Subgroups — C₃×#66107 #11755784

Order 960.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4062	C₂	1	2	yes	maximal, complemented
7	C₃×#4061	C₂	1	2	yes	maximal, complemented
8	C₃×#4058	C₂	1	2	yes	maximal, complemented
9	C₃×#4057	C₂	1	2	yes	maximal, complemented
10	C₃×#4055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#66107	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
16	C₂²×C₃×Dic₅	—	2	1	no	—
17	C₃×#713	C₂²	1	1	yes	characteristic, complemented
18	C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
19	C₃×#711	—	2	1	no	—
20	C₃×#711	—	2	1	no	—
21	C₃×#711	—	2	1	no	—
22	C₃×#711	C₂²	1	2	yes	—
23	C₃×#711	C₂²	1	2	yes	complemented
24	C₃×#711	C₂²	1	1	yes	characteristic, complemented
25	C₃×D₄×D₅	—	2	1	no	—
26	C₃×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₃×#709	—	2	1	no	—
28	C₃×#709	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₅	—	2	1	no	—
30	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
33	C₃×C₅×D₈	C₂²	1	2	yes	complemented
34	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₃×#689	C₂²	1	2	yes	complemented
36	C₃×#687	C₂²	1	2	yes	complemented
37	C₃×#687	C₂²	1	2	yes	complemented
38	C₃×#686	C₂²	1	2	yes	complemented
39	C₃×#681	C₂²	1	1	yes	characteristic, complemented
40	C₃×Dic₂₀	C₂²	1	2	yes	complemented
41	C₃×#677	C₂²	1	2	yes	complemented
42	C₃×#676	C₂²	1	2	yes	complemented
43	C₃×C₈×D₅	C₂²	1	2	yes	complemented
44	C₃×#575	—	5	1	no	maximal, Hall
45	D₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#711	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
48	#4097	C₂×C₃	1	1	yes	characteristic, complemented
49	#4078	C₂×C₃	1	1	yes	characteristic, complemented
50	#4062	C₂×C₃	1	2	yes	complemented
51	#4061	C₂×C₃	1	2	yes	complemented
52	#4058	C₂×C₃	1	2	yes	complemented
53	#4057	C₂×C₃	1	2	yes	complemented
54	#4055	C₂×C₃	1	1	yes	characteristic, complemented
55	D₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂³×C₃×C₅	—	2	1	no	—
57	C₂²×C₃×D₅	—	2	1	no	—
58	C₂²×C₃×D₅	D₄	1	1	yes	characteristic
59	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₃×C₅×D₄	—	2	1	no	—
61	C₃×C₅×D₄	—	2	1	no	—
62	C₃×C₅×D₄	C₂³	1	2	yes	—
63	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	—	2	1	no	—
65	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₂²⋊D₅	—	2	1	no	—
67	C₃×C₂²⋊D₅	—	2	1	no	—
68	C₃×C₂²⋊D₅	—	2	2	no	—
69	C₃×C₂²⋊D₅	—	2	2	no	—
70	C₃×C₂²⋊D₅	—	2	1	no	—
71	C₂×C₃×Dic₅	—	2	1	no	—
72	C₂×C₃×Dic₅	—	2	1	no	—
73	C₂×C₃×Dic₅	—	2	2	no	—
74	C₂×C₃×Dic₅	—	2	2	no	—
75	C₂×C₃×Dic₅	D₄	1	1	yes	characteristic
76	C₃×D₂₀	—	2	1	no	—
77	C₃×D₂₀	C₂³	1	1	yes	characteristic
78	C₃×C₄×D₅	—	2	1	no	—
79	C₃×C₄×D₅	—	2	1	no	—
80	C₃×C₄×D₅	—	2	1	no	—
81	C₃×C₄×D₅	D₄	1	1	yes	characteristic
82	C₃×C₄×D₅	D₄	1	1	yes	characteristic
83	C₃×C₄×D₅	C₂³	1	1	yes	characteristic
84	C₃×C₄×D₅	C₂³	1	1	yes	characteristic
85	C₃×Dic₁₀	—	2	1	no	—
86	C₃×Dic₁₀	—	2	1	no	—
87	C₃×Dic₁₀	C₂³	1	2	yes	—
88	C₃×Dic₁₀	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₃×#168	C₂³	1	2	yes	—
91	C₂×C₃×#41	—	5	1	no	—
92	C₂×C₃×#41	—	5	1	no	—
93	C₃×#137	—	5	1	no	—
94	C₃×#137	—	5	2	no	—
95	C₃×#137	—	5	1	no	—
96	C₃×AGL(1,ℤ/8)	—	5	1	no	—
97	C₃×AGL(1,ℤ/8)	—	5	2	no	—
98	C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
99	C₃×#135	—	5	2	no	—
100	C₃×#135	—	5	2	no	—
101	C₂×C₃×M₁₆	—	5	1	no	—
102	C₅×#41	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊D₅	—	2	1	no	—
105	C₂²×Dic₅	—	2	1	no	—
106	#713	C₂²×C₃	1	1	yes	characteristic, complemented
107	Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
108	#711	—	2	1	no	—
109	#711	—	2	1	no	—
110	#711	—	2	1	no	—
111	#711	C₂²×C₃	1	2	yes	—
112	#711	C₂²×C₃	1	2	yes	complemented
113	#711	C₂²×C₃	1	1	yes	characteristic, complemented
114	D₄×D₅	—	2	1	no	—
115	D₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
116	#709	—	2	1	no	—
117	#709	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×D₅	—	2	1	no	—
119	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
122	C₅×D₈	C₂²×C₃	1	2	yes	complemented
123	C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
124	#689	C₂²×C₃	1	2	yes	complemented
125	#687	C₂²×C₃	1	2	yes	complemented
126	#687	C₂²×C₃	1	2	yes	complemented
127	#686	C₂²×C₃	1	2	yes	complemented
128	#681	C₂²×C₃	1	1	yes	characteristic, complemented
129	Dic₂₀	C₂²×C₃	1	2	yes	complemented
130	#677	C₂²×C₃	1	2	yes	complemented
131	#676	C₂²×C₃	1	2	yes	complemented
132	C₈×D₅	C₂²×C₃	1	2	yes	complemented
133	#575	—	5	1	no	Sylow
134	C₂²×C₃×C₅	—	2	2	no	—
135	C₂²×C₃×C₅	—	2	1	no	—
136	C₂²×C₃×C₅	—	4	2	no	—
137	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×D₅	—	2	1	no	—
139	C₂×C₃×D₅	—	4	1	no	—
140	C₂×C₃×D₅	—	4	2	no	—
141	C₂×C₃×D₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×D₅	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×Dic₅	—	2	1	no	—
147	C₃×Dic₅	—	2	2	no	—
148	C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
149	C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
150	C₃×#41	—	5	1	no	—
151	C₃×#41	—	5	2	no	—
152	C₃×#41	—	5	2	no	—
153	C₃×#41	—	5	1	no	—
154	C₃×#41	—	5	1	no	—
155	C₃×#41	—	10	1	no	—
156	C₃×#41	—	10	1	no	—
157	C₃×#41	—	10	1	no	—
158	C₃×#41	—	10	1	no	—
159	C₃×#41	C₂×D₅	1	1	yes	characteristic
160	C₂×C₃×Q₈	—	5	1	no	—
161	C₂×C₃×Q₈	—	5	1	no	—
162	C₂×C₃×D₄	—	5	1	no	—
163	C₂×C₃×D₄	—	10	1	no	—
164	C₂×C₃×D₄	—	10	1	no	—
165	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	10	1	no	—
168	C₂²×C₃×C₄	—	10	1	no	—
169	C₃×Q₁₆	—	5	2	no	—
170	C₃×Q₁₆	—	5	2	no	—
171	C₃×SD₁₆	—	5	2	no	—
172	C₃×SD₁₆	—	5	2	no	—
173	C₃×SD₁₆	—	5	2	no	—
174	C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
175	C₃×D₈	—	5	2	no	—
176	C₃×D₈	C₂×D₅	1	2	yes	complemented
177	C₃×M₁₆	—	5	1	no	—
178	C₃×M₁₆	—	5	2	no	—
179	C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
180	C₂×C₃×C₈	—	5	2	no	—
181	C₂³×C₅	—	2	1	no	—
182	C₂²×D₅	—	2	1	no	—
183	C₂²×D₅	C₃×D₄	1	1	yes	characteristic
184	C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
185	C₅×D₄	—	2	1	no	—
186	C₅×D₄	—	2	1	no	—
187	C₅×D₄	C₂³×C₃	1	2	yes	—
188	C₅×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂²⋊D₅	—	2	1	no	—
192	C₂²⋊D₅	—	2	1	no	—
193	C₂²⋊D₅	—	2	2	no	—
194	C₂²⋊D₅	—	2	2	no	—
195	C₂²⋊D₅	—	2	1	no	—
196	C₂×Dic₅	—	2	1	no	—
197	C₂×Dic₅	—	2	1	no	—
198	C₂×Dic₅	—	2	2	no	—
199	C₂×Dic₅	—	2	2	no	—
200	C₂×Dic₅	C₃×D₄	1	1	yes	characteristic
201	D₂₀	—	2	1	no	—
202	D₂₀	C₂³×C₃	1	1	yes	characteristic
203	C₄×D₅	—	2	1	no	—
204	C₄×D₅	—	2	1	no	—
205	C₄×D₅	—	2	1	no	—
206	C₄×D₅	C₃×D₄	1	1	yes	characteristic
207	C₄×D₅	C₃×D₄	1	1	yes	characteristic
208	C₄×D₅	C₂³×C₃	1	1	yes	characteristic
209	C₄×D₅	C₂³×C₃	1	1	yes	characteristic
210	Dic₁₀	—	2	1	no	—
211	Dic₁₀	—	2	1	no	—
212	Dic₁₀	C₂³×C₃	1	2	yes	—
213	Dic₁₀	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₈	C₂³×C₃	1	2	yes	—
215	#168	C₂³×C₃	1	2	yes	—
216	C₂×#41	—	5	1	no	—
217	C₂×#41	—	5	1	no	—
218	#137	—	5	1	no	—
219	#137	—	5	2	no	—
220	#137	—	5	1	no	—
221	AGL(1,ℤ/8)	—	5	1	no	—
222	AGL(1,ℤ/8)	—	5	2	no	—
223	AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
224	#135	—	5	2	no	—
225	#135	—	5	2	no	—
226	C₂×M₁₆	—	5	1	no	—
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	4	1	no	—
229	C₂×C₃×C₅	—	4	2	no	—
230	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₃×D₅	—	2	1	no	—
232	C₃×D₅	—	2	1	no	—
233	C₃×D₅	—	4	1	no	—
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	5	1	no	—
236	C₂³×C₃	—	10	1	no	—
237	C₃×Q₈	—	5	2	no	—
238	C₃×Q₈	—	5	1	no	—
239	C₃×Q₈	—	10	1	no	—
240	C₃×Q₈	—	10	1	no	—
241	C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
242	C₃×D₄	—	2	1	no	—
243	C₃×D₄	—	2	1	no	—
244	C₃×D₄	—	5	1	no	—
245	C₃×D₄	—	10	1	no	—
246	C₃×D₄	—	10	1	no	—
247	C₃×D₄	—	10	1	no	—
248	C₃×D₄	—	10	2	no	—
249	C₃×D₄	—	10	2	no	—
250	C₃×D₄	—	10	1	no	—
251	C₃×D₄	C₂²×D₅	1	2	yes	—
252	C₃×D₄	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	1	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	10	1	no	—
260	C₂×C₃×C₄	—	10	1	no	—
261	C₂×C₃×C₄	—	10	1	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	2	no	—
264	C₂×C₃×C₄	—	10	1	no	—
265	C₂×C₃×C₄	—	10	1	no	—
266	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₃×C₈	—	5	2	no	—
268	C₃×C₈	C₂²×D₅	1	2	yes	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×D₅	—	2	1	no	—
274	C₂×D₅	—	4	1	no	—
275	C₂×D₅	—	4	2	no	—
276	C₂×D₅	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×D₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
281	Dic₅	—	2	1	no	—
282	Dic₅	—	2	2	no	—
283	Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
284	Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
285	#41	—	5	1	no	—
286	#41	—	5	2	no	—
287	#41	—	5	1	no	—
288	#41	—	5	2	no	—
289	#41	—	5	1	no	—
290	#41	—	10	1	no	—
291	#41	—	10	1	no	—
292	#41	—	10	1	no	—
293	#41	—	10	1	no	—
294	#41	C₂×C₃×D₅	1	1	yes	characteristic
295	C₂×Q₈	—	5	1	no	—
296	C₂×Q₈	—	5	1	no	—
297	C₂×D₄	—	5	1	no	—
298	C₂×D₄	—	10	1	no	—
299	C₂×D₄	—	10	1	no	—
300	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	10	1	no	—
303	C₂²×C₄	—	10	1	no	—
304	Q₁₆	—	5	2	no	—
305	Q₁₆	—	5	2	no	—
306	SD₁₆	—	5	2	no	—
307	SD₁₆	—	5	2	no	—
308	SD₁₆	—	5	2	no	—
309	SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
310	D₈	—	5	2	no	—
311	D₈	C₂×C₃×D₅	1	2	yes	complemented
312	M₁₆	—	5	1	no	—
313	M₁₆	—	5	2	no	—
314	M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
315	C₂×C₈	—	5	2	no	—
316	C₃×C₅	#575	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	5	1	no	—
321	C₂²×C₃	—	5	1	no	—
322	C₂²×C₃	—	10	1	no	—
323	C₂²×C₃	—	20	1	no	—
324	C₂²×C₃	—	20	2	no	—
325	C₂²×C₃	D₄×D₅	1	1	yes	characteristic
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	5	1	no	—
328	C₃×C₄	—	5	1	no	—
329	C₃×C₄	—	10	1	no	—
330	C₃×C₄	—	10	2	no	—
331	C₃×C₄	D₄×D₅	1	1	yes	characteristic
332	C₃×C₄	C₂³×D₅	1	1	yes	characteristic
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	4	1	no	—
335	C₂×C₅	—	4	2	no	—
336	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
337	D₅	—	2	1	no	—
338	D₅	—	2	1	no	—
339	D₅	—	4	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	5	1	no	—
342	C₂³	—	10	1	no	—
343	Q₈	—	5	1	no	—
344	Q₈	—	5	2	no	—
345	Q₈	—	10	1	no	—
346	Q₈	—	10	1	no	—
347	Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	5	1	no	—
351	D₄	—	10	1	no	—
352	D₄	—	10	1	no	—
353	D₄	—	10	1	no	—
354	D₄	—	10	2	no	—
355	D₄	—	10	2	no	—
356	D₄	—	10	1	no	—
357	D₄	C₂²×C₃×D₅	1	2	yes	—
358	D₄	C₂²×C₃×D₅	1	1	yes	characteristic
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	5	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	5	1	no	—
364	C₂×C₄	—	5	1	no	—
365	C₂×C₄	—	10	1	no	—
366	C₂×C₄	—	10	1	no	—
367	C₂×C₄	—	10	1	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	—	10	1	no	—
372	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₈	—	5	2	no	—
374	C₈	C₂²×C₃×D₅	1	2	yes	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	4	2	no	—
377	C₂×C₃	—	4	1	no	—
378	C₂×C₃	—	10	1	no	—
379	C₂×C₃	—	10	1	no	—
380	C₂×C₃	—	20	1	no	—
381	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
382	C₅	C₃×#575	1	1	yes	characteristic, complemented, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	5	1	no	—
387	C₂²	—	5	1	no	—
388	C₂²	—	10	1	no	—
389	C₂²	—	20	1	no	—
390	C₂²	—	20	2	no	—
391	C₂²	C₃×D₄×D₅	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	5	1	no	—
394	C₄	—	5	1	no	—
395	C₄	—	10	1	no	—
396	C₄	—	10	2	no	—
397	C₄	C₃×D₄×D₅	1	1	yes	characteristic
398	C₄	C₂³×C₃×D₅	1	1	yes	characteristic
399	C₃	#66107	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	2	1	no	—
401	C₂	—	4	2	no	—
402	C₂	—	4	1	no	—
403	C₂	—	10	1	no	—
404	C₂	—	10	1	no	—
405	C₂	—	20	1	no	—
406	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂×C₃×C₅	C₂²×D₄
hypercenter	C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₃×#575
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×#41	C₂	semidirect
2. C₂×C₃×#711	C₂	semidirect
3. C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#4097	C₂	semidirect
5. C₃×#4078	C₂	semidirect
6. C₃×#4062	C₂	semidirect
7. C₃×#4061	C₂	semidirect
8. C₃×#4058	C₂	semidirect
9. C₃×#4057	C₂	semidirect
10. C₃×#4055	C₂	semidirect
11. C₃×D₅×M₁₆	C₂	semidirect
12. #66107	C₃	direct (N × H)
14. C₂×C₃×C₅×D₄	C₂²	semidirect
17. C₃×#713	C₂²	semidirect
18. C₃×Q₈×D₅	C₂²	semidirect
23. C₃×#711	C₂²	semidirect
24. C₃×#711	C₂²	semidirect
26. C₃×D₄×D₅	C₂²	semidirect
31. C₂×C₃×Dic₁₀	C₂²	semidirect
32. C₃×C₅×SD₁₆	C₂²	semidirect
33. C₃×C₅×D₈	C₂²	semidirect
34. C₃×C₅×M₁₆	C₂²	semidirect
35. C₃×#689	C₂²	semidirect
36. C₃×#687	C₂²	semidirect
37. C₃×#687	C₂²	semidirect
38. C₃×#686	C₂²	semidirect
39. C₃×#681	C₂²	semidirect
40. C₃×Dic₂₀	C₂²	semidirect
41. C₃×#677	C₂²	semidirect
42. C₃×#676	C₂²	semidirect
43. C₃×C₈×D₅	C₂²	semidirect
45. D₅×#41	C₂×C₃	semidirect
46. C₂×#711	C₂×C₃	semidirect
47. C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
48. #4097	C₂×C₃	semidirect
49. #4078	C₂×C₃	semidirect
50. #4062	C₂×C₃	semidirect
51. #4061	C₂×C₃	semidirect
52. #4058	C₂×C₃	semidirect
53. #4057	C₂×C₃	semidirect
54. #4055	C₂×C₃	semidirect
55. D₅×M₁₆	C₂×C₃	semidirect
98. C₃×AGL(1,ℤ/8)	D₅	semidirect
103. C₂×C₅×D₄	C₂²×C₃	semidirect
106. #713	C₂²×C₃	semidirect
107. Q₈×D₅	C₂²×C₃	semidirect
112. #711	C₂²×C₃	semidirect
113. #711	C₂²×C₃	semidirect
115. D₄×D₅	C₂²×C₃	semidirect
120. C₂×Dic₁₀	C₂²×C₃	semidirect
121. C₅×SD₁₆	C₂²×C₃	semidirect
122. C₅×D₈	C₂²×C₃	semidirect
123. C₅×M₁₆	C₂²×C₃	semidirect
124. #689	C₂²×C₃	semidirect
125. #687	C₂²×C₃	semidirect
126. #687	C₂²×C₃	semidirect
127. #686	C₂²×C₃	semidirect
128. #681	C₂²×C₃	semidirect
129. Dic₂₀	C₂²×C₃	semidirect
130. #677	C₂²×C₃	semidirect
131. #676	C₂²×C₃	semidirect
132. C₈×D₅	C₂²×C₃	semidirect
165. C₂×C₃×D₄	C₂×D₅	semidirect
174. C₃×SD₁₆	C₂×D₅	semidirect
176. C₃×D₈	C₂×D₅	semidirect
179. C₃×M₁₆	C₂×D₅	semidirect
223. AGL(1,ℤ/8)	C₃×D₅	semidirect
300. C₂×D₄	C₂×C₃×D₅	semidirect
309. SD₁₆	C₂×C₃×D₅	semidirect
311. D₈	C₂×C₃×D₅	semidirect
314. M₁₆	C₂×C₃×D₅	semidirect
316. C₃×C₅	#575	semidirect
382. C₅	C₃×#575	semidirect
399. C₃	#66107	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×#41	2
C₂×C₃×#711	2
C₃×C₅×AGL(1,ℤ/8)	2
C₃×#4097	2
C₃×#4078	2
C₃×#4062	2
C₃×#4061	2
C₃×#4058	2
C₃×#4057	2
C₃×#4055	2
C₃×D₅×M₁₆	2
#66107	3
C₃×#575	5

Subgroups — C3×#66107 #11755784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66107 #11755784