Subgroups — C₃×#87283 #11906069

Order 1152.

3529 conjugacy classes of subgroups.

The subgroup lattice has 530 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	C₂×C₃×#1010	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5832	C₂	1	3	yes	maximal, complemented
4	C₃×#5831	C₂	1	4	yes	maximal, complemented
5	C₃×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5825	C₂	1	3	yes	maximal, complemented
7	C₃×#5806	C₂	1	12	yes	maximal, complemented
8	C₃×#5805	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×#936	C₂	1	3	yes	maximal, complemented
10	C₃×#3500	—	3	1	no	maximal
11	#87283	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₃²×H(5,𝔽₂)	—	2	8	no	—
13	C₂×C₃²×#41	C₂²	1	3	yes	—
14	C₂×C₃²×#41	C₂²	1	2	yes	—
15	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×D₄	C₂²	1	3	yes	—
17	C₂²×C₃²×D₄	C₂²	1	6	yes	—
18	C₃×#1010	—	2	8	no	—
19	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
20	C₂×C₃×#237	C₂²	1	6	yes	complemented
21	C₂×C₃×#235	C₂²	1	3	yes	complemented
22	C₂²×C₃×Dic₆	C₂²	1	3	yes	complemented
23	C₃×#953	C₂²	1	12	yes	complemented
24	C₂×C₃×#217	C₂²	1	12	yes	complemented
25	C₃×#947	C₂²	1	1	yes	characteristic, complemented
26	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
27	C₃×#944	C₂²	1	3	yes	complemented
28	C₃×#940	C₂²	1	3	yes	complemented
29	C₃×#939	C₂²	1	12	yes	complemented
30	C₃×#938	C₂²	1	12	yes	complemented
31	C₃×#936	C₂²	1	3	yes	complemented
32	C₃×#936	C₂²	1	6	yes	complemented
33	C₃×#936	C₂²	1	12	yes	complemented
34	C₃×#935	C₂²	1	12	yes	complemented
35	C₃×D₄×Dic₃	C₂²	1	6	yes	complemented
36	C₃×C₄×#67	C₂²	1	12	yes	complemented
37	C₃×#926	C₂²	1	3	yes	complemented
38	C₃×#924	C₂²	1	12	yes	complemented
39	C₂×C₃×C₄×Dic₃	C₂²	1	3	yes	complemented
40	C₂×C₃×2₋¹⁺⁴	—	3	1	no	—
41	C₂×C₃×H(5,𝔽₂)	—	2	1	no	—
42	C₂×C₃×H(5,𝔽₂)	D₃	1	1	yes	characteristic, complemented
43	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#1010	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#548	—	3	4	no	—
46	C₃×#546	—	3	12	no	—
47	C₃×#536	—	3	3	no	—
48	C₃×#535	—	3	3	no	—
49	C₃×#532	—	3	3	no	—
50	C₂×C₃×#124	—	3	3	no	—
51	C₃×C₄×#41	—	3	1	no	—
52	#5832	C₂×C₃	1	3	yes	complemented
53	#5831	C₂×C₃	1	4	yes	complemented
54	Dic₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
55	#5825	C₂×C₃	1	3	yes	complemented
56	#5806	C₂×C₃	1	12	yes	complemented
57	#5805	C₂×C₃	1	3	yes	complemented
58	C₂×#936	C₂×C₃	1	3	yes	complemented
59	C₂⁴×C₃²	C₂³	1	6	yes	—
60	C₃²×#41	—	2	8	no	—
61	C₃²×#41	—	2	12	no	—
62	C₃²×#41	D₄	1	8	yes	complemented
63	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
65	C₂×C₃²×D₄	—	2	24	no	—
66	C₂×C₃²×D₄	—	2	12	no	—
67	C₂×C₃²×D₄	C₂³	1	6	yes	—
68	C₂×C₃²×D₄	C₂³	1	3	yes	—
69	C₂×C₃²×D₄	C₂³	1	6	yes	—
70	C₂×C₃²×D₄	C₂³	1	3	yes	—
71	C₂²×C₃²×C₄	C₂³	1	6	yes	—
72	C₂²×C₃²×C₄	C₂³	1	3	yes	—
73	C₂×C₃×#67	C₂³	1	6	yes	—
74	C₂×C₃×#67	C₂³	1	12	yes	—
75	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
76	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
77	C₃×D₃×Q₈	—	2	8	no	—
78	C₃×#237	—	2	24	no	—
79	C₃×#235	—	2	12	no	—
80	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
82	C₂×C₃×Dic₆	—	2	12	no	—
83	C₂×C₃×Dic₆	C₂³	1	6	yes	—
84	C₂×C₃×Dic₆	C₂³	1	3	yes	—
85	C₃×#217	C₂³	1	24	yes	—
86	C₃×#217	C₂³	1	6	yes	—
87	C₃×#217	C₂³	1	12	yes	—
88	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
89	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
90	C₃×Dic₃⋊C₄	C₂³	1	12	yes	—
91	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
92	C₃×C₄×Dic₃	C₂³	1	3	yes	—
93	C₃×C₄×Dic₃	C₂³	1	6	yes	—
94	#3500	—	3	1	no	Sylow
95	C₃×2₋¹⁺⁴	—	6	8	no	—
96	C₃×H(5,𝔽₂)	—	2	16	no	—
97	C₃×H(5,𝔽₂)	—	2	8	no	—
98	C₃×H(5,𝔽₂)	—	2	8	no	—
99	C₂×C₃×#41	—	2	3	no	—
100	C₂×C₃×#41	—	2	2	no	—
101	C₂×C₃×#41	—	2	1	no	—
102	C₂×C₃×#41	—	3	6	no	—
103	C₂×C₃×#41	—	3	3	no	—
104	C₂×C₃×#41	C₂×D₃	1	3	yes	—
105	C₂×C₃×#41	C₂×D₃	1	2	yes	—
106	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
108	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
109	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₃×Q₈	—	3	2	no	—
111	C₂²×C₃×Q₈	—	3	3	no	—
112	C₂²×C₃×D₄	—	2	3	no	—
113	C₂²×C₃×D₄	—	2	6	no	—
114	C₂²×C₃×D₄	C₂×D₃	1	3	yes	—
115	C₂²×C₃×D₄	C₂×D₃	1	6	yes	—
116	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
117	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
118	#1010	—	2	8	no	—
119	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
120	C₂×#237	C₂²×C₃	1	6	yes	complemented
121	C₂×#235	C₂²×C₃	1	3	yes	complemented
122	C₂²×Dic₆	C₂²×C₃	1	3	yes	complemented
123	C₃×C₄⋊Q₈	—	3	3	no	—
124	C₃×#127	—	3	3	no	—
125	C₃×#124	—	3	1	no	—
126	C₃×#124	—	3	3	no	—
127	C₃×#124	—	3	6	no	—
128	C₃×#124	—	3	12	no	—
129	C₃×#123	—	3	12	no	—
130	C₃×C₂²⋊Q₈	—	3	12	no	—
131	C₃×#121	—	3	12	no	—
132	C₃×#121	—	3	12	no	—
133	C₃×#120	—	3	12	no	—
134	C₃×C₄×Q₈	—	3	2	no	—
135	C₃×C₄×D₄	—	3	6	no	—
136	C₃×C₄×D₄	—	3	12	no	—
137	C₃×#117	—	3	3	no	—
138	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
139	C₂×C₃×C₄²	—	3	3	no	—
140	#953	C₂²×C₃	1	12	yes	complemented
141	C₂×#217	C₂²×C₃	1	12	yes	complemented
142	#947	C₂²×C₃	1	1	yes	characteristic, complemented
143	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
144	#944	C₂²×C₃	1	3	yes	complemented
145	#940	C₂²×C₃	1	3	yes	complemented
146	#939	C₂²×C₃	1	12	yes	complemented
147	#938	C₂²×C₃	1	12	yes	complemented
148	#936	C₂²×C₃	1	3	yes	complemented
149	#936	C₂²×C₃	1	6	yes	complemented
150	#936	C₂²×C₃	1	12	yes	complemented
151	#935	C₂²×C₃	1	12	yes	complemented
152	D₄×Dic₃	C₂²×C₃	1	6	yes	complemented
153	C₄×#67	C₂²×C₃	1	12	yes	complemented
154	#926	C₂²×C₃	1	3	yes	complemented
155	#924	C₂²×C₃	1	12	yes	complemented
156	C₂×C₄×Dic₃	C₂²×C₃	1	3	yes	complemented
157	C₂³×C₃²	—	2	12	no	—
158	C₂³×C₃²	—	4	12	no	—
159	C₂³×C₃²	C₂⁴	1	6	yes	—
160	C₂³×C₃²	C₂⁴	1	3	yes	—
161	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
162	C₃²×Q₈	—	2	2	no	—
163	C₃²×Q₈	C₂×D₄	1	4	yes	—
164	C₃²×D₄	—	2	12	no	—
165	C₃²×D₄	—	2	6	no	—
166	C₃²×D₄	—	2	12	no	—
167	C₃²×D₄	C₂×D₄	1	12	yes	—
168	C₂×C₃²×C₄	—	2	12	no	—
169	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
170	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
171	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
173	C₃×#67	—	2	12	no	—
174	C₃×#67	—	4	12	no	—
175	C₂×C₃×Dic₃	—	2	12	no	—
176	C₂×C₃×Dic₃	—	4	6	no	—
177	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
178	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
179	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
180	C₃×D₁₂	—	2	2	no	—
181	C₃×C₄×D₃	—	2	12	no	—
182	C₃×Dic₆	—	2	6	no	—
183	C₃×Dic₆	—	2	12	no	—
184	C₂×2₋¹⁺⁴	—	3	1	no	—
185	C₂×H(5,𝔽₂)	C₃×D₃	1	1	yes	characteristic, complemented
186	#548	—	3	4	no	—
187	#546	—	3	12	no	—
188	#536	—	3	3	no	—
189	#535	—	3	3	no	—
190	#532	—	3	3	no	—
191	C₂×#124	—	3	3	no	—
192	C₄×#41	—	3	1	no	—
193	C₂⁴×C₃	—	2	6	no	—
194	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
195	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
196	C₃×#41	—	2	16	no	—
197	C₃×#41	—	2	24	no	—
198	C₃×#41	—	2	8	no	—
199	C₃×#41	—	2	8	no	—
200	C₃×#41	—	2	12	no	—
201	C₃×#41	—	2	12	no	—
202	C₃×#41	—	2	8	no	—
203	C₃×#41	—	6	24	no	—
204	C₃×#41	—	6	12	no	—
205	C₃×#41	#67	1	8	yes	complemented
206	C₃×#41	C₃×D₄	1	8	yes	complemented
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	—	2	1	no	—
209	C₂×C₃×Q₈	—	3	6	no	—
210	C₂×C₃×Q₈	—	3	3	no	—
211	C₂×C₃×Q₈	—	6	8	no	—
212	C₂×C₃×Q₈	—	6	12	no	—
213	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₃×D₄	—	2	48	no	—
218	C₂×C₃×D₄	—	2	24	no	—
219	C₂×C₃×D₄	—	2	24	no	—
220	C₂×C₃×D₄	—	2	24	no	—
221	C₂×C₃×D₄	—	2	12	no	—
222	C₂×C₃×D₄	—	2	12	no	—
223	C₂×C₃×D₄	—	2	6	no	—
224	C₂×C₃×D₄	—	2	6	no	—
225	C₂×C₃×D₄	—	2	3	no	—
226	C₂×C₃×D₄	—	2	3	no	—
227	C₂×C₃×D₄	—	3	6	no	—
228	C₂×C₃×D₄	—	3	12	no	—
229	C₂×C₃×D₄	—	3	1	no	—
230	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
231	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
232	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
233	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
234	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
235	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
236	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
237	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
238	C₂²×C₃×C₄	—	2	6	no	—
239	C₂²×C₃×C₄	—	2	3	no	—
240	C₂²×C₃×C₄	—	3	6	no	—
241	C₂²×C₃×C₄	—	3	6	no	—
242	C₂²×C₃×C₄	—	3	6	no	—
243	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
244	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
245	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
246	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
247	C₂×#67	C₂³×C₃	1	6	yes	—
248	C₂×#67	C₂³×C₃	1	12	yes	—
249	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
250	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
251	D₃×Q₈	—	2	8	no	—
252	#237	—	2	24	no	—
253	#235	—	2	12	no	—
254	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
256	C₂×Dic₆	—	2	12	no	—
257	C₂×Dic₆	C₂³×C₃	1	6	yes	—
258	C₂×Dic₆	C₂³×C₃	1	3	yes	—
259	C₃×C₄⋊C₄	—	3	12	no	—
260	C₃×C₄⋊C₄	—	3	6	no	—
261	C₃×C₂²⋊C₄	—	3	12	no	—
262	C₃×C₂²⋊C₄	—	3	24	no	—
263	C₃×C₂²⋊C₄	—	3	6	no	—
264	C₃×C₂²⋊C₄	—	3	4	no	—
265	C₃×C₄²	—	3	1	no	—
266	C₃×C₄²	—	3	3	no	—
267	C₃×C₄²	—	3	6	no	—
268	#217	C₂³×C₃	1	24	yes	—
269	#217	C₂³×C₃	1	6	yes	—
270	#217	C₂³×C₃	1	12	yes	—
271	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
272	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
273	Dic₃⋊C₄	C₂³×C₃	1	12	yes	—
274	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
275	C₄×Dic₃	C₂³×C₃	1	3	yes	—
276	C₄×Dic₃	C₂³×C₃	1	6	yes	—
277	C₂²×C₃²	—	2	6	no	—
278	C₂²×C₃²	—	2	6	no	—
279	C₂²×C₃²	—	2	12	no	—
280	C₂²×C₃²	—	8	12	no	—
281	C₂²×C₃²	C₂²×D₄	1	6	yes	—
282	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
283	C₂×C₃×D₃	—	2	2	no	—
284	C₂×C₃×D₃	—	2	4	no	—
285	C₃²×C₄	—	2	2	no	—
286	C₃²×C₄	C₂²×D₄	1	2	yes	—
287	C₃²×C₄	C₂²×D₄	1	6	yes	—
288	C₃×Dic₃	—	2	6	no	—
289	C₃×Dic₃	—	2	2	no	—
290	C₃×Dic₃	—	2	6	no	—
291	2₋¹⁺⁴	—	6	8	no	—
292	H(5,𝔽₂)	—	2	8	no	—
293	C₂×#41	—	3	6	no	—
294	C₂×#41	—	3	3	no	—
295	C₂×#41	C₂×C₃×D₃	1	3	yes	—
296	C₂×#41	C₂×C₃×D₃	1	2	yes	—
297	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
298	C₂²×Q₈	—	3	2	no	—
299	C₂²×Q₈	—	3	3	no	—
300	C₂²×D₄	C₂×C₃×D₃	1	3	yes	—
301	C₂²×D₄	C₂×C₃×D₃	1	6	yes	—
302	C₄⋊Q₈	—	3	3	no	—
303	#127	—	3	3	no	—
304	#124	—	3	1	no	—
305	#124	—	3	3	no	—
306	#124	—	3	6	no	—
307	#124	—	3	12	no	—
308	#123	—	3	12	no	—
309	C₂²⋊Q₈	—	3	12	no	—
310	#121	—	3	12	no	—
311	#121	—	3	12	no	—
312	#120	—	3	12	no	—
313	C₄×Q₈	—	3	2	no	—
314	C₄×D₄	—	3	6	no	—
315	C₄×D₄	—	3	12	no	—
316	#117	—	3	3	no	—
317	C₂×C₂²⋊C₄	—	3	12	no	—
318	C₂×C₄²	—	3	3	no	—
319	C₂³×C₃	—	2	24	no	—
320	C₂³×C₃	—	2	12	no	—
321	C₂³×C₃	—	2	12	no	—
322	C₂³×C₃	—	2	6	no	—
323	C₂³×C₃	—	2	3	no	—
324	C₂³×C₃	—	3	2	no	—
325	C₂³×C₃	—	4	12	no	—
326	C₂³×C₃	—	4	12	no	—
327	C₂³×C₃	—	8	12	no	—
328	C₂³×C₃	C₂³×D₃	1	6	yes	—
329	C₂³×C₃	C₂³×D₃	1	3	yes	—
330	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
331	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
332	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
333	C₃×Q₈	—	2	4	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₃×Q₈	—	2	4	no	—
337	C₃×Q₈	—	6	12	no	—
338	C₃×Q₈	—	6	6	no	—
339	C₃×Q₈	C₂×#67	1	4	yes	—
340	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
341	C₃×D₄	—	2	24	no	—
342	C₃×D₄	—	2	24	no	—
343	C₃×D₄	—	2	12	no	—
344	C₃×D₄	—	2	12	no	—
345	C₃×D₄	—	2	12	no	—
346	C₃×D₄	—	2	12	no	—
347	C₃×D₄	—	2	6	no	—
348	C₃×D₄	—	2	6	no	—
349	C₃×D₄	—	2	12	no	—
350	C₃×D₄	—	2	12	no	—
351	C₃×D₄	—	6	12	no	—
352	C₃×D₄	—	6	2	no	—
353	C₃×D₄	—	12	12	no	—
354	C₃×D₄	C₂×#67	1	12	yes	—
355	C₃×D₄	C₂×C₃×D₄	1	12	yes	—
356	C₂×C₃×C₄	—	2	24	no	—
357	C₂×C₃×C₄	—	2	12	no	—
358	C₂×C₃×C₄	—	2	12	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	3	no	—
362	C₂×C₃×C₄	—	2	12	no	—
363	C₂×C₃×C₄	—	3	2	no	—
364	C₂×C₃×C₄	—	3	6	no	—
365	C₂×C₃×C₄	—	3	6	no	—
366	C₂×C₃×C₄	—	6	12	no	—
367	C₂×C₃×C₄	—	6	12	no	—
368	C₂×C₃×C₄	—	12	6	no	—
369	C₂×C₃×C₄	C₂×#67	1	12	yes	—
370	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
371	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
372	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
374	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
377	#67	—	2	12	no	—
378	#67	—	4	12	no	—
379	C₂×Dic₃	—	2	12	no	—
380	C₂×Dic₃	—	4	6	no	—
381	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
382	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
383	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
384	D₁₂	—	2	2	no	—
385	C₄×D₃	—	2	12	no	—
386	Dic₆	—	2	6	no	—
387	Dic₆	—	2	12	no	—
388	C₂×C₃²	—	2	6	no	—
389	C₂×C₃²	—	4	6	no	—
390	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
391	C₂×C₃²	#585	1	2	yes	—
392	C₃×D₃	—	4	2	no	—
393	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
394	#41	—	2	8	no	—
395	#41	—	2	12	no	—
396	#41	—	6	24	no	—
397	#41	—	6	12	no	—
398	#41	C₃×#67	1	8	yes	complemented
399	C₂×Q₈	—	3	6	no	—
400	C₂×Q₈	—	3	3	no	—
401	C₂×Q₈	—	6	8	no	—
402	C₂×Q₈	—	6	12	no	—
403	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
404	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
405	C₂×D₄	—	2	24	no	—
406	C₂×D₄	—	2	12	no	—
407	C₂×D₄	—	3	6	no	—
408	C₂×D₄	—	3	12	no	—
409	C₂×D₄	—	3	1	no	—
410	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
411	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
412	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
413	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
414	C₂²×C₄	—	3	6	no	—
415	C₂²×C₄	—	3	6	no	—
416	C₂²×C₄	—	3	6	no	—
417	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
418	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
419	C₄⋊C₄	—	3	6	no	—
420	C₄⋊C₄	—	3	12	no	—
421	C₂²⋊C₄	—	3	12	no	—
422	C₂²⋊C₄	—	3	24	no	—
423	C₂²⋊C₄	—	3	6	no	—
424	C₂²⋊C₄	—	3	4	no	—
425	C₄²	—	3	1	no	—
426	C₄²	—	3	3	no	—
427	C₄²	—	3	6	no	—
428	C₂²×C₃	—	2	6	no	—
429	C₂²×C₃	—	2	6	no	—
430	C₂²×C₃	—	2	12	no	—
431	C₂²×C₃	—	2	12	no	—
432	C₂²×C₃	—	2	6	no	—
433	C₂²×C₃	—	2	6	no	—
434	C₂²×C₃	—	2	12	no	—
435	C₂²×C₃	—	2	6	no	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	4	6	no	—
438	C₂²×C₃	—	4	12	no	—
439	C₂²×C₃	—	6	4	no	—
440	C₂²×C₃	—	6	2	no	—
441	C₂²×C₃	—	8	12	no	—
442	C₂²×C₃	—	8	12	no	—
443	C₂²×C₃	—	8	24	no	—
444	C₂²×C₃	C₂²×#67	1	6	yes	—
445	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
446	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
447	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
448	C₂×D₃	—	2	2	no	—
449	C₂×D₃	—	2	4	no	—
450	C₃×C₄	—	2	4	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	6	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	6	2	no	—
456	C₃×C₄	—	6	6	no	—
457	C₃×C₄	—	6	6	no	—
458	C₃×C₄	C₂²×#67	1	6	yes	—
459	C₃×C₄	C₂²×#67	1	2	yes	—
460	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
461	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
462	Dic₃	—	2	6	no	—
463	Dic₃	—	2	2	no	—
464	Dic₃	—	2	6	no	—
465	C₃²	#3500	1	1	yes	characteristic, complemented, Sylow
466	C₂³	—	2	12	no	—
467	C₂³	—	3	2	no	—
468	C₂³	—	4	12	no	—
469	C₂³	C₂³×C₃×D₃	1	6	yes	—
470	C₂³	C₂³×C₃×D₃	1	3	yes	—
471	Q₈	—	2	2	no	—
472	Q₈	—	6	12	no	—
473	Q₈	—	6	6	no	—
474	Q₈	C₂×C₃×#67	1	4	yes	—
475	D₄	—	2	12	no	—
476	D₄	—	2	12	no	—
477	D₄	—	2	6	no	—
478	D₄	—	6	12	no	—
479	D₄	—	6	2	no	—
480	D₄	—	12	12	no	—
481	D₄	C₂×C₃×#67	1	12	yes	—
482	C₂×C₄	—	2	12	no	—
483	C₂×C₄	—	3	2	no	—
484	C₂×C₄	—	3	6	no	—
485	C₂×C₄	—	3	6	no	—
486	C₂×C₄	—	6	12	no	—
487	C₂×C₄	—	6	12	no	—
488	C₂×C₄	—	12	6	no	—
489	C₂×C₄	C₂×C₃×#67	1	12	yes	—
490	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
491	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
492	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
493	C₂×C₃	—	2	6	no	—
494	C₂×C₃	—	2	6	no	—
495	C₂×C₃	—	2	2	no	—
496	C₂×C₃	—	2	1	no	—
497	C₂×C₃	—	4	6	no	—
498	C₂×C₃	—	4	12	no	—
499	C₂×C₃	—	4	6	no	—
500	C₂×C₃	—	4	6	no	—
501	C₂×C₃	—	12	2	no	—
502	C₂×C₃	#5966	1	2	yes	—
503	C₂×C₃	C₂³×#67	1	1	yes	characteristic
504	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
505	C₂×C₃	C₃×#585	1	2	yes	—
506	D₃	—	4	2	no	—
507	C₂²	—	2	6	no	—
508	C₂²	—	2	12	no	—
509	C₂²	—	2	6	no	—
510	C₂²	—	6	4	no	—
511	C₂²	—	6	2	no	—
512	C₂²	—	8	12	no	—
513	C₂²	C₂²×C₃×#67	1	6	yes	—
514	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	6	2	no	—
517	C₄	—	6	6	no	—
518	C₄	—	6	6	no	—
519	C₄	C₂²×C₃×#67	1	6	yes	—
520	C₄	C₂²×C₃×#67	1	2	yes	—
521	C₃	—	2	1	no	—
522	C₃	#87283	1	1	yes	characteristic, direct product factor
523	C₃	C₃×#3500	1	1	yes	characteristic, complemented
524	C₂	—	2	6	no	—
525	C₂	—	4	6	no	—
526	C₂	—	12	2	no	—
527	C₂	C₃×#5966	1	2	yes	—
528	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×#3500
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. C₂×C₃×#1010	C₂	semidirect
3. C₃×#5832	C₂	semidirect
4. C₃×#5831	C₂	semidirect
5. C₃×Dic₃×#41	C₂	semidirect
6. C₃×#5825	C₂	semidirect
7. C₃×#5806	C₂	semidirect
8. C₃×#5805	C₂	semidirect
9. C₂×C₃×#936	C₂	semidirect
11. #87283	C₃	direct (N × H)
19. C₂×C₃×D₃×Q₈	C₂²	semidirect
20. C₂×C₃×#237	C₂²	semidirect
21. C₂×C₃×#235	C₂²	semidirect
22. C₂²×C₃×Dic₆	C₂²	semidirect
23. C₃×#953	C₂²	semidirect
24. C₂×C₃×#217	C₂²	semidirect
25. C₃×#947	C₂²	semidirect
26. C₃×Q₈×Dic₃	C₂²	semidirect
27. C₃×#944	C₂²	semidirect
28. C₃×#940	C₂²	semidirect
29. C₃×#939	C₂²	semidirect
30. C₃×#938	C₂²	semidirect
31. C₃×#936	C₂²	semidirect
32. C₃×#936	C₂²	semidirect
33. C₃×#936	C₂²	semidirect
34. C₃×#935	C₂²	semidirect
35. C₃×D₄×Dic₃	C₂²	semidirect
36. C₃×C₄×#67	C₂²	semidirect
37. C₃×#926	C₂²	semidirect
38. C₃×#924	C₂²	semidirect
39. C₂×C₃×C₄×Dic₃	C₂²	semidirect
42. C₂×C₃×H(5,𝔽₂)	D₃	semidirect
43. C₂×C₃×H(5,𝔽₂)	C₂×C₃	semidirect
44. C₂×#1010	C₂×C₃	semidirect
52. #5832	C₂×C₃	semidirect
53. #5831	C₂×C₃	semidirect
54. Dic₃×#41	C₂×C₃	semidirect
55. #5825	C₂×C₃	semidirect
56. #5806	C₂×C₃	semidirect
57. #5805	C₂×C₃	semidirect
58. C₂×#936	C₂×C₃	semidirect
62. C₃²×#41	D₄	semidirect
119. C₂×D₃×Q₈	C₂²×C₃	semidirect
120. C₂×#237	C₂²×C₃	semidirect
121. C₂×#235	C₂²×C₃	semidirect
122. C₂²×Dic₆	C₂²×C₃	semidirect
140. #953	C₂²×C₃	semidirect
141. C₂×#217	C₂²×C₃	semidirect
142. #947	C₂²×C₃	semidirect
143. Q₈×Dic₃	C₂²×C₃	semidirect
144. #944	C₂²×C₃	semidirect
145. #940	C₂²×C₃	semidirect
146. #939	C₂²×C₃	semidirect
147. #938	C₂²×C₃	semidirect
148. #936	C₂²×C₃	semidirect
149. #936	C₂²×C₃	semidirect
150. #936	C₂²×C₃	semidirect
151. #935	C₂²×C₃	semidirect
152. D₄×Dic₃	C₂²×C₃	semidirect
153. C₄×#67	C₂²×C₃	semidirect
154. #926	C₂²×C₃	semidirect
155. #924	C₂²×C₃	semidirect
156. C₂×C₄×Dic₃	C₂²×C₃	semidirect
185. C₂×H(5,𝔽₂)	C₃×D₃	semidirect
205. C₃×#41	#67	semidirect
206. C₃×#41	C₃×D₄	semidirect
398. #41	C₃×#67	semidirect
465. C₃²	#3500	semidirect
522. C₃	#87283	direct (N × H)
523. C₃	C₃×#3500	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
C₂×C₃×#1010	2
C₃×#5832	2
C₃×#5831	2
C₃×Dic₃×#41	2
C₃×#5825	2
C₃×#5806	2
C₃×#5805	2
C₂×C₃×#936	2
C₃×#3500	3
#87283	3

Subgroups — C3×#87283 #11906069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87283 #11906069