Subgroups — C₂×#11748094 #14429462

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91309	C₂	1	2	yes	maximal
4	C₂×#91103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90961	C₂	1	2	yes	maximal, complemented
6	#11748094	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65432	—	3	1	no	maximal, Hall
8	C₂×C₅×#235	C₂²	1	1	yes	characteristic
9	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×#6710	C₂²	1	2	yes	—
12	C₂×C₅×#208	C₂²	1	1	yes	characteristic
13	C₅×#901	—	2	2	no	—
14	C₅×#901	C₂²	1	4	yes	—
15	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
16	C₂×C₅×D₃×C₈	—	2	1	no	—
17	C₂×C₃×Dic₂₀	—	2	1	no	—
18	C₂×C₃×Dic₂₀	—	2	1	no	—
19	C₂×C₃×Dic₂₀	—	2	2	no	—
20	C₂×C₃×Dic₂₀	C₂²	1	4	yes	complemented
21	C₂×#6661	—	2	2	no	—
22	#91309	—	2	4	no	—
23	#91309	C₂²	1	8	yes	—
24	C₂×#6656	—	2	2	no	—
25	#91103	C₂²	1	4	yes	complemented
26	#90961	C₂²	1	8	yes	complemented
27	C₂×#5192	—	5	1	no	maximal, Hall
28	C₂×C₅×#131	—	3	1	no	—
29	C₂×#4097	—	3	2	no	—
30	C₂²×Dic₂₀	D₃	1	1	yes	characteristic, complemented
31	#65432	—	3	8	no	—
32	C₂×#3956	—	3	2	no	—
33	C₂×#3951	—	3	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	1	no	—
36	C₅×#235	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	D₄	1	2	yes	—
39	C₅×#235	C₂³	1	2	yes	—
40	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	—	2	2	no	—
44	C₂×C₃×Dic₁₀	—	2	2	no	—
45	C₂×C₃×Dic₁₀	—	2	2	no	—
46	C₂×C₃×Dic₁₀	—	2	2	no	—
47	C₂×C₃×Dic₁₀	—	2	2	no	—
48	C₂×C₃×Dic₁₀	—	2	2	no	—
49	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
50	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	#6710	—	2	2	no	—
55	#6710	C₂³	1	4	yes	—
56	C₂×C₃⋊#168	—	2	2	no	—
57	C₅×#208	—	2	1	no	—
58	C₅×#208	C₂³	1	2	yes	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
61	C₅×D₃×C₈	—	2	4	no	—
62	C₃×Dic₂₀	—	2	4	no	—
63	C₃×Dic₂₀	—	2	4	no	—
64	#6661	—	2	8	no	—
65	#6656	—	2	8	no	—
66	C₂²×C₃×Q₁₆	—	5	1	no	—
67	C₂×#942	—	5	2	no	—
68	C₂×#901	D₅	1	1	yes	characteristic
69	C₂×#836	—	5	2	no	—
70	#5192	—	5	8	no	—
71	C₂×#819	—	5	1	no	—
72	C₂×C₅×#41	—	3	1	no	—
73	C₂²×Dic₁₀	C₂×D₃	1	2	yes	—
74	C₅×#131	—	3	4	no	—
75	C₅×#131	—	6	2	no	—
76	C₂×C₅×M₁₆	—	3	1	no	—
77	C₂×C₅×M₁₆	—	6	1	no	—
78	C₂²×C₅×C₈	—	6	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	#4097	—	3	8	no	—
81	#4097	—	6	4	no	—
82	C₂×#689	—	6	2	no	—
83	C₂×#687	—	6	2	no	—
84	C₂×#681	—	3	2	no	—
85	C₂×Dic₂₀	—	2	1	no	—
86	C₂×Dic₂₀	—	2	1	no	—
87	C₂×Dic₂₀	—	2	2	no	—
88	C₂×Dic₂₀	C₂×D₃	1	4	yes	complemented
89	#3956	—	3	8	no	—
90	#3951	—	3	4	no	—
91	C₂×#473	—	15	1	no	Sylow
92	C₂³×C₃×C₅	#41	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₅×#67	—	2	2	no	—
101	C₅×#67	—	2	2	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₅×D₁₂	—	2	1	no	—
104	C₅×D₁₂	C₂×D₄	1	2	yes	—
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₅×Dic₆	—	2	1	no	—
108	C₅×Dic₆	C₂×D₄	1	2	yes	—
109	C₂×C₃×Dic₅	—	2	4	no	—
110	C₂×C₃×Dic₅	—	4	2	no	—
111	C₂×C₃×Dic₅	—	4	2	no	—
112	C₃×Dic₁₀	—	2	4	no	—
113	C₃×Dic₁₀	—	2	4	no	—
114	C₃×Dic₁₀	—	4	2	no	—
115	C₃×Dic₁₀	—	4	2	no	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
118	C₃⋊#168	—	2	4	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₂²×C₃×Q₈	—	5	2	no	—
121	C₂×#235	C₂×D₅	1	1	yes	characteristic
122	C₂×C₃×Q₁₆	—	5	4	no	—
123	C₂×C₃×Q₁₆	—	10	1	no	—
124	C₂×C₃×Q₁₆	—	10	1	no	—
125	C₂×C₃×Q₁₆	—	10	2	no	—
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂×#216	—	10	2	no	—
128	#942	—	5	8	no	—
129	#942	—	10	4	no	—
130	C₂×#215	—	10	2	no	—
131	C₂×#208	—	5	2	no	—
132	C₂×#208	C₂×D₅	1	1	yes	characteristic
133	#901	—	2	2	no	—
134	#901	C₂×D₅	1	4	yes	—
135	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
136	C₂×D₃×C₈	—	2	1	no	—
137	#836	—	5	8	no	—
138	#819	—	5	4	no	—
139	C₅×#41	—	3	2	no	—
140	C₅×#41	—	3	2	no	—
141	C₅×#41	—	6	1	no	—
142	C₅×#41	—	6	1	no	—
143	C₂×C₅×Q₈	—	3	1	no	—
144	C₂×C₅×D₄	—	3	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×Dic₅	—	2	2	no	—
149	C₂×Dic₁₀	—	2	2	no	—
150	C₂×Dic₁₀	—	2	2	no	—
151	C₂×Dic₁₀	—	2	2	no	—
152	C₂×Dic₁₀	—	2	2	no	—
153	C₂×Dic₁₀	—	2	2	no	—
154	C₂×Dic₁₀	C₂²×D₃	1	4	yes	—
155	C₅×M₁₆	—	3	2	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₅×M₁₆	—	6	4	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₂×C₅×C₈	—	6	4	no	—
160	C₂×C₅×C₈	#67	1	1	yes	characteristic
161	C₂×C₅×C₈	#67	1	1	yes	characteristic
162	C₂×C₅×C₈	#67	1	2	yes	—
163	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
164	#689	—	6	8	no	—
165	#687	—	6	8	no	—
166	#681	—	3	4	no	—
167	#681	—	6	2	no	—
168	C₂×#168	—	6	2	no	—
169	Dic₂₀	—	2	4	no	—
170	Dic₂₀	—	2	4	no	—
171	C₂×#137	—	15	2	no	—
172	C₂²×Q₁₆	—	5	1	no	—
173	C₂×#131	—	3	1	no	—
174	#473	—	15	8	no	—
175	C₂×#108	—	15	1	no	—
176	C₂×#101	—	15	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	#121	1	1	yes	characteristic
179	C₂²×C₃×C₅	#121	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	4	2	no	—
183	C₃×C₄×C₅	#121	1	1	yes	characteristic
184	C₃×C₄×C₅	#121	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×Dic₅	—	4	4	no	—
188	C₅×Dic₃	—	2	2	no	—
189	C₂×C₃×Q₈	—	5	4	no	—
190	C₂×C₃×Q₈	—	10	2	no	—
191	C₂×C₃×Q₈	—	10	2	no	—
192	C₂×C₃×Q₈	—	10	2	no	—
193	C₂×C₃×Q₈	—	10	2	no	—
194	C₂×C₃×Q₈	—	10	2	no	—
195	C₂²×C₃×C₄	—	10	2	no	—
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₂×#67	—	2	1	no	—
198	#235	—	2	1	no	—
199	#235	—	2	1	no	—
200	#235	D₂₀	1	2	yes	—
201	#235	C₂²×D₅	1	2	yes	—
202	C₂×D₁₂	D₂₀	1	1	yes	characteristic
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×Dic₆	D₂₀	1	1	yes	characteristic
205	C₃×Q₁₆	—	10	4	no	—
206	C₃×Q₁₆	—	10	4	no	—
207	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
210	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
211	#216	—	10	8	no	—
212	#215	—	10	8	no	—
213	#208	—	2	1	no	—
214	#208	—	5	4	no	—
215	#208	—	10	2	no	—
216	#208	C₂²×D₅	1	2	yes	—
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	10	2	no	—
219	ΓL(1,𝔽₂₅)	—	2	4	no	—
220	D₃×C₈	—	2	4	no	—
221	C₂³×C₅	—	6	1	no	—
222	C₂³×C₅	#237	1	1	yes	characteristic
223	C₅×Q₈	—	3	2	no	—
224	C₅×Q₈	—	6	1	no	—
225	C₅×D₄	—	3	2	no	—
226	C₅×D₄	—	6	2	no	—
227	C₅×D₄	—	6	2	no	—
228	C₅×D₄	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	2	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	#237	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₂×Dic₅	—	2	4	no	—
239	C₂×Dic₅	—	4	2	no	—
240	C₂×Dic₅	—	4	2	no	—
241	Dic₁₀	—	2	4	no	—
242	Dic₁₀	—	2	4	no	—
243	Dic₁₀	—	4	2	no	—
244	Dic₁₀	—	4	2	no	—
245	C₅×C₈	—	6	2	no	—
246	C₅×C₈	C₂×#67	1	2	yes	—
247	C₅×C₈	C₂×#67	1	2	yes	—
248	#168	—	6	4	no	—
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	—	5	2	no	—
251	#137	—	15	8	no	—
252	#137	—	30	4	no	—
253	C₂×Q₁₆	—	5	4	no	—
254	C₂×Q₁₆	—	10	1	no	—
255	C₂×Q₁₆	—	10	1	no	—
256	C₂×Q₁₆	—	10	2	no	—
257	C₂×Q₁₆	—	30	2	no	—
258	C₂×SD₁₆	—	30	2	no	—
259	#131	—	3	4	no	—
260	#131	—	6	2	no	—
261	C₂×M₁₆	—	3	1	no	—
262	C₂×M₁₆	—	6	1	no	—
263	C₂×M₁₆	—	15	2	no	—
264	C₂²×C₈	—	6	1	no	—
265	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
266	#108	—	15	4	no	—
267	#101	—	15	8	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	#473	1	2	yes	complemented
271	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
272	C₅×D₃	—	4	2	no	—
273	C₂³×C₃	#709	1	1	yes	characteristic
274	C₂²×D₃	—	2	1	no	—
275	C₃×Q₈	—	10	4	no	—
276	C₃×Q₈	—	10	4	no	—
277	C₃×Q₈	—	20	2	no	—
278	C₃×Q₈	—	20	2	no	—
279	C₂×C₃×C₄	—	10	4	no	—
280	C₂×C₃×C₄	—	20	2	no	—
281	C₂×C₃×C₄	—	20	2	no	—
282	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
284	C₂×C₃×C₄	#709	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	#67	—	2	2	no	—
289	#67	—	2	2	no	—
290	C₂×Dic₃	—	2	1	no	—
291	D₁₂	—	2	1	no	—
292	D₁₂	C₂×D₂₀	1	2	yes	—
293	C₄×D₃	—	2	2	no	—
294	C₄×D₃	—	2	2	no	—
295	Dic₆	—	2	1	no	—
296	Dic₆	C₂×D₂₀	1	2	yes	—
297	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
298	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
299	C₃⋊C₈	—	2	2	no	—
300	C₃⋊C₈	—	10	4	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	#938	1	1	yes	characteristic
305	C₂²×C₅	#938	1	1	yes	characteristic
306	C₂²×C₅	C₂×#237	1	1	yes	characteristic
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	#938	1	1	yes	characteristic
309	C₄×C₅	#938	1	1	yes	characteristic
310	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
311	C₄×C₅	C₂²×#67	1	1	yes	characteristic
312	Dic₅	—	4	4	no	—
313	#41	—	3	2	no	—
314	#41	—	3	2	no	—
315	#41	—	6	1	no	—
316	#41	—	6	1	no	—
317	C₂×Q₈	—	3	1	no	—
318	C₂×Q₈	—	5	4	no	—
319	C₂×Q₈	—	10	2	no	—
320	C₂×Q₈	—	10	2	no	—
321	C₂×Q₈	—	10	2	no	—
322	C₂×Q₈	—	10	2	no	—
323	C₂×Q₈	—	10	2	no	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂²×C₄	—	6	1	no	—
327	C₂²×C₄	—	10	2	no	—
328	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
329	Q₁₆	—	10	4	no	—
330	Q₁₆	—	10	4	no	—
331	Q₁₆	—	30	8	no	—
332	SD₁₆	—	30	8	no	—
333	M₁₆	—	3	2	no	—
334	M₁₆	—	6	1	no	—
335	M₁₆	—	6	4	no	—
336	M₁₆	—	15	4	no	—
337	M₁₆	—	30	2	no	—
338	C₂×C₈	—	6	1	no	—
339	C₂×C₈	—	6	4	no	—
340	C₂×C₈	—	30	2	no	—
341	C₂×C₈	#1201	1	1	yes	characteristic
342	C₂×C₈	#1201	1	1	yes	characteristic
343	C₂×C₈	#1201	1	2	yes	—
344	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	#4076	1	1	yes	characteristic
348	C₂²×C₃	#4076	1	1	yes	characteristic
349	C₂²×C₃	C₂×#709	1	1	yes	characteristic
350	C₂×D₃	—	2	2	no	—
351	C₂×D₃	—	4	2	no	—
352	C₃×C₄	—	20	4	no	—
353	C₃×C₄	#4076	1	1	yes	characteristic
354	C₃×C₄	#4076	1	1	yes	characteristic
355	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
356	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
357	Dic₃	—	2	2	no	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	12	2	no	—
361	C₂×C₅	#5192	1	2	yes	complemented
362	C₂×C₅	C₂×#938	1	1	yes	characteristic
363	C₂³	—	6	1	no	—
364	C₂³	#6765	1	1	yes	characteristic
365	Q₈	—	3	2	no	—
366	Q₈	—	6	1	no	—
367	Q₈	—	10	4	no	—
368	Q₈	—	10	4	no	—
369	Q₈	—	20	2	no	—
370	Q₈	—	20	2	no	—
371	D₄	—	3	2	no	—
372	D₄	—	6	2	no	—
373	D₄	—	6	2	no	—
374	D₄	—	6	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	10	4	no	—
379	C₂×C₄	—	20	2	no	—
380	C₂×C₄	—	20	2	no	—
381	C₂×C₄	#6765	1	1	yes	characteristic
382	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
383	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
384	C₂×C₄	C₂×#1201	1	1	yes	characteristic
385	C₂×C₄	C₂×#1201	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
387	C₈	—	6	2	no	—
388	C₈	—	30	4	no	—
389	C₈	C₂×#1201	1	2	yes	—
390	C₈	C₂×#1201	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	#65432	1	2	yes	complemented
394	C₂×C₃	C₂×#4076	1	1	yes	characteristic
395	D₃	—	4	2	no	—
396	C₅	C₂×#5192	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	6	2	no	—
399	C₂²	—	12	2	no	—
400	C₂²	#91456	1	1	yes	characteristic
401	C₂²	#91456	1	1	yes	characteristic
402	C₂²	C₂×#6765	1	1	yes	characteristic
403	C₄	—	6	2	no	—
404	C₄	—	20	4	no	—
405	C₄	#91456	1	1	yes	characteristic
406	C₄	#91456	1	1	yes	characteristic
407	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
408	C₄	C₂²×#1201	1	1	yes	characteristic
409	C₃	C₂×#65432	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	12	2	no	—
413	C₂	#11748094	1	2	yes	direct product factor
414	C₂	C₂×#91456	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#91456
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#473
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₂₀	C₂	semidirect
4. C₂×#91103	C₂	semidirect
5. C₂×#90961	C₂	semidirect
6. #11748094	C₂	direct (N × H)
20. C₂×C₃×Dic₂₀	C₂²	semidirect
25. #91103	C₂²	semidirect
26. #90961	C₂²	semidirect
30. C₂²×Dic₂₀	D₃	semidirect
88. C₂×Dic₂₀	C₂×D₃	semidirect
270. C₂×C₃×C₅	#473	semidirect
345. C₃×C₅	C₂×#473	semidirect
361. C₂×C₅	#5192	semidirect
393. C₂×C₃	#65432	semidirect
396. C₅	C₂×#5192	semidirect
409. C₃	C₂×#65432	semidirect
413. C₂	#11748094	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×C₅×#901	2
C₂²×C₃×Dic₂₀	2
C₂×#91309	2
C₂×#91103	2
C₂×#90961	2
#11748094	2
C₂×#65432	3
C₂×#5192	5

Subgroups — C2×#11748094 #14429462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748094 #14429462