Subgroups — C₅×D₄×#67 #11756186

Order 960.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#953	C₂	1	2	yes	maximal, complemented
5	C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#939	C₂	1	2	yes	maximal, complemented
7	C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#937	C₂	1	2	yes	maximal, complemented
9	C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄²	—	3	1	no	maximal, Hall
13	C₂⁴×C₃×C₅	C₂²	1	2	yes	complemented
14	C₂³×C₅×D₃	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₄	—	2	4	no	—
16	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#67	—	2	8	no	—
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₅×#67	C₂²	1	2	yes	complemented
24	C₂×C₅×#67	C₂²	1	2	yes	complemented
25	C₂×C₅×#67	C₂²	1	2	yes	complemented
26	C₂×C₅×#67	C₂²	1	2	yes	complemented
27	C₂²×C₅×Dic₃	C₂²	1	2	yes	complemented
28	C₅×D₃×D₄	—	2	4	no	—
29	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₅×#217	C₂²	1	1	yes	characteristic, complemented
32	C₅×#217	C₂²	1	2	yes	complemented
33	C₅×#217	C₂²	1	2	yes	complemented
34	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	D₄×#67	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₅×D₄	—	3	2	no	—
41	C₂²×C₅×D₄	—	3	1	no	—
42	C₂²×C₅×D₄	D₃	1	1	yes	characteristic, complemented
43	C₅×#127	—	3	1	no	—
44	C₅×#121	—	3	1	no	—
45	C₅×#121	—	3	2	no	—
46	C₅×#121	—	3	1	no	—
47	C₅×#120	—	3	2	no	—
48	C₅×#120	—	3	2	no	—
49	C₄×C₅×D₄	—	3	1	no	—
50	C₄×C₅×D₄	—	3	1	no	—
51	C₂³×C₃×C₅	—	2	4	no	—
52	C₂³×C₃×C₅	—	2	4	no	—
53	C₂³×C₃×C₅	—	4	2	no	—
54	C₂³×C₃×C₅	C₂³	1	2	yes	—
55	C₂³×C₃×C₅	C₂³	1	2	yes	—
56	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×D₃	—	2	4	no	—
58	C₂²×C₅×D₃	—	2	4	no	—
59	C₂²×C₅×D₃	—	4	2	no	—
60	C₂²×C₅×D₃	C₂³	1	2	yes	—
61	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₃×C₅×D₄	—	2	4	no	—
63	C₃×C₅×D₄	—	2	2	no	—
64	C₃×C₅×D₄	D₄	1	4	yes	complemented
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₅×#67	—	2	4	no	—
69	C₅×#67	—	2	4	no	—
70	C₅×#67	—	2	4	no	—
71	C₅×#67	—	2	4	no	—
72	C₅×#67	—	4	2	no	—
73	C₅×#67	D₄	1	4	yes	direct product factor
74	C₂×C₅×Dic₃	—	2	4	no	—
75	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₅×Dic₃	C₂³	1	2	yes	—
78	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₅×D₁₂	—	2	2	no	—
80	C₄×C₅×D₃	—	2	2	no	—
81	C₂²×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×#67	C₂×C₅	1	2	yes	complemented
83	C₂×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
84	#953	C₂×C₅	1	2	yes	complemented
85	#940	C₂×C₅	1	1	yes	characteristic, complemented
86	#939	C₂×C₅	1	2	yes	complemented
87	#938	C₂×C₅	1	1	yes	characteristic, complemented
88	#937	C₂×C₅	1	2	yes	complemented
89	D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
90	#930	C₂×C₅	1	1	yes	characteristic, complemented
91	C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂⁴×C₅	—	3	2	no	—
93	C₂⁴×C₅	C₂×D₃	1	2	yes	complemented
94	C₂×C₅×D₄	—	2	4	no	—
95	C₂×C₅×D₄	—	3	1	no	—
96	C₂×C₅×D₄	—	3	2	no	—
97	C₂×C₅×D₄	—	3	2	no	—
98	C₂×C₅×D₄	—	3	2	no	—
99	C₂×C₅×D₄	—	3	2	no	—
100	C₂×C₅×D₄	—	3	2	no	—
101	C₂×C₅×D₄	—	3	1	no	—
102	C₂×C₅×D₄	—	6	8	no	—
103	C₂×C₅×D₄	—	6	4	no	—
104	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×D₄	C₂×D₃	1	2	yes	complemented
106	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
107	C₂²×C₄×C₅	—	3	2	no	—
108	C₂²×C₄×C₅	—	3	1	no	—
109	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
110	C₅×C₄⋊C₄	—	3	1	no	—
111	C₅×C₄⋊C₄	—	3	1	no	—
112	C₅×C₂²⋊C₄	—	3	1	no	—
113	C₅×C₂²⋊C₄	—	3	2	no	—
114	C₅×C₂²⋊C₄	—	3	2	no	—
115	C₅×C₂²⋊C₄	—	3	1	no	—
116	C₅×C₂²⋊C₄	—	3	2	no	—
117	C₄²×C₅	—	3	1	no	—
118	D₄²	—	3	1	no	Sylow
119	C₂²×C₃×C₅	—	2	2	no	—
120	C₂²×C₃×C₅	—	2	1	no	—
121	C₂²×C₃×C₅	—	2	2	no	—
122	C₂²×C₃×C₅	—	2	1	no	—
123	C₂²×C₃×C₅	—	2	2	no	—
124	C₂²×C₃×C₅	—	2	2	no	—
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	4	8	no	—
127	C₂²×C₃×C₅	C₂×D₄	1	2	yes	complemented
128	C₂²×C₃×C₅	C₂×D₄	1	4	yes	complemented
129	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
130	C₂×C₅×D₃	—	2	1	no	—
131	C₂×C₅×D₃	—	2	1	no	—
132	C₂×C₅×D₃	—	2	2	no	—
133	C₂×C₅×D₃	—	2	2	no	—
134	C₂×C₅×D₃	—	2	2	no	—
135	C₂×C₅×D₃	—	4	8	no	—
136	C₂×C₅×D₃	C₂×D₄	1	2	yes	complemented
137	C₃×C₄×C₅	—	2	1	no	—
138	C₃×C₄×C₅	C₂×D₄	1	2	yes	complemented
139	C₅×Dic₃	—	2	1	no	—
140	C₅×Dic₃	—	2	2	no	—
141	C₅×Dic₃	—	2	1	no	—
142	C₅×Dic₃	C₂×D₄	1	2	yes	complemented
143	C₂⁴×C₃	C₂²×C₅	1	2	yes	complemented
144	C₂³×D₃	C₂²×C₅	1	2	yes	complemented
145	C₂×C₃×D₄	—	2	4	no	—
146	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
148	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
150	C₂×#67	—	2	8	no	—
151	C₂×#67	C₂²×C₅	1	1	yes	characteristic
152	C₂×#67	C₂²×C₅	1	2	yes	complemented
153	C₂×#67	C₂²×C₅	1	2	yes	complemented
154	C₂×#67	C₂²×C₅	1	2	yes	complemented
155	C₂×#67	C₂²×C₅	1	2	yes	complemented
156	C₂×#67	C₂²×C₅	1	2	yes	complemented
157	C₂²×Dic₃	C₂²×C₅	1	2	yes	complemented
158	D₃×D₄	—	2	4	no	—
159	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
160	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
161	#217	C₂²×C₅	1	1	yes	characteristic, complemented
162	#217	C₂²×C₅	1	2	yes	complemented
163	#217	C₂²×C₅	1	2	yes	complemented
164	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
165	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
166	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
167	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₂³×C₅	—	2	4	no	—
170	C₂³×C₅	—	2	4	no	—
171	C₂³×C₅	—	3	1	no	—
172	C₂³×C₅	—	3	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	6	4	no	—
175	C₂³×C₅	—	6	4	no	—
176	C₂³×C₅	—	12	2	no	—
177	C₂³×C₅	C₂²×D₃	1	2	yes	—
178	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂³×C₅	C₂²×D₃	1	2	yes	—
180	C₅×D₄	—	2	4	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	3	4	no	—
183	C₅×D₄	—	6	4	no	—
184	C₅×D₄	—	6	4	no	—
185	C₅×D₄	—	6	4	no	—
186	C₅×D₄	—	6	4	no	—
187	C₅×D₄	—	6	2	no	—
188	C₅×D₄	—	12	2	no	—
189	C₅×D₄	#67	1	4	yes	direct product factor
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	3	1	no	—
192	C₂×C₄×C₅	—	3	1	no	—
193	C₂×C₄×C₅	—	3	2	no	—
194	C₂×C₄×C₅	—	3	1	no	—
195	C₂×C₄×C₅	—	6	4	no	—
196	C₂×C₄×C₅	—	6	2	no	—
197	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₂²×D₄	—	3	2	no	—
200	C₂²×D₄	—	3	1	no	—
201	C₂²×D₄	C₅×D₃	1	1	yes	characteristic, complemented
202	#127	—	3	1	no	—
203	#121	—	3	1	no	—
204	#121	—	3	2	no	—
205	#121	—	3	1	no	—
206	#120	—	3	2	no	—
207	#120	—	3	2	no	—
208	C₄×D₄	—	3	1	no	—
209	C₄×D₄	—	3	1	no	—
210	C₂×C₃×C₅	—	2	4	no	—
211	C₂×C₃×C₅	—	2	2	no	—
212	C₂×C₃×C₅	—	4	2	no	—
213	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₅×D₃	—	2	2	no	—
217	C₅×D₃	—	4	2	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	4	2	no	—
221	C₂³×C₃	C₂³×C₅	1	2	yes	—
222	C₂³×C₃	C₂³×C₅	1	2	yes	—
223	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
224	C₂²×D₃	—	2	4	no	—
225	C₂²×D₃	—	2	4	no	—
226	C₂²×D₃	—	4	2	no	—
227	C₂²×D₃	C₂³×C₅	1	2	yes	—
228	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
229	C₃×D₄	—	2	4	no	—
230	C₃×D₄	—	2	2	no	—
231	C₃×D₄	C₅×D₄	1	4	yes	complemented
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
235	#67	—	2	4	no	—
236	#67	—	2	4	no	—
237	#67	—	2	4	no	—
238	#67	—	2	4	no	—
239	#67	—	4	2	no	—
240	#67	C₅×D₄	1	4	yes	direct product factor
241	C₂×Dic₃	—	2	4	no	—
242	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
243	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
244	C₂×Dic₃	C₂³×C₅	1	2	yes	—
245	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
246	D₁₂	—	2	2	no	—
247	C₄×D₃	—	2	2	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	3	2	no	—
256	C₂²×C₅	—	4	8	no	—
257	C₂²×C₅	—	6	1	no	—
258	C₂²×C₅	—	6	1	no	—
259	C₂²×C₅	—	6	2	no	—
260	C₂²×C₅	—	6	2	no	—
261	C₂²×C₅	—	6	2	no	—
262	C₂²×C₅	—	12	8	no	—
263	C₂²×C₅	D₃×D₄	1	2	yes	complemented
264	C₂²×C₅	C₂×#67	1	4	yes	complemented
265	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	3	2	no	—
268	C₄×C₅	—	6	2	no	—
269	C₄×C₅	—	6	1	no	—
270	C₄×C₅	—	6	1	no	—
271	C₄×C₅	C₂×#67	1	2	yes	complemented
272	C₂⁴	—	3	2	no	—
273	C₂⁴	C₂×C₅×D₃	1	2	yes	complemented
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	3	1	no	—
276	C₂×D₄	—	3	2	no	—
277	C₂×D₄	—	3	2	no	—
278	C₂×D₄	—	3	2	no	—
279	C₂×D₄	—	3	2	no	—
280	C₂×D₄	—	3	2	no	—
281	C₂×D₄	—	3	1	no	—
282	C₂×D₄	—	6	8	no	—
283	C₂×D₄	—	6	4	no	—
284	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₂×D₄	C₂×C₅×D₃	1	2	yes	complemented
286	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
287	C₂²×C₄	—	3	2	no	—
288	C₂²×C₄	—	3	1	no	—
289	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
290	C₄⋊C₄	—	3	1	no	—
291	C₄⋊C₄	—	3	1	no	—
292	C₂²⋊C₄	—	3	1	no	—
293	C₂²⋊C₄	—	3	2	no	—
294	C₂²⋊C₄	—	3	2	no	—
295	C₂²⋊C₄	—	3	1	no	—
296	C₂²⋊C₄	—	3	2	no	—
297	C₄²	—	3	1	no	—
298	C₃×C₅	D₄²	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	2	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	4	8	no	—
307	C₂²×C₃	C₂×C₅×D₄	1	2	yes	complemented
308	C₂²×C₃	C₂×C₅×D₄	1	4	yes	complemented
309	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
310	C₂×D₃	—	2	1	no	—
311	C₂×D₃	—	2	1	no	—
312	C₂×D₃	—	2	2	no	—
313	C₂×D₃	—	2	2	no	—
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	—	4	8	no	—
316	C₂×D₃	C₂×C₅×D₄	1	2	yes	complemented
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	C₂×C₅×D₄	1	2	yes	complemented
319	Dic₃	—	2	1	no	—
320	Dic₃	—	2	2	no	—
321	Dic₃	—	2	1	no	—
322	Dic₃	C₂×C₅×D₄	1	2	yes	complemented
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	2	4	no	—
325	C₂×C₅	—	4	2	no	—
326	C₂×C₅	—	6	2	no	—
327	C₂×C₅	—	12	2	no	—
328	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
329	C₂×C₅	#1004	1	1	yes	characteristic
330	C₂×C₅	C₂²×#67	1	1	yes	characteristic
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	3	1	no	—
334	C₂³	—	3	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	6	4	no	—
337	C₂³	—	6	4	no	—
338	C₂³	—	12	2	no	—
339	C₂³	C₂²×C₅×D₃	1	2	yes	—
340	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₂³	C₂²×C₅×D₃	1	2	yes	—
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	3	4	no	—
345	D₄	—	6	4	no	—
346	D₄	—	6	4	no	—
347	D₄	—	6	4	no	—
348	D₄	—	6	4	no	—
349	D₄	—	6	2	no	—
350	D₄	—	12	2	no	—
351	D₄	C₅×#67	1	4	yes	direct product factor
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	3	1	no	—
354	C₂×C₄	—	3	1	no	—
355	C₂×C₄	—	3	2	no	—
356	C₂×C₄	—	3	1	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
361	C₂×C₃	—	2	4	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
367	D₃	—	2	2	no	—
368	D₃	—	4	2	no	—
369	C₅	D₄×#67	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	3	2	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	6	1	no	—
380	C₂²	—	6	1	no	—
381	C₂²	—	6	2	no	—
382	C₂²	—	6	2	no	—
383	C₂²	—	6	2	no	—
384	C₂²	—	12	8	no	—
385	C₂²	C₅×D₃×D₄	1	2	yes	complemented
386	C₂²	C₂×C₅×#67	1	4	yes	complemented
387	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	3	2	no	—
390	C₄	—	6	2	no	—
391	C₄	—	6	1	no	—
392	C₄	—	6	1	no	—
393	C₄	C₂×C₅×#67	1	2	yes	complemented
394	C₃	C₅×D₄²	1	1	yes	characteristic, complemented, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	2	4	no	—
397	C₂	—	4	2	no	—
398	C₂	—	6	2	no	—
399	C₂	—	12	2	no	—
400	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
401	C₂	C₅×#1004	1	1	yes	characteristic
402	C₂	C₂²×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×D₄	D₃
hypocenter	C₃	C₅×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₅×#67	C₂	semidirect
3. C₂×C₅×D₃×D₄	C₂	semidirect
4. C₅×#953	C₂	semidirect
5. C₅×#940	C₂	semidirect
6. C₅×#939	C₂	semidirect
7. C₅×#938	C₂	semidirect
8. C₅×#937	C₂	semidirect
9. C₅×D₄×Dic₃	C₂	semidirect
10. C₅×#930	C₂	semidirect
11. C₄×C₅×#67	C₂	semidirect
13. C₂⁴×C₃×C₅	C₂²	semidirect
14. C₂³×C₅×D₃	C₂²	semidirect
17. C₂×C₃×C₅×D₄	C₂²	semidirect
18. C₂×C₃×C₅×D₄	C₂²	semidirect
19. C₂²×C₃×C₄×C₅	C₂²	semidirect
22. C₂×C₅×#67	C₂²	semidirect
23. C₂×C₅×#67	C₂²	semidirect
24. C₂×C₅×#67	C₂²	semidirect
25. C₂×C₅×#67	C₂²	semidirect
26. C₂×C₅×#67	C₂²	semidirect
27. C₂²×C₅×Dic₃	C₂²	semidirect
29. C₂×C₅×D₁₂	C₂²	semidirect
30. C₂×C₄×C₅×D₃	C₂²	semidirect
31. C₅×#217	C₂²	semidirect
32. C₅×#217	C₂²	semidirect
33. C₅×#217	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₅×C₄⋊Dic₃	C₂²	semidirect
37. C₅×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₅×Dic₃	C₂²	semidirect
39. D₄×#67	C₅	direct (N × H)
42. C₂²×C₅×D₄	D₃	semidirect
64. C₃×C₅×D₄	D₄	semidirect
73. C₅×#67	D₄	direct (N × H)
81. C₂²×C₃×D₄	C₂×C₅	semidirect
82. C₂²×#67	C₂×C₅	semidirect
83. C₂×D₃×D₄	C₂×C₅	semidirect
84. #953	C₂×C₅	semidirect
85. #940	C₂×C₅	semidirect
86. #939	C₂×C₅	semidirect
87. #938	C₂×C₅	semidirect
88. #937	C₂×C₅	semidirect
89. D₄×Dic₃	C₂×C₅	semidirect
90. #930	C₂×C₅	semidirect
91. C₄×#67	C₂×C₅	semidirect
93. C₂⁴×C₅	C₂×D₃	semidirect
105. C₂×C₅×D₄	C₂×D₃	semidirect
106. C₂×C₅×D₄	C₂×D₃	semidirect
109. C₂²×C₄×C₅	C₂×D₃	semidirect
127. C₂²×C₃×C₅	C₂×D₄	semidirect
128. C₂²×C₃×C₅	C₂×D₄	semidirect
136. C₂×C₅×D₃	C₂×D₄	semidirect
138. C₃×C₄×C₅	C₂×D₄	semidirect
142. C₅×Dic₃	C₂×D₄	semidirect
143. C₂⁴×C₃	C₂²×C₅	semidirect
144. C₂³×D₃	C₂²×C₅	semidirect
147. C₂×C₃×D₄	C₂²×C₅	semidirect
148. C₂×C₃×D₄	C₂²×C₅	semidirect
149. C₂²×C₃×C₄	C₂²×C₅	semidirect
152. C₂×#67	C₂²×C₅	semidirect
153. C₂×#67	C₂²×C₅	semidirect
154. C₂×#67	C₂²×C₅	semidirect
155. C₂×#67	C₂²×C₅	semidirect
156. C₂×#67	C₂²×C₅	semidirect
157. C₂²×Dic₃	C₂²×C₅	semidirect
159. C₂×D₁₂	C₂²×C₅	semidirect
160. C₂×C₄×D₃	C₂²×C₅	semidirect
161. #217	C₂²×C₅	semidirect
162. #217	C₂²×C₅	semidirect
163. #217	C₂²×C₅	semidirect
164. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
165. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
166. C₄⋊Dic₃	C₂²×C₅	semidirect
167. Dic₃⋊C₄	C₂²×C₅	semidirect
168. C₄×Dic₃	C₂²×C₅	semidirect
189. C₅×D₄	#67	direct (N × H)
201. C₂²×D₄	C₅×D₃	semidirect
231. C₃×D₄	C₅×D₄	semidirect
240. #67	C₅×D₄	direct (N × H)
263. C₂²×C₅	D₃×D₄	semidirect
264. C₂²×C₅	C₂×#67	semidirect
271. C₄×C₅	C₂×#67	semidirect
273. C₂⁴	C₂×C₅×D₃	semidirect
285. C₂×D₄	C₂×C₅×D₃	semidirect
286. C₂×D₄	C₂×C₅×D₃	semidirect
289. C₂²×C₄	C₂×C₅×D₃	semidirect
298. C₃×C₅	D₄²	semidirect
307. C₂²×C₃	C₂×C₅×D₄	semidirect
308. C₂²×C₃	C₂×C₅×D₄	semidirect
316. C₂×D₃	C₂×C₅×D₄	semidirect
318. C₃×C₄	C₂×C₅×D₄	semidirect
322. Dic₃	C₂×C₅×D₄	semidirect
351. D₄	C₅×#67	direct (N × H)
369. C₅	D₄×#67	direct (N × H)
385. C₂²	C₅×D₃×D₄	semidirect
386. C₂²	C₂×C₅×#67	semidirect
393. C₄	C₂×C₅×#67	semidirect
394. C₃	C₅×D₄²	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×D₄	2
C₂²×C₅×#67	2
C₂×C₅×D₃×D₄	2
C₅×#953	2
C₅×#940	2
C₅×#939	2
C₅×#938	2
C₅×#937	2
C₅×D₄×Dic₃	2
C₅×#930	2
C₄×C₅×#67	2
C₅×D₄²	3
D₄×#67	5

Subgroups — C5×D4×#67 #11756186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×#67 #11756186