Subgroups — C₃×#87284 #11904278

Order 1152.

4249 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5830	C₂	1	2	yes	maximal, complemented
4	C₃×#5829	C₂	1	8	yes	maximal, complemented
5	C₃×#5828	C₂	1	2	yes	maximal, complemented
6	C₃×#5804	C₂	1	4	yes	maximal, complemented
7	C₃×D₄×#67	C₂	1	8	yes	maximal, complemented
8	C₂×C₃×#937	C₂	1	4	yes	maximal, complemented
9	C₃×#5798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3484	—	3	1	no	maximal
11	#87284	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
13	C₃²×H(5,𝔽₂)	—	2	8	no	—
14	C₂×C₃²×#41	C₂²	1	2	yes	complemented
15	C₂×C₃²×#41	C₂²	1	4	yes	complemented
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×D₄	C₂²	1	4	yes	complemented
18	C₂²×C₃²×D₄	C₂²	1	4	yes	complemented
19	C₂²×C₃×#67	C₂²	1	2	yes	complemented
20	C₂²×C₃×#67	C₂²	1	8	yes	complemented
21	C₂×C₃×D₃×D₄	—	2	8	no	—
22	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
23	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
25	C₃×#953	C₂²	1	8	yes	complemented
26	C₂×C₃×#217	C₂²	1	4	yes	complemented
27	C₃×#947	C₂²	1	4	yes	complemented
28	C₃×#946	C₂²	1	4	yes	complemented
29	C₃×#940	C₂²	1	4	yes	complemented
30	C₃×#939	C₂²	1	16	yes	complemented
31	C₃×#938	C₂²	1	4	yes	complemented
32	C₃×#937	C₂²	1	4	yes	complemented
33	C₃×#937	C₂²	1	16	yes	complemented
34	C₃×#937	C₂²	1	8	yes	complemented
35	C₃×#935	C₂²	1	4	yes	complemented
36	C₃×D₄×Dic₃	C₂²	1	8	yes	complemented
37	C₃×#930	C₂²	1	8	yes	complemented
38	C₃×#929	C₂²	1	8	yes	complemented
39	C₃×C₄×#67	C₂²	1	8	yes	complemented
40	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
41	C₃×#926	C₂²	1	2	yes	complemented
42	C₂×C₃×H(5,𝔽₂)	—	2	1	no	—
43	C₂×C₃×H(5,𝔽₂)	D₃	1	1	yes	characteristic, complemented
44	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×D₄	—	3	1	no	—
46	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#546	—	3	8	no	—
48	C₃×D₄²	—	3	8	no	—
49	C₃×#535	—	3	2	no	—
50	C₃×#534	—	3	4	no	—
51	C₃×#525	—	3	2	no	—
52	C₂×C₃×#120	—	3	4	no	—
53	C₃×#518	—	3	1	no	—
54	#5830	C₂×C₃	1	2	yes	complemented
55	#5829	C₂×C₃	1	8	yes	complemented
56	#5828	C₂×C₃	1	2	yes	complemented
57	#5804	C₂×C₃	1	4	yes	complemented
58	D₄×#67	C₂×C₃	1	8	yes	complemented
59	C₂×#937	C₂×C₃	1	4	yes	complemented
60	#5798	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃²	C₂³	1	2	yes	—
62	C₂⁴×C₃²	C₂³	1	4	yes	complemented
63	C₂³×C₃×D₃	—	2	8	no	—
64	C₂³×C₃×D₃	—	4	8	no	—
65	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
66	C₂³×C₃×D₃	C₂³	1	8	yes	—
67	C₂³×C₃×D₃	C₂³	1	2	yes	—
68	C₃²×#41	—	2	16	no	—
69	C₃²×#41	—	2	8	no	—
70	C₂×C₃²×Q₈	C₂³	1	2	yes	complemented
71	C₂×C₃²×D₄	—	2	16	no	—
72	C₂×C₃²×D₄	—	2	16	no	—
73	C₂×C₃²×D₄	D₄	1	8	yes	complemented
74	C₂×C₃²×D₄	C₂³	1	4	yes	—
75	C₂×C₃²×D₄	C₂³	1	4	yes	—
76	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
77	C₂×C₃²×D₄	C₂³	1	2	yes	complemented
78	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
80	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
81	C₂×C₃×#67	—	2	8	no	—
82	C₂×C₃×#67	—	4	16	no	—
83	C₂×C₃×#67	C₂³	1	8	yes	—
84	C₂×C₃×#67	C₂³	1	8	yes	—
85	C₂×C₃×#67	C₂³	1	16	yes	complemented
86	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₃×Dic₃	C₂³	1	8	yes	complemented
88	C₃×D₃×D₄	—	2	32	no	—
89	C₂×C₃×D₁₂	—	2	4	no	—
90	C₂×C₃×D₁₂	C₂³	1	4	yes	—
91	C₂×C₃×C₄×D₃	—	2	4	no	—
92	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
93	C₃×#217	C₂³	1	4	yes	—
94	C₃×#217	C₂³	1	8	yes	complemented
95	C₃×#217	C₂³	1	8	yes	complemented
96	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
97	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
98	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
99	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
100	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
101	#3484	—	3	1	no	Sylow
102	C₂⁵×C₃	—	3	2	no	—
103	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
104	C₃×H(5,𝔽₂)	—	2	16	no	—
105	C₃×H(5,𝔽₂)	—	2	8	no	—
106	C₃×H(5,𝔽₂)	—	2	8	no	—
107	C₂×C₃×#41	—	2	2	no	—
108	C₂×C₃×#41	—	2	4	no	—
109	C₂×C₃×#41	C₂×D₃	1	2	yes	complemented
110	C₂×C₃×#41	C₂×D₃	1	4	yes	complemented
111	C₂×C₃×#41	C₂²×C₃	1	2	yes	complemented
112	C₂×C₃×#41	C₂²×C₃	1	4	yes	complemented
113	C₂²×C₃×D₄	—	2	1	no	—
114	C₂²×C₃×D₄	—	2	4	no	—
115	C₂²×C₃×D₄	—	2	4	no	—
116	C₂²×C₃×D₄	—	3	2	no	—
117	C₂²×C₃×D₄	—	3	8	no	—
118	C₂²×C₃×D₄	—	3	8	no	—
119	C₂²×C₃×D₄	—	3	1	no	—
120	C₂²×C₃×D₄	—	6	8	no	—
121	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂×D₃	1	4	yes	complemented
123	C₂²×C₃×D₄	C₂×D₃	1	4	yes	complemented
124	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	complemented
126	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	complemented
127	C₂³×C₃×C₄	—	3	1	no	—
128	C₂²×#67	C₂²×C₃	1	2	yes	complemented
129	C₂²×#67	C₂²×C₃	1	8	yes	complemented
130	C₂×D₃×D₄	—	2	8	no	—
131	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
132	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₃×#127	—	3	4	no	—
135	C₃×#124	—	3	4	no	—
136	C₃×#123	—	3	4	no	—
137	C₃×#123	—	3	8	no	—
138	C₃×C₂²⋊Q₈	—	3	4	no	—
139	C₃×#121	—	3	4	no	—
140	C₃×#121	—	3	16	no	—
141	C₃×#121	—	3	8	no	—
142	C₃×#120	—	3	8	no	—
143	C₃×#120	—	3	4	no	—
144	C₃×#120	—	3	8	no	—
145	C₃×#120	—	3	16	no	—
146	C₃×C₄×D₄	—	3	8	no	—
147	C₃×C₄×D₄	—	3	8	no	—
148	C₃×#117	—	3	2	no	—
149	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
150	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
151	#953	C₂²×C₃	1	8	yes	complemented
152	C₂×#217	C₂²×C₃	1	4	yes	complemented
153	#947	C₂²×C₃	1	4	yes	complemented
154	#946	C₂²×C₃	1	4	yes	complemented
155	#940	C₂²×C₃	1	4	yes	complemented
156	#939	C₂²×C₃	1	16	yes	complemented
157	#938	C₂²×C₃	1	4	yes	complemented
158	#937	C₂²×C₃	1	4	yes	complemented
159	#937	C₂²×C₃	1	16	yes	complemented
160	#937	C₂²×C₃	1	8	yes	complemented
161	#935	C₂²×C₃	1	4	yes	complemented
162	D₄×Dic₃	C₂²×C₃	1	8	yes	complemented
163	#930	C₂²×C₃	1	8	yes	complemented
164	#929	C₂²×C₃	1	8	yes	complemented
165	C₄×#67	C₂²×C₃	1	8	yes	complemented
166	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
167	#926	C₂²×C₃	1	2	yes	complemented
168	C₂³×C₃²	—	2	8	no	—
169	C₂³×C₃²	—	4	4	no	—
170	C₂³×C₃²	—	4	8	no	—
171	C₂³×C₃²	C₂×D₄	1	8	yes	complemented
172	C₂³×C₃²	C₂⁴	1	4	yes	—
173	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
174	C₂³×C₃²	C₂⁴	1	4	yes	—
175	C₂²×C₃×D₃	—	2	2	no	—
176	C₂²×C₃×D₃	—	2	4	no	—
177	C₂²×C₃×D₃	—	2	4	no	—
178	C₂²×C₃×D₃	—	2	16	no	—
179	C₂²×C₃×D₃	—	2	16	no	—
180	C₂²×C₃×D₃	—	4	8	no	—
181	C₂²×C₃×D₃	—	4	4	no	—
182	C₂²×C₃×D₃	—	4	32	no	—
183	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
184	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
185	C₃²×Q₈	—	2	4	no	—
186	C₃²×D₄	—	2	8	no	—
187	C₃²×D₄	—	2	16	no	—
188	C₃²×D₄	—	2	4	no	—
189	C₃²×D₄	C₂×D₄	1	16	yes	complemented
190	C₂×C₃²×C₄	—	2	8	no	—
191	C₂×C₃²×C₄	—	2	8	no	—
192	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
193	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
194	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
195	C₃×#67	—	2	16	no	—
196	C₃×#67	—	2	16	no	—
197	C₃×#67	—	4	16	no	—
198	C₂×C₃×Dic₃	—	2	2	no	—
199	C₂×C₃×Dic₃	—	4	8	no	—
200	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
201	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
202	C₃×D₁₂	—	2	8	no	—
203	C₃×C₄×D₃	—	2	8	no	—
204	C₂×H(5,𝔽₂)	C₃×D₃	1	1	yes	characteristic, complemented
205	C₂³×D₄	—	3	1	no	—
206	#546	—	3	8	no	—
207	D₄²	—	3	8	no	—
208	#535	—	3	2	no	—
209	#534	—	3	4	no	—
210	#525	—	3	2	no	—
211	C₂×#120	—	3	4	no	—
212	#518	—	3	1	no	—
213	C₂⁴×C₃	—	2	2	no	—
214	C₂⁴×C₃	—	2	4	no	—
215	C₂⁴×C₃	—	3	1	no	—
216	C₂⁴×C₃	—	3	8	no	—
217	C₂⁴×C₃	—	3	2	no	—
218	C₂⁴×C₃	—	6	8	no	—
219	C₂⁴×C₃	—	12	8	no	—
220	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
221	C₂⁴×C₃	C₂²×D₃	1	4	yes	complemented
222	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
223	C₂⁴×C₃	C₂³×C₃	1	4	yes	complemented
224	C₂³×D₃	—	2	8	no	—
225	C₂³×D₃	—	4	8	no	—
226	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
227	C₂³×D₃	C₂³×C₃	1	8	yes	—
228	C₂³×D₃	C₂³×C₃	1	2	yes	—
229	C₃×#41	—	2	32	no	—
230	C₃×#41	—	2	16	no	—
231	C₃×#41	—	2	16	no	—
232	C₃×#41	—	2	16	no	—
233	C₃×#41	—	2	8	no	—
234	C₃×#41	—	2	8	no	—
235	C₂×C₃×Q₈	—	2	2	no	—
236	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	complemented
237	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	complemented
238	C₂×C₃×D₄	—	2	32	no	—
239	C₂×C₃×D₄	—	2	32	no	—
240	C₂×C₃×D₄	—	2	16	no	—
241	C₂×C₃×D₄	—	2	16	no	—
242	C₂×C₃×D₄	—	2	16	no	—
243	C₂×C₃×D₄	—	2	16	no	—
244	C₂×C₃×D₄	—	2	8	no	—
245	C₂×C₃×D₄	—	2	4	no	—
246	C₂×C₃×D₄	—	2	4	no	—
247	C₂×C₃×D₄	—	2	8	no	—
248	C₂×C₃×D₄	—	2	2	no	—
249	C₂×C₃×D₄	—	3	8	no	—
250	C₂×C₃×D₄	—	3	8	no	—
251	C₂×C₃×D₄	—	3	16	no	—
252	C₂×C₃×D₄	—	3	4	no	—
253	C₂×C₃×D₄	—	6	8	no	—
254	C₂×C₃×D₄	—	6	32	no	—
255	C₂×C₃×D₄	—	6	4	no	—
256	C₂×C₃×D₄	—	12	16	no	—
257	C₂×C₃×D₄	#67	1	8	yes	complemented
258	C₂×C₃×D₄	C₃×D₄	1	8	yes	complemented
259	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
260	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
261	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
262	C₂×C₃×D₄	C₂²×D₃	1	2	yes	complemented
263	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
264	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
265	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
266	C₂×C₃×D₄	C₂³×C₃	1	2	yes	complemented
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	4	no	—
269	C₂²×C₃×C₄	—	2	4	no	—
270	C₂²×C₃×C₄	—	3	1	no	—
271	C₂²×C₃×C₄	—	3	8	no	—
272	C₂²×C₃×C₄	—	3	4	no	—
273	C₂²×C₃×C₄	—	6	4	no	—
274	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
276	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
277	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
279	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
280	C₂×#67	—	2	8	no	—
281	C₂×#67	—	4	16	no	—
282	C₂×#67	C₂³×C₃	1	8	yes	—
283	C₂×#67	C₂³×C₃	1	8	yes	—
284	C₂×#67	C₂³×C₃	1	16	yes	complemented
285	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₂²×Dic₃	C₂³×C₃	1	8	yes	complemented
287	D₃×D₄	—	2	32	no	—
288	C₂×D₁₂	—	2	4	no	—
289	C₂×D₁₂	C₂³×C₃	1	4	yes	—
290	C₂×C₄×D₃	—	2	4	no	—
291	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
292	C₃×C₄⋊C₄	—	3	8	no	—
293	C₃×C₄⋊C₄	—	3	4	no	—
294	C₃×C₂²⋊C₄	—	3	4	no	—
295	C₃×C₂²⋊C₄	—	3	8	no	—
296	C₃×C₂²⋊C₄	—	3	8	no	—
297	C₃×C₂²⋊C₄	—	3	8	no	—
298	C₃×C₂²⋊C₄	—	3	16	no	—
299	C₃×C₄²	—	3	4	no	—
300	#217	C₂³×C₃	1	4	yes	—
301	#217	C₂³×C₃	1	8	yes	complemented
302	#217	C₂³×C₃	1	8	yes	complemented
303	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
304	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
305	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
306	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
307	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
308	C₂²×C₃²	—	2	4	no	—
309	C₂²×C₃²	—	2	8	no	—
310	C₂²×C₃²	—	2	2	no	—
311	C₂²×C₃²	—	2	8	no	—
312	C₂²×C₃²	—	4	8	no	—
313	C₂²×C₃²	—	8	8	no	—
314	C₂²×C₃²	C₂²×D₄	1	2	yes	—
315	C₂²×C₃²	C₂²×D₄	1	8	yes	—
316	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
317	C₂×C₃×D₃	—	2	8	no	—
318	C₂×C₃×D₃	—	2	2	no	—
319	C₂×C₃×D₃	—	2	2	no	—
320	C₂×C₃×D₃	—	2	4	no	—
321	C₂×C₃×D₃	—	2	8	no	—
322	C₂×C₃×D₃	—	4	32	no	—
323	C₂×C₃×D₃	—	4	8	no	—
324	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	complemented
325	C₃²×C₄	—	2	4	no	—
326	C₃²×C₄	C₂²×D₄	1	4	yes	—
327	C₃×Dic₃	—	2	2	no	—
328	C₃×Dic₃	—	2	8	no	—
329	C₂⁵	—	3	2	no	—
330	H(5,𝔽₂)	—	2	8	no	—
331	C₂×#41	C₂×C₃×D₃	1	2	yes	complemented
332	C₂×#41	C₂×C₃×D₃	1	4	yes	complemented
333	C₂²×D₄	—	3	2	no	—
334	C₂²×D₄	—	3	8	no	—
335	C₂²×D₄	—	3	8	no	—
336	C₂²×D₄	—	3	1	no	—
337	C₂²×D₄	—	6	8	no	—
338	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
339	C₂²×D₄	C₂×C₃×D₃	1	4	yes	complemented
340	C₂²×D₄	C₂×C₃×D₃	1	4	yes	complemented
341	C₂³×C₄	—	3	1	no	—
342	#127	—	3	4	no	—
343	#124	—	3	4	no	—
344	#123	—	3	4	no	—
345	#123	—	3	8	no	—
346	C₂²⋊Q₈	—	3	4	no	—
347	#121	—	3	4	no	—
348	#121	—	3	16	no	—
349	#121	—	3	8	no	—
350	#120	—	3	8	no	—
351	#120	—	3	4	no	—
352	#120	—	3	8	no	—
353	#120	—	3	16	no	—
354	C₄×D₄	—	3	8	no	—
355	C₄×D₄	—	3	8	no	—
356	#117	—	3	2	no	—
357	C₂×C₂²⋊C₄	—	3	4	no	—
358	C₂×C₂²⋊C₄	—	3	8	no	—
359	C₂³×C₃	—	2	16	no	—
360	C₂³×C₃	—	2	8	no	—
361	C₂³×C₃	—	2	8	no	—
362	C₂³×C₃	—	2	4	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	4	no	—
365	C₂³×C₃	—	2	8	no	—
366	C₂³×C₃	—	3	2	no	—
367	C₂³×C₃	—	3	4	no	—
368	C₂³×C₃	—	4	4	no	—
369	C₂³×C₃	—	4	4	no	—
370	C₂³×C₃	—	4	8	no	—
371	C₂³×C₃	—	4	8	no	—
372	C₂³×C₃	—	6	4	no	—
373	C₂³×C₃	—	6	16	no	—
374	C₂³×C₃	—	6	2	no	—
375	C₂³×C₃	—	6	16	no	—
376	C₂³×C₃	—	6	4	no	—
377	C₂³×C₃	—	8	4	no	—
378	C₂³×C₃	—	8	8	no	—
379	C₂³×C₃	—	12	8	no	—
380	C₂³×C₃	—	12	4	no	—
381	C₂³×C₃	—	12	32	no	—
382	C₂³×C₃	C₂×#67	1	8	yes	complemented
383	C₂³×C₃	C₂×C₃×D₄	1	8	yes	complemented
384	C₂³×C₃	C₂³×D₃	1	4	yes	—
385	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
386	C₂³×C₃	C₂³×D₃	1	4	yes	—
387	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
388	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
389	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
390	C₂²×D₃	—	2	2	no	—
391	C₂²×D₃	—	2	4	no	—
392	C₂²×D₃	—	2	4	no	—
393	C₂²×D₃	—	2	16	no	—
394	C₂²×D₃	—	2	16	no	—
395	C₂²×D₃	—	4	8	no	—
396	C₂²×D₃	—	4	4	no	—
397	C₂²×D₃	—	4	32	no	—
398	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
399	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
400	C₃×Q₈	—	2	8	no	—
401	C₃×Q₈	—	2	4	no	—
402	C₃×Q₈	—	2	4	no	—
403	C₃×D₄	—	2	16	no	—
404	C₃×D₄	—	2	32	no	—
405	C₃×D₄	—	2	8	no	—
406	C₃×D₄	—	2	8	no	—
407	C₃×D₄	—	2	16	no	—
408	C₃×D₄	—	2	8	no	—
409	C₃×D₄	—	2	16	no	—
410	C₃×D₄	—	2	4	no	—
411	C₃×D₄	—	2	4	no	—
412	C₃×D₄	—	2	16	no	—
413	C₃×D₄	—	6	16	no	—
414	C₃×D₄	—	6	16	no	—
415	C₃×D₄	—	6	8	no	—
416	C₃×D₄	—	12	16	no	—
417	C₃×D₄	C₂×#67	1	16	yes	complemented
418	C₃×D₄	C₂×C₃×D₄	1	16	yes	complemented
419	C₂×C₃×C₄	—	2	16	no	—
420	C₂×C₃×C₄	—	2	16	no	—
421	C₂×C₃×C₄	—	2	8	no	—
422	C₂×C₃×C₄	—	2	8	no	—
423	C₂×C₃×C₄	—	2	8	no	—
424	C₂×C₃×C₄	—	2	8	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	4	no	—
428	C₂×C₃×C₄	—	3	8	no	—
429	C₂×C₃×C₄	—	3	2	no	—
430	C₂×C₃×C₄	—	6	2	no	—
431	C₂×C₃×C₄	—	6	8	no	—
432	C₂×C₃×C₄	—	12	8	no	—
433	C₂×C₃×C₄	C₂×#67	1	4	yes	complemented
434	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
435	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
436	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
437	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
438	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
439	#67	—	2	16	no	—
440	#67	—	2	16	no	—
441	#67	—	4	16	no	—
442	C₂×Dic₃	—	2	2	no	—
443	C₂×Dic₃	—	4	8	no	—
444	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
445	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
446	D₁₂	—	2	8	no	—
447	C₄×D₃	—	2	8	no	—
448	C₂×C₃²	—	2	2	no	—
449	C₂×C₃²	—	2	8	no	—
450	C₂×C₃²	—	4	4	no	—
451	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
452	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₃×D₃	—	2	4	no	—
454	C₃×D₃	—	4	4	no	—
455	C₂⁴	—	3	1	no	—
456	C₂⁴	—	3	8	no	—
457	C₂⁴	—	3	2	no	—
458	C₂⁴	—	6	8	no	—
459	C₂⁴	—	12	8	no	—
460	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
461	C₂⁴	C₂²×C₃×D₃	1	4	yes	complemented
462	#41	—	2	16	no	—
463	#41	—	2	8	no	—
464	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	complemented
465	C₂×D₄	—	2	16	no	—
466	C₂×D₄	—	2	16	no	—
467	C₂×D₄	—	3	8	no	—
468	C₂×D₄	—	3	8	no	—
469	C₂×D₄	—	3	16	no	—
470	C₂×D₄	—	3	4	no	—
471	C₂×D₄	—	6	8	no	—
472	C₂×D₄	—	6	32	no	—
473	C₂×D₄	—	6	4	no	—
474	C₂×D₄	—	12	16	no	—
475	C₂×D₄	C₃×#67	1	8	yes	complemented
476	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
477	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
478	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
479	C₂×D₄	C₂²×C₃×D₃	1	2	yes	complemented
480	C₂²×C₄	—	3	1	no	—
481	C₂²×C₄	—	3	8	no	—
482	C₂²×C₄	—	3	4	no	—
483	C₂²×C₄	—	6	4	no	—
484	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
486	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
487	C₄⋊C₄	—	3	4	no	—
488	C₄⋊C₄	—	3	8	no	—
489	C₂²⋊C₄	—	3	4	no	—
490	C₂²⋊C₄	—	3	8	no	—
491	C₂²⋊C₄	—	3	8	no	—
492	C₂²⋊C₄	—	3	8	no	—
493	C₂²⋊C₄	—	3	16	no	—
494	C₄²	—	3	4	no	—
495	C₂²×C₃	—	2	8	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	8	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	8	no	—
500	C₂²×C₃	—	2	8	no	—
501	C₂²×C₃	—	2	4	no	—
502	C₂²×C₃	—	2	4	no	—
503	C₂²×C₃	—	2	8	no	—
504	C₂²×C₃	—	2	8	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	3	4	no	—
508	C₂²×C₃	—	4	8	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	8	no	—
511	C₂²×C₃	—	4	8	no	—
512	C₂²×C₃	—	4	8	no	—
513	C₂²×C₃	—	6	8	no	—
514	C₂²×C₃	—	6	2	no	—
515	C₂²×C₃	—	6	2	no	—
516	C₂²×C₃	—	6	8	no	—
517	C₂²×C₃	—	6	4	no	—
518	C₂²×C₃	—	8	8	no	—
519	C₂²×C₃	—	8	8	no	—
520	C₂²×C₃	—	8	8	no	—
521	C₂²×C₃	—	8	16	no	—
522	C₂²×C₃	—	12	32	no	—
523	C₂²×C₃	—	12	8	no	—
524	C₂²×C₃	C₂²×#67	1	8	yes	—
525	C₂²×C₃	C₂²×#67	1	2	yes	—
526	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
527	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
528	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
529	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
530	C₂×D₃	—	2	8	no	—
531	C₂×D₃	—	2	2	no	—
532	C₂×D₃	—	2	2	no	—
533	C₂×D₃	—	2	4	no	—
534	C₂×D₃	—	2	8	no	—
535	C₂×D₃	—	4	32	no	—
536	C₂×D₃	—	4	8	no	—
537	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
538	C₃×C₄	—	2	8	no	—
539	C₃×C₄	—	2	4	no	—
540	C₃×C₄	—	2	4	no	—
541	C₃×C₄	—	2	4	no	—
542	C₃×C₄	—	6	8	no	—
543	C₃×C₄	—	6	2	no	—
544	C₃×C₄	C₂²×#67	1	4	yes	—
545	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
546	Dic₃	—	2	2	no	—
547	Dic₃	—	2	8	no	—
548	C₃²	#3484	1	1	yes	characteristic, complemented, Sylow
549	C₂³	—	2	8	no	—
550	C₂³	—	3	2	no	—
551	C₂³	—	3	4	no	—
552	C₂³	—	4	4	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	6	4	no	—
555	C₂³	—	6	16	no	—
556	C₂³	—	6	2	no	—
557	C₂³	—	6	16	no	—
558	C₂³	—	6	4	no	—
559	C₂³	—	12	8	no	—
560	C₂³	—	12	4	no	—
561	C₂³	—	12	32	no	—
562	C₂³	C₂×C₃×#67	1	8	yes	complemented
563	C₂³	C₂³×C₃×D₃	1	4	yes	—
564	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
565	C₂³	C₂³×C₃×D₃	1	4	yes	—
566	Q₈	—	2	4	no	—
567	D₄	—	2	8	no	—
568	D₄	—	2	16	no	—
569	D₄	—	2	4	no	—
570	D₄	—	6	16	no	—
571	D₄	—	6	16	no	—
572	D₄	—	6	8	no	—
573	D₄	—	12	16	no	—
574	D₄	C₂×C₃×#67	1	16	yes	complemented
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	3	8	no	—
578	C₂×C₄	—	3	2	no	—
579	C₂×C₄	—	6	2	no	—
580	C₂×C₄	—	6	8	no	—
581	C₂×C₄	—	12	8	no	—
582	C₂×C₄	C₂×C₃×#67	1	4	yes	complemented
583	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
584	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
585	C₂×C₃	—	2	2	no	—
586	C₂×C₃	—	2	8	no	—
587	C₂×C₃	—	2	2	no	—
588	C₂×C₃	—	2	8	no	—
589	C₂×C₃	—	2	2	no	—
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	4	2	no	—
592	C₂×C₃	—	4	8	no	—
593	C₂×C₃	—	4	8	no	—
594	C₂×C₃	—	4	4	no	—
595	C₂×C₃	—	4	4	no	—
596	C₂×C₃	—	6	4	no	—
597	C₂×C₃	—	12	4	no	—
598	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
599	C₂×C₃	C₂³×#67	1	1	yes	characteristic
600	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
601	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
602	D₃	—	2	4	no	—
603	D₃	—	4	4	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	3	4	no	—
609	C₂²	—	4	8	no	—
610	C₂²	—	6	8	no	—
611	C₂²	—	6	2	no	—
612	C₂²	—	6	2	no	—
613	C₂²	—	6	8	no	—
614	C₂²	—	6	4	no	—
615	C₂²	—	8	8	no	—
616	C₂²	—	12	32	no	—
617	C₂²	—	12	8	no	—
618	C₂²	C₂²×C₃×#67	1	8	yes	—
619	C₂²	C₂²×C₃×#67	1	2	yes	—
620	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
621	C₄	—	2	4	no	—
622	C₄	—	6	8	no	—
623	C₄	—	6	2	no	—
624	C₄	C₂²×C₃×#67	1	4	yes	—
625	C₃	—	2	1	no	—
626	C₃	#87284	1	1	yes	characteristic, direct product factor
627	C₃	C₃×#3484	1	1	yes	characteristic, complemented
628	C₂	—	2	2	no	—
629	C₂	—	2	8	no	—
630	C₂	—	4	4	no	—
631	C₂	—	6	4	no	—
632	C₂	—	12	4	no	—
633	C₂	C₃×D₃×H(5,𝔽₂)	1	2	yes	—
634	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×H(5,𝔽₂)	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×H(5,𝔽₂)	D₃
hypocenter	C₃	C₃×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×H(5,𝔽₂)	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₃×#5830	C₂	semidirect
4. C₃×#5829	C₂	semidirect
5. C₃×#5828	C₂	semidirect
6. C₃×#5804	C₂	semidirect
7. C₃×D₄×#67	C₂	semidirect
8. C₂×C₃×#937	C₂	semidirect
9. C₃×#5798	C₂	semidirect
11. #87284	C₃	direct (N × H)
12. C₂⁴×C₃×D₃	C₂²	semidirect
14. C₂×C₃²×#41	C₂²	semidirect
15. C₂×C₃²×#41	C₂²	semidirect
17. C₂²×C₃²×D₄	C₂²	semidirect
18. C₂²×C₃²×D₄	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
22. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂²×C₃×D₁₂	C₂²	semidirect
24. C₂²×C₃×C₄×D₃	C₂²	semidirect
25. C₃×#953	C₂²	semidirect
26. C₂×C₃×#217	C₂²	semidirect
27. C₃×#947	C₂²	semidirect
28. C₃×#946	C₂²	semidirect
29. C₃×#940	C₂²	semidirect
30. C₃×#939	C₂²	semidirect
31. C₃×#938	C₂²	semidirect
32. C₃×#937	C₂²	semidirect
33. C₃×#937	C₂²	semidirect
34. C₃×#937	C₂²	semidirect
35. C₃×#935	C₂²	semidirect
36. C₃×D₄×Dic₃	C₂²	semidirect
37. C₃×#930	C₂²	semidirect
38. C₃×#929	C₂²	semidirect
39. C₃×C₄×#67	C₂²	semidirect
40. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₃×#926	C₂²	semidirect
43. C₂×C₃×H(5,𝔽₂)	D₃	semidirect
44. C₂×C₃×H(5,𝔽₂)	C₂×C₃	semidirect
46. C₂²×D₃×D₄	C₂×C₃	semidirect
54. #5830	C₂×C₃	semidirect
55. #5829	C₂×C₃	semidirect
56. #5828	C₂×C₃	semidirect
57. #5804	C₂×C₃	semidirect
58. D₄×#67	C₂×C₃	semidirect
59. C₂×#937	C₂×C₃	semidirect
60. #5798	C₂×C₃	semidirect
62. C₂⁴×C₃²	C₂³	semidirect
70. C₂×C₃²×Q₈	C₂³	semidirect
73. C₂×C₃²×D₄	D₄	semidirect
76. C₂×C₃²×D₄	C₂³	semidirect
77. C₂×C₃²×D₄	C₂³	semidirect
79. C₂²×C₃²×C₄	C₂³	semidirect
80. C₂²×C₃²×C₄	C₂³	semidirect
85. C₂×C₃×#67	C₂³	semidirect
87. C₂²×C₃×Dic₃	C₂³	semidirect
94. C₃×#217	C₂³	semidirect
95. C₃×#217	C₂³	semidirect
97. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
98. C₃×C₄⋊Dic₃	C₂³	semidirect
99. C₃×Dic₃⋊C₄	C₂³	semidirect
100. C₃×C₄×Dic₃	C₂³	semidirect
103. C₂⁴×D₃	C₂²×C₃	semidirect
109. C₂×C₃×#41	C₂×D₃	semidirect
110. C₂×C₃×#41	C₂×D₃	semidirect
111. C₂×C₃×#41	C₂²×C₃	semidirect
112. C₂×C₃×#41	C₂²×C₃	semidirect
122. C₂²×C₃×D₄	C₂×D₃	semidirect
123. C₂²×C₃×D₄	C₂×D₃	semidirect
125. C₂²×C₃×D₄	C₂²×C₃	semidirect
126. C₂²×C₃×D₄	C₂²×C₃	semidirect
128. C₂²×#67	C₂²×C₃	semidirect
129. C₂²×#67	C₂²×C₃	semidirect
131. C₂×D₃×D₄	C₂²×C₃	semidirect
132. C₂²×D₁₂	C₂²×C₃	semidirect
133. C₂²×C₄×D₃	C₂²×C₃	semidirect
151. #953	C₂²×C₃	semidirect
152. C₂×#217	C₂²×C₃	semidirect
153. #947	C₂²×C₃	semidirect
154. #946	C₂²×C₃	semidirect
155. #940	C₂²×C₃	semidirect
156. #939	C₂²×C₃	semidirect
157. #938	C₂²×C₃	semidirect
158. #937	C₂²×C₃	semidirect
159. #937	C₂²×C₃	semidirect
160. #937	C₂²×C₃	semidirect
161. #935	C₂²×C₃	semidirect
162. D₄×Dic₃	C₂²×C₃	semidirect
163. #930	C₂²×C₃	semidirect
164. #929	C₂²×C₃	semidirect
165. C₄×#67	C₂²×C₃	semidirect
166. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
167. #926	C₂²×C₃	semidirect
171. C₂³×C₃²	C₂×D₄	semidirect
189. C₃²×D₄	C₂×D₄	semidirect
192. C₂×C₃²×C₄	C₂×D₄	semidirect
204. C₂×H(5,𝔽₂)	C₃×D₃	semidirect
221. C₂⁴×C₃	C₂²×D₃	semidirect
223. C₂⁴×C₃	C₂³×C₃	semidirect
236. C₂×C₃×Q₈	C₂²×D₃	semidirect
237. C₂×C₃×Q₈	C₂³×C₃	semidirect
257. C₂×C₃×D₄	#67	semidirect
258. C₂×C₃×D₄	C₃×D₄	semidirect
261. C₂×C₃×D₄	C₂²×D₃	semidirect
262. C₂×C₃×D₄	C₂²×D₃	semidirect
265. C₂×C₃×D₄	C₂³×C₃	semidirect
266. C₂×C₃×D₄	C₂³×C₃	semidirect
275. C₂²×C₃×C₄	C₂²×D₃	semidirect
276. C₂²×C₃×C₄	C₂²×D₃	semidirect
278. C₂²×C₃×C₄	C₂³×C₃	semidirect
279. C₂²×C₃×C₄	C₂³×C₃	semidirect
284. C₂×#67	C₂³×C₃	semidirect
286. C₂²×Dic₃	C₂³×C₃	semidirect
301. #217	C₂³×C₃	semidirect
302. #217	C₂³×C₃	semidirect
304. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
305. C₄⋊Dic₃	C₂³×C₃	semidirect
306. Dic₃⋊C₄	C₂³×C₃	semidirect
307. C₄×Dic₃	C₂³×C₃	semidirect
324. C₂×C₃×D₃	H(5,𝔽₂)	semidirect
331. C₂×#41	C₂×C₃×D₃	semidirect
332. C₂×#41	C₂×C₃×D₃	semidirect
339. C₂²×D₄	C₂×C₃×D₃	semidirect
340. C₂²×D₄	C₂×C₃×D₃	semidirect
382. C₂³×C₃	C₂×#67	semidirect
383. C₂³×C₃	C₂×C₃×D₄	semidirect
417. C₃×D₄	C₂×#67	semidirect
418. C₃×D₄	C₂×C₃×D₄	semidirect
433. C₂×C₃×C₄	C₂×#67	semidirect
434. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
461. C₂⁴	C₂²×C₃×D₃	semidirect
464. C₂×Q₈	C₂²×C₃×D₃	semidirect
475. C₂×D₄	C₃×#67	semidirect
478. C₂×D₄	C₂²×C₃×D₃	semidirect
479. C₂×D₄	C₂²×C₃×D₃	semidirect
485. C₂²×C₄	C₂²×C₃×D₃	semidirect
486. C₂²×C₄	C₂²×C₃×D₃	semidirect
537. C₂×D₃	C₃×H(5,𝔽₂)	semidirect
548. C₃²	#3484	semidirect
562. C₂³	C₂×C₃×#67	semidirect
574. D₄	C₂×C₃×#67	semidirect
582. C₂×C₄	C₂×C₃×#67	semidirect
626. C₃	#87284	direct (N × H)
627. C₃	C₃×#3484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×H(5,𝔽₂)	2
C₂²×C₃×D₃×D₄	2
C₃×#5830	2
C₃×#5829	2
C₃×#5828	2
C₃×#5804	2
C₃×D₄×#67	2
C₂×C₃×#937	2
C₃×#5798	2
C₃×#3484	3
#87284	3

Subgroups — C3×#87284 #11904278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87284 #11904278