Subgroups — C₂×#72229544 #72231566

Order 7200.

1688 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₃⋊#1043	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃⋊#1043	—	3	1	no	maximal
3	C₂×C₃×Dic₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
4	#72229544	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄⋊(C₃⋊#1043)	—	3	1	no	maximal
6	C₂²×C₃⋊(C₃⋊#1043)	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₃²×C₅⋊D₅	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊(C₃⋊#1043)	—	2	2	no	—
9	C₂×C₃⋊(C₃⋊#1043)	C₂²	1	2	yes	—
10	C₂×C₃×C₃⋊#1043	—	2	2	no	—
11	C₂×C₃×C₃⋊#1043	C₂²	1	2	yes	—
12	C₂×C₃×C₃⋊#1039	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅²×Dic₃	C₄	1	1	yes	characteristic, complemented
14	C₃×Dic₃×C₅⋊D₅	C₄	1	2	yes	complemented
15	C₃×Dic₃×C₅⋊D₅	C₂²	1	2	yes	—
16	C₂×Dic₃⋊ΓL(1,𝔽₁₆)	—	5	6	no	maximal
17	C₂²×C₃⋊#1043	—	3	1	no	—
18	C₂²×C₃⋊#1043	—	3	1	no	—
19	C₂²×C₃⋊#1043	—	6	1	no	—
20	C₂²×C₃⋊#1043	D₃	1	1	yes	characteristic
21	C₂²×C₃×#1043	—	3	1	no	—
22	C₂×C₃×C₄×C₅⋊D₅	—	3	1	no	—
23	C₂×Dic₃×C₅⋊D₅	D₃	1	1	yes	characteristic
24	C₄⋊(C₃⋊#1043)	—	3	4	no	—
25	Dic₃⋊#1043	—	3	4	no	—
26	C₂²×C₃²×C₅²	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃²×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃²×C₅⋊D₅	D₄	1	2	yes	—
29	C₂×C₃²×C₅⋊D₅	Q₈	1	2	yes	—
30	C₂×C₃²×C₅⋊D₅	C₂³	1	1	yes	characteristic
31	C₃⋊(C₃⋊#1043)	—	2	2	no	—
32	C₃×C₃⋊#1043	—	2	2	no	—
33	C₃×C₃⋊#1039	C₂×C₄	1	2	yes	complemented
34	C₃×C₅²×Dic₃	C₂×C₄	1	2	yes	complemented
35	C₂×C₄⋊#1043	—	9	1	no	Hall
36	C₂²×C₃⋊ΓL(1,𝔽₁₆)	—	5	6	no	—
37	C₂²×C₃×ΓL(1,𝔽₁₆)	—	5	6	no	—
38	C₂×C₃×D₅×Dic₃	—	5	6	no	—
39	Dic₃⋊ΓL(1,𝔽₁₆)	—	5	24	no	—
40	C₂²×C₃×C₅⋊D₅	—	2	1	no	—
41	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	1	yes	characteristic
42	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	1	yes	characteristic
43	C₂×C₃⋊#1043	—	2	2	no	—
44	C₂×C₃⋊#1043	—	3	2	no	—
45	C₂×C₃⋊#1043	—	3	2	no	—
46	C₂×C₃⋊#1043	—	6	2	no	—
47	C₂×C₃⋊#1043	—	6	2	no	—
48	C₂×C₃⋊#1043	—	6	2	no	—
49	C₂×C₃⋊#1043	—	6	2	no	—
50	C₂×C₃⋊#1043	—	6	2	no	—
51	C₂×C₃⋊#1043	C₂×D₃	1	2	yes	—
52	C₂×C₃×#1043	—	3	2	no	—
53	C₂×C₃×#1043	—	6	2	no	—
54	C₂×C₃×C₄×C₅²	—	3	1	no	—
55	C₂×C₃⋊#1039	Dic₃	1	1	yes	characteristic, complemented
56	C₂×C₅²×Dic₃	Dic₃	1	1	yes	characteristic, complemented
57	C₂×C₃×#1039	—	3	1	no	—
58	C₃×C₄×C₅⋊D₅	—	3	2	no	—
59	C₃×C₄×C₅⋊D₅	—	3	2	no	—
60	Dic₃×C₅⋊D₅	Dic₃	1	2	yes	complemented
61	Dic₃×C₅⋊D₅	C₂×D₃	1	2	yes	—
62	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	15	6	no	—
63	C₂×Dic₃⋊AGL(1,𝔽₅)	—	15	6	no	—
64	C₂×C₃²×C₅²	C₄⋊C₄	1	2	yes	complemented
65	C₂×C₃²×C₅²	C₂²×C₄	1	1	yes	characteristic
66	C₃²×C₅⋊D₅	C₄⋊C₄	1	2	yes	complemented
67	C₃²×C₅⋊D₅	C₂×D₄	1	1	yes	characteristic
68	C₃²×C₅⋊D₅	C₂×Q₈	1	1	yes	characteristic
69	C₂²×#1043	—	3	1	no	—
70	C₂²×#1043	—	9	1	no	—
71	C₂×C₄×C₅⋊D₅	—	3	1	no	—
72	C₄⋊#1043	—	9	4	no	—
73	C₂²×C₃²×D₅	—	5	6	no	—
74	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	5	12	no	—
75	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	10	12	no	—
76	C₂×C₃×ΓL(1,𝔽₁₆)	—	5	12	no	—
77	C₂×C₃×ΓL(1,𝔽₁₆)	—	10	12	no	—
78	C₂×C₃×Dic₁₅	—	5	6	no	—
79	C₂×C₃×C₅×Dic₃	AGL(1,𝔽₅)	1	6	yes	complemented
80	C₃×D₅×Dic₃	—	5	12	no	—
81	C₃×D₅×Dic₃	—	5	12	no	—
82	C₂²×C₃×C₅²	—	2	1	no	—
83	C₂²×C₃×C₅²	C₄×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₅²	C₂×Dic₃	1	1	yes	characteristic
85	C₂×C₃×C₅⋊D₅	—	2	1	no	—
86	C₂×C₃×C₅⋊D₅	—	2	2	no	—
87	C₂×C₃×C₅⋊D₅	—	2	2	no	—
88	C₂×C₃×C₅⋊D₅	—	2	1	no	—
89	C₂×C₃×C₅⋊D₅	Dic₆	1	2	yes	—
90	C₂×C₃×C₅⋊D₅	Dic₆	1	2	yes	—
91	C₂×C₃×C₅⋊D₅	C₄×D₃	1	1	yes	characteristic
92	C₂×C₃×C₅⋊D₅	D₁₂	1	2	yes	—
93	C₂×C₃×C₅⋊D₅	C₂×Dic₃	1	1	yes	characteristic
94	C₂×C₃×C₅⋊D₅	#67	1	2	yes	—
95	C₂×C₃×C₅⋊D₅	C₂²×D₃	1	1	yes	characteristic
96	C₂×C₃×C₅⋊D₅	C₂²×D₃	1	1	yes	characteristic
97	C₃⋊#1043	—	2	2	no	—
98	C₃⋊#1043	—	6	2	no	—
99	C₃⋊#1043	—	6	2	no	—
100	C₃⋊#1043	—	6	2	no	—
101	C₃⋊#1043	—	6	2	no	—
102	C₃×#1043	—	6	2	no	—
103	C₃×C₄×C₅²	—	3	2	no	—
104	C₃⋊#1039	C₂×Dic₃	1	2	yes	complemented
105	C₅²×Dic₃	C₂×Dic₃	1	2	yes	complemented
106	C₃×#1039	—	3	2	no	—
107	C₂×Dic₃⋊Dic₃	—	25	1	no	Hall
108	C₂²×ΓL(1,𝔽₁₆)	—	5	6	no	—
109	C₂²×ΓL(1,𝔽₁₆)	—	15	6	no	—
110	C₂²×ΓL(1,𝔽₁₆)	—	15	6	no	—
111	C₂²×ΓL(1,𝔽₁₆)	—	30	6	no	—
112	C₂²×C₃×AGL(1,𝔽₅)	—	15	6	no	—
113	C₂×C₃×C₄×D₅	—	15	6	no	—
114	C₂×D₅×Dic₃	—	5	6	no	—
115	C₄⋊ΓL(1,𝔽₁₆)	—	15	24	no	—
116	Dic₃⋊AGL(1,𝔽₅)	—	15	24	no	—
117	C₃²×C₅²	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
118	C₂²×C₅⋊D₅	D₃²	1	1	yes	characteristic
119	C₂×#1043	—	3	2	no	—
120	C₂×#1043	—	6	2	no	—
121	C₂×#1043	—	9	2	no	—
122	C₂×#1043	—	18	2	no	—
123	C₂×C₄×C₅²	—	3	1	no	—
124	C₂×#1039	—	3	1	no	—
125	C₄×C₅⋊D₅	—	3	2	no	—
126	C₄×C₅⋊D₅	—	3	2	no	—
127	C₂²×C₃²×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	—
128	C₂×C₃²×D₅	—	5	12	no	—
129	C₂×C₃²×D₅	—	5	12	no	—
130	C₂×C₃²×D₅	—	5	6	no	—
131	C₂×C₃²×D₅	—	5	6	no	—
132	C₃⋊ΓL(1,𝔽₁₆)	—	10	12	no	—
133	C₃×ΓL(1,𝔽₁₆)	—	10	12	no	—
134	C₃×Dic₁₅	—	5	12	no	—
135	C₃×C₅×Dic₃	C₂×AGL(1,𝔽₅)	1	12	yes	complemented
136	C₂×C₄⋊AGL(1,𝔽₅)	—	45	6	no	—
137	C₂×C₃×C₅²	—	2	2	no	—
138	C₂×C₃×C₅²	—	2	1	no	—
139	C₂×C₃×C₅²	Dic₃⋊C₄	1	2	yes	complemented
140	C₂×C₃×C₅²	C₄⋊Dic₃	1	2	yes	complemented
141	C₂×C₃×C₅²	C₂×C₄×D₃	1	1	yes	characteristic
142	C₂×C₃×C₅²	C₂²×Dic₃	1	1	yes	characteristic
143	C₃×C₅⋊D₅	—	2	2	no	—
144	C₃×C₅⋊D₅	—	2	1	no	—
145	C₃×C₅⋊D₅	—	2	1	no	—
146	C₃×C₅⋊D₅	Dic₃⋊C₄	1	2	yes	complemented
147	C₃×C₅⋊D₅	C₄⋊Dic₃	1	2	yes	complemented
148	C₃×C₅⋊D₅	C₂×Dic₆	1	1	yes	characteristic
149	C₃×C₅⋊D₅	C₂×Dic₆	1	1	yes	characteristic
150	C₃×C₅⋊D₅	C₂×D₁₂	1	1	yes	characteristic
151	C₃×C₅⋊D₅	C₂×#67	1	1	yes	characteristic
152	C₂²×C₃⋊Dic₃	—	25	1	no	—
153	C₂²×C₃×Dic₃	—	25	1	no	—
154	C₂²×C₃×Dic₃	—	25	1	no	—
155	Dic₃⋊Dic₃	—	25	4	no	—
156	C₂²×C₃×D₅	—	5	6	no	—
157	C₂²×C₃×D₅	—	5	6	no	—
158	C₂²×C₃×D₅	—	10	6	no	—
159	C₂×ΓL(1,𝔽₁₆)	—	5	12	no	—
160	C₂×ΓL(1,𝔽₁₆)	—	10	12	no	—
161	C₂×ΓL(1,𝔽₁₆)	—	15	12	no	—
162	C₂×ΓL(1,𝔽₁₆)	—	15	12	no	—
163	C₂×ΓL(1,𝔽₁₆)	—	30	12	no	—
164	C₂×ΓL(1,𝔽₁₆)	—	30	12	no	—
165	C₂×ΓL(1,𝔽₁₆)	—	30	12	no	—
166	C₂×ΓL(1,𝔽₁₆)	—	30	12	no	—
167	C₂×ΓL(1,𝔽₁₆)	—	30	12	no	—
168	C₂×C₃×AGL(1,𝔽₅)	—	15	12	no	—
169	C₂×C₃×AGL(1,𝔽₅)	—	30	12	no	—
170	C₂×C₃×C₄×C₅	—	3	6	no	—
171	C₂×Dic₁₅	—	5	6	no	—
172	C₂×C₅×Dic₃	ΓL(1,𝔽₁₆)	1	6	yes	complemented
173	C₂×C₃×Dic₅	—	15	6	no	—
174	C₃×C₄×D₅	—	15	12	no	—
175	C₃×C₄×D₅	—	15	12	no	—
176	D₅×Dic₃	—	5	12	no	—
177	D₅×Dic₃	—	5	12	no	—
178	C₂²×C₅²	D₃×Dic₃	1	1	yes	characteristic
179	C₂×C₅⋊D₅	D₃×Dic₃	1	1	yes	characteristic
180	C₂×C₅⋊D₅	#626	1	2	yes	—
181	C₂×C₅⋊D₅	#627	1	2	yes	—
182	C₂×C₅⋊D₅	C₂×D₃²	1	1	yes	characteristic
183	#1043	—	6	2	no	—
184	#1043	—	18	2	no	—
185	C₄×C₅²	—	3	2	no	—
186	#1039	—	3	2	no	—
187	C₂×C₄⋊Dic₃	—	75	1	no	—
188	C₂×Dic₃⋊C₄	—	75	1	no	—
189	C₂×C₃²×C₅	C₄⋊AGL(1,𝔽₅)	1	12	yes	complemented
190	C₂×C₃²×C₅	C₂²×AGL(1,𝔽₅)	1	6	yes	—
191	C₃²×D₅	—	5	6	no	—
192	C₃²×D₅	—	5	12	no	—
193	C₃²×D₅	—	5	6	no	—
194	C₂²×AGL(1,𝔽₅)	—	15	6	no	—
195	C₂²×AGL(1,𝔽₅)	—	45	6	no	—
196	C₂×C₄×D₅	—	15	6	no	—
197	C₄⋊AGL(1,𝔽₅)	—	45	24	no	—
198	C₃×C₅²	—	2	1	no	—
199	C₃×C₅²	C₂×Dic₃⋊C₄	1	1	yes	characteristic, complemented
200	C₃×C₅²	C₂×C₄⋊Dic₃	1	1	yes	characteristic, complemented
201	C₂³×C₃²	—	25	1	no	—
202	C₂×C₃⋊Dic₃	—	25	2	no	—
203	C₂×C₃⋊Dic₃	—	50	2	no	—
204	C₂×C₃×Dic₃	—	25	1	no	—
205	C₂×C₃×Dic₃	—	25	2	no	—
206	C₂×C₃×Dic₃	—	25	2	no	—
207	C₂×C₃×Dic₃	—	25	2	no	—
208	C₂×C₃×Dic₃	—	50	2	no	—
209	C₂×C₃×Dic₃	#1043	1	1	yes	characteristic, complemented
210	C₂²×C₃×C₅	—	2	6	no	—
211	C₂²×C₃×C₅	D₃×AGL(1,𝔽₅)	1	6	yes	—
212	C₂²×C₃×C₅	C₂×ΓL(1,𝔽₁₆)	1	6	yes	—
213	C₂×C₃×D₅	—	5	12	no	—
214	C₂×C₃×D₅	—	5	12	no	—
215	C₂×C₃×D₅	—	5	12	no	—
216	C₂×C₃×D₅	—	5	12	no	—
217	C₂×C₃×D₅	—	5	6	no	—
218	C₂×C₃×D₅	—	5	6	no	—
219	C₂×C₃×D₅	—	5	6	no	—
220	C₂×C₃×D₅	—	5	6	no	—
221	C₂×C₃×D₅	—	10	6	no	—
222	C₂×C₃×D₅	—	10	12	no	—
223	C₂×C₃×D₅	—	10	6	no	—
224	C₂×C₃×D₅	—	10	12	no	—
225	ΓL(1,𝔽₁₆)	—	10	12	no	—
226	ΓL(1,𝔽₁₆)	—	30	12	no	—
227	ΓL(1,𝔽₁₆)	—	30	12	no	—
228	ΓL(1,𝔽₁₆)	—	30	12	no	—
229	ΓL(1,𝔽₁₆)	—	30	12	no	—
230	C₃×AGL(1,𝔽₅)	—	30	12	no	—
231	C₃×C₄×C₅	—	3	12	no	—
232	Dic₁₅	—	5	12	no	—
233	C₃×Dic₅	—	15	12	no	—
234	C₅×Dic₃	C₂×ΓL(1,𝔽₁₆)	1	12	yes	complemented
235	C₂×C₅²	Dic₃⋊Dic₃	1	2	yes	complemented
236	C₂×C₅²	C₂×D₃×Dic₃	1	1	yes	characteristic
237	C₅⋊D₅	Dic₃⋊Dic₃	1	2	yes	complemented
238	C₅⋊D₅	C₂×#626	1	1	yes	characteristic
239	C₅⋊D₅	C₂×#627	1	1	yes	characteristic
240	C₂²×C₃×C₄	—	75	1	no	—
241	C₂²×C₃×C₄	—	75	1	no	—
242	C₂²×Dic₃	—	25	1	no	—
243	C₂²×Dic₃	—	25	1	no	—
244	C₂²×Dic₃	—	75	1	no	—
245	C₂²×Dic₃	—	75	1	no	—
246	C₂²×Dic₃	—	150	1	no	—
247	C₄⋊Dic₃	—	75	4	no	—
248	Dic₃⋊C₄	—	75	4	no	—
249	C₃²×C₅	C₂×C₄⋊AGL(1,𝔽₅)	1	6	yes	complemented
250	C₂²×D₅	—	5	6	no	—
251	C₂×AGL(1,𝔽₅)	—	15	12	no	—
252	C₂×AGL(1,𝔽₅)	—	30	12	no	—
253	C₂×AGL(1,𝔽₅)	—	45	12	no	—
254	C₂×AGL(1,𝔽₅)	—	90	12	no	—
255	C₂×C₄×C₅	—	3	6	no	—
256	C₂×Dic₅	—	15	6	no	—
257	C₄×D₅	—	15	12	no	—
258	C₄×D₅	—	15	12	no	—
259	C₂²×C₃²	—	25	2	no	—
260	C₂²×C₃²	—	25	2	no	—
261	C₂²×C₃²	—	25	1	no	—
262	C₂²×C₃²	—	25	1	no	—
263	C₂²×C₃²	C₂×#1043	1	1	yes	characteristic
264	C₃⋊Dic₃	—	50	2	no	—
265	C₃×Dic₃	—	25	2	no	—
266	C₃×Dic₃	—	50	2	no	—
267	C₃×Dic₃	C₂×#1043	1	2	yes	complemented
268	C₂×C₄⋊C₄	—	225	1	no	Sylow
269	C₂×C₃×C₅	—	2	6	no	—
270	C₂×C₃×C₅	—	2	12	no	—
271	C₂×C₃×C₅	Dic₃⋊AGL(1,𝔽₅)	1	12	yes	complemented
272	C₂×C₃×C₅	C₄⋊ΓL(1,𝔽₁₆)	1	12	yes	complemented
273	C₂×C₃×C₅	C₂×D₃×AGL(1,𝔽₅)	1	6	yes	—
274	C₂×C₃×C₅	C₂²×ΓL(1,𝔽₁₆)	1	6	yes	—
275	C₃×D₅	—	5	12	no	—
276	C₃×D₅	—	5	6	no	—
277	C₃×D₅	—	5	6	no	—
278	C₃×D₅	—	5	12	no	—
279	C₃×D₅	—	5	6	no	—
280	C₃×D₅	—	5	6	no	—
281	C₃×D₅	—	10	6	no	—
282	C₃×D₅	—	10	12	no	—
283	C₃×D₅	—	10	6	no	—
284	C₅²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₃	—	25	1	no	—
286	C₂³×C₃	—	25	1	no	—
287	C₂³×C₃	—	50	1	no	—
288	C₂×C₃×C₄	—	3	1	no	—
289	C₂×C₃×C₄	—	75	2	no	—
290	C₂×C₃×C₄	—	75	2	no	—
291	C₂×C₃×C₄	—	75	1	no	—
292	C₂×C₃×C₄	—	75	2	no	—
293	C₂×C₃×C₄	—	150	2	no	—
294	C₂×Dic₃	—	25	1	no	—
295	C₂×Dic₃	—	25	2	no	—
296	C₂×Dic₃	—	25	2	no	—
297	C₂×Dic₃	—	25	2	no	—
298	C₂×Dic₃	—	50	2	no	—
299	C₂×Dic₃	—	75	2	no	—
300	C₂×Dic₃	—	75	2	no	—
301	C₂×Dic₃	—	150	2	no	—
302	C₂×Dic₃	—	150	2	no	—
303	C₂×Dic₃	—	150	2	no	—
304	C₂×Dic₃	—	150	2	no	—
305	C₂×Dic₃	—	150	2	no	—
306	C₂×Dic₃	C₃⋊#1043	1	1	yes	characteristic, complemented
307	C₂²×C₅	D₃×ΓL(1,𝔽₁₆)	1	6	yes	—
308	C₂×D₅	—	5	6	no	—
309	C₂×D₅	—	5	6	no	—
310	C₂×D₅	—	5	12	no	—
311	C₂×D₅	—	5	12	no	—
312	AGL(1,𝔽₅)	—	30	12	no	—
313	AGL(1,𝔽₅)	—	90	12	no	—
314	C₄×C₅	—	3	12	no	—
315	Dic₅	—	15	12	no	—
316	C₂×C₃²	—	25	1	no	—
317	C₂×C₃²	—	25	2	no	—
318	C₂×C₃²	—	25	1	no	—
319	C₂×C₃²	C₄⋊#1043	1	2	yes	complemented
320	C₂×C₃²	C₂²×#1043	1	1	yes	characteristic
321	C₂²×C₄	—	75	1	no	—
322	C₂²×C₄	—	75	1	no	—
323	C₂²×C₄	—	225	1	no	—
324	C₄⋊C₄	—	225	4	no	—
325	C₃×C₅	—	2	6	no	—
326	C₃×C₅	C₂×Dic₃⋊AGL(1,𝔽₅)	1	6	yes	complemented
327	C₃×C₅	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	25	1	no	—
330	C₂²×C₃	—	25	1	no	—
331	C₂²×C₃	—	25	2	no	—
332	C₂²×C₃	—	25	2	no	—
333	C₂²×C₃	—	25	1	no	—
334	C₂²×C₃	—	25	1	no	—
335	C₂²×C₃	—	25	2	no	—
336	C₂²×C₃	—	25	2	no	—
337	C₂²×C₃	—	50	1	no	—
338	C₂²×C₃	—	50	2	no	—
339	C₂²×C₃	—	50	1	no	—
340	C₂²×C₃	—	50	2	no	—
341	C₂²×C₃	D₃×#1043	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₃⋊#1043	1	1	yes	characteristic
343	C₃×C₄	—	3	2	no	—
344	C₃×C₄	—	75	2	no	—
345	C₃×C₄	—	150	2	no	—
346	Dic₃	—	25	2	no	—
347	Dic₃	—	50	2	no	—
348	Dic₃	—	150	2	no	—
349	Dic₃	—	150	2	no	—
350	Dic₃	—	150	2	no	—
351	Dic₃	—	150	2	no	—
352	Dic₃	C₂×C₃⋊#1043	1	2	yes	complemented
353	C₂×C₅	Dic₃⋊ΓL(1,𝔽₁₆)	1	12	yes	complemented
354	C₂×C₅	C₂×D₃×ΓL(1,𝔽₁₆)	1	6	yes	—
355	D₅	—	5	12	no	—
356	D₅	—	5	6	no	—
357	D₅	—	5	6	no	—
358	C₃²	C₂×C₄⋊#1043	1	1	yes	characteristic, complemented, Sylow
359	C₂³	—	25	1	no	—
360	C₂×C₄	—	3	1	no	—
361	C₂×C₄	—	75	2	no	—
362	C₂×C₄	—	75	2	no	—
363	C₂×C₄	—	75	1	no	—
364	C₂×C₄	—	75	2	no	—
365	C₂×C₄	—	150	2	no	—
366	C₂×C₄	—	450	2	no	—
367	C₂×C₄	—	225	2	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	2	no	—
370	C₂×C₃	—	25	1	no	—
371	C₂×C₃	—	25	2	no	—
372	C₂×C₃	—	25	1	no	—
373	C₂×C₃	—	25	1	no	—
374	C₂×C₃	—	25	1	no	—
375	C₂×C₃	—	25	2	no	—
376	C₂×C₃	—	50	1	no	—
377	C₂×C₃	—	50	1	no	—
378	C₂×C₃	—	50	2	no	—
379	C₂×C₃	Dic₃⋊#1043	1	2	yes	complemented
380	C₂×C₃	C₄⋊(C₃⋊#1043)	1	2	yes	complemented
381	C₂×C₃	C₂×D₃×#1043	1	1	yes	characteristic
382	C₂×C₃	C₂²×C₃⋊#1043	1	1	yes	characteristic
383	C₅	C₂×Dic₃⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
384	C₂²	—	25	1	no	—
385	C₂²	—	25	1	no	—
386	C₂²	—	25	2	no	—
387	C₂²	—	25	2	no	—
388	C₂²	D₃×C₃⋊#1043	1	1	yes	characteristic
389	C₄	—	3	2	no	—
390	C₄	—	75	2	no	—
391	C₄	—	150	2	no	—
392	C₄	—	450	2	no	—
393	C₃	—	2	1	no	—
394	C₃	C₂×C₄⋊(C₃⋊#1043)	1	1	yes	characteristic, complemented
395	C₃	C₂×Dic₃⋊#1043	1	1	yes	characteristic, complemented
396	C₂	—	25	1	no	—
397	C₂	—	25	1	no	—
398	C₂	—	25	2	no	—
399	C₂	#72229544	1	2	yes	direct product factor
400	C₂	C₂×D₃×C₃⋊#1043	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₃⋊#1043
commutator	C₂×C₃²×C₅²	C₂²×C₄
Frattini	C₂	C₂×D₃×C₃⋊#1043
Fitting, socle	C₂²×C₃²×C₅²	C₂×C₄
prime radical	C₂²×C₃²×C₅⋊D₅	C₂²
cosocle	C₂×C₃²×C₅⋊D₅	C₂³
hypocenter	C₃²×C₅²	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃²×C₅² ▷ C₃²×C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
4. #72229544	C₂	direct (N × H)
12. C₂×C₃×C₃⋊#1039	C₄	semidirect
13. C₂×C₃×C₅²×Dic₃	C₄	semidirect
14. C₃×Dic₃×C₅⋊D₅	C₄	semidirect
33. C₃×C₃⋊#1039	C₂×C₄	semidirect
34. C₃×C₅²×Dic₃	C₂×C₄	semidirect
55. C₂×C₃⋊#1039	Dic₃	semidirect
56. C₂×C₅²×Dic₃	Dic₃	semidirect
60. Dic₃×C₅⋊D₅	Dic₃	semidirect
64. C₂×C₃²×C₅²	C₄⋊C₄	semidirect
66. C₃²×C₅⋊D₅	C₄⋊C₄	semidirect
79. C₂×C₃×C₅×Dic₃	AGL(1,𝔽₅)	semidirect
104. C₃⋊#1039	C₂×Dic₃	semidirect
105. C₅²×Dic₃	C₂×Dic₃	semidirect
117. C₃²×C₅²	C₂×C₄⋊C₄	semidirect
135. C₃×C₅×Dic₃	C₂×AGL(1,𝔽₅)	semidirect
139. C₂×C₃×C₅²	Dic₃⋊C₄	semidirect
140. C₂×C₃×C₅²	C₄⋊Dic₃	semidirect
146. C₃×C₅⋊D₅	Dic₃⋊C₄	semidirect
147. C₃×C₅⋊D₅	C₄⋊Dic₃	semidirect
172. C₂×C₅×Dic₃	ΓL(1,𝔽₁₆)	semidirect
189. C₂×C₃²×C₅	C₄⋊AGL(1,𝔽₅)	semidirect
199. C₃×C₅²	C₂×Dic₃⋊C₄	semidirect
200. C₃×C₅²	C₂×C₄⋊Dic₃	semidirect
209. C₂×C₃×Dic₃	#1043	semidirect
234. C₅×Dic₃	C₂×ΓL(1,𝔽₁₆)	semidirect
235. C₂×C₅²	Dic₃⋊Dic₃	semidirect
237. C₅⋊D₅	Dic₃⋊Dic₃	semidirect
249. C₃²×C₅	C₂×C₄⋊AGL(1,𝔽₅)	semidirect
267. C₃×Dic₃	C₂×#1043	semidirect
271. C₂×C₃×C₅	Dic₃⋊AGL(1,𝔽₅)	semidirect
272. C₂×C₃×C₅	C₄⋊ΓL(1,𝔽₁₆)	semidirect
284. C₅²	C₂×Dic₃⋊Dic₃	semidirect
306. C₂×Dic₃	C₃⋊#1043	semidirect
319. C₂×C₃²	C₄⋊#1043	semidirect
326. C₃×C₅	C₂×Dic₃⋊AGL(1,𝔽₅)	semidirect
327. C₃×C₅	C₂×C₄⋊ΓL(1,𝔽₁₆)	semidirect
352. Dic₃	C₂×C₃⋊#1043	semidirect
353. C₂×C₅	Dic₃⋊ΓL(1,𝔽₁₆)	semidirect
358. C₃²	C₂×C₄⋊#1043	semidirect
379. C₂×C₃	Dic₃⋊#1043	semidirect
380. C₂×C₃	C₄⋊(C₃⋊#1043)	semidirect
383. C₅	C₂×Dic₃⋊ΓL(1,𝔽₁₆)	semidirect
394. C₃	C₂×C₄⋊(C₃⋊#1043)	semidirect
395. C₃	C₂×Dic₃⋊#1043	semidirect
399. C₂	#72229544	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₃⋊#1043	2
C₂×Dic₃⋊#1043	3
C₂×C₃×Dic₃×C₅⋊D₅	2
#72229544	2
C₂×C₄⋊(C₃⋊#1043)	3
C₂²×C₃⋊(C₃⋊#1043)	2
C₂×Dic₃⋊ΓL(1,𝔽₁₆)	5

Subgroups — C2×#72229544 #72231566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72229544 #72231566