Subgroups — C₅×#87268 #14480638

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5833	C₂	1	4	yes	maximal, complemented
4	C₅×#5832	C₂	1	4	yes	maximal, complemented
5	C₅×#5830	C₂	1	2	yes	maximal, complemented
6	C₅×#5828	C₂	1	4	yes	maximal, complemented
7	C₅×#5825	C₂	1	2	yes	maximal, complemented
8	C₅×#5816	C₂	1	2	yes	maximal, complemented
9	C₅×#5805	C₂	1	2	yes	maximal, complemented
10	C₅×#5804	C₂	1	4	yes	maximal, complemented
11	C₅×#5791	C₂	1	4	yes	maximal, complemented
12	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#3449	—	3	1	no	maximal, Hall
14	C₂×C₃×C₅×#41	—	2	8	no	—
15	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
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	2	yes	—
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
24	C₂²×C₅×#67	C₂²	1	2	yes	—
25	C₂×C₅×#235	—	2	8	no	—
26	C₂×C₅×#235	C₂²	1	2	yes	—
27	C₂×C₅×#235	C₂²	1	2	yes	—
28	C₂×C₅×#235	C₂²	1	2	yes	complemented
29	C₂×C₅×#235	C₂²	1	2	yes	complemented
30	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
32	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
33	C₅×#953	C₂²	1	8	yes	complemented
34	C₂×C₅×#217	C₂²	1	2	yes	—
35	C₅×#947	C₂²	1	4	yes	complemented
36	C₅×#946	C₂²	1	8	yes	complemented
37	C₅×#944	C₂²	1	4	yes	complemented
38	C₅×#940	C₂²	1	4	yes	complemented
39	C₅×#939	C₂²	1	16	yes	complemented
40	C₅×#938	C₂²	1	8	yes	complemented
41	C₅×#937	C₂²	1	8	yes	complemented
42	C₅×#936	C₂²	1	4	yes	complemented
43	C₅×#935	C₂²	1	8	yes	complemented
44	C₅×#930	C₂²	1	8	yes	complemented
45	C₅×#929	C₂²	1	8	yes	complemented
46	C₄×C₅×#67	C₂²	1	16	yes	complemented
47	C₅×#926	C₂²	1	2	yes	complemented
48	C₅×#926	C₂²	1	2	yes	complemented
49	C₅×#926	C₂²	1	2	yes	complemented
50	C₅×#926	C₂²	1	2	yes	complemented
51	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
52	C₅×#924	C₂²	1	8	yes	complemented
53	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
54	#87268	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂²×C₅×#41	—	3	1	no	—
56	C₂²×C₅×#41	D₃	1	1	yes	characteristic, complemented
57	C₅×#537	—	3	4	no	—
58	C₅×#536	—	3	2	no	—
59	C₅×#536	—	3	2	no	—
60	C₅×#535	—	3	2	no	—
61	C₅×#535	—	3	2	no	—
62	C₅×#534	—	3	4	no	—
63	C₅×#532	—	3	4	no	—
64	C₅×#525	—	3	4	no	—
65	C₅×#525	—	3	4	no	—
66	C₂×C₅×#117	—	3	1	no	—
67	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₅×D₃	C₂³	1	2	yes	—
70	C₃×C₅×#41	—	2	8	no	—
71	C₃×C₅×#41	—	2	8	no	—
72	C₃×C₅×#41	—	2	8	no	—
73	C₃×C₅×#41	—	2	8	no	—
74	C₂×C₃×C₅×Q₈	—	2	4	no	—
75	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
76	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	—	2	4	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
80	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
81	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
82	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
83	C₂²×C₃×C₄×C₅	—	2	8	no	—
84	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
85	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
86	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
87	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₅×#67	—	2	8	no	—
95	C₂×C₅×#67	C₂³	1	4	yes	—
96	C₂×C₅×#67	C₂³	1	4	yes	—
97	C₂×C₅×#67	C₂³	1	16	yes	—
98	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
99	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
100	C₅×#235	—	2	8	no	—
101	C₅×#235	—	2	8	no	—
102	C₅×#235	—	2	8	no	—
103	C₅×#235	—	2	8	no	—
104	C₂×C₅×D₁₂	—	2	4	no	—
105	C₂×C₅×D₁₂	C₂³	1	2	yes	—
106	C₂×C₅×D₁₂	C₂³	1	2	yes	—
107	C₂×C₄×C₅×D₃	—	2	8	no	—
108	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
109	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
110	C₂×C₅×Dic₆	—	2	4	no	—
111	C₂×C₅×Dic₆	C₂³	1	2	yes	—
112	C₂×C₅×Dic₆	C₂³	1	2	yes	—
113	C₅×#217	C₂³	1	16	yes	—
114	C₅×#217	C₂³	1	4	yes	—
115	C₅×#217	C₂³	1	4	yes	—
116	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
117	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
118	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
119	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
120	C₄×C₅×Dic₃	C₂³	1	4	yes	—
121	C₄×C₅×Dic₃	C₂³	1	4	yes	—
122	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
124	#5833	C₂×C₅	1	4	yes	complemented
125	#5832	C₂×C₅	1	4	yes	complemented
126	#5830	C₂×C₅	1	2	yes	complemented
127	#5828	C₂×C₅	1	4	yes	complemented
128	#5825	C₂×C₅	1	2	yes	complemented
129	#5816	C₂×C₅	1	2	yes	complemented
130	#5805	C₂×C₅	1	2	yes	complemented
131	#5804	C₂×C₅	1	4	yes	complemented
132	#5791	C₂×C₅	1	4	yes	complemented
133	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×C₅×#41	—	2	8	no	—
135	C₂×C₅×#41	—	3	2	no	—
136	C₂×C₅×#41	—	3	2	no	—
137	C₂×C₅×#41	—	3	2	no	—
138	C₂×C₅×#41	—	3	2	no	—
139	C₂×C₅×#41	—	6	8	no	—
140	C₂×C₅×#41	C₂×D₃	1	2	yes	—
141	C₂×C₅×#41	C₂×D₃	1	2	yes	—
142	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
143	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
144	C₂²×C₅×Q₈	—	3	1	no	—
145	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
146	C₂²×C₅×D₄	—	3	2	no	—
147	C₂²×C₅×D₄	—	3	1	no	—
148	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
149	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
150	C₂³×C₄×C₅	—	3	2	no	—
151	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
152	C₂³×C₄×C₅	C₂×D₃	1	2	yes	complemented
153	C₅×C₄⋊Q₈	—	3	4	no	—
154	C₅×#127	—	3	4	no	—
155	C₅×#124	—	3	4	no	—
156	C₅×#124	—	3	4	no	—
157	C₅×#123	—	3	8	no	—
158	C₅×#123	—	3	8	no	—
159	C₅×C₂²⋊Q₈	—	3	8	no	—
160	C₅×C₂²⋊Q₈	—	3	8	no	—
161	C₅×#121	—	3	8	no	—
162	C₅×#121	—	3	16	no	—
163	C₅×#121	—	3	8	no	—
164	C₅×#120	—	3	8	no	—
165	C₅×#120	—	3	8	no	—
166	C₄×C₅×D₄	—	3	16	no	—
167	C₅×#117	—	3	2	no	—
168	C₅×#117	—	3	2	no	—
169	C₅×#117	—	3	2	no	—
170	C₅×#117	—	3	2	no	—
171	C₂×C₅×C₄⋊C₄	—	3	2	no	—
172	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
173	C₂×C₄²×C₅	—	3	2	no	—
174	#3449	—	3	1	no	Sylow
175	C₂³×C₃×C₅	—	2	4	no	—
176	C₂³×C₃×C₅	—	4	2	no	—
177	C₂³×C₃×C₅	—	4	4	no	—
178	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
179	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
180	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
181	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
182	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
183	C₂²×C₅×D₃	—	2	4	no	—
184	C₂²×C₅×D₃	—	4	4	no	—
185	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
186	C₃×C₅×Q₈	—	2	4	no	—
187	C₃×C₅×Q₈	—	2	4	no	—
188	C₃×C₅×D₄	—	2	8	no	—
189	C₃×C₅×D₄	—	2	8	no	—
190	C₃×C₅×D₄	—	2	4	no	—
191	C₃×C₅×D₄	—	2	4	no	—
192	C₂×C₃×C₄×C₅	—	2	4	no	—
193	C₂×C₃×C₄×C₅	—	2	8	no	—
194	C₂×C₃×C₄×C₅	—	2	8	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
196	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
197	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
198	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
200	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
201	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
206	C₅×#67	—	2	8	no	—
207	C₅×#67	—	2	8	no	—
208	C₅×#67	—	4	16	no	—
209	C₂×C₅×Dic₃	—	2	4	no	—
210	C₂×C₅×Dic₃	—	4	4	no	—
211	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
212	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
213	C₅×D₁₂	—	2	4	no	—
214	C₅×D₁₂	—	2	4	no	—
215	C₄×C₅×D₃	—	2	8	no	—
216	C₄×C₅×D₃	—	2	8	no	—
217	C₅×Dic₆	—	2	4	no	—
218	C₅×Dic₆	—	2	4	no	—
219	C₂×C₃×#41	—	2	8	no	—
220	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
221	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
222	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
223	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
224	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
225	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
226	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
227	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
229	C₂²×#67	C₂²×C₅	1	2	yes	—
230	C₂×#235	—	2	8	no	—
231	C₂×#235	C₂²×C₅	1	2	yes	—
232	C₂×#235	C₂²×C₅	1	2	yes	—
233	C₂×#235	C₂²×C₅	1	2	yes	complemented
234	C₂×#235	C₂²×C₅	1	2	yes	complemented
235	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
236	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
237	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
238	#953	C₂²×C₅	1	8	yes	complemented
239	C₂×#217	C₂²×C₅	1	2	yes	—
240	#947	C₂²×C₅	1	4	yes	complemented
241	#946	C₂²×C₅	1	8	yes	complemented
242	#944	C₂²×C₅	1	4	yes	complemented
243	#940	C₂²×C₅	1	4	yes	complemented
244	#939	C₂²×C₅	1	16	yes	complemented
245	#938	C₂²×C₅	1	8	yes	complemented
246	#937	C₂²×C₅	1	8	yes	complemented
247	#936	C₂²×C₅	1	4	yes	complemented
248	#935	C₂²×C₅	1	8	yes	complemented
249	#930	C₂²×C₅	1	8	yes	complemented
250	#929	C₂²×C₅	1	8	yes	complemented
251	C₄×#67	C₂²×C₅	1	16	yes	complemented
252	#926	C₂²×C₅	1	2	yes	complemented
253	#926	C₂²×C₅	1	2	yes	complemented
254	#926	C₂²×C₅	1	2	yes	complemented
255	#926	C₂²×C₅	1	2	yes	complemented
256	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
257	#924	C₂²×C₅	1	8	yes	complemented
258	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
259	C₂⁴×C₅	—	3	2	no	—
260	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
261	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
262	C₅×#41	—	2	8	no	—
263	C₅×#41	—	2	8	no	—
264	C₅×#41	—	2	8	no	—
265	C₅×#41	—	2	8	no	—
266	C₅×#41	—	6	8	no	—
267	C₅×#41	—	6	8	no	—
268	C₅×#41	—	6	8	no	—
269	C₅×#41	—	6	8	no	—
270	C₂×C₅×Q₈	—	2	4	no	—
271	C₂×C₅×Q₈	—	3	2	no	—
272	C₂×C₅×Q₈	—	3	2	no	—
273	C₂×C₅×Q₈	—	6	4	no	—
274	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
275	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
276	C₂×C₅×D₄	—	2	8	no	—
277	C₂×C₅×D₄	—	2	4	no	—
278	C₂×C₅×D₄	—	3	4	no	—
279	C₂×C₅×D₄	—	3	4	no	—
280	C₂×C₅×D₄	—	3	16	no	—
281	C₂×C₅×D₄	—	3	2	no	—
282	C₂×C₅×D₄	—	3	2	no	—
283	C₂×C₅×D₄	—	6	8	no	—
284	C₂×C₅×D₄	—	6	4	no	—
285	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
286	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
287	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
288	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
289	C₂²×C₄×C₅	—	2	8	no	—
290	C₂²×C₄×C₅	—	3	2	no	—
291	C₂²×C₄×C₅	—	3	4	no	—
292	C₂²×C₄×C₅	—	3	4	no	—
293	C₂²×C₄×C₅	—	3	4	no	—
294	C₂²×C₄×C₅	—	6	8	no	—
295	C₂²×C₄×C₅	#67	1	8	yes	complemented
296	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
297	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
298	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
299	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
305	C₅×C₄⋊C₄	—	3	4	no	—
306	C₅×C₄⋊C₄	—	3	4	no	—
307	C₅×C₄⋊C₄	—	3	16	no	—
308	C₅×C₂²⋊C₄	—	3	4	no	—
309	C₅×C₂²⋊C₄	—	3	4	no	—
310	C₅×C₂²⋊C₄	—	3	16	no	—
311	C₅×C₂²⋊C₄	—	3	16	no	—
312	C₄²×C₅	—	3	4	no	—
313	C₄²×C₅	—	3	4	no	—
314	C₂²×#41	—	3	1	no	—
315	C₂²×#41	C₅×D₃	1	1	yes	characteristic, complemented
316	#537	—	3	4	no	—
317	#536	—	3	2	no	—
318	#536	—	3	2	no	—
319	#535	—	3	2	no	—
320	#535	—	3	2	no	—
321	#534	—	3	4	no	—
322	#532	—	3	4	no	—
323	#525	—	3	4	no	—
324	#525	—	3	4	no	—
325	C₂×#117	—	3	1	no	—
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	2	2	no	—
329	C₂²×C₃×C₅	—	2	4	no	—
330	C₂²×C₃×C₅	—	2	8	no	—
331	C₂²×C₃×C₅	—	4	4	no	—
332	C₂²×C₃×C₅	—	4	8	no	—
333	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
334	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
335	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
336	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
337	C₂×C₅×D₃	—	2	4	no	—
338	C₂×C₅×D₃	—	2	8	no	—
339	C₂×C₅×D₃	—	4	8	no	—
340	C₃×C₄×C₅	—	2	4	no	—
341	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
342	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
343	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
344	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
345	C₅×Dic₃	—	2	4	no	—
346	C₅×Dic₃	—	2	8	no	—
347	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
348	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
349	C₂³×D₃	C₂³×C₅	1	2	yes	—
350	C₃×#41	—	2	8	no	—
351	C₃×#41	—	2	8	no	—
352	C₃×#41	—	2	8	no	—
353	C₃×#41	—	2	8	no	—
354	C₂×C₃×Q₈	—	2	4	no	—
355	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
356	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
357	C₂×C₃×D₄	—	2	8	no	—
358	C₂×C₃×D₄	—	2	4	no	—
359	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
360	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
361	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
362	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
363	C₂²×C₃×C₄	—	2	8	no	—
364	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
365	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
366	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
367	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
368	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×#67	—	2	8	no	—
375	C₂×#67	C₂³×C₅	1	4	yes	—
376	C₂×#67	C₂³×C₅	1	4	yes	—
377	C₂×#67	C₂³×C₅	1	16	yes	—
378	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
379	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
380	#235	—	2	8	no	—
381	#235	—	2	8	no	—
382	#235	—	2	8	no	—
383	#235	—	2	8	no	—
384	C₂×D₁₂	—	2	4	no	—
385	C₂×D₁₂	C₂³×C₅	1	2	yes	—
386	C₂×D₁₂	C₂³×C₅	1	2	yes	—
387	C₂×C₄×D₃	—	2	8	no	—
388	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
389	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
390	C₂×Dic₆	—	2	4	no	—
391	C₂×Dic₆	C₂³×C₅	1	2	yes	—
392	C₂×Dic₆	C₂³×C₅	1	2	yes	—
393	#217	C₂³×C₅	1	16	yes	—
394	#217	C₂³×C₅	1	4	yes	—
395	#217	C₂³×C₅	1	4	yes	—
396	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
397	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
398	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
399	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
400	C₄×Dic₃	C₂³×C₅	1	4	yes	—
401	C₄×Dic₃	C₂³×C₅	1	4	yes	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	3	4	no	—
404	C₂³×C₅	—	4	2	no	—
405	C₂³×C₅	—	4	4	no	—
406	C₂³×C₅	—	6	4	no	—
407	C₂³×C₅	—	12	4	no	—
408	C₂³×C₅	C₂×#67	1	4	yes	—
409	C₂³×C₅	C₂³×D₃	1	4	yes	—
410	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
411	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
412	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
413	C₅×Q₈	—	2	4	no	—
414	C₅×Q₈	—	2	4	no	—
415	C₅×Q₈	—	6	4	no	—
416	C₅×Q₈	—	6	4	no	—
417	C₅×D₄	—	2	8	no	—
418	C₅×D₄	—	2	8	no	—
419	C₅×D₄	—	2	4	no	—
420	C₅×D₄	—	2	4	no	—
421	C₅×D₄	—	6	8	no	—
422	C₅×D₄	—	6	8	no	—
423	C₅×D₄	—	6	4	no	—
424	C₅×D₄	—	6	4	no	—
425	C₅×D₄	—	12	16	no	—
426	C₂×C₄×C₅	—	2	4	no	—
427	C₂×C₄×C₅	—	2	8	no	—
428	C₂×C₄×C₅	—	2	8	no	—
429	C₂×C₄×C₅	—	3	8	no	—
430	C₂×C₄×C₅	—	3	4	no	—
431	C₂×C₄×C₅	—	6	4	no	—
432	C₂×C₄×C₅	—	6	8	no	—
433	C₂×C₄×C₅	—	6	8	no	—
434	C₂×C₄×C₅	—	12	4	no	—
435	C₂×C₄×C₅	C₂×#67	1	4	yes	—
436	C₂×C₄×C₅	C₂×#67	1	4	yes	—
437	C₂×C₄×C₅	C₂×#67	1	4	yes	—
438	C₂×C₄×C₅	C₂×#67	1	4	yes	—
439	C₂×C₄×C₅	C₂×#67	1	4	yes	—
440	C₂×C₄×C₅	C₂×#67	1	4	yes	—
441	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
442	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
444	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
445	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
446	C₂×#41	—	2	8	no	—
447	C₂×#41	—	3	2	no	—
448	C₂×#41	—	3	2	no	—
449	C₂×#41	—	3	2	no	—
450	C₂×#41	—	3	2	no	—
451	C₂×#41	—	6	8	no	—
452	C₂×#41	C₂×C₅×D₃	1	2	yes	—
453	C₂×#41	C₂×C₅×D₃	1	2	yes	—
454	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
455	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
456	C₂²×Q₈	—	3	1	no	—
457	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
458	C₂²×D₄	—	3	2	no	—
459	C₂²×D₄	—	3	1	no	—
460	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
461	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
462	C₂³×C₄	—	3	2	no	—
463	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
464	C₂³×C₄	C₂×C₅×D₃	1	2	yes	complemented
465	C₄⋊Q₈	—	3	4	no	—
466	#127	—	3	4	no	—
467	#124	—	3	4	no	—
468	#124	—	3	4	no	—
469	#123	—	3	8	no	—
470	#123	—	3	8	no	—
471	C₂²⋊Q₈	—	3	8	no	—
472	C₂²⋊Q₈	—	3	8	no	—
473	#121	—	3	8	no	—
474	#121	—	3	16	no	—
475	#121	—	3	8	no	—
476	#120	—	3	8	no	—
477	#120	—	3	8	no	—
478	C₄×D₄	—	3	16	no	—
479	#117	—	3	2	no	—
480	#117	—	3	2	no	—
481	#117	—	3	2	no	—
482	#117	—	3	2	no	—
483	C₂×C₄⋊C₄	—	3	2	no	—
484	C₂×C₂²⋊C₄	—	3	2	no	—
485	C₂×C₄²	—	3	2	no	—
486	C₂×C₃×C₅	—	2	2	no	—
487	C₂×C₃×C₅	—	2	2	no	—
488	C₂×C₃×C₅	—	2	2	no	—
489	C₂×C₃×C₅	—	4	4	no	—
490	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
491	C₂×C₃×C₅	#585	1	2	yes	—
492	C₅×D₃	—	4	4	no	—
493	C₂³×C₃	—	2	4	no	—
494	C₂³×C₃	—	4	2	no	—
495	C₂³×C₃	—	4	4	no	—
496	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
497	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
498	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
499	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
500	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
501	C₂²×D₃	—	2	4	no	—
502	C₂²×D₃	—	4	4	no	—
503	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
504	C₃×Q₈	—	2	4	no	—
505	C₃×Q₈	—	2	4	no	—
506	C₃×D₄	—	2	8	no	—
507	C₃×D₄	—	2	8	no	—
508	C₃×D₄	—	2	4	no	—
509	C₃×D₄	—	2	4	no	—
510	C₂×C₃×C₄	—	2	4	no	—
511	C₂×C₃×C₄	—	2	8	no	—
512	C₂×C₃×C₄	—	2	8	no	—
513	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
514	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
515	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
516	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
517	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
518	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
519	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
520	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
524	#67	—	2	8	no	—
525	#67	—	2	8	no	—
526	#67	—	4	16	no	—
527	C₂×Dic₃	—	2	4	no	—
528	C₂×Dic₃	—	4	4	no	—
529	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
530	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
531	D₁₂	—	2	4	no	—
532	D₁₂	—	2	4	no	—
533	C₄×D₃	—	2	8	no	—
534	C₄×D₃	—	2	8	no	—
535	Dic₆	—	2	4	no	—
536	Dic₆	—	2	4	no	—
537	C₂²×C₅	—	2	2	no	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	8	no	—
541	C₂²×C₅	—	2	4	no	—
542	C₂²×C₅	—	4	4	no	—
543	C₂²×C₅	—	4	8	no	—
544	C₂²×C₅	—	6	8	no	—
545	C₂²×C₅	—	6	4	no	—
546	C₂²×C₅	—	12	8	no	—
547	C₂²×C₅	C₂²×#67	1	2	yes	—
548	C₂²×C₅	C₂²×#67	1	2	yes	—
549	C₂²×C₅	C₂²×#67	1	2	yes	—
550	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
551	C₄×C₅	—	2	4	no	—
552	C₄×C₅	—	6	8	no	—
553	C₄×C₅	—	6	4	no	—
554	C₄×C₅	C₂²×#67	1	2	yes	—
555	C₄×C₅	C₂²×#67	1	2	yes	—
556	C₄×C₅	C₂²×#67	1	2	yes	—
557	C₄×C₅	C₂²×#67	1	2	yes	—
558	C₂⁴	—	3	2	no	—
559	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
560	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
561	#41	—	2	8	no	—
562	#41	—	2	8	no	—
563	#41	—	2	8	no	—
564	#41	—	2	8	no	—
565	#41	—	6	8	no	—
566	#41	—	6	8	no	—
567	#41	—	6	8	no	—
568	#41	—	6	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	3	2	no	—
571	C₂×Q₈	—	3	2	no	—
572	C₂×Q₈	—	6	4	no	—
573	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
574	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	3	4	no	—
578	C₂×D₄	—	3	4	no	—
579	C₂×D₄	—	3	16	no	—
580	C₂×D₄	—	3	2	no	—
581	C₂×D₄	—	3	2	no	—
582	C₂×D₄	—	6	8	no	—
583	C₂×D₄	—	6	4	no	—
584	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
585	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
586	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
587	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
588	C₂²×C₄	—	2	8	no	—
589	C₂²×C₄	—	3	2	no	—
590	C₂²×C₄	—	3	4	no	—
591	C₂²×C₄	—	3	4	no	—
592	C₂²×C₄	—	3	4	no	—
593	C₂²×C₄	—	6	8	no	—
594	C₂²×C₄	C₅×#67	1	8	yes	complemented
595	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
596	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
597	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
598	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
602	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
604	C₄⋊C₄	—	3	4	no	—
605	C₄⋊C₄	—	3	4	no	—
606	C₄⋊C₄	—	3	16	no	—
607	C₂²⋊C₄	—	3	4	no	—
608	C₂²⋊C₄	—	3	4	no	—
609	C₂²⋊C₄	—	3	16	no	—
610	C₂²⋊C₄	—	3	16	no	—
611	C₄²	—	3	4	no	—
612	C₄²	—	3	4	no	—
613	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	2	no	—
617	C₂²×C₃	—	2	4	no	—
618	C₂²×C₃	—	2	8	no	—
619	C₂²×C₃	—	4	4	no	—
620	C₂²×C₃	—	4	8	no	—
621	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
622	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
623	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
624	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
625	C₂×D₃	—	2	4	no	—
626	C₂×D₃	—	2	8	no	—
627	C₂×D₃	—	4	8	no	—
628	C₃×C₄	—	2	4	no	—
629	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
630	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
631	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
632	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
633	Dic₃	—	2	4	no	—
634	Dic₃	—	2	8	no	—
635	C₂×C₅	—	2	2	no	—
636	C₂×C₅	—	2	2	no	—
637	C₂×C₅	—	2	2	no	—
638	C₂×C₅	—	4	4	no	—
639	C₂×C₅	—	12	4	no	—
640	C₂×C₅	#5964	1	2	yes	—
641	C₂×C₅	C₂³×#67	1	1	yes	characteristic
642	C₂³	—	2	4	no	—
643	C₂³	—	3	4	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	6	4	no	—
647	C₂³	—	12	4	no	—
648	C₂³	C₂×C₅×#67	1	4	yes	—
649	C₂³	C₂³×C₅×D₃	1	4	yes	—
650	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
651	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
652	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
653	Q₈	—	2	4	no	—
654	Q₈	—	2	4	no	—
655	Q₈	—	6	4	no	—
656	Q₈	—	6	4	no	—
657	D₄	—	2	8	no	—
658	D₄	—	2	8	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	4	no	—
661	D₄	—	6	8	no	—
662	D₄	—	6	8	no	—
663	D₄	—	6	4	no	—
664	D₄	—	6	4	no	—
665	D₄	—	12	16	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	3	8	no	—
670	C₂×C₄	—	3	4	no	—
671	C₂×C₄	—	6	4	no	—
672	C₂×C₄	—	6	8	no	—
673	C₂×C₄	—	6	8	no	—
674	C₂×C₄	—	12	4	no	—
675	C₂×C₄	C₂×C₅×#67	1	4	yes	—
676	C₂×C₄	C₂×C₅×#67	1	4	yes	—
677	C₂×C₄	C₂×C₅×#67	1	4	yes	—
678	C₂×C₄	C₂×C₅×#67	1	4	yes	—
679	C₂×C₄	C₂×C₅×#67	1	4	yes	—
680	C₂×C₄	C₂×C₅×#67	1	4	yes	—
681	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
682	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
683	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
684	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
685	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
686	C₂×C₃	—	2	2	no	—
687	C₂×C₃	—	2	2	no	—
688	C₂×C₃	—	2	2	no	—
689	C₂×C₃	—	4	4	no	—
690	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
691	C₂×C₃	C₅×#585	1	2	yes	—
692	D₃	—	4	4	no	—
693	C₅	#87268	1	1	yes	characteristic, direct product factor, Sylow
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	8	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	8	no	—
701	C₂²	—	6	8	no	—
702	C₂²	—	6	4	no	—
703	C₂²	—	12	8	no	—
704	C₂²	C₂²×C₅×#67	1	2	yes	—
705	C₂²	C₂²×C₅×#67	1	2	yes	—
706	C₂²	C₂²×C₅×#67	1	2	yes	—
707	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
708	C₄	—	2	4	no	—
709	C₄	—	6	8	no	—
710	C₄	—	6	4	no	—
711	C₄	C₂²×C₅×#67	1	2	yes	—
712	C₄	C₂²×C₅×#67	1	2	yes	—
713	C₄	C₂²×C₅×#67	1	2	yes	—
714	C₄	C₂²×C₅×#67	1	2	yes	—
715	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
716	C₂	—	2	2	no	—
717	C₂	—	2	2	no	—
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	—	12	4	no	—
721	C₂	C₅×#5964	1	2	yes	—
722	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₅×#5833	C₂	semidirect
4. C₅×#5832	C₂	semidirect
5. C₅×#5830	C₂	semidirect
6. C₅×#5828	C₂	semidirect
7. C₅×#5825	C₂	semidirect
8. C₅×#5816	C₂	semidirect
9. C₅×#5805	C₂	semidirect
10. C₅×#5804	C₂	semidirect
11. C₅×#5791	C₂	semidirect
12. C₂×C₅×#926	C₂	semidirect
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
23. C₂³×C₃×C₄×C₅	C₂²	semidirect
28. C₂×C₅×#235	C₂²	semidirect
29. C₂×C₅×#235	C₂²	semidirect
30. C₂²×C₅×D₁₂	C₂²	semidirect
31. C₂²×C₄×C₅×D₃	C₂²	semidirect
32. C₂²×C₅×Dic₆	C₂²	semidirect
33. C₅×#953	C₂²	semidirect
35. C₅×#947	C₂²	semidirect
36. C₅×#946	C₂²	semidirect
37. C₅×#944	C₂²	semidirect
38. C₅×#940	C₂²	semidirect
39. C₅×#939	C₂²	semidirect
40. C₅×#938	C₂²	semidirect
41. C₅×#937	C₂²	semidirect
42. C₅×#936	C₂²	semidirect
43. C₅×#935	C₂²	semidirect
44. C₅×#930	C₂²	semidirect
45. C₅×#929	C₂²	semidirect
46. C₄×C₅×#67	C₂²	semidirect
47. C₅×#926	C₂²	semidirect
48. C₅×#926	C₂²	semidirect
49. C₅×#926	C₂²	semidirect
50. C₅×#926	C₂²	semidirect
51. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
52. C₅×#924	C₂²	semidirect
53. C₂×C₄×C₅×Dic₃	C₂²	semidirect
54. #87268	C₅	direct (N × H)
56. C₂²×C₅×#41	D₃	semidirect
84. C₂²×C₃×C₄×C₅	D₄	semidirect
122. C₂²×C₃×#41	C₂×C₅	semidirect
123. C₂²×#235	C₂×C₅	semidirect
124. #5833	C₂×C₅	semidirect
125. #5832	C₂×C₅	semidirect
126. #5830	C₂×C₅	semidirect
127. #5828	C₂×C₅	semidirect
128. #5825	C₂×C₅	semidirect
129. #5816	C₂×C₅	semidirect
130. #5805	C₂×C₅	semidirect
131. #5804	C₂×C₅	semidirect
132. #5791	C₂×C₅	semidirect
133. C₂×#926	C₂×C₅	semidirect
142. C₂×C₅×#41	C₂×D₃	semidirect
143. C₂×C₅×#41	C₂×D₃	semidirect
145. C₂²×C₅×Q₈	C₂×D₃	semidirect
149. C₂²×C₅×D₄	C₂×D₃	semidirect
152. C₂³×C₄×C₅	C₂×D₃	semidirect
222. C₂×C₃×#41	C₂²×C₅	semidirect
223. C₂×C₃×#41	C₂²×C₅	semidirect
224. C₂²×C₃×Q₈	C₂²×C₅	semidirect
226. C₂²×C₃×D₄	C₂²×C₅	semidirect
228. C₂³×C₃×C₄	C₂²×C₅	semidirect
233. C₂×#235	C₂²×C₅	semidirect
234. C₂×#235	C₂²×C₅	semidirect
235. C₂²×D₁₂	C₂²×C₅	semidirect
236. C₂²×C₄×D₃	C₂²×C₅	semidirect
237. C₂²×Dic₆	C₂²×C₅	semidirect
238. #953	C₂²×C₅	semidirect
240. #947	C₂²×C₅	semidirect
241. #946	C₂²×C₅	semidirect
242. #944	C₂²×C₅	semidirect
243. #940	C₂²×C₅	semidirect
244. #939	C₂²×C₅	semidirect
245. #938	C₂²×C₅	semidirect
246. #937	C₂²×C₅	semidirect
247. #936	C₂²×C₅	semidirect
248. #935	C₂²×C₅	semidirect
249. #930	C₂²×C₅	semidirect
250. #929	C₂²×C₅	semidirect
251. C₄×#67	C₂²×C₅	semidirect
252. #926	C₂²×C₅	semidirect
253. #926	C₂²×C₅	semidirect
254. #926	C₂²×C₅	semidirect
255. #926	C₂²×C₅	semidirect
256. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
257. #924	C₂²×C₅	semidirect
258. C₂×C₄×Dic₃	C₂²×C₅	semidirect
295. C₂²×C₄×C₅	#67	semidirect
315. C₂²×#41	C₅×D₃	semidirect
364. C₂²×C₃×C₄	C₅×D₄	semidirect
454. C₂×#41	C₂×C₅×D₃	semidirect
455. C₂×#41	C₂×C₅×D₃	semidirect
457. C₂²×Q₈	C₂×C₅×D₃	semidirect
461. C₂²×D₄	C₂×C₅×D₃	semidirect
464. C₂³×C₄	C₂×C₅×D₃	semidirect
594. C₂²×C₄	C₅×#67	semidirect
613. C₃×C₅	#3449	semidirect
693. C₅	#87268	direct (N × H)
715. C₃	C₅×#3449	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×#41	2
C₂²×C₅×#235	2
C₅×#5833	2
C₅×#5832	2
C₅×#5830	2
C₅×#5828	2
C₅×#5825	2
C₅×#5816	2
C₅×#5805	2
C₅×#5804	2
C₅×#5791	2
C₂×C₅×#926	2
C₅×#3449	3
#87268	5

Subgroups — C5×#87268 #14480638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87268 #14480638