Subgroups — C₂×C₅×#5594 #14495254

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#953	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#937	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×#936	C₂	1	3	yes	maximal, complemented
5	C₅×#5594	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#885	C₂	1	6	yes	maximal, complemented
7	C₂×C₅×H(3,𝔽₄)	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
11	C₂²×C₅×#67	C₂²	1	6	yes	—
12	C₂²×C₅×Dic₆	C₂²	1	3	yes	complemented
13	C₃×C₅×#120	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
15	C₅×#953	C₂²	1	16	yes	complemented
16	C₂×C₅×#217	C₂²	1	6	yes	complemented
17	C₂×C₅×#217	C₂²	1	3	yes	complemented
18	C₅×#937	C₂²	1	24	yes	complemented
19	C₅×#936	C₂²	1	24	yes	complemented
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
21	C₂×C₄×C₅×Dic₃	C₂²	1	3	yes	complemented
22	C₅×#885	C₂²	1	48	yes	complemented
23	C₂×#5594	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₅×H(3,𝔽₄)	—	3	16	no	—
25	C₂×C₅×#124	—	3	3	no	—
26	C₂×C₅×#124	—	3	6	no	—
27	C₂×C₅×#120	—	3	2	no	—
28	C₂×C₅×#120	—	3	3	no	—
29	C₂×C₅×#120	D₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	4	6	no	—
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	4	yes	complemented
34	C₂³×C₅×D₃	—	4	6	no	—
35	C₂³×C₅×D₃	C₂³	1	2	yes	—
36	C₂³×C₅×D₃	C₂³	1	4	yes	complemented
37	C₂×C₃×C₅×D₄	—	4	6	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	12	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
40	C₂×C₅×#67	—	4	12	no	—
41	C₂×C₅×#67	C₂³	1	24	yes	—
42	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
43	C₂×C₅×Dic₆	—	4	6	no	—
44	C₂×C₅×Dic₆	C₂³	1	12	yes	complemented
45	C₃×C₅×C₂²⋊C₄	C₂³	1	12	yes	complemented
46	C₅×#217	C₂³	1	24	yes	complemented
47	C₅×#217	C₂³	1	12	yes	complemented
48	C₅×(C₂×D₃)⋊C₄	C₂³	1	24	yes	complemented
49	C₄×C₅×Dic₃	C₂³	1	12	yes	complemented
50	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
51	C₂×#953	C₂×C₅	1	2	yes	complemented
52	C₂×#937	C₂×C₅	1	3	yes	complemented
53	C₂×#936	C₂×C₅	1	3	yes	complemented
54	#5594	C₂×C₅	1	16	yes	direct product factor
55	C₂×#885	C₂×C₅	1	6	yes	complemented
56	C₂⁵×C₅	—	3	1	no	—
57	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic, complemented
58	C₂²×C₅×Q₈	—	3	3	no	—
59	C₂²×C₅×D₄	—	3	6	no	—
60	C₂²×C₅×D₄	C₂×D₃	1	3	yes	—
61	C₅×#124	—	3	24	no	—
62	C₅×#124	—	3	48	no	—
63	C₅×#120	—	3	16	no	—
64	C₅×#120	—	3	24	no	—
65	C₅×#120	C₂×D₃	1	8	yes	complemented
66	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
68	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
69	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	3	yes	complemented
70	C₂×C₄²×C₅	—	3	3	no	—
71	C₂×H(3,𝔽₄)	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	12	no	—
73	C₂³×C₃×C₅	—	2	6	no	—
74	C₂³×C₃×C₅	—	2	6	no	—
75	C₂³×C₃×C₅	—	4	12	no	—
76	C₂³×C₃×C₅	—	4	16	no	—
77	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	12	no	—
81	C₂²×C₅×D₃	—	4	12	no	—
82	C₂²×C₅×D₃	—	4	16	no	—
83	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
84	C₃×C₅×D₄	—	4	12	no	—
85	C₂×C₃×C₄×C₅	—	2	6	no	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
87	C₅×#67	—	4	24	no	—
88	C₂×C₅×Dic₃	—	2	12	no	—
89	C₂×C₅×Dic₃	C₂⁴	1	12	yes	—
90	C₅×Dic₆	—	4	12	no	—
91	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic, complemented
92	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
93	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
94	C₂²×#67	C₂²×C₅	1	6	yes	—
95	C₂²×Dic₆	C₂²×C₅	1	3	yes	complemented
96	C₃×#120	C₂²×C₅	1	8	yes	complemented
97	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
98	#953	C₂²×C₅	1	16	yes	complemented
99	C₂×#217	C₂²×C₅	1	6	yes	complemented
100	C₂×#217	C₂²×C₅	1	3	yes	complemented
101	#937	C₂²×C₅	1	24	yes	complemented
102	#936	C₂²×C₅	1	24	yes	complemented
103	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	6	yes	complemented
104	C₂×C₄×Dic₃	C₂²×C₅	1	3	yes	complemented
105	#885	C₂²×C₅	1	48	yes	complemented
106	C₂⁴×C₅	—	3	2	no	—
107	C₂⁴×C₅	—	3	4	no	—
108	C₂⁴×C₅	—	4	6	no	—
109	C₂⁴×C₅	—	12	6	no	—
110	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
111	C₂⁴×C₅	C₂²×D₃	1	3	yes	—
112	C₂⁴×C₅	C₂²×D₃	1	4	yes	complemented
113	C₂×C₅×Q₈	—	3	12	no	—
114	C₂×C₅×Q₈	—	12	6	no	—
115	C₂×C₅×D₄	—	3	24	no	—
116	C₂×C₅×D₄	—	4	6	no	—
117	C₂×C₅×D₄	—	12	12	no	—
118	C₂×C₅×D₄	C₂²×D₃	1	12	yes	—
119	C₂²×C₄×C₅	—	3	6	no	—
120	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
121	C₅×C₂²⋊C₄	—	3	12	no	—
122	C₅×C₂²⋊C₄	—	3	24	no	—
123	C₅×C₂²⋊C₄	—	3	24	no	—
124	C₅×C₂²⋊C₄	C₂²×D₃	1	12	yes	complemented
125	C₄²×C₅	—	3	12	no	—
126	H(3,𝔽₄)	—	3	16	no	—
127	C₂×#124	—	3	3	no	—
128	C₂×#124	—	3	6	no	—
129	C₂×#120	—	3	2	no	—
130	C₂×#120	—	3	3	no	—
131	C₂×#120	C₅×D₃	1	1	yes	characteristic, complemented
132	C₂²×C₃×C₅	—	2	12	no	—
133	C₂²×C₃×C₅	—	2	6	no	—
134	C₂²×C₃×C₅	—	2	6	no	—
135	C₂²×C₃×C₅	—	4	16	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	—	4	12	no	—
138	C₂²×C₃×C₅	H(5,𝔽₂)	1	6	yes	—
139	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
140	C₂×C₅×D₃	—	2	12	no	—
141	C₂×C₅×D₃	—	4	16	no	—
142	C₂×C₅×D₃	—	4	8	no	—
143	C₃×C₄×C₅	—	2	6	no	—
144	C₅×Dic₃	—	2	12	no	—
145	C₂⁴×C₃	—	4	6	no	—
146	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
147	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
148	C₂⁴×C₃	C₂³×C₅	1	4	yes	complemented
149	C₂³×D₃	—	4	6	no	—
150	C₂³×D₃	C₂³×C₅	1	2	yes	—
151	C₂³×D₃	C₂³×C₅	1	4	yes	complemented
152	C₂×C₃×D₄	—	4	6	no	—
153	C₂×C₃×D₄	C₂³×C₅	1	12	yes	—
154	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
155	C₂×#67	—	4	12	no	—
156	C₂×#67	C₂³×C₅	1	24	yes	—
157	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
158	C₂×Dic₆	—	4	6	no	—
159	C₂×Dic₆	C₂³×C₅	1	12	yes	complemented
160	C₃×C₂²⋊C₄	C₂³×C₅	1	12	yes	complemented
161	#217	C₂³×C₅	1	24	yes	complemented
162	#217	C₂³×C₅	1	12	yes	complemented
163	(C₂×D₃)⋊C₄	C₂³×C₅	1	24	yes	complemented
164	C₄×Dic₃	C₂³×C₅	1	12	yes	complemented
165	C₂³×C₅	—	2	6	no	—
166	C₂³×C₅	—	2	6	no	—
167	C₂³×C₅	—	2	12	no	—
168	C₂³×C₅	—	3	4	no	—
169	C₂³×C₅	—	4	12	no	—
170	C₂³×C₅	—	4	16	no	—
171	C₂³×C₅	—	6	12	no	—
172	C₂³×C₅	—	12	12	no	—
173	C₂³×C₅	—	12	16	no	—
174	C₂³×C₅	C₂³×D₃	1	2	yes	—
175	C₂³×C₅	C₂³×D₃	1	6	yes	—
176	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
177	C₅×Q₈	—	12	12	no	—
178	C₅×D₄	—	4	12	no	—
179	C₅×D₄	—	12	24	no	—
180	C₂×C₄×C₅	—	2	6	no	—
181	C₂×C₄×C₅	—	3	12	no	—
182	C₂×C₄×C₅	—	6	12	no	—
183	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
184	C₂⁵	—	3	1	no	—
185	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic, complemented
186	C₂²×Q₈	—	3	3	no	—
187	C₂²×D₄	—	3	6	no	—
188	C₂²×D₄	C₂×C₅×D₃	1	3	yes	—
189	#124	—	3	24	no	—
190	#124	—	3	48	no	—
191	#120	—	3	16	no	—
192	#120	—	3	24	no	—
193	#120	C₂×C₅×D₃	1	8	yes	complemented
194	C₂×C₂²⋊C₄	—	3	3	no	—
195	C₂×C₂²⋊C₄	—	3	6	no	—
196	C₂×C₂²⋊C₄	—	3	6	no	—
197	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	3	yes	complemented
198	C₂×C₄²	—	3	3	no	—
199	C₂×C₃×C₅	—	4	2	no	—
200	C₂×C₃×C₅	—	4	6	no	—
201	C₂×C₃×C₅	H(3,𝔽₄)	1	4	yes	complemented
202	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	3	yes	—
203	C₅×D₃	—	4	4	no	—
204	C₂³×C₃	—	2	12	no	—
205	C₂³×C₃	—	2	6	no	—
206	C₂³×C₃	—	2	6	no	—
207	C₂³×C₃	—	4	12	no	—
208	C₂³×C₃	—	4	16	no	—
209	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
210	C₂³×C₃	C₂⁴×C₅	1	6	yes	—
211	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
212	C₂²×D₃	—	2	12	no	—
213	C₂²×D₃	—	4	12	no	—
214	C₂²×D₃	—	4	16	no	—
215	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
216	C₃×D₄	—	4	12	no	—
217	C₂×C₃×C₄	—	2	6	no	—
218	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
219	#67	—	4	24	no	—
220	C₂×Dic₃	—	2	12	no	—
221	C₂×Dic₃	C₂⁴×C₅	1	12	yes	—
222	Dic₆	—	4	12	no	—
223	C₂²×C₅	—	2	6	no	—
224	C₂²×C₅	—	2	6	no	—
225	C₂²×C₅	—	2	12	no	—
226	C₂²×C₅	—	4	16	no	—
227	C₂²×C₅	—	4	12	no	—
228	C₂²×C₅	—	4	4	no	—
229	C₂²×C₅	—	6	12	no	—
230	C₂²×C₅	—	12	16	no	—
231	C₂²×C₅	—	12	8	no	—
232	C₂²×C₅	#1004	1	6	yes	—
233	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
234	C₄×C₅	—	2	6	no	—
235	C₄×C₅	—	6	12	no	—
236	C₂⁴	—	3	2	no	—
237	C₂⁴	—	3	4	no	—
238	C₂⁴	—	4	6	no	—
239	C₂⁴	—	12	6	no	—
240	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
241	C₂⁴	C₂²×C₅×D₃	1	3	yes	—
242	C₂⁴	C₂²×C₅×D₃	1	4	yes	complemented
243	C₂×Q₈	—	3	12	no	—
244	C₂×Q₈	—	12	6	no	—
245	C₂×D₄	—	3	24	no	—
246	C₂×D₄	—	4	6	no	—
247	C₂×D₄	—	12	12	no	—
248	C₂×D₄	C₂²×C₅×D₃	1	12	yes	—
249	C₂²×C₄	—	3	6	no	—
250	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
251	C₂²⋊C₄	—	3	12	no	—
252	C₂²⋊C₄	—	3	24	no	—
253	C₂²⋊C₄	—	3	24	no	—
254	C₂²⋊C₄	C₂²×C₅×D₃	1	12	yes	complemented
255	C₄²	—	3	12	no	—
256	C₃×C₅	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Hall
257	C₂²×C₃	—	2	12	no	—
258	C₂²×C₃	—	2	6	no	—
259	C₂²×C₃	—	2	6	no	—
260	C₂²×C₃	—	4	16	no	—
261	C₂²×C₃	—	4	4	no	—
262	C₂²×C₃	—	4	12	no	—
263	C₂²×C₃	C₅×H(5,𝔽₂)	1	6	yes	—
264	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
265	C₂×D₃	—	2	12	no	—
266	C₂×D₃	—	4	16	no	—
267	C₂×D₃	—	4	8	no	—
268	C₃×C₄	—	2	6	no	—
269	Dic₃	—	2	12	no	—
270	C₂×C₅	—	4	6	no	—
271	C₂×C₅	—	4	2	no	—
272	C₂×C₅	—	12	4	no	—
273	C₂×C₅	#5594	1	4	yes	direct product factor
274	C₂×C₅	C₂×#1004	1	3	yes	—
275	C₂³	—	2	6	no	—
276	C₂³	—	2	6	no	—
277	C₂³	—	2	12	no	—
278	C₂³	—	3	4	no	—
279	C₂³	—	4	12	no	—
280	C₂³	—	4	16	no	—
281	C₂³	—	6	12	no	—
282	C₂³	—	12	12	no	—
283	C₂³	—	12	16	no	—
284	C₂³	C₂³×C₅×D₃	1	2	yes	—
285	C₂³	C₂³×C₅×D₃	1	6	yes	—
286	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
287	Q₈	—	12	12	no	—
288	D₄	—	4	12	no	—
289	D₄	—	12	24	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	3	12	no	—
292	C₂×C₄	—	6	12	no	—
293	C₂×C₄	C₂³×C₅×D₃	1	6	yes	—
294	C₂×C₃	—	4	2	no	—
295	C₂×C₃	—	4	6	no	—
296	C₂×C₃	C₅×H(3,𝔽₄)	1	4	yes	complemented
297	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	3	yes	—
298	D₃	—	4	4	no	—
299	C₅	C₂×#5594	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²	—	2	6	no	—
301	C₂²	—	2	6	no	—
302	C₂²	—	2	12	no	—
303	C₂²	—	4	16	no	—
304	C₂²	—	4	12	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	6	12	no	—
307	C₂²	—	12	16	no	—
308	C₂²	—	12	8	no	—
309	C₂²	C₅×#1004	1	6	yes	—
310	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
311	C₄	—	2	6	no	—
312	C₄	—	6	12	no	—
313	C₃	C₂×C₅×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
314	C₂	—	4	6	no	—
315	C₂	—	4	2	no	—
316	C₂	—	12	4	no	—
317	C₂	C₅×#5594	1	4	yes	direct product factor
318	C₂	C₂×C₅×#1004	1	3	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#120	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#120	D₃
hypocenter	C₃	C₂×C₅×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#120	C₂	semidirect
2. C₂×C₅×#953	C₂	semidirect
3. C₂×C₅×#937	C₂	semidirect
4. C₂×C₅×#936	C₂	semidirect
5. C₅×#5594	C₂	direct (N × H)
6. C₂×C₅×#885	C₂	semidirect
8. C₂⁵×C₃×C₅	C₂²	semidirect
9. C₂⁴×C₅×D₃	C₂²	semidirect
12. C₂²×C₅×Dic₆	C₂²	semidirect
13. C₃×C₅×#120	C₂²	semidirect
14. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
15. C₅×#953	C₂²	semidirect
16. C₂×C₅×#217	C₂²	semidirect
17. C₂×C₅×#217	C₂²	semidirect
18. C₅×#937	C₂²	semidirect
19. C₅×#936	C₂²	semidirect
20. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₂×C₄×C₅×Dic₃	C₂²	semidirect
22. C₅×#885	C₂²	semidirect
23. C₂×#5594	C₅	direct (N × H)
29. C₂×C₅×#120	D₃	semidirect
33. C₂⁴×C₃×C₅	C₂³	semidirect
36. C₂³×C₅×D₃	C₂³	semidirect
44. C₂×C₅×Dic₆	C₂³	semidirect
45. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
46. C₅×#217	C₂³	semidirect
47. C₅×#217	C₂³	semidirect
48. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
49. C₄×C₅×Dic₃	C₂³	semidirect
50. C₂×C₃×#120	C₂×C₅	semidirect
51. C₂×#953	C₂×C₅	semidirect
52. C₂×#937	C₂×C₅	semidirect
53. C₂×#936	C₂×C₅	semidirect
54. #5594	C₂×C₅	direct (N × H)
55. C₂×#885	C₂×C₅	semidirect
57. C₂⁵×C₅	C₂×D₃	semidirect
65. C₅×#120	C₂×D₃	semidirect
69. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
91. C₂⁵×C₃	C₂²×C₅	semidirect
92. C₂⁴×D₃	C₂²×C₅	semidirect
95. C₂²×Dic₆	C₂²×C₅	semidirect
96. C₃×#120	C₂²×C₅	semidirect
97. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
98. #953	C₂²×C₅	semidirect
99. C₂×#217	C₂²×C₅	semidirect
100. C₂×#217	C₂²×C₅	semidirect
101. #937	C₂²×C₅	semidirect
102. #936	C₂²×C₅	semidirect
103. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
104. C₂×C₄×Dic₃	C₂²×C₅	semidirect
105. #885	C₂²×C₅	semidirect
112. C₂⁴×C₅	C₂²×D₃	semidirect
124. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
131. C₂×#120	C₅×D₃	semidirect
148. C₂⁴×C₃	C₂³×C₅	semidirect
151. C₂³×D₃	C₂³×C₅	semidirect
159. C₂×Dic₆	C₂³×C₅	semidirect
160. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
161. #217	C₂³×C₅	semidirect
162. #217	C₂³×C₅	semidirect
163. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
164. C₄×Dic₃	C₂³×C₅	semidirect
185. C₂⁵	C₂×C₅×D₃	semidirect
193. #120	C₂×C₅×D₃	semidirect
197. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
201. C₂×C₃×C₅	H(3,𝔽₄)	semidirect
242. C₂⁴	C₂²×C₅×D₃	semidirect
254. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
256. C₃×C₅	C₂×H(3,𝔽₄)	semidirect
273. C₂×C₅	#5594	direct (N × H)
296. C₂×C₃	C₅×H(3,𝔽₄)	semidirect
299. C₅	C₂×#5594	direct (N × H)
313. C₃	C₂×C₅×H(3,𝔽₄)	semidirect
317. C₂	C₅×#5594	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#120	2
C₂×C₅×#953	2
C₂×C₅×#937	2
C₂×C₅×#936	2
C₅×#5594	2
C₂×C₅×#885	2
C₂×C₅×H(3,𝔽₄)	3
C₂×#5594	5

Subgroups — C2×C5×#5594 #14495254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5594 #14495254