—	3	2	no	—
605	#125	C₂×C₅×D₃	1	2	yes	complemented
606	C₂²⋊Q₈	—	3	4	no	—
607	C₂²⋊Q₈	—	3	2	no	—
608	C₂²⋊Q₈	—	3	4	no	—
609	C₂²⋊Q₈	—	3	2	no	—
610	C₂²⋊Q₈	—	3	4	no	—
611	C₂²⋊Q₈	—	3	4	no	—
612	C₂²⋊Q₈	—	3	4	no	—
613	C₂²⋊Q₈	—	3	4	no	—
614	C₂²⋊Q₈	—	3	2	no	—
615	C₂²⋊Q₈	—	3	4	no	—
616	C₂²⋊Q₈	—	3	4	no	—
617	C₂²⋊Q₈	—	3	4	no	—
618	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
619	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
620	C₄×Q₈	—	3	1	no	—
621	C₄×Q₈	—	3	2	no	—
622	C₄×Q₈	—	3	1	no	—
623	C₄×Q₈	—	3	1	no	—
624	C₄×Q₈	—	3	2	no	—
625	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
626	C₄×D₄	—	3	2	no	—
627	C₄×D₄	—	3	1	no	—
628	C₄×D₄	—	3	4	no	—
629	C₄×D₄	—	3	2	no	—
630	C₄×D₄	—	3	2	no	—
631	C₄×D₄	—	3	1	no	—
632	C₄×D₄	—	3	4	no	—
633	C₄×D₄	—	3	2	no	—
634	C₄×D₄	—	3	2	no	—
635	C₄×D₄	—	3	1	no	—
636	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
637	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	—	3	4	no	—
639	C₂×C₄⋊C₄	—	3	2	no	—
640	C₂×C₄⋊C₄	—	3	1	no	—
641	C₂×C₄⋊C₄	—	3	4	no	—
642	C₂×C₄⋊C₄	—	3	2	no	—
643	C₂×C₄⋊C₄	—	3	4	no	—
644	C₂×C₄⋊C₄	—	3	2	no	—
645	C₂×C₄⋊C₄	—	3	2	no	—
646	C₂×C₄⋊C₄	—	3	1	no	—
647	C₂×C₄⋊C₄	—	3	2	no	—
648	C₂×C₄⋊C₄	—	3	2	no	—
649	C₂×C₄⋊C₄	—	3	4	no	—
650	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
651	C₂×C₂²⋊C₄	—	3	4	no	—
652	C₂×C₂²⋊C₄	—	3	2	no	—
653	C₂×C₄²	—	3	2	no	—
654	C₂×C₄²	—	3	1	no	—
655	C₂×C₃×C₅	—	2	4	no	—
656	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
657	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
658	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₅×D₃	—	2	4	no	—
660	C₅×D₃	#554	1	4	yes	direct product factor
661	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
662	C₂²×D₃	—	2	4	no	—
663	C₂²×D₃	—	2	4	no	—
664	C₂²×D₃	C₂×C₅×Q₈	1	8	yes	—
665	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
666	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
667	C₃×Q₈	—	2	2	no	—
668	C₃×Q₈	—	4	2	no	—
669	C₃×D₄	C₂×C₅×Q₈	1	4	yes	complemented
670	C₂×C₃×C₄	—	2	4	no	—
671	C₂×C₃×C₄	—	4	4	no	—
672	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
673	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
674	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
675	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
676	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
677	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
678	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
679	#67	C₂×C₅×Q₈	1	8	yes	complemented
680	C₂×Dic₃	—	2	4	no	—
681	C₂×Dic₃	—	4	4	no	—
682	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
683	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
684	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
685	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
686	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
687	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
688	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
689	D₁₂	C₂×C₅×Q₈	1	4	yes	complemented
690	C₄×D₃	—	2	4	no	—
691	C₄×D₃	—	2	4	no	—
692	C₄×D₃	—	2	4	no	—
693	C₄×D₃	—	2	8	no	—
694	C₄×D₃	—	2	2	no	—
695	C₄×D₃	—	2	4	no	—
696	C₄×D₃	—	2	4	no	—
697	C₄×D₃	—	4	4	no	—
698	C₄×D₃	—	4	4	no	—
699	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
700	C₄×D₃	C₅×#41	1	4	yes	—
701	Dic₆	—	2	2	no	—
702	Dic₆	—	2	4	no	—
703	Dic₆	—	4	4	no	—
704	Dic₆	—	4	2	no	—
705	C₂²×C₅	—	2	2	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	3	2	no	—
708	C₂²×C₅	—	3	2	no	—
709	C₂²×C₅	—	3	2	no	—
710	C₂²×C₅	—	3	4	no	—
711	C₂²×C₅	—	6	16	no	—
712	C₂²×C₅	—	6	2	no	—
713	C₂²×C₅	—	6	2	no	—
714	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	—
715	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	4	no	—
720	C₄×C₅	—	2	1	no	—
721	C₄×C₅	—	3	2	no	—
722	C₄×C₅	—	3	2	no	—
723	C₄×C₅	—	6	2	no	—
724	C₄×C₅	—	6	2	no	—
725	C₄×C₅	—	6	2	no	—
726	C₄×C₅	—	6	4	no	—
727	C₄×C₅	—	6	1	no	—
728	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
729	C₄×C₅	D₃×#41	1	2	yes	—
730	C₂⁴	—	3	2	no	—
731	C₂×Q₈	—	3	2	no	—
732	C₂×Q₈	—	3	1	no	—
733	C₂×Q₈	—	3	4	no	—
734	C₂×Q₈	—	3	2	no	—
735	C₂×Q₈	—	6	4	no	—
736	C₂×Q₈	—	12	4	no	—
737	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
739	C₂×D₄	—	3	2	no	—
740	C₂×D₄	—	3	8	no	—
741	C₂×D₄	—	3	1	no	—
742	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
743	C₂²×C₄	—	3	1	no	—
744	C₂²×C₄	—	3	1	no	—
745	C₂²×C₄	—	3	2	no	—
746	C₂²×C₄	—	3	4	no	—
747	C₂²×C₄	—	3	2	no	—
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	3	2	no	—
750	C₂²×C₄	—	3	2	no	—
751	C₂²×C₄	—	3	4	no	—
752	C₂²×C₄	—	3	2	no	—
753	C₂²×C₄	—	3	2	no	—
754	C₂²×C₄	—	3	4	no	—
755	C₂²×C₄	—	3	4	no	—
756	C₂²×C₄	—	6	8	no	—
757	C₂²×C₄	—	12	8	no	—
758	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
759	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
760	C₄⋊C₄	—	3	2	no	—
761	C₄⋊C₄	—	3	1	no	—
762	C₄⋊C₄	—	3	4	no	—
763	C₄⋊C₄	—	3	4	no	—
764	C₄⋊C₄	—	3	4	no	—
765	C₄⋊C₄	—	3	4	no	—
766	C₄⋊C₄	—	3	2	no	—
767	C₄⋊C₄	—	3	2	no	—
768	C₄⋊C₄	—	3	1	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	2	no	—
771	C₄⋊C₄	—	3	2	no	—
772	C₄⋊C₄	—	3	2	no	—
773	C₄⋊C₄	—	3	2	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	4	no	—
776	C₄⋊C₄	—	3	4	no	—
777	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
779	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
780	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
782	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
783	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
784	C₂²⋊C₄	—	3	4	no	—
785	C₂²⋊C₄	—	3	2	no	—
786	C₂²⋊C₄	—	3	4	no	—
787	C₂²⋊C₄	—	3	2	no	—
788	C₂²⋊C₄	—	3	2	no	—
789	C₂²⋊C₄	—	3	4	no	—
790	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
791	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
792	C₄²	—	3	2	no	—
793	C₄²	—	3	2	no	—
794	C₄²	—	3	2	no	—
795	C₄²	—	3	1	no	—
796	C₄²	—	3	1	no	—
797	C₄²	—	3	1	no	—
798	C₄²	C₂²×C₅×D₃	1	2	yes	—
799	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
800	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	C₂²×C₅×Q₈	1	4	yes	—
804	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
805	C₂×D₃	—	2	2	no	—
806	C₂×D₃	—	2	2	no	—
807	C₂×D₃	—	2	16	no	—
808	C₂×D₃	C₂²×C₅×Q₈	1	4	yes	—
809	C₂×D₃	C₂²×C₅×Q₈	1	2	yes	—
810	C₂×D₃	C₂×C₅×#41	1	2	yes	—
811	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
812	C₃×C₄	—	2	2	no	—
813	C₃×C₄	—	2	2	no	—
814	C₃×C₄	—	2	1	no	—
815	C₃×C₄	—	2	4	no	—
816	C₃×C₄	—	2	2	no	—
817	C₃×C₄	C₂²×C₅×Q₈	1	2	yes	—
818	C₃×C₄	C₂×C₅×#41	1	2	yes	—
819	Dic₃	—	2	2	no	—
820	Dic₃	—	2	2	no	—
821	Dic₃	—	2	1	no	—
822	Dic₃	—	2	4	no	—
823	Dic₃	—	2	2	no	—
824	Dic₃	C₂²×C₅×Q₈	1	2	yes	—
825	Dic₃	C₂×C₅×#41	1	2	yes	—
826	C₂×C₅	—	2	4	no	—
827	C₂×C₅	—	3	4	no	—
828	C₂×C₅	—	6	4	no	—
829	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
830	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
831	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
832	C₂³	—	3	1	no	—
833	C₂³	—	3	8	no	—
834	C₂³	—	3	2	no	—
835	C₂³	—	6	4	no	—
836	C₂³	—	6	4	no	—
837	C₂³	C₂³×C₅×D₃	1	2	yes	—
838	Q₈	—	2	2	no	—
839	Q₈	—	4	2	no	—
840	Q₈	—	6	4	no	—
841	Q₈	—	6	2	no	—
842	Q₈	—	12	4	no	—
843	Q₈	—	12	2	no	—
844	D₄	—	3	8	no	—
845	D₄	—	3	4	no	—
846	D₄	C₅×D₃×Q₈	1	4	yes	complemented
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	3	1	no	—
849	C₂×C₄	—	3	1	no	—
850	C₂×C₄	—	3	4	no	—
851	C₂×C₄	—	3	4	no	—
852	C₂×C₄	—	3	2	no	—
853	C₂×C₄	—	3	1	no	—
854	C₂×C₄	—	3	2	no	—
855	C₂×C₄	—	3	2	no	—
856	C₂×C₄	—	3	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	6	4	no	—
859	C₂×C₄	—	6	4	no	—
860	C₂×C₄	—	6	4	no	—
861	C₂×C₄	—	6	8	no	—
862	C₂×C₄	—	6	4	no	—
863	C₂×C₄	—	6	2	no	—
864	C₂×C₄	—	6	4	no	—
865	C₂×C₄	—	6	4	no	—
866	C₂×C₄	—	12	4	no	—
867	C₂×C₄	—	12	4	no	—
868	C₂×C₄	—	12	4	no	—
869	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
870	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
871	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
872	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
873	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
874	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
876	C₂×C₃	—	2	4	no	—
877	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
878	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
879	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
880	D₃	—	2	4	no	—
881	D₃	C₅×#554	1	4	yes	direct product factor
882	C₅	D₃×#554	1	1	yes	characteristic, direct product factor, Sylow
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	3	2	no	—
886	C₂²	—	3	2	no	—
887	C₂²	—	3	2	no	—
888	C₂²	—	3	4	no	—
889	C₂²	—	6	16	no	—
890	C₂²	—	6	2	no	—
891	C₂²	—	6	2	no	—
892	C₂²	C₂×C₅×D₃×Q₈	1	4	yes	—
893	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	1	no	—
899	C₄	—	3	2	no	—
900	C₄	—	3	2	no	—
901	C₄	—	6	2	no	—
902	C₄	—	6	2	no	—
903	C₄	—	6	2	no	—
904	C₄	—	6	4	no	—
905	C₄	—	6	1	no	—
906	C₄	C₂×C₅×D₃×Q₈	1	2	yes	—
907	C₄	C₅×D₃×#41	1	2	yes	—
908	C₃	C₂×C₅×#554	1	1	yes	characteristic, complemented, Sylow
909	C₂	—	2	4	no	—
910	C₂	—	3	4	no	—
911	C₂	—	6	4	no	—
912	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
913	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
914	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#554	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#554	D₃
hypocenter	C₃	C₂×C₅×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#554

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
2. C₅×#5730	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₅×#5690	C₂	semidirect
5. C₅×D₃×#125	C₂	semidirect
6. C₅×#5636	C₂	semidirect
7. C₅×#5635	C₂	semidirect
8. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
9. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₅×#5579	C₂	semidirect
11. C₄×C₅×D₃×Q₈	C₂	semidirect
14. C₅×#5543	C₂	semidirect
15. C₅×#5539	C₂	semidirect
16. C₅×#5511	C₂	semidirect
17. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#125	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₃×C₄×C₅×Q₈	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₅×#946	C₂²	semidirect
33. C₅×#946	C₂²	semidirect
34. C₅×Q₈×Dic₃	C₂²	semidirect
35. C₅×#944	C₂²	semidirect
40. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
41. C₅×#924	C₂²	semidirect
42. C₅×#924	C₂²	semidirect
43. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
44. C₅×#897	C₂²	semidirect
45. C₅×#897	C₂²	semidirect
46. C₅×#896	C₂²	semidirect
47. C₅×#896	C₂²	semidirect
48. C₅×#896	C₂²	semidirect
58. C₅×D₃×C₄⋊C₄	C₂²	semidirect
59. C₅×D₃×C₄⋊C₄	C₂²	semidirect
60. C₅×D₃×C₄⋊C₄	C₂²	semidirect
61. C₅×#890	C₂²	semidirect
62. C₅×#890	C₂²	semidirect
63. C₅×#889	C₂²	semidirect
64. C₅×#889	C₂²	semidirect
65. C₅×#888	C₂²	semidirect
66. C₅×#888	C₂²	semidirect
67. C₅×#887	C₂²	semidirect
68. C₅×#887	C₂²	semidirect
73. C₅×#878	C₂²	semidirect
74. C₅×#878	C₂²	semidirect
75. C₅×#878	C₂²	semidirect
80. C₅×#870	C₂²	semidirect
81. C₅×#869	C₂²	semidirect
82. C₄×C₅×Dic₆	C₂²	semidirect
83. C₄×C₅×Dic₆	C₂²	semidirect
84. D₃×#554	C₅	direct (N × H)
93. C₅×#554	D₃	direct (N × H)
113. C₅×D₃×D₄	Q₈	semidirect
172. C₃×#554	C₂×C₅	semidirect
173. #5730	C₂×C₅	semidirect
174. D₃×C₄⋊Q₈	C₂×C₅	semidirect
175. #5690	C₂×C₅	semidirect
176. D₃×#125	C₂×C₅	semidirect
177. #5636	C₂×C₅	semidirect
178. #5635	C₂×C₅	semidirect
179. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
180. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
181. #5579	C₂×C₅	semidirect
182. C₄×D₃×Q₈	C₂×C₅	semidirect
185. #5543	C₂×C₅	semidirect
186. #5539	C₂×C₅	semidirect
187. #5511	C₂×C₅	semidirect
188. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
198. C₅×C₄⋊Q₈	C₂×D₃	semidirect
204. C₅×#125	C₂×D₃	semidirect
217. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
218. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
224. C₄×C₅×Q₈	C₂×D₃	semidirect
249. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
263. C₃×C₅×D₄	C₂×Q₈	semidirect
273. C₅×#67	C₂×Q₈	semidirect
283. C₅×D₁₂	C₂×Q₈	semidirect
304. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
305. C₃×#125	C₂²×C₅	semidirect
306. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
307. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
308. C₃×C₄×Q₈	C₂²×C₅	semidirect
311. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
312. #946	C₂²×C₅	semidirect
313. #946	C₂²×C₅	semidirect
314. Q₈×Dic₃	C₂²×C₅	semidirect
315. #944	C₂²×C₅	semidirect
320. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
321. #924	C₂²×C₅	semidirect
322. #924	C₂²×C₅	semidirect
323. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
324. #897	C₂²×C₅	semidirect
325. #897	C₂²×C₅	semidirect
326. #896	C₂²×C₅	semidirect
327. #896	C₂²×C₅	semidirect
328. #896	C₂²×C₅	semidirect
338. D₃×C₄⋊C₄	C₂²×C₅	semidirect
339. D₃×C₄⋊C₄	C₂²×C₅	semidirect
340. D₃×C₄⋊C₄	C₂²×C₅	semidirect
341. #890	C₂²×C₅	semidirect
342. #890	C₂²×C₅	semidirect
343. #889	C₂²×C₅	semidirect
344. #889	C₂²×C₅	semidirect
345. #888	C₂²×C₅	semidirect
346. #888	C₂²×C₅	semidirect
347. #887	C₂²×C₅	semidirect
348. #887	C₂²×C₅	semidirect
353. #878	C₂²×C₅	semidirect
354. #878	C₂²×C₅	semidirect
355. #878	C₂²×C₅	semidirect
360. #870	C₂²×C₅	semidirect
361. #869	C₂²×C₅	semidirect
362. C₄×Dic₆	C₂²×C₅	semidirect
363. C₄×Dic₆	C₂²×C₅	semidirect
442. #554	C₅×D₃	direct (N × H)
487. D₃×D₄	C₅×Q₈	semidirect
560. C₅×D₄	D₃×Q₈	semidirect
599. C₄⋊Q₈	C₂×C₅×D₃	semidirect
605. #125	C₂×C₅×D₃	semidirect
618. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
619. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
625. C₄×Q₈	C₂×C₅×D₃	semidirect
650. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
660. C₅×D₃	#554	direct (N × H)
669. C₃×D₄	C₂×C₅×Q₈	semidirect
679. #67	C₂×C₅×Q₈	semidirect
689. D₁₂	C₂×C₅×Q₈	semidirect
800. C₃×C₅	C₂×#554	semidirect
846. D₄	C₅×D₃×Q₈	semidirect
881. D₃	C₅×#554	direct (N × H)
882. C₅	D₃×#554	direct (N × H)
908. C₃	C₂×C₅×#554	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#554	2
C₅×#5730	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5690	2
C₅×D₃×#125	2
C₅×#5636	2
C₅×#5635	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5579	2
C₄×C₅×D₃×Q₈	2
C₄×C₅×D₃×D₄	2
C₅×#5543	2
C₅×#5539	2
C₅×#5511	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#554	3
D₃×#554	5

Subgroups — C5×D3×#554 #14483784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#554 #14483784