Subgroups — C₃²×#5830 #13179206

Order 1728.

2660 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#947	C₂	1	2	yes	maximal, complemented
4	C₃²×#940	C₂	1	2	yes	maximal, complemented
5	C₃²×#937	C₂	1	4	yes	maximal, complemented
6	C₃²×#930	C₂	1	4	yes	maximal, complemented
7	C₃²×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#535	—	3	1	no	maximal
9	C₃×#5830	C₃	1	4	yes	maximal, direct product factor
10	C₂³×C₃²×D₃	C₂²	1	2	yes	—
11	C₃³×#41	—	2	4	no	—
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃³×D₄	C₂²	1	2	yes	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
17	C₂×C₃²×#67	C₂²	1	8	yes	complemented
18	C₂×C₃²×D₁₂	—	2	4	no	—
19	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
20	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
21	C₃²×#217	C₂²	1	2	yes	—
22	C₃²×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
23	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	complemented
24	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	—	2	4	no	—
26	C₂×C₃²×#41	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃²×#41	C₂×C₃	1	4	yes	complemented
28	C₂²×C₃²×D₄	—	3	1	no	—
29	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
30	C₃²×#127	—	3	2	no	—
31	C₃²×#124	—	3	2	no	—
32	C₃²×#121	—	3	4	no	—
33	C₃²×#120	—	3	4	no	—
34	C₃²×#117	—	3	1	no	—
35	C₃×#947	C₂×C₃	1	8	yes	complemented
36	C₃×#940	C₂×C₃	1	8	yes	complemented
37	C₃×#937	C₂×C₃	1	16	yes	complemented
38	C₃×#930	C₂×C₃	1	16	yes	complemented
39	C₃×#926	C₂×C₃	1	4	yes	complemented
40	C₂³×C₃³	C₂³	1	2	yes	—
41	C₂³×C₃³	C₂³	1	1	yes	characteristic
42	C₂²×C₃²×D₃	—	2	4	no	—
43	C₂²×C₃²×D₃	—	4	4	no	—
44	C₂²×C₃²×D₃	C₂³	1	4	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₃³×D₄	—	2	4	no	—
47	C₃³×D₄	—	2	2	no	—
48	C₂×C₃³×C₄	—	2	4	no	—
49	C₂×C₃³×C₄	D₄	1	4	yes	complemented
50	C₂×C₃³×C₄	C₂³	1	2	yes	—
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
53	C₃²×#67	—	4	8	no	—
54	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
55	C₃²×D₁₂	—	2	4	no	—
56	C₃²×D₁₂	—	2	4	no	—
57	C₃×#535	—	3	4	no	—
58	#5830	C₃²	1	1	yes	characteristic, direct product factor
59	C₂⁴×C₃²	—	3	2	no	—
60	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
61	C₃²×#41	—	2	32	no	—
62	C₃²×#41	—	2	4	no	—
63	C₃²×#41	—	2	16	no	—
64	C₂×C₃²×Q₈	—	2	4	no	—
65	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
66	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
67	C₂×C₃²×D₄	—	2	8	no	—
68	C₂×C₃²×D₄	—	2	4	no	—
69	C₂×C₃²×D₄	—	3	8	no	—
70	C₂×C₃²×D₄	—	3	2	no	—
71	C₂×C₃²×D₄	—	3	2	no	—
72	C₂×C₃²×D₄	—	6	4	no	—
73	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
74	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
75	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
76	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
77	C₂²×C₃²×C₄	—	2	4	no	—
78	C₂²×C₃²×C₄	—	2	8	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	complemented
81	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
82	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	complemented
83	C₂×C₃×#67	C₂²×C₃	1	32	yes	complemented
84	C₂×C₃×D₁₂	—	2	16	no	—
85	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
86	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
87	C₃²×C₄⋊C₄	—	3	2	no	—
88	C₃²×C₂²⋊C₄	—	3	2	no	—
89	C₃²×C₂²⋊C₄	—	3	8	no	—
90	C₃²×C₄²	—	3	2	no	—
91	C₃×#217	C₂²×C₃	1	8	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	32	yes	complemented
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	complemented
94	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
95	C₂²×C₃³	—	2	2	no	—
96	C₂²×C₃³	—	2	2	no	—
97	C₂²×C₃³	—	2	4	no	—
98	C₂²×C₃³	C₂×D₄	1	2	yes	—
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₂×C₃²×D₃	—	2	4	no	—
101	C₂×C₃²×D₃	—	2	8	no	—
102	C₂×C₃²×D₃	—	4	8	no	—
103	C₃³×C₄	—	2	2	no	—
104	C₃³×C₄	C₂×D₄	1	2	yes	—
105	C₃³×C₄	C₂×D₄	1	2	yes	—
106	C₃²×Dic₃	—	2	4	no	—
107	C₂×C₃×#41	—	2	4	no	—
108	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
109	C₂×C₃×#41	C₂×C₃²	1	1	yes	characteristic, complemented
110	C₂²×C₃×D₄	—	3	4	no	—
111	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
112	C₃×#127	—	3	8	no	—
113	C₃×#124	—	3	8	no	—
114	C₃×#121	—	3	16	no	—
115	C₃×#120	—	3	16	no	—
116	C₃×#117	—	3	4	no	—
117	#947	C₂×C₃²	1	2	yes	complemented
118	#940	C₂×C₃²	1	2	yes	complemented
119	#937	C₂×C₃²	1	4	yes	complemented
120	#930	C₂×C₃²	1	4	yes	complemented
121	#926	C₂×C₃²	1	1	yes	characteristic, complemented
122	C₂³×C₃²	—	2	8	no	—
123	C₂³×C₃²	—	2	4	no	—
124	C₂³×C₃²	—	3	4	no	—
125	C₂³×C₃²	—	6	4	no	—
126	C₂³×C₃²	—	12	4	no	—
127	C₂³×C₃²	C₂²×D₃	1	2	yes	—
128	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
129	C₂³×C₃²	C₂³×C₃	1	8	yes	—
130	C₂³×C₃²	C₂³×C₃	1	4	yes	—
131	C₂²×C₃×D₃	—	2	16	no	—
132	C₂²×C₃×D₃	—	4	16	no	—
133	C₂²×C₃×D₃	C₂³×C₃	1	16	yes	—
134	C₃²×Q₈	—	2	16	no	—
135	C₃²×Q₈	—	2	2	no	—
136	C₃²×Q₈	—	2	8	no	—
137	C₃²×D₄	—	2	32	no	—
138	C₃²×D₄	—	2	16	no	—
139	C₃²×D₄	—	2	4	no	—
140	C₃²×D₄	—	2	16	no	—
141	C₃²×D₄	—	2	2	no	—
142	C₃²×D₄	—	2	8	no	—
143	C₃²×D₄	—	6	4	no	—
144	C₃²×D₄	—	6	4	no	—
145	C₃²×D₄	—	12	8	no	—
146	C₂×C₃²×C₄	—	2	32	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	—	2	16	no	—
149	C₂×C₃²×C₄	—	2	16	no	—
150	C₂×C₃²×C₄	—	2	4	no	—
151	C₂×C₃²×C₄	—	2	8	no	—
152	C₂×C₃²×C₄	—	2	4	no	—
153	C₂×C₃²×C₄	—	3	4	no	—
154	C₂×C₃²×C₄	#67	1	4	yes	complemented
155	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
156	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
157	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
160	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
161	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
162	C₃×#67	—	4	32	no	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
164	C₃×D₁₂	—	2	16	no	—
165	C₃×D₁₂	—	2	16	no	—
166	#535	—	3	1	no	Sylow
167	C₂×C₃³	—	2	2	no	—
168	C₂×C₃³	—	4	2	no	—
169	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
171	C₃²×D₃	—	4	4	no	—
172	C₂⁴×C₃	—	3	8	no	—
173	C₂³×D₃	C₂²×C₃²	1	2	yes	—
174	C₃×#41	—	2	32	no	—
175	C₃×#41	—	2	16	no	—
176	C₃×#41	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	4	no	—
178	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
179	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
180	C₂×C₃×D₄	—	2	8	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	3	32	no	—
183	C₂×C₃×D₄	—	3	8	no	—
184	C₂×C₃×D₄	—	3	8	no	—
185	C₂×C₃×D₄	—	6	16	no	—
186	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
187	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
188	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	—
189	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	8	no	—
192	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
193	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	complemented
194	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	complemented
196	C₂×#67	C₂²×C₃²	1	8	yes	complemented
197	C₂×D₁₂	—	2	4	no	—
198	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
199	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
200	C₃×C₄⋊C₄	—	3	8	no	—
201	C₃×C₂²⋊C₄	—	3	8	no	—
202	C₃×C₂²⋊C₄	—	3	32	no	—
203	C₃×C₄²	—	3	8	no	—
204	#217	C₂²×C₃²	1	2	yes	—
205	(C₂×D₃)⋊C₄	C₂²×C₃²	1	8	yes	complemented
206	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
207	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	2	4	no	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	—	2	8	no	—
213	C₂²×C₃²	—	2	4	no	—
214	C₂²×C₃²	—	2	8	no	—
215	C₂²×C₃²	—	2	8	no	—
216	C₂²×C₃²	—	2	16	no	—
217	C₂²×C₃²	—	4	8	no	—
218	C₂²×C₃²	—	4	16	no	—
219	C₂²×C₃²	—	6	8	no	—
220	C₂²×C₃²	—	6	4	no	—
221	C₂²×C₃²	—	12	8	no	—
222	C₂²×C₃²	C₂×#67	1	2	yes	—
223	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
224	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
225	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
226	C₂×C₃×D₃	—	2	16	no	—
227	C₂×C₃×D₃	—	2	32	no	—
228	C₂×C₃×D₃	—	4	32	no	—
229	C₃²×C₄	—	2	16	no	—
230	C₃²×C₄	—	2	2	no	—
231	C₃²×C₄	—	2	8	no	—
232	C₃²×C₄	—	2	8	no	—
233	C₃²×C₄	—	2	8	no	—
234	C₃²×C₄	—	6	4	no	—
235	C₃²×C₄	C₂×#67	1	2	yes	—
236	C₃²×C₄	C₂×#67	1	2	yes	—
237	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
238	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
239	C₃×Dic₃	—	2	16	no	—
240	C₂×#41	C₃²×D₃	1	1	yes	characteristic, complemented
241	C₂²×D₄	—	3	1	no	—
242	#127	—	3	2	no	—
243	#124	—	3	2	no	—
244	#121	—	3	4	no	—
245	#120	—	3	4	no	—
246	#117	—	3	1	no	—
247	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	8	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	3	16	no	—
251	C₂³×C₃	—	6	16	no	—
252	C₂³×C₃	—	12	16	no	—
253	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
254	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
255	C₂³×C₃	C₂³×C₃²	1	2	yes	—
256	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
257	C₂²×D₃	—	2	4	no	—
258	C₂²×D₃	—	4	4	no	—
259	C₂²×D₃	C₂³×C₃²	1	4	yes	—
260	C₃×Q₈	—	2	16	no	—
261	C₃×Q₈	—	2	8	no	—
262	C₃×Q₈	—	2	2	no	—
263	C₃×D₄	—	2	32	no	—
264	C₃×D₄	—	2	16	no	—
265	C₃×D₄	—	2	16	no	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	8	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	6	16	no	—
270	C₃×D₄	—	6	16	no	—
271	C₃×D₄	—	12	32	no	—
272	C₂×C₃×C₄	—	2	32	no	—
273	C₂×C₃×C₄	—	2	16	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	16	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	3	16	no	—
280	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
281	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
285	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
286	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
288	#67	—	4	8	no	—
289	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
290	D₁₂	—	2	4	no	—
291	D₁₂	—	2	4	no	—
292	C₂×C₃²	—	2	2	no	—
293	C₂×C₃²	—	2	8	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	8	no	—
296	C₂×C₃²	—	4	8	no	—
297	C₂×C₃²	—	4	16	no	—
298	C₂×C₃²	—	4	2	no	—
299	C₂×C₃²	—	4	8	no	—
300	C₂×C₃²	—	12	4	no	—
301	C₂×C₃²	#1009	1	2	yes	—
302	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
303	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
304	C₂×C₃²	C₃×H(5,𝔽₂)	1	8	yes	—
305	C₃×D₃	—	4	16	no	—
306	C₂⁴	—	3	2	no	—
307	#41	—	2	4	no	—
308	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
309	C₂×D₄	—	3	8	no	—
310	C₂×D₄	—	3	2	no	—
311	C₂×D₄	—	3	2	no	—
312	C₂×D₄	—	6	4	no	—
313	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
314	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
315	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	complemented
317	C₄⋊C₄	—	3	2	no	—
318	C₂²⋊C₄	—	3	2	no	—
319	C₂²⋊C₄	—	3	8	no	—
320	C₄²	—	3	2	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	16	no	—
324	C₂²×C₃	—	2	16	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	4	16	no	—
332	C₂²×C₃	—	6	32	no	—
333	C₂²×C₃	—	6	16	no	—
334	C₂²×C₃	—	12	32	no	—
335	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
336	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
337	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
338	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
339	C₂×D₃	—	2	4	no	—
340	C₂×D₃	—	2	8	no	—
341	C₂×D₃	—	4	8	no	—
342	C₃×C₄	—	2	16	no	—
343	C₃×C₄	—	2	8	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	8	no	—
346	C₃×C₄	—	2	8	no	—
347	C₃×C₄	—	6	16	no	—
348	C₃×C₄	C₂×C₃×#67	1	8	yes	—
349	C₃×C₄	C₂×C₃×#67	1	8	yes	—
350	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
351	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
352	Dic₃	—	2	4	no	—
353	C₃²	—	2	4	no	—
354	C₃²	#5830	1	1	yes	characteristic, direct product factor
355	C₃²	C₃×#535	1	4	yes	complemented
356	C₂³	—	3	4	no	—
357	C₂³	—	6	4	no	—
358	C₂³	—	12	4	no	—
359	C₂³	C₂²×C₃²×D₃	1	2	yes	—
360	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	6	4	no	—
365	D₄	—	6	4	no	—
366	D₄	—	12	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	3	4	no	—
369	C₂×C₄	C₃²×#67	1	4	yes	complemented
370	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
371	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
373	C₂×C₃	—	2	8	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	2	8	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	4	8	no	—
378	C₂×C₃	—	4	16	no	—
379	C₂×C₃	—	4	8	no	—
380	C₂×C₃	—	4	2	no	—
381	C₂×C₃	—	12	16	no	—
382	C₂×C₃	C₃×#1009	1	8	yes	—
383	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
384	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
385	C₂×C₃	C₃²×H(5,𝔽₂)	1	2	yes	—
386	D₃	—	4	4	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	6	8	no	—
391	C₂²	—	6	4	no	—
392	C₂²	—	12	8	no	—
393	C₂²	C₂×C₃²×#67	1	2	yes	—
394	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	6	4	no	—
397	C₄	C₂×C₃²×#67	1	2	yes	—
398	C₄	C₂×C₃²×#67	1	2	yes	—
399	C₃	—	2	4	no	—
400	C₃	C₃×#5830	1	4	yes	direct product factor
401	C₃	C₃²×#535	1	1	yes	characteristic, complemented
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	—	12	4	no	—
405	C₂	C₃²×#1009	1	2	yes	—
406	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₃²×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂²×C₃²×D₁₂	C₂	semidirect
3. C₃²×#947	C₂	semidirect
4. C₃²×#940	C₂	semidirect
5. C₃²×#937	C₂	semidirect
6. C₃²×#930	C₂	semidirect
7. C₃²×#926	C₂	semidirect
9. C₃×#5830	C₃	direct (N × H)
12. C₂×C₃³×Q₈	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
16. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂×C₃²×#67	C₂²	semidirect
22. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
23. C₃²×C₄⋊Dic₃	C₂²	semidirect
24. C₃²×C₄×Dic₃	C₂²	semidirect
26. C₂×C₃²×#41	D₃	semidirect
27. C₂×C₃²×#41	C₂×C₃	semidirect
29. C₂²×C₃×D₁₂	C₂×C₃	semidirect
35. C₃×#947	C₂×C₃	semidirect
36. C₃×#940	C₂×C₃	semidirect
37. C₃×#937	C₂×C₃	semidirect
38. C₃×#930	C₂×C₃	semidirect
39. C₃×#926	C₂×C₃	semidirect
49. C₂×C₃³×C₄	D₄	semidirect
58. #5830	C₃²	direct (N × H)
65. C₂×C₃²×Q₈	C₂×D₃	semidirect
66. C₂×C₃²×Q₈	C₂²×C₃	semidirect
74. C₂×C₃²×D₄	C₂×D₃	semidirect
76. C₂×C₃²×D₄	C₂²×C₃	semidirect
80. C₂²×C₃²×C₄	C₂×D₃	semidirect
82. C₂²×C₃²×C₄	C₂²×C₃	semidirect
83. C₂×C₃×#67	C₂²×C₃	semidirect
92. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
93. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
94. C₃×C₄×Dic₃	C₂²×C₃	semidirect
108. C₂×C₃×#41	C₃×D₃	semidirect
109. C₂×C₃×#41	C₂×C₃²	semidirect
111. C₂²×D₁₂	C₂×C₃²	semidirect
117. #947	C₂×C₃²	semidirect
118. #940	C₂×C₃²	semidirect
119. #937	C₂×C₃²	semidirect
120. #930	C₂×C₃²	semidirect
121. #926	C₂×C₃²	semidirect
154. C₂×C₃²×C₄	#67	semidirect
155. C₂×C₃²×C₄	C₃×D₄	semidirect
178. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
179. C₂×C₃×Q₈	C₂²×C₃²	semidirect
187. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
189. C₂×C₃×D₄	C₂²×C₃²	semidirect
193. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
195. C₂²×C₃×C₄	C₂²×C₃²	semidirect
196. C₂×#67	C₂²×C₃²	semidirect
205. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
206. C₄⋊Dic₃	C₂²×C₃²	semidirect
207. C₄×Dic₃	C₂²×C₃²	semidirect
240. C₂×#41	C₃²×D₃	semidirect
247. C₃³	#535	semidirect
280. C₂×C₃×C₄	C₃×#67	semidirect
281. C₂×C₃×C₄	C₃²×D₄	semidirect
308. C₂×Q₈	C₂×C₃²×D₃	semidirect
314. C₂×D₄	C₂×C₃²×D₃	semidirect
316. C₂²×C₄	C₂×C₃²×D₃	semidirect
354. C₃²	#5830	direct (N × H)
355. C₃²	C₃×#535	semidirect
369. C₂×C₄	C₃²×#67	semidirect
400. C₃	C₃×#5830	direct (N × H)
401. C₃	C₃²×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃³×#41	2
C₂²×C₃²×D₁₂	2
C₃²×#947	2
C₃²×#940	2
C₃²×#937	2
C₃²×#930	2
C₃²×#926	2
C₃²×#535	3
C₃×#5830	3

Subgroups — C32×#5830 #13179206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5830 #13179206