Subgroups — C₂×C₃×#5805 #11900995

Order 1152.

4473 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#953	C₂	1	4	yes	maximal, complemented
4	C₃×#5805	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#940	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#938	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#936	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#535	—	3	1	no	maximal
10	C₂×#5805	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂⁵×C₃²	C₂²	1	2	yes	—
12	C₂²×C₃²×D₄	—	2	8	no	—
13	C₂²×C₃²×D₄	C₂²	1	2	yes	—
14	C₂²×C₃²×D₄	C₂²	1	2	yes	—
15	C₂²×C₃²×D₄	C₂²	1	8	yes	complemented
16	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#67	C₂²	1	2	yes	—
18	C₂²×C₃×#67	C₂²	1	8	yes	complemented
19	C₂×C₃×#235	—	2	8	no	—
20	C₂×C₃×#235	C₂²	1	8	yes	complemented
21	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
23	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
24	C₃×#953	C₂²	1	32	yes	complemented
25	C₂×C₃×#217	C₂²	1	2	yes	—
26	C₂×C₃×#217	C₂²	1	8	yes	complemented
27	C₃×#940	C₂²	1	16	yes	complemented
28	C₃×#938	C₂²	1	32	yes	complemented
29	C₃×#936	C₂²	1	16	yes	complemented
30	C₃×#926	C₂²	1	8	yes	complemented
31	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
32	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
33	C₂²×C₃×#41	—	3	1	no	—
34	C₂³×C₃×D₄	—	2	1	no	—
35	C₂³×C₃×D₄	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#235	C₂×C₃	1	1	yes	characteristic, complemented
38	C₃×#535	—	3	16	no	—
39	C₂×C₃×#127	—	3	2	no	—
40	C₂×C₃×#124	—	3	2	no	—
41	C₂×C₃×#121	—	3	4	no	—
42	C₂×C₃×#120	—	3	4	no	—
43	C₂×C₃×#117	—	3	1	no	—
44	C₂×#953	C₂×C₃	1	4	yes	complemented
45	#5805	C₂×C₃	1	16	yes	direct product factor
46	C₂×#940	C₂×C₃	1	2	yes	complemented
47	C₂×#938	C₂×C₃	1	4	yes	complemented
48	C₂×#936	C₂×C₃	1	2	yes	complemented
49	C₂×#926	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂⁴×C₃²	—	2	8	no	—
51	C₂⁴×C₃²	—	4	8	no	—
52	C₂⁴×C₃²	C₂³	1	4	yes	—
53	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
54	C₂⁴×C₃²	C₂³	1	8	yes	—
55	C₂³×C₃×D₃	C₂³	1	2	yes	—
56	C₂×C₃²×D₄	—	2	8	no	—
57	C₂×C₃²×D₄	—	2	8	no	—
58	C₂×C₃²×D₄	—	2	32	no	—
59	C₂×C₃²×D₄	C₂³	1	8	yes	—
60	C₂×C₃²×D₄	C₂³	1	8	yes	—
61	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
62	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂³	1	4	yes	—
65	C₂×C₃×#67	—	2	8	no	—
66	C₂×C₃×#67	—	4	16	no	—
67	C₂×C₃×#67	C₂³	1	8	yes	—
68	C₂×C₃×#67	C₂³	1	32	yes	complemented
69	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
70	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
71	C₃×#235	—	2	32	no	—
72	C₂×C₃×D₁₂	—	2	4	no	—
73	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
74	C₂×C₃×C₄×D₃	—	2	8	no	—
75	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
76	C₂×C₃×Dic₆	—	2	4	no	—
77	C₂×C₃×Dic₆	C₂³	1	4	yes	complemented
78	C₃×#217	C₂³	1	8	yes	—
79	C₃×#217	C₂³	1	32	yes	complemented
80	C₃×C₄⋊Dic₃	C₂³	1	8	yes	complemented
81	C₃×C₄×Dic₃	C₂³	1	8	yes	complemented
82	C₂×#535	—	3	1	no	Sylow
83	C₂⁵×C₃	—	2	2	no	—
84	C₂⁵×C₃	C₂×D₃	1	2	yes	—
85	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
86	C₂×C₃×#41	—	3	8	no	—
87	C₂×C₃×#41	—	6	8	no	—
88	C₂²×C₃×Q₈	—	3	1	no	—
89	C₂²×C₃×D₄	—	2	16	no	—
90	C₂²×C₃×D₄	—	2	8	no	—
91	C₂²×C₃×D₄	—	2	8	no	—
92	C₂²×C₃×D₄	—	2	2	no	—
93	C₂²×C₃×D₄	—	2	2	no	—
94	C₂²×C₃×D₄	—	2	8	no	—
95	C₂²×C₃×D₄	—	3	2	no	—
96	C₂²×C₃×D₄	—	3	8	no	—
97	C₂²×C₃×D₄	—	3	1	no	—
98	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
99	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
100	C₂²×C₃×D₄	C₂×D₃	1	8	yes	complemented
101	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
102	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
103	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	complemented
104	C₂³×C₃×C₄	—	2	1	no	—
105	C₂³×C₃×C₄	—	3	2	no	—
106	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
107	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂²×#67	C₂²×C₃	1	2	yes	—
109	C₂²×#67	C₂²×C₃	1	8	yes	complemented
110	C₂×#235	—	2	8	no	—
111	C₂×#235	C₂²×C₃	1	8	yes	complemented
112	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
114	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₃×#127	—	3	16	no	—
116	C₃×#124	—	3	16	no	—
117	C₃×#121	—	3	32	no	—
118	C₃×#120	—	3	32	no	—
119	C₃×#117	—	3	8	no	—
120	C₂×C₃×C₄⋊C₄	—	3	2	no	—
121	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
122	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
123	C₂×C₃×C₄²	—	3	2	no	—
124	#953	C₂²×C₃	1	32	yes	complemented
125	C₂×#217	C₂²×C₃	1	2	yes	—
126	C₂×#217	C₂²×C₃	1	8	yes	complemented
127	#940	C₂²×C₃	1	16	yes	complemented
128	#938	C₂²×C₃	1	32	yes	complemented
129	#936	C₂²×C₃	1	16	yes	complemented
130	#926	C₂²×C₃	1	8	yes	complemented
131	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
132	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
133	C₂³×C₃²	—	2	4	no	—
134	C₂³×C₃²	—	2	16	no	—
135	C₂³×C₃²	—	2	8	no	—
136	C₂³×C₃²	—	2	16	no	—
137	C₂³×C₃²	—	4	16	no	—
138	C₂³×C₃²	—	4	32	no	—
139	C₂³×C₃²	C₂×D₄	1	4	yes	—
140	C₂³×C₃²	C₂⁴	1	8	yes	—
141	C₂³×C₃²	C₂⁴	1	2	yes	—
142	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
143	C₂²×C₃×D₃	—	2	4	no	—
144	C₂²×C₃×D₃	—	2	8	no	—
145	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
146	C₃²×D₄	—	2	16	no	—
147	C₃²×D₄	—	2	16	no	—
148	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
149	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
150	C₂×C₃²×C₄	C₂×D₄	1	16	yes	complemented
151	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
152	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
153	C₃×#67	—	2	16	no	—
154	C₃×#67	—	4	32	no	—
155	C₂×C₃×Dic₃	—	2	4	no	—
156	C₂×C₃×Dic₃	—	2	8	no	—
157	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
158	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
159	C₃×D₁₂	—	2	8	no	—
160	C₃×C₄×D₃	—	2	16	no	—
161	C₃×Dic₆	—	2	8	no	—
162	C₂²×#41	—	3	1	no	—
163	C₂³×D₄	C₃×D₃	1	1	yes	characteristic, complemented
164	#535	—	3	16	no	—
165	C₂×#127	—	3	2	no	—
166	C₂×#124	—	3	2	no	—
167	C₂×#121	—	3	4	no	—
168	C₂×#120	—	3	4	no	—
169	C₂×#117	—	3	1	no	—
170	C₂⁴×C₃	—	2	16	no	—
171	C₂⁴×C₃	—	2	8	no	—
172	C₂⁴×C₃	—	2	8	no	—
173	C₂⁴×C₃	—	2	1	no	—
174	C₂⁴×C₃	—	2	4	no	—
175	C₂⁴×C₃	—	2	8	no	—
176	C₂⁴×C₃	—	3	2	no	—
177	C₂⁴×C₃	—	4	8	no	—
178	C₂⁴×C₃	—	4	8	no	—
179	C₂⁴×C₃	—	4	16	no	—
180	C₂⁴×C₃	C₂²×D₃	1	4	yes	—
181	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
182	C₂⁴×C₃	C₂²×D₃	1	8	yes	—
183	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
184	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
185	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
186	C₂³×D₃	C₂³×C₃	1	2	yes	—
187	C₃×#41	—	6	32	no	—
188	C₂×C₃×Q₈	—	3	4	no	—
189	C₂×C₃×Q₈	—	6	4	no	—
190	C₂×C₃×D₄	—	2	16	no	—
191	C₂×C₃×D₄	—	2	16	no	—
192	C₂×C₃×D₄	—	2	64	no	—
193	C₂×C₃×D₄	—	2	8	no	—
194	C₂×C₃×D₄	—	2	8	no	—
195	C₂×C₃×D₄	—	2	32	no	—
196	C₂×C₃×D₄	—	2	8	no	—
197	C₂×C₃×D₄	—	2	8	no	—
198	C₂×C₃×D₄	—	2	32	no	—
199	C₂×C₃×D₄	—	2	8	no	—
200	C₂×C₃×D₄	—	2	8	no	—
201	C₂×C₃×D₄	—	3	8	no	—
202	C₂×C₃×D₄	—	3	32	no	—
203	C₂×C₃×D₄	—	3	4	no	—
204	C₂×C₃×D₄	—	6	8	no	—
205	C₂×C₃×D₄	—	6	4	no	—
206	C₂×C₃×D₄	—	12	16	no	—
207	C₂×C₃×D₄	C₂²×D₃	1	8	yes	—
208	C₂×C₃×D₄	C₂²×D₃	1	8	yes	—
209	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
210	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
211	C₂²×C₃×C₄	—	2	8	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	—	2	4	no	—
215	C₂²×C₃×C₄	—	3	4	no	—
216	C₂²×C₃×C₄	—	3	2	no	—
217	C₂²×C₃×C₄	—	3	8	no	—
218	C₂²×C₃×C₄	—	6	8	no	—
219	C₂²×C₃×C₄	#67	1	8	yes	complemented
220	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
221	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
224	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
227	C₂×#67	—	2	8	no	—
228	C₂×#67	—	4	16	no	—
229	C₂×#67	C₂³×C₃	1	8	yes	—
230	C₂×#67	C₂³×C₃	1	32	yes	complemented
231	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
232	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
233	#235	—	2	32	no	—
234	C₂×D₁₂	—	2	4	no	—
235	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
236	C₂×C₄×D₃	—	2	8	no	—
237	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
238	C₂×Dic₆	—	2	4	no	—
239	C₂×Dic₆	C₂³×C₃	1	4	yes	complemented
240	C₃×C₄⋊C₄	—	3	8	no	—
241	C₃×C₂²⋊C₄	—	3	8	no	—
242	C₃×C₂²⋊C₄	—	3	32	no	—
243	C₃×C₄²	—	3	8	no	—
244	#217	C₂³×C₃	1	8	yes	—
245	#217	C₂³×C₃	1	32	yes	complemented
246	C₄⋊Dic₃	C₂³×C₃	1	8	yes	complemented
247	C₄×Dic₃	C₂³×C₃	1	8	yes	complemented
248	C₂²×C₃²	—	2	8	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	8	no	—
251	C₂²×C₃²	—	2	16	no	—
252	C₂²×C₃²	—	4	32	no	—
253	C₂²×C₃²	—	4	16	no	—
254	C₂²×C₃²	C₂²×D₄	1	4	yes	—
255	C₂²×C₃²	C₂²×D₄	1	2	yes	—
256	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
257	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
258	C₂×C₃×D₃	—	2	4	no	—
259	C₂×C₃×D₃	—	2	8	no	—
260	C₂×C₃×D₃	—	4	8	no	—
261	C₃²×C₄	C₂²×D₄	1	4	yes	—
262	C₃²×C₄	C₂²×D₄	1	4	yes	—
263	C₃×Dic₃	—	2	4	no	—
264	C₃×Dic₃	—	2	8	no	—
265	C₂⁵	C₂×C₃×D₃	1	2	yes	—
266	C₂×#41	—	3	8	no	—
267	C₂×#41	—	6	8	no	—
268	C₂²×Q₈	—	3	1	no	—
269	C₂²×D₄	—	2	8	no	—
270	C₂²×D₄	—	3	2	no	—
271	C₂²×D₄	—	3	8	no	—
272	C₂²×D₄	—	3	1	no	—
273	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
274	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
275	C₂²×D₄	C₂×C₃×D₃	1	8	yes	complemented
276	C₂³×C₄	—	3	2	no	—
277	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
278	#127	—	3	16	no	—
279	#124	—	3	16	no	—
280	#121	—	3	32	no	—
281	#120	—	3	32	no	—
282	#117	—	3	8	no	—
283	C₂×C₄⋊C₄	—	3	2	no	—
284	C₂×C₂²⋊C₄	—	3	2	no	—
285	C₂×C₂²⋊C₄	—	3	8	no	—
286	C₂×C₄²	—	3	2	no	—
287	C₂³×C₃	—	2	8	no	—
288	C₂³×C₃	—	2	4	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	—	2	32	no	—
291	C₂³×C₃	—	2	16	no	—
292	C₂³×C₃	—	2	16	no	—
293	C₂³×C₃	—	2	16	no	—
294	C₂³×C₃	—	2	8	no	—
295	C₂³×C₃	—	2	16	no	—
296	C₂³×C₃	—	2	8	no	—
297	C₂³×C₃	—	2	16	no	—
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	—	2	1	no	—
300	C₂³×C₃	—	2	8	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	3	4	no	—
303	C₂³×C₃	—	4	16	no	—
304	C₂³×C₃	—	4	16	no	—
305	C₂³×C₃	—	4	16	no	—
306	C₂³×C₃	—	4	32	no	—
307	C₂³×C₃	—	4	64	no	—
308	C₂³×C₃	—	4	32	no	—
309	C₂³×C₃	—	4	32	no	—
310	C₂³×C₃	—	6	8	no	—
311	C₂³×C₃	—	6	4	no	—
312	C₂³×C₃	C₂×#67	1	4	yes	—
313	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
314	C₂³×C₃	C₂³×D₃	1	8	yes	—
315	C₂³×C₃	C₂³×D₃	1	2	yes	—
316	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
317	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
318	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
319	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
320	C₂²×D₃	—	2	4	no	—
321	C₂²×D₃	—	2	8	no	—
322	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
323	C₃×Q₈	—	6	8	no	—
324	C₃×D₄	—	2	32	no	—
325	C₃×D₄	—	2	32	no	—
326	C₃×D₄	—	2	16	no	—
327	C₃×D₄	—	2	16	no	—
328	C₃×D₄	—	2	16	no	—
329	C₃×D₄	—	2	16	no	—
330	C₃×D₄	—	6	16	no	—
331	C₃×D₄	—	6	8	no	—
332	C₃×D₄	—	12	32	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	16	no	—
338	C₂×C₃×C₄	—	3	8	no	—
339	C₂×C₃×C₄	—	3	4	no	—
340	C₂×C₃×C₄	—	6	8	no	—
341	C₂×C₃×C₄	—	6	4	no	—
342	C₂×C₃×C₄	—	6	16	no	—
343	C₂×C₃×C₄	C₂×#67	1	4	yes	—
344	C₂×C₃×C₄	C₂×#67	1	4	yes	—
345	C₂×C₃×C₄	C₂×#67	1	16	yes	complemented
346	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
347	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
348	C₂×C₃×C₄	C₂×C₃×D₄	1	16	yes	complemented
349	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
350	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
351	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
352	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
353	#67	—	2	16	no	—
354	#67	—	4	32	no	—
355	C₂×Dic₃	—	2	4	no	—
356	C₂×Dic₃	—	2	8	no	—
357	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
358	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
359	D₁₂	—	2	8	no	—
360	C₄×D₃	—	2	16	no	—
361	Dic₆	—	2	8	no	—
362	C₂×C₃²	—	2	4	no	—
363	C₂×C₃²	—	4	8	no	—
364	C₂×C₃²	#535	1	4	yes	complemented
365	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
366	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₃×D₃	—	4	4	no	—
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	3	2	no	—
370	C₂⁴	—	4	8	no	—
371	C₂⁴	C₂²×C₃×D₃	1	4	yes	—
372	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₂⁴	C₂²×C₃×D₃	1	8	yes	—
374	#41	—	6	32	no	—
375	C₂×Q₈	—	3	4	no	—
376	C₂×Q₈	—	6	4	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	32	no	—
380	C₂×D₄	—	3	8	no	—
381	C₂×D₄	—	3	32	no	—
382	C₂×D₄	—	3	4	no	—
383	C₂×D₄	—	6	8	no	—
384	C₂×D₄	—	6	4	no	—
385	C₂×D₄	—	12	16	no	—
386	C₂×D₄	C₂²×C₃×D₃	1	8	yes	—
387	C₂×D₄	C₂²×C₃×D₃	1	8	yes	—
388	C₂²×C₄	—	3	4	no	—
389	C₂²×C₄	—	3	2	no	—
390	C₂²×C₄	—	3	8	no	—
391	C₂²×C₄	—	6	8	no	—
392	C₂²×C₄	C₃×#67	1	8	yes	complemented
393	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
396	C₄⋊C₄	—	3	8	no	—
397	C₂²⋊C₄	—	3	8	no	—
398	C₂²⋊C₄	—	3	32	no	—
399	C₄²	—	3	8	no	—
400	C₂²×C₃	—	2	16	no	—
401	C₂²×C₃	—	2	8	no	—
402	C₂²×C₃	—	2	4	no	—
403	C₂²×C₃	—	2	4	no	—
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	8	no	—
406	C₂²×C₃	—	2	16	no	—
407	C₂²×C₃	—	2	16	no	—
408	C₂²×C₃	—	2	8	no	—
409	C₂²×C₃	—	2	8	no	—
410	C₂²×C₃	—	2	16	no	—
411	C₂²×C₃	—	2	4	no	—
412	C₂²×C₃	—	2	4	no	—
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	4	16	no	—
416	C₂²×C₃	—	4	64	no	—
417	C₂²×C₃	—	4	32	no	—
418	C₂²×C₃	—	4	32	no	—
419	C₂²×C₃	—	4	32	no	—
420	C₂²×C₃	—	4	16	no	—
421	C₂²×C₃	—	4	16	no	—
422	C₂²×C₃	—	6	8	no	—
423	C₂²×C₃	—	6	4	no	—
424	C₂²×C₃	—	12	8	no	—
425	C₂²×C₃	#1004	1	4	yes	—
426	C₂²×C₃	C₂²×#67	1	4	yes	—
427	C₂²×C₃	C₂²×#67	1	2	yes	—
428	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
429	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
430	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
431	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
432	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
433	C₂×D₃	—	2	4	no	—
434	C₂×D₃	—	2	8	no	—
435	C₂×D₃	—	4	8	no	—
436	C₃×C₄	—	2	4	no	—
437	C₃×C₄	—	2	4	no	—
438	C₃×C₄	—	6	8	no	—
439	C₃×C₄	—	6	4	no	—
440	C₃×C₄	C₂²×#67	1	4	yes	—
441	C₃×C₄	C₂²×#67	1	4	yes	—
442	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
443	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
444	Dic₃	—	2	4	no	—
445	Dic₃	—	2	8	no	—
446	C₃²	C₂×#535	1	1	yes	characteristic, complemented, Sylow
447	C₂³	—	2	4	no	—
448	C₂³	—	2	16	no	—
449	C₂³	—	2	16	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	3	4	no	—
452	C₂³	—	4	16	no	—
453	C₂³	—	4	32	no	—
454	C₂³	—	6	8	no	—
455	C₂³	—	6	4	no	—
456	C₂³	C₂×C₃×#67	1	4	yes	—
457	C₂³	C₂³×C₃×D₃	1	8	yes	—
458	C₂³	C₂³×C₃×D₃	1	2	yes	—
459	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
460	Q₈	—	6	8	no	—
461	D₄	—	2	16	no	—
462	D₄	—	2	16	no	—
463	D₄	—	6	16	no	—
464	D₄	—	6	8	no	—
465	D₄	—	12	32	no	—
466	C₂×C₄	—	3	8	no	—
467	C₂×C₄	—	3	4	no	—
468	C₂×C₄	—	6	8	no	—
469	C₂×C₄	—	6	4	no	—
470	C₂×C₄	—	6	16	no	—
471	C₂×C₄	C₂×C₃×#67	1	4	yes	—
472	C₂×C₄	C₂×C₃×#67	1	4	yes	—
473	C₂×C₄	C₂×C₃×#67	1	16	yes	complemented
474	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
475	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
476	C₂×C₃	—	2	8	no	—
477	C₂×C₃	—	2	4	no	—
478	C₂×C₃	—	2	4	no	—
479	C₂×C₃	—	2	4	no	—
480	C₂×C₃	—	2	2	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	4	16	no	—
483	C₂×C₃	—	4	8	no	—
484	C₂×C₃	—	4	8	no	—
485	C₂×C₃	—	12	4	no	—
486	C₂×C₃	#5805	1	4	yes	direct product factor
487	C₂×C₃	C₃×#535	1	4	yes	complemented
488	C₂×C₃	C₂×#1004	1	2	yes	—
489	C₂×C₃	C₂³×#67	1	1	yes	characteristic
490	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
491	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
492	D₃	—	4	4	no	—
493	C₂²	—	2	8	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	16	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	4	32	no	—
498	C₂²	—	4	16	no	—
499	C₂²	—	6	8	no	—
500	C₂²	—	6	4	no	—
501	C₂²	—	12	8	no	—
502	C₂²	C₃×#1004	1	4	yes	—
503	C₂²	C₂²×C₃×#67	1	4	yes	—
504	C₂²	C₂²×C₃×#67	1	2	yes	—
505	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
506	C₄	—	6	8	no	—
507	C₄	—	6	4	no	—
508	C₄	C₂²×C₃×#67	1	4	yes	—
509	C₄	C₂²×C₃×#67	1	4	yes	—
510	C₃	—	2	1	no	—
511	C₃	C₂×#5805	1	1	yes	characteristic, direct product factor
512	C₃	C₂×C₃×#535	1	1	yes	characteristic, complemented
513	C₂	—	2	4	no	—
514	C₂	—	4	8	no	—
515	C₂	—	12	4	no	—
516	C₂	C₃×#5805	1	4	yes	direct product factor
517	C₂	C₂×C₃×#1004	1	2	yes	—
518	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂³×C₃²×D₄	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂³×C₃×D₄	D₃
hypocenter	C₃	C₂×C₃×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×D₄	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₂×C₃×#953	C₂	semidirect
4. C₃×#5805	C₂	direct (N × H)
5. C₂×C₃×#940	C₂	semidirect
6. C₂×C₃×#938	C₂	semidirect
7. C₂×C₃×#936	C₂	semidirect
8. C₂×C₃×#926	C₂	semidirect
10. C₂×#5805	C₃	direct (N × H)
15. C₂²×C₃²×D₄	C₂²	semidirect
18. C₂²×C₃×#67	C₂²	semidirect
20. C₂×C₃×#235	C₂²	semidirect
21. C₂²×C₃×D₁₂	C₂²	semidirect
22. C₂²×C₃×C₄×D₃	C₂²	semidirect
23. C₂²×C₃×Dic₆	C₂²	semidirect
24. C₃×#953	C₂²	semidirect
26. C₂×C₃×#217	C₂²	semidirect
27. C₃×#940	C₂²	semidirect
28. C₃×#938	C₂²	semidirect
29. C₃×#936	C₂²	semidirect
30. C₃×#926	C₂²	semidirect
31. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
32. C₂×C₃×C₄×Dic₃	C₂²	semidirect
35. C₂³×C₃×D₄	D₃	semidirect
36. C₂³×C₃×D₄	C₂×C₃	semidirect
37. C₂²×#235	C₂×C₃	semidirect
44. C₂×#953	C₂×C₃	semidirect
45. #5805	C₂×C₃	direct (N × H)
46. C₂×#940	C₂×C₃	semidirect
47. C₂×#938	C₂×C₃	semidirect
48. C₂×#936	C₂×C₃	semidirect
49. C₂×#926	C₂×C₃	semidirect
61. C₂²×C₃²×C₄	D₄	semidirect
68. C₂×C₃×#67	C₂³	semidirect
73. C₂×C₃×D₁₂	C₂³	semidirect
75. C₂×C₃×C₄×D₃	C₂³	semidirect
77. C₂×C₃×Dic₆	C₂³	semidirect
79. C₃×#217	C₂³	semidirect
80. C₃×C₄⋊Dic₃	C₂³	semidirect
81. C₃×C₄×Dic₃	C₂³	semidirect
100. C₂²×C₃×D₄	C₂×D₃	semidirect
103. C₂²×C₃×D₄	C₂²×C₃	semidirect
109. C₂²×#67	C₂²×C₃	semidirect
111. C₂×#235	C₂²×C₃	semidirect
112. C₂²×D₁₂	C₂²×C₃	semidirect
113. C₂²×C₄×D₃	C₂²×C₃	semidirect
114. C₂²×Dic₆	C₂²×C₃	semidirect
124. #953	C₂²×C₃	semidirect
126. C₂×#217	C₂²×C₃	semidirect
127. #940	C₂²×C₃	semidirect
128. #938	C₂²×C₃	semidirect
129. #936	C₂²×C₃	semidirect
130. #926	C₂²×C₃	semidirect
131. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
132. C₂×C₄×Dic₃	C₂²×C₃	semidirect
150. C₂×C₃²×C₄	C₂×D₄	semidirect
163. C₂³×D₄	C₃×D₃	semidirect
219. C₂²×C₃×C₄	#67	semidirect
220. C₂²×C₃×C₄	C₃×D₄	semidirect
230. C₂×#67	C₂³×C₃	semidirect
235. C₂×D₁₂	C₂³×C₃	semidirect
237. C₂×C₄×D₃	C₂³×C₃	semidirect
239. C₂×Dic₆	C₂³×C₃	semidirect
245. #217	C₂³×C₃	semidirect
246. C₄⋊Dic₃	C₂³×C₃	semidirect
247. C₄×Dic₃	C₂³×C₃	semidirect
275. C₂²×D₄	C₂×C₃×D₃	semidirect
345. C₂×C₃×C₄	C₂×#67	semidirect
348. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
364. C₂×C₃²	#535	semidirect
392. C₂²×C₄	C₃×#67	semidirect
446. C₃²	C₂×#535	semidirect
473. C₂×C₄	C₂×C₃×#67	semidirect
486. C₂×C₃	#5805	direct (N × H)
487. C₂×C₃	C₃×#535	semidirect
511. C₃	C₂×#5805	direct (N × H)
512. C₃	C₂×C₃×#535	semidirect
516. C₂	C₃×#5805	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²×D₄	2
C₂²×C₃×#235	2
C₂×C₃×#953	2
C₃×#5805	2
C₂×C₃×#940	2
C₂×C₃×#938	2
C₂×C₃×#936	2
C₂×C₃×#926	2
C₂×C₃×#535	3
C₂×#5805	3

Subgroups — C2×C3×#5805 #11900995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5805 #11900995