Subgroups — #14281941

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752499	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746304	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64704	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745840	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745839	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601220	—	3	1	no	maximal, Hall
9	C₄×D₆₀	C₂²	1	1	yes	characteristic
10	C₂×C₅×D₃×C₈	—	2	1	no	—
11	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
13	#91460	C₄	1	1	yes	characteristic
14	C₄×#1203	—	2	1	no	—
15	#91386	—	2	1	no	—
16	#91381	C₄	1	1	yes	characteristic
17	#91380	—	2	1	no	—
18	#91374	C₄	1	1	yes	characteristic
19	#91369	C₄	1	1	yes	characteristic
20	#91351	—	2	1	no	—
21	C₂×#6650	—	2	1	no	—
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₃×C₄×#168	C₂²	1	1	yes	characteristic
27	#90953	—	2	1	no	—
28	#68234	—	5	1	no	maximal, Hall
29	#65813	—	3	1	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₄×#681	—	3	1	no	—
32	#64704	—	3	1	no	—
33	#64704	D₃	1	1	yes	characteristic, complemented
34	#64703	—	3	1	no	—
35	#64703	—	3	1	no	—
36	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₅	—	2	1	no	—
38	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
42	C₂×#1203	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
45	#6714	—	2	1	no	—
46	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃⋊#168	—	2	1	no	—
48	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
50	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
51	C₂×C₅×C₃⋊C₈	—	2	1	no	—
52	C₅×D₃×C₈	—	4	2	no	—
53	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
54	C₃×#683	—	2	1	no	—
55	C₃×C₄×Dic₅	—	2	1	no	—
56	C₂×C₃×#168	—	2	1	no	—
57	#6669	—	2	1	no	—
58	#6669	—	2	1	no	—
59	#6668	—	2	1	no	—
60	#6667	—	2	1	no	—
61	#6667	—	2	1	no	—
62	#6667	—	2	1	no	—
63	(C₂×D₃)⋊Dic₅	—	2	1	no	—
64	#6650	—	2	4	no	—
65	#5580	—	5	1	no	—
66	D₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
67	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
68	C₃×Q₈⋊C₈	—	5	1	no	—
69	#4535	—	5	1	no	—
70	#4483	—	5	1	no	—
71	#4459	—	5	1	no	—
72	C₂²×C₅×C₈	—	6	1	no	—
73	C₂×C₄²×C₅	—	3	1	no	—
74	#4076	—	3	1	no	—
75	#4075	—	6	1	no	—
76	C₄×C₂²⋊D₅	—	6	1	no	—
77	#4070	—	3	1	no	—
78	C₂×#681	—	6	1	no	—
79	#4022	—	6	1	no	—
80	#4021	—	3	1	no	—
81	C₄×D₂₀	—	3	1	no	—
82	#4018	—	6	1	no	—
83	#4016	—	3	1	no	—
84	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
85	C₅×C₄⋊C₈	—	3	1	no	—
86	C₅×C₄⋊C₈	—	6	1	no	—
87	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
88	#3935	—	6	1	no	—
89	C₄×#168	—	3	1	no	—
90	C₄×#168	C₂×D₃	1	1	yes	characteristic
91	#1483	—	15	1	no	Sylow
92	C₂²×D₁₅	—	2	1	no	—
93	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	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×Dic₁₅	—	2	1	no	—
98	D₆₀	—	2	1	no	—
99	D₆₀	—	2	1	no	—
100	C₄×D₁₅	—	4	1	no	—
101	C₄×D₁₅	—	4	1	no	—
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	1	no	—
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₂×C₃×Dic₅	—	2	1	no	—
111	C₂×C₃×Dic₅	—	2	1	no	—
112	C₃×Dic₁₀	—	2	1	no	—
113	C₃×Dic₁₀	—	2	1	no	—
114	#1203	—	4	2	no	—
115	C₃×C₅×C₈	—	4	1	no	—
116	C₃⋊#168	—	2	2	no	—
117	C₃×#168	—	2	2	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₃×C₄×Q₈	—	5	1	no	—
120	#947	—	5	1	no	—
121	#946	—	5	1	no	—
122	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
123	C₂×D₃×C₈	—	2	1	no	—
124	#898	—	10	1	no	—
125	#895	—	5	1	no	—
126	#894	—	10	1	no	—
127	#890	—	5	1	no	—
128	C₄×D₁₂	—	5	1	no	—
129	C₄×D₁₂	—	10	1	no	—
130	#872	—	10	1	no	—
131	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
132	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
133	C₃×C₄×C₈	—	5	1	no	—
134	#815	—	10	1	no	—
135	Dic₃⋊C₈	—	2	1	no	—
136	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
137	C₄×C₃⋊C₈	—	5	1	no	—
138	C₂²×C₄×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂×C₂²⋊D₅	—	6	1	no	—
142	C₂×D₂₀	—	3	1	no	—
143	C₂×C₄×D₅	—	6	1	no	—
144	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₂×C₅×C₈	—	12	2	no	—
148	C₄²×C₅	—	3	1	no	—
149	C₄²×C₅	—	3	1	no	—
150	C₄²×C₅	—	3	1	no	—
151	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²⋊Dic₅	—	6	1	no	—
153	#685	—	6	1	no	—
154	#685	—	6	1	no	—
155	#685	—	6	1	no	—
156	#685	—	6	1	no	—
157	C₄⋊Dic₅	—	3	1	no	—
158	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
159	#683	—	2	1	no	—
160	#683	—	6	1	no	—
161	#683	—	6	1	no	—
162	#683	—	6	1	no	—
163	C₄×Dic₅	—	2	1	no	—
164	#681	—	6	4	no	—
165	C₂×#168	—	2	1	no	—
166	C₂×#168	—	6	1	no	—
167	#529	—	15	1	no	—
168	C₂×C₄⋊C₈	—	3	1	no	—
169	C₄×M₁₆	—	15	1	no	—
170	Q₈⋊C₈	—	5	1	no	—
171	Q₈⋊C₈	—	15	1	no	—
172	D₄⋊C₈	—	15	1	no	—
173	D₄⋊C₈	—	15	1	no	—
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×D₁₅	—	4	1	no	—
176	C₂×D₁₅	—	4	1	no	—
177	C₂×D₁₅	—	4	1	no	—
178	C₂×C₅×D₃	—	2	1	no	—
179	C₂×C₅×D₃	—	2	1	no	—
180	C₂×C₅×D₃	#104	1	2	yes	—
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	#131	1	1	yes	characteristic
183	C₃×C₄×C₅	#131	1	1	yes	characteristic
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₃×C₄×C₅	#137	1	1	yes	characteristic
186	Dic₁₅	—	4	1	no	—
187	C₃×Dic₅	—	4	1	no	—
188	C₃×Dic₅	—	4	1	no	—
189	C₅×Dic₃	—	2	1	no	—
190	C₅×Dic₃	—	2	1	no	—
191	C₅×Dic₃	—	2	1	no	—
192	C₂×C₃×Q₈	—	5	1	no	—
193	C₂×D₁₂	—	5	1	no	—
194	C₂×D₁₂	—	10	1	no	—
195	C₂×C₄×D₃	—	10	1	no	—
196	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
197	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
198	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	—	10	1	no	—
201	C₃×C₄⋊C₄	—	5	1	no	—
202	C₃×C₄⋊C₄	—	10	1	no	—
203	C₃×C₄²	—	10	1	no	—
204	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	—	10	1	no	—
206	(C₂×D₃)⋊C₄	—	10	1	no	—
207	(C₂×D₃)⋊C₄	—	10	1	no	—
208	(C₂×D₃)⋊C₄	—	10	1	no	—
209	(C₂×D₃)⋊C₄	—	10	1	no	—
210	C₄⋊Dic₃	—	5	1	no	—
211	C₄⋊Dic₃	—	10	1	no	—
212	Dic₃⋊C₄	—	10	1	no	—
213	Dic₃⋊C₄	—	10	1	no	—
214	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
215	C₄×Dic₃	D₂₀	1	1	yes	characteristic
216	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	10	1	no	—
219	ΓL(1,𝔽₂₅)	—	10	4	no	—
220	D₃×C₈	—	4	2	no	—
221	C₂³×C₅	—	3	1	no	—
222	C₂²×D₅	—	6	1	no	—
223	C₂×C₄×C₅	—	3	1	no	—
224	C₂×C₄×C₅	—	3	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	1	no	—
228	C₂×C₄×C₅	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	1	no	—
231	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
234	C₂²⋊D₅	—	12	2	no	—
235	C₂×Dic₅	—	2	1	no	—
236	C₂×Dic₅	—	2	1	no	—
237	C₂×Dic₅	—	6	1	no	—
238	D₂₀	—	6	1	no	—
239	D₂₀	—	6	1	no	—
240	C₄×D₅	—	12	1	no	—
241	C₄×D₅	—	12	1	no	—
242	Dic₁₀	—	2	1	no	—
243	Dic₁₀	—	2	1	no	—
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	12	1	no	—
246	#168	—	2	2	no	—
247	#168	—	6	2	no	—
248	C₂×M₁₆	—	30	1	no	—
249	C₂²×C₈	—	6	1	no	—
250	#126	—	30	1	no	—
251	#125	—	15	1	no	—
252	#124	—	15	1	no	—
253	#123	—	30	1	no	—
254	C₂²⋊Q₈	—	15	1	no	—
255	#121	—	15	1	no	—
256	C₄×Q₈	—	5	1	no	—
257	C₄×D₄	—	15	1	no	—
258	C₄×D₄	—	30	1	no	—
259	#117	—	30	1	no	—
260	C₂×C₄²	—	3	1	no	—
261	C₄⋊C₈	—	3	1	no	—
262	C₄⋊C₈	—	6	1	no	—
263	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
264	#97	—	30	1	no	—
265	C₄×C₈	—	5	1	no	—
266	C₄×C₈	—	15	1	no	—
267	C₂×C₃×C₅	#408	1	1	yes	characteristic
268	C₂×C₃×C₅	#417	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
270	D₁₅	—	8	1	no	—
271	C₅×D₃	—	2	2	no	—
272	C₂²×D₃	—	10	1	no	—
273	C₂²×D₃	#685	1	1	yes	characteristic
274	C₃×Q₈	—	10	1	no	—
275	C₃×Q₈	—	10	1	no	—
276	C₂×C₃×C₄	—	10	1	no	—
277	C₂×C₃×C₄	—	10	1	no	—
278	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×Dic₃	—	10	1	no	—
282	C₂×Dic₃	#685	1	1	yes	characteristic
283	C₂×Dic₃	#685	1	1	yes	characteristic
284	C₂×Dic₃	#685	1	1	yes	characteristic
285	D₁₂	—	10	1	no	—
286	D₁₂	—	10	1	no	—
287	D₁₂	—	20	2	no	—
288	C₄×D₃	—	2	2	no	—
289	C₄×D₃	—	2	1	no	—
290	C₄×D₃	—	2	1	no	—
291	C₄×D₃	—	2	1	no	—
292	C₄×D₃	—	2	1	no	—
293	C₄×D₃	—	20	1	no	—
294	C₄×D₃	—	20	1	no	—
295	C₃×C₈	—	4	1	no	—
296	C₃×C₈	—	10	2	no	—
297	C₃⋊C₈	—	4	1	no	—
298	C₃⋊C₈	—	10	2	no	—
299	C₂²×C₅	—	3	2	no	—
300	C₂²×C₅	—	6	1	no	—
301	C₂²×C₅	—	6	1	no	—
302	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×D₅	—	12	1	no	—
304	C₂×D₅	—	12	1	no	—
305	C₂×D₅	—	12	1	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	6	1	no	—
308	C₄×C₅	—	6	1	no	—
309	C₄×C₅	—	6	1	no	—
310	C₄×C₅	#901	1	1	yes	characteristic
311	C₄×C₅	#907	1	1	yes	characteristic
312	C₄×C₅	#914	1	1	yes	characteristic
313	C₄×C₅	#918	1	1	yes	characteristic
314	Dic₅	—	4	1	no	—
315	Dic₅	—	4	1	no	—
316	Dic₅	—	12	1	no	—
317	C₂×Q₈	—	5	1	no	—
318	C₂×D₄	—	15	1	no	—
319	C₂×D₄	—	30	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	3	1	no	—
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	30	1	no	—
324	M₁₆	—	30	4	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	6	1	no	—
327	C₂×C₈	—	10	1	no	—
328	C₂×C₈	—	12	2	no	—
329	C₂×C₈	—	30	1	no	—
330	C₄⋊C₄	—	5	1	no	—
331	C₄⋊C₄	—	10	1	no	—
332	C₄⋊C₄	—	15	1	no	—
333	C₄⋊C₄	—	30	1	no	—
334	C₄⋊C₄	—	30	1	no	—
335	C₄⋊C₄	—	30	1	no	—
336	C₂²⋊C₄	—	30	1	no	—
337	C₂²⋊C₄	—	30	1	no	—
338	C₂²⋊C₄	—	30	1	no	—
339	C₂²⋊C₄	—	30	1	no	—
340	C₂²⋊C₄	—	30	1	no	—
341	C₄²	—	3	1	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	3	1	no	—
344	C₄²	—	10	1	no	—
345	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
346	C₃×C₅	#1483	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	C₂×#685	1	1	yes	characteristic
348	C₂×D₃	—	2	1	no	—
349	C₂×D₃	—	2	1	no	—
350	C₂×D₃	—	20	1	no	—
351	C₂×D₃	—	20	1	no	—
352	C₂×D₃	—	20	1	no	—
353	C₂×D₃	#3957	1	2	yes	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	20	1	no	—
356	C₃×C₄	—	20	1	no	—
357	C₃×C₄	#4047	1	1	yes	characteristic
358	C₃×C₄	#4047	1	1	yes	characteristic
359	C₃×C₄	#4078	1	1	yes	characteristic
360	C₃×C₄	#4088	1	1	yes	characteristic
361	Dic₃	—	2	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	—	20	1	no	—
365	C₂×C₅	—	6	2	no	—
366	C₂×C₅	#4727	1	1	yes	characteristic
367	C₂×C₅	#4803	1	1	yes	characteristic
368	C₂×C₅	D₃×#104	1	1	yes	characteristic
369	D₅	—	24	1	no	—
370	C₂³	—	3	1	no	—
371	C₂³	—	30	1	no	—
372	Q₈	—	10	1	no	—
373	Q₈	—	10	1	no	—
374	D₄	—	30	1	no	—
375	D₄	—	30	1	no	—
376	D₄	—	60	2	no	—
377	C₂×C₄	—	3	1	no	—
378	C₂×C₄	—	3	1	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	10	1	no	—
386	C₂×C₄	—	10	1	no	—
387	C₂×C₄	—	30	1	no	—
388	C₂×C₄	—	60	1	no	—
389	C₂×C₄	—	60	1	no	—
390	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
391	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
392	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
393	C₈	—	4	1	no	—
394	C₈	—	10	2	no	—
395	C₈	—	12	1	no	—
396	C₈	—	30	2	no	—
397	C₂×C₃	#65255	1	1	yes	characteristic
398	C₂×C₃	#65399	1	1	yes	characteristic
399	C₂×C₃	C₂×#3957	1	1	yes	characteristic
400	D₃	—	2	2	no	—
401	D₃	—	40	1	no	—
402	C₅	#68234	1	1	yes	characteristic, complemented, Sylow
403	C₂²	—	3	2	no	—
404	C₂²	—	6	1	no	—
405	C₂²	—	6	1	no	—
406	C₂²	—	60	1	no	—
407	C₂²	—	60	1	no	—
408	C₂²	—	60	1	no	—
409	C₂²	D₃×#685	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	6	1	no	—
412	C₄	—	6	1	no	—
413	C₄	—	6	1	no	—
414	C₄	—	20	1	no	—
415	C₄	—	20	1	no	—
416	C₄	—	60	1	no	—
417	C₄	#91265	1	1	yes	characteristic
418	C₄	#91267	1	1	yes	characteristic
419	C₄	#91496	1	1	yes	characteristic
420	C₄	#91520	1	1	yes	characteristic
421	C₃	#10601220	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	6	2	no	—
423	C₂	—	120	1	no	—
424	C₂	#11747505	1	1	yes	characteristic
425	C₂	#11748139	1	1	yes	characteristic
426	C₂	D₃×#3957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₅×C₄⋊C₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	#91460	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	#1483
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₅×D₃×C₄⋊C₈	C₂	semidirect
3. C₄×#6650	C₂	semidirect
4. #11746304	C₂	semidirect
5. C₃×#64704	C₂	semidirect
6. #11745840	C₂	semidirect
7. #11745839	C₂	semidirect
33. #64704	D₃	semidirect
66. D₃×C₄⋊C₈	D₅	semidirect
346. C₃×C₅	#1483	semidirect
402. C₅	#68234	semidirect
421. C₃	#10601220	semidirect

Maximal subgroups

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

subgroup	index
#11752499	2
C₅×D₃×C₄⋊C₈	2
C₄×#6650	2
#11746304	2
C₃×#64704	2
#11745840	2
#11745839	2
#10601220	3
#68234	5