Subgroups — C₃×#35278 #10653885

Order 768.

2746 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#540	C₂	1	2	yes	maximal, complemented
2	C₃×#2867	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2856	C₂	1	2	yes	maximal, complemented
5	C₃×#2641	C₂	1	2	yes	maximal, complemented
6	C₃×#2619	C₂	1	2	yes	maximal, complemented
7	C₃×#2445	C₂	1	8	yes	maximal, complemented
8	C₃×#2428	C₂	1	8	yes	maximal, complemented
9	C₃×#2328	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#127	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	#35278	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#540	—	2	16	no	—
14	C₂×C₃×#127	C₂²	1	2	yes	—
15	C₂×C₃×#127	C₂²	1	2	yes	—
16	C₂×C₃×#127	C₂²	1	2	yes	—
17	C₂×C₃×#127	C₂²	1	8	yes	—
18	C₂×C₃×#125	C₂²	1	2	yes	—
19	C₂×C₃×#123	C₂²	1	8	yes	—
20	C₂×C₃×#121	C₂²	1	4	yes	—
21	C₂×C₃×#121	C₂²	1	8	yes	—
22	C₂×C₃×#121	C₂²	1	8	yes	—
23	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄×D₄	C₂²	1	8	yes	—
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
28	C₃×#394	C₂²	1	8	yes	—
29	C₃×#394	C₂²	1	16	yes	—
30	C₃×#392	C₂²	1	8	yes	—
31	C₃×#390	C₂²	1	4	yes	—
32	C₃×#390	C₂²	1	4	yes	—
33	C₃×#390	C₂²	1	8	yes	—
34	C₃×#390	C₂²	1	8	yes	—
35	C₃×#389	C₂²	1	8	yes	—
36	C₃×#386	C₂²	1	16	yes	—
37	C₃×#384	C₂²	1	2	yes	—
38	C₃×#382	C₂²	1	2	yes	—
39	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
40	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
41	C₃×#376	C₂²	1	1	yes	characteristic
42	C₃×#376	C₂²	1	1	yes	characteristic
43	C₃×C₄³	C₂²	1	1	yes	characteristic
44	C₃×C₄³	C₂²	1	1	yes	characteristic
45	C₂×#540	C₂×C₃	1	2	yes	complemented
46	#2867	C₂×C₃	1	1	yes	characteristic, complemented
47	#2859	C₂×C₃	1	1	yes	characteristic, complemented
48	#2856	C₂×C₃	1	2	yes	complemented
49	#2641	C₂×C₃	1	2	yes	complemented
50	#2619	C₂×C₃	1	2	yes	complemented
51	#2445	C₂×C₃	1	8	yes	complemented
52	#2428	C₂×C₃	1	8	yes	complemented
53	#2328	C₂×C₃	1	2	yes	complemented
54	C₄×#127	C₂×C₃	1	2	yes	complemented
55	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₃×D₄	C₂³	1	4	yes	—
57	C₂²×C₃×D₄	C₂³	1	8	yes	—
58	C₂²×C₃×D₄	C₂³	1	8	yes	—
59	C₂²×C₃×D₄	C₂³	1	8	yes	—
60	C₂²×C₃×D₄	C₂³	1	8	yes	—
61	C₂³×C₃×C₄	C₂³	1	2	yes	—
62	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
63	C₂³×C₃×C₄	C₂³	1	8	yes	—
64	C₃×#127	—	2	8	no	—
65	C₃×#127	—	2	8	no	—
66	C₃×#127	—	2	8	no	—
67	C₃×#127	—	4	16	no	—
68	C₃×#125	—	2	8	no	—
69	C₃×#123	—	2	32	no	—
70	C₃×#121	—	2	16	no	—
71	C₃×#121	—	2	32	no	—
72	C₃×#121	—	4	16	no	—
73	C₃×C₄×D₄	—	2	16	no	—
74	C₃×C₄×D₄	—	4	16	no	—
75	C₃×#117	—	2	4	no	—
76	C₃×#117	D₄	1	8	yes	complemented
77	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
83	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
88	C₂×C₃×C₄²	—	2	4	no	—
89	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂³	1	4	yes	—
91	C₂×C₃×C₄²	C₂³	1	4	yes	—
92	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂³	1	2	yes	—
94	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
98	C₃×#95	C₂³	1	4	yes	—
99	C₃×#95	C₂³	1	4	yes	—
100	C₃×#95	C₂³	1	8	yes	—
101	#540	—	2	16	no	—
102	C₂×#127	C₂²×C₃	1	2	yes	—
103	C₂×#127	C₂²×C₃	1	2	yes	—
104	C₂×#127	C₂²×C₃	1	2	yes	—
105	C₂×#127	C₂²×C₃	1	8	yes	—
106	C₂×#125	C₂²×C₃	1	2	yes	—
107	C₂×#123	C₂²×C₃	1	8	yes	—
108	C₂×#121	C₂²×C₃	1	4	yes	—
109	C₂×#121	C₂²×C₃	1	8	yes	—
110	C₂×#121	C₂²×C₃	1	8	yes	—
111	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
112	C₂×C₄×D₄	C₂²×C₃	1	8	yes	—
113	C₂×#117	C₂²×C₃	1	1	yes	characteristic
114	C₂×#117	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
116	#394	C₂²×C₃	1	8	yes	—
117	#394	C₂²×C₃	1	16	yes	—
118	#392	C₂²×C₃	1	8	yes	—
119	#390	C₂²×C₃	1	4	yes	—
120	#390	C₂²×C₃	1	8	yes	—
121	#390	C₂²×C₃	1	4	yes	—
122	#390	C₂²×C₃	1	8	yes	—
123	#389	C₂²×C₃	1	8	yes	—
124	#386	C₂²×C₃	1	16	yes	—
125	#384	C₂²×C₃	1	2	yes	—
126	#382	C₂²×C₃	1	2	yes	—
127	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
128	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
129	#376	C₂²×C₃	1	1	yes	characteristic
130	#376	C₂²×C₃	1	1	yes	characteristic
131	C₄³	C₂²×C₃	1	1	yes	characteristic
132	C₄³	C₂²×C₃	1	1	yes	characteristic
133	C₂⁴×C₃	C₂⁴	1	8	yes	—
134	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×D₄	—	2	16	no	—
136	C₂×C₃×D₄	—	2	8	no	—
137	C₂×C₃×D₄	—	2	16	no	—
138	C₂×C₃×D₄	—	2	8	no	—
139	C₂×C₃×D₄	—	2	8	no	—
140	C₂×C₃×D₄	—	2	16	no	—
141	C₂×C₃×D₄	—	2	16	no	—
142	C₂×C₃×D₄	—	2	16	no	—
143	C₂×C₃×D₄	—	2	16	no	—
144	C₂×C₃×D₄	—	4	16	no	—
145	C₂×C₃×D₄	—	4	16	no	—
146	C₂×C₃×D₄	—	4	16	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	4	no	—
150	C₂²×C₃×C₄	—	2	8	no	—
151	C₂²×C₃×C₄	—	2	16	no	—
152	C₂²×C₃×C₄	—	4	16	no	—
153	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
154	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
155	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
156	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
157	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
158	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
159	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
161	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
163	C₃×C₄⋊C₄	—	2	8	no	—
164	C₃×C₄⋊C₄	—	2	16	no	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	2	16	no	—
167	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
168	C₃×C₂²⋊C₄	—	2	16	no	—
169	C₃×C₂²⋊C₄	—	2	16	no	—
170	C₃×C₂²⋊C₄	—	2	4	no	—
171	C₃×C₂²⋊C₄	—	4	16	no	—
172	C₃×C₂²⋊C₄	—	4	16	no	—
173	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
174	C₃×C₄²	—	2	4	no	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	2	8	no	—
178	C₃×C₄²	—	2	8	no	—
179	C₃×C₄²	C₂×D₄	1	4	yes	—
180	C₃×C₄²	C₂×D₄	1	4	yes	—
181	C₃×C₄²	#41	1	4	yes	—
182	C₃×C₄²	#41	1	4	yes	—
183	C₂²×D₄	C₂³×C₃	1	4	yes	—
184	C₂²×D₄	C₂³×C₃	1	8	yes	—
185	C₂²×D₄	C₂³×C₃	1	8	yes	—
186	C₂²×D₄	C₂³×C₃	1	8	yes	—
187	C₂²×D₄	C₂³×C₃	1	8	yes	—
188	C₂³×C₄	C₂³×C₃	1	2	yes	—
189	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₂³×C₄	C₂³×C₃	1	8	yes	—
191	#127	—	2	8	no	—
192	#127	—	2	8	no	—
193	#127	—	2	8	no	—
194	#127	—	4	16	no	—
195	#125	—	2	8	no	—
196	#123	—	2	32	no	—
197	#121	—	2	16	no	—
198	#121	—	2	32	no	—
199	#121	—	4	16	no	—
200	C₄×D₄	—	2	16	no	—
201	C₄×D₄	—	4	16	no	—
202	#117	—	2	4	no	—
203	#117	C₃×D₄	1	8	yes	complemented
204	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
205	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
206	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
207	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
208	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
210	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
211	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
212	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
215	C₂×C₄²	—	2	4	no	—
216	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₃	1	4	yes	—
218	C₂×C₄²	C₂³×C₃	1	4	yes	—
219	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₃	1	2	yes	—
221	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
225	#95	C₂³×C₃	1	4	yes	—
226	#95	C₂³×C₃	1	4	yes	—
227	#95	C₂³×C₃	1	8	yes	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	2	8	no	—
232	C₂³×C₃	—	2	8	no	—
233	C₂³×C₃	—	2	8	no	—
234	C₂³×C₃	—	2	16	no	—
235	C₂³×C₃	—	2	16	no	—
236	C₂³×C₃	C₂²×D₄	1	2	yes	—
237	C₂³×C₃	C₂⁵	1	1	yes	characteristic
238	C₃×D₄	—	4	16	no	—
239	C₃×D₄	—	4	32	no	—
240	C₃×D₄	—	8	16	no	—
241	C₃×D₄	—	8	16	no	—
242	C₃×D₄	—	8	16	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	2	8	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	16	no	—
255	C₂×C₃×C₄	—	4	8	no	—
256	C₂×C₃×C₄	—	8	16	no	—
257	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
258	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
259	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
261	C₂×C₃×C₄	C₂×#41	1	4	yes	—
262	C₂×C₃×C₄	C₂×#41	1	2	yes	—
263	C₂×C₃×C₄	C₂×#41	1	2	yes	—
264	C₂×C₃×C₄	C₂×#41	1	4	yes	—
265	C₂×C₃×C₄	H(5,𝔽₂)	1	8	yes	—
266	C₂⁴	C₂⁴×C₃	1	8	yes	—
267	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	16	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	16	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	16	no	—
279	C₂×D₄	—	4	16	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	16	no	—
285	C₂²×C₄	—	4	16	no	—
286	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
294	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	16	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	16	no	—
300	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	2	16	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	4	16	no	—
305	C₂²⋊C₄	—	4	16	no	—
306	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
307	C₄²	—	2	4	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	8	no	—
311	C₄²	—	2	8	no	—
312	C₄²	C₂×C₃×D₄	1	4	yes	—
313	C₄²	C₂×C₃×D₄	1	4	yes	—
314	C₄²	C₃×#41	1	4	yes	—
315	C₄²	C₃×#41	1	4	yes	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	4	no	—
318	C₂²×C₃	—	4	2	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	8	no	—
321	C₂²×C₃	—	4	16	no	—
322	C₂²×C₃	—	4	8	no	—
323	C₂²×C₃	—	4	8	no	—
324	C₂²×C₃	—	4	16	no	—
325	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	4	2	no	—
334	C₃×C₄	—	4	8	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	#532	1	4	yes	—
337	C₃×C₄	#540	1	8	yes	complemented
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	16	no	—
345	C₂³	—	2	16	no	—
346	C₂³	C₂²×C₃×D₄	1	2	yes	—
347	C₂³	C₂⁵×C₃	1	1	yes	characteristic
348	D₄	—	4	16	no	—
349	D₄	—	4	32	no	—
350	D₄	—	8	16	no	—
351	D₄	—	8	16	no	—
352	D₄	—	8	16	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	16	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	8	16	no	—
367	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
368	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
369	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
370	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
371	C₂×C₄	C₂×C₃×#41	1	4	yes	—
372	C₂×C₄	C₂×C₃×#41	1	2	yes	—
373	C₂×C₄	C₂×C₃×#41	1	2	yes	—
374	C₂×C₄	C₂×C₃×#41	1	4	yes	—
375	C₂×C₄	C₃×H(5,𝔽₂)	1	8	yes	—
376	C₂×C₃	—	4	2	no	—
377	C₂×C₃	—	8	8	no	—
378	C₂×C₃	C₂×#532	1	1	yes	characteristic
379	C₂×C₃	C₂×#540	1	2	yes	—
380	C₂×C₃	#3498	1	2	yes	—
381	C₂×C₃	#3508	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	16	no	—
391	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
392	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
393	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
394	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
395	C₄	—	2	2	no	—
396	C₄	—	2	4	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	8	no	—
401	C₄	—	4	2	no	—
402	C₄	C₃×#532	1	4	yes	—
403	C₄	C₃×#540	1	8	yes	complemented
404	C₃	#35278	1	1	yes	characteristic, direct product factor, Sylow
405	C₂	—	4	2	no	—
406	C₂	—	8	8	no	—
407	C₂	C₂×C₃×#532	1	1	yes	characteristic
408	C₂	C₂×C₃×#540	1	2	yes	—
409	C₂	C₃×#3498	1	2	yes	—
410	C₂	C₃×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#540	C₂	semidirect
2. C₃×#2867	C₂	semidirect
3. C₃×#2859	C₂	semidirect
4. C₃×#2856	C₂	semidirect
5. C₃×#2641	C₂	semidirect
6. C₃×#2619	C₂	semidirect
7. C₃×#2445	C₂	semidirect
8. C₃×#2428	C₂	semidirect
9. C₃×#2328	C₂	semidirect
10. C₃×C₄×#127	C₂	semidirect
11. C₃×C₄×#117	C₂	semidirect
12. #35278	C₃	direct (N × H)
45. C₂×#540	C₂×C₃	semidirect
46. #2867	C₂×C₃	semidirect
47. #2859	C₂×C₃	semidirect
48. #2856	C₂×C₃	semidirect
49. #2641	C₂×C₃	semidirect
50. #2619	C₂×C₃	semidirect
51. #2445	C₂×C₃	semidirect
52. #2428	C₂×C₃	semidirect
53. #2328	C₂×C₃	semidirect
54. C₄×#127	C₂×C₃	semidirect
55. C₄×#117	C₂×C₃	semidirect
76. C₃×#117	D₄	semidirect
203. #117	C₃×D₄	semidirect
337. C₃×C₄	#540	semidirect
403. C₄	C₃×#540	semidirect
404. C₃	#35278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#540	2
C₃×#2867	2
C₃×#2859	2
C₃×#2856	2
C₃×#2641	2
C₃×#2619	2
C₃×#2445	2
C₃×#2428	2
C₃×#2328	2
C₃×C₄×#127	2
C₃×C₄×#117	2
#35278	3

Subgroups — C3×#35278 #10653885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35278 #10653885