Subgroups — C₃×#3559 #87443

Order 384.

1024 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	2	yes	maximal, complemented
2	C₃×#562	C₂	1	2	yes	maximal, complemented
3	C₃×#554	C₂	1	2	yes	maximal, complemented
4	C₃×#553	C₂	1	2	yes	maximal, complemented
5	C₃×#553	C₂	1	2	yes	maximal, complemented
6	C₃×#547	C₂	1	4	yes	maximal, complemented
7	C₃×#547	C₂	1	2	yes	maximal, complemented
8	C₃×#544	C₂	1	2	yes	maximal, complemented
9	C₃×#540	C₂	1	2	yes	maximal, complemented
10	C₃×#539	C₂	1	2	yes	maximal, complemented
11	C₃×#539	C₂	1	4	yes	maximal, complemented
12	C₃×#537	C₂	1	2	yes	maximal, complemented
13	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	#3559	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×#41	C₂²	1	2	yes	—
18	C₂×C₃×#41	C₂²	1	4	yes	—
19	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
20	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃×#127	C₂²	1	1	yes	characteristic
23	C₃×#126	C₂²	1	4	yes	—
24	C₃×#126	C₂²	1	4	yes	—
25	C₃×#126	C₂²	1	2	yes	—
26	C₃×#125	C₂²	1	2	yes	—
27	C₃×#125	C₂²	1	1	yes	characteristic
28	C₃×#125	C₂²	1	2	yes	—
29	C₃×#125	C₂²	1	2	yes	—
30	C₃×#125	C₂²	1	2	yes	—
31	C₃×#125	C₂²	1	4	yes	—
32	C₃×#125	C₂²	1	2	yes	—
33	C₃×#124	C₂²	1	1	yes	characteristic
34	C₃×#124	C₂²	1	2	yes	—
35	C₃×#123	C₂²	1	4	yes	—
36	C₃×#123	C₂²	1	4	yes	—
37	C₃×#123	C₂²	1	4	yes	—
38	C₃×#123	C₂²	1	2	yes	—
39	C₃×#123	C₂²	1	4	yes	—
40	C₃×#123	C₂²	1	4	yes	—
41	C₃×#123	C₂²	1	4	yes	—
42	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
43	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
44	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
49	C₃×#121	C₂²	1	4	yes	—
50	C₃×#121	C₂²	1	4	yes	—
51	C₃×#121	C₂²	1	1	yes	characteristic
52	C₃×#121	C₂²	1	2	yes	—
53	C₃×#121	C₂²	1	2	yes	—
54	C₃×#121	C₂²	1	4	yes	—
55	C₃×#121	C₂²	1	4	yes	—
56	C₃×#121	C₂²	1	2	yes	—
57	C₃×#121	C₂²	1	2	yes	—
58	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
59	C₃×C₄×D₄	C₂²	1	2	yes	—
60	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
61	C₃×C₄×D₄	C₂²	1	2	yes	—
62	C₃×C₄×D₄	C₂²	1	2	yes	—
63	C₃×C₄×D₄	C₂²	1	4	yes	—
64	C₃×C₄×D₄	C₂²	1	4	yes	—
65	C₃×C₄×D₄	C₂²	1	2	yes	—
66	C₃×C₄×D₄	C₂²	1	2	yes	—
67	C₃×#117	C₂²	1	2	yes	—
68	C₃×#117	C₂²	1	2	yes	—
69	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	—
74	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
76	#563	C₂×C₃	1	2	yes	complemented
77	#562	C₂×C₃	1	2	yes	complemented
78	#554	C₂×C₃	1	2	yes	complemented
79	#553	C₂×C₃	1	2	yes	complemented
80	#553	C₂×C₃	1	2	yes	complemented
81	#547	C₂×C₃	1	4	yes	complemented
82	#547	C₂×C₃	1	2	yes	complemented
83	#544	C₂×C₃	1	2	yes	complemented
84	#540	C₂×C₃	1	2	yes	complemented
85	#539	C₂×C₃	1	2	yes	complemented
86	#539	C₂×C₃	1	4	yes	complemented
87	#537	C₂×C₃	1	2	yes	complemented
88	#532	C₂×C₃	1	1	yes	characteristic, complemented
89	#529	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×#125	C₂×C₃	1	1	yes	characteristic, complemented
91	C₃×#41	—	4	4	no	—
92	C₃×#41	—	4	8	no	—
93	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×Q₈	C₂³	1	4	yes	—
95	C₂×C₃×Q₈	C₂³	1	2	yes	—
96	C₂×C₃×D₄	C₂³	1	2	yes	—
97	C₂×C₃×D₄	C₂³	1	2	yes	—
98	C₂×C₃×D₄	C₂³	1	4	yes	—
99	C₂×C₃×D₄	C₂³	1	4	yes	—
100	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
101	C₂×C₃×D₄	C₂³	1	2	yes	—
102	C₂×C₃×D₄	C₂³	1	4	yes	—
103	C₂×C₃×D₄	C₂³	1	2	yes	—
104	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂³	1	2	yes	—
107	C₂²×C₃×C₄	C₂³	1	2	yes	—
108	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂³	1	2	yes	—
110	C₂²×C₃×C₄	C₂³	1	4	yes	—
111	C₂²×C₃×C₄	C₂³	1	4	yes	—
112	C₂²×C₃×C₄	C₂³	1	4	yes	—
113	C₂²×C₃×C₄	C₂³	1	4	yes	—
114	C₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃×C₄²	C₂³	1	1	yes	characteristic
147	C₃×C₄²	C₂³	1	1	yes	characteristic
148	C₃×C₄²	C₂³	1	1	yes	characteristic
149	C₃×C₄²	C₂³	1	1	yes	characteristic
150	C₃×C₄²	C₂³	1	2	yes	—
151	C₃×C₄²	C₂³	1	4	yes	—
152	C₂×#41	C₂²×C₃	1	2	yes	—
153	C₂×#41	C₂²×C₃	1	4	yes	—
154	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
155	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
156	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
157	#127	C₂²×C₃	1	1	yes	characteristic
158	#126	C₂²×C₃	1	2	yes	—
159	#126	C₂²×C₃	1	4	yes	—
160	#126	C₂²×C₃	1	4	yes	—
161	#125	C₂²×C₃	1	2	yes	—
162	#125	C₂²×C₃	1	2	yes	—
163	#125	C₂²×C₃	1	2	yes	—
164	#125	C₂²×C₃	1	2	yes	—
165	#125	C₂²×C₃	1	1	yes	characteristic
166	#125	C₂²×C₃	1	4	yes	—
167	#125	C₂²×C₃	1	2	yes	—
168	#124	C₂²×C₃	1	1	yes	characteristic
169	#124	C₂²×C₃	1	2	yes	—
170	#123	C₂²×C₃	1	2	yes	—
171	#123	C₂²×C₃	1	4	yes	—
172	#123	C₂²×C₃	1	4	yes	—
173	#123	C₂²×C₃	1	4	yes	—
174	#123	C₂²×C₃	1	4	yes	—
175	#123	C₂²×C₃	1	4	yes	—
176	#123	C₂²×C₃	1	4	yes	—
177	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
178	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
179	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
180	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
181	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
182	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
183	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
184	#121	C₂²×C₃	1	1	yes	characteristic
185	#121	C₂²×C₃	1	2	yes	—
186	#121	C₂²×C₃	1	2	yes	—
187	#121	C₂²×C₃	1	4	yes	—
188	#121	C₂²×C₃	1	4	yes	—
189	#121	C₂²×C₃	1	4	yes	—
190	#121	C₂²×C₃	1	2	yes	—
191	#121	C₂²×C₃	1	4	yes	—
192	#121	C₂²×C₃	1	2	yes	—
193	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₄×D₄	C₂²×C₃	1	2	yes	—
195	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
196	C₄×D₄	C₂²×C₃	1	2	yes	—
197	C₄×D₄	C₂²×C₃	1	2	yes	—
198	C₄×D₄	C₂²×C₃	1	4	yes	—
199	C₄×D₄	C₂²×C₃	1	4	yes	—
200	C₄×D₄	C₂²×C₃	1	2	yes	—
201	C₄×D₄	C₂²×C₃	1	2	yes	—
202	#117	C₂²×C₃	1	2	yes	—
203	#117	C₂²×C₃	1	2	yes	—
204	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	—
209	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
210	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
211	C₂³×C₃	C₂⁴	1	2	yes	—
212	C₂³×C₃	C₂⁴	1	4	yes	—
213	C₂³×C₃	C₂⁴	1	1	yes	characteristic
214	C₃×Q₈	—	4	1	no	—
215	C₃×Q₈	—	4	4	no	—
216	C₃×Q₈	—	4	2	no	—
217	C₃×D₄	—	2	4	no	—
218	C₃×D₄	—	2	8	no	—
219	C₃×D₄	—	2	4	no	—
220	C₃×D₄	—	4	4	no	—
221	C₃×D₄	—	4	2	no	—
222	C₃×D₄	—	4	1	no	—
223	C₃×D₄	—	4	4	no	—
224	C₃×D₄	—	4	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	4	4	no	—
231	C₂×C₃×C₄	—	4	1	no	—
232	C₂×C₃×C₄	—	4	4	no	—
233	C₂×C₃×C₄	—	4	4	no	—
234	C₂×C₃×C₄	—	4	4	no	—
235	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂⁴	1	2	yes	—
237	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂⁴	1	2	yes	—
242	C₂×C₃×C₄	C₂⁴	1	4	yes	—
243	C₂×C₃×C₄	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄	C₂⁴	1	4	yes	—
245	C₂×C₃×C₄	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
247	#41	—	4	4	no	—
248	#41	—	4	8	no	—
249	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
250	C₂×Q₈	C₂³×C₃	1	4	yes	—
251	C₂×Q₈	C₂³×C₃	1	2	yes	—
252	C₂×D₄	C₂³×C₃	1	2	yes	—
253	C₂×D₄	C₂³×C₃	1	2	yes	—
254	C₂×D₄	C₂³×C₃	1	4	yes	—
255	C₂×D₄	C₂³×C₃	1	4	yes	—
256	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
257	C₂×D₄	C₂³×C₃	1	2	yes	—
258	C₂×D₄	C₂³×C₃	1	4	yes	—
259	C₂×D₄	C₂³×C₃	1	2	yes	—
260	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₃	1	2	yes	—
263	C₂²×C₄	C₂³×C₃	1	2	yes	—
264	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₃	1	2	yes	—
266	C₂²×C₄	C₂³×C₃	1	4	yes	—
267	C₂²×C₄	C₂³×C₃	1	4	yes	—
268	C₂²×C₄	C₂³×C₃	1	4	yes	—
269	C₂²×C₄	C₂³×C₃	1	4	yes	—
270	C₄⋊C₄	C₂³×C₃	1	2	yes	—
271	C₄⋊C₄	C₂³×C₃	1	4	yes	—
272	C₄⋊C₄	C₂³×C₃	1	2	yes	—
273	C₄⋊C₄	C₂³×C₃	1	2	yes	—
274	C₄⋊C₄	C₂³×C₃	1	2	yes	—
275	C₄⋊C₄	C₂³×C₃	1	4	yes	—
276	C₄⋊C₄	C₂³×C₃	1	4	yes	—
277	C₄⋊C₄	C₂³×C₃	1	4	yes	—
278	C₄⋊C₄	C₂³×C₃	1	4	yes	—
279	C₄⋊C₄	C₂³×C₃	1	2	yes	—
280	C₄⋊C₄	C₂³×C₃	1	4	yes	—
281	C₄⋊C₄	C₂³×C₃	1	4	yes	—
282	C₄⋊C₄	C₂³×C₃	1	2	yes	—
283	C₄⋊C₄	C₂³×C₃	1	2	yes	—
284	C₄⋊C₄	C₂³×C₃	1	2	yes	—
285	C₄⋊C₄	C₂³×C₃	1	2	yes	—
286	C₄⋊C₄	C₂³×C₃	1	4	yes	—
287	C₄⋊C₄	C₂³×C₃	1	2	yes	—
288	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
289	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
291	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
292	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
293	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
294	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
295	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
296	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
297	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
298	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
299	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
300	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
301	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
302	C₄²	C₂³×C₃	1	1	yes	characteristic
303	C₄²	C₂³×C₃	1	1	yes	characteristic
304	C₄²	C₂³×C₃	1	1	yes	characteristic
305	C₄²	C₂³×C₃	1	1	yes	characteristic
306	C₄²	C₂³×C₃	1	2	yes	—
307	C₄²	C₂³×C₃	1	4	yes	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₃	C₂⁵	1	1	yes	characteristic
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	4	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
330	C₂³	C₂⁴×C₃	1	2	yes	—
331	C₂³	C₂⁴×C₃	1	4	yes	—
332	C₂³	C₂⁴×C₃	1	1	yes	characteristic
333	Q₈	—	4	4	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	1	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	8	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
355	C₂×C₄	C₂⁴×C₃	1	2	yes	—
356	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
357	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
358	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
359	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
360	C₂×C₄	C₂⁴×C₃	1	2	yes	—
361	C₂×C₄	C₂⁴×C₃	1	4	yes	—
362	C₂×C₄	C₂⁴×C₃	1	2	yes	—
363	C₂×C₄	C₂⁴×C₃	1	4	yes	—
364	C₂×C₄	C₂⁴×C₃	1	4	yes	—
365	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	4	2	no	—
368	C₂×C₃	—	4	4	no	—
369	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂×C₃	#585	1	1	yes	characteristic
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
381	C₂²	C₂⁵×C₃	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	4	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
394	C₃	#3559	1	1	yes	characteristic, direct product factor, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	4	2	no	—
397	C₂	—	4	4	no	—
398	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
400	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#563	C₂	semidirect
2. C₃×#562	C₂	semidirect
3. C₃×#554	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#553	C₂	semidirect
6. C₃×#547	C₂	semidirect
7. C₃×#547	C₂	semidirect
8. C₃×#544	C₂	semidirect
9. C₃×#540	C₂	semidirect
10. C₃×#539	C₂	semidirect
11. C₃×#539	C₂	semidirect
12. C₃×#537	C₂	semidirect
13. C₃×#532	C₂	semidirect
14. C₃×#529	C₂	semidirect
15. C₂×C₃×#125	C₂	semidirect
16. #3559	C₃	direct (N × H)
76. #563	C₂×C₃	semidirect
77. #562	C₂×C₃	semidirect
78. #554	C₂×C₃	semidirect
79. #553	C₂×C₃	semidirect
80. #553	C₂×C₃	semidirect
81. #547	C₂×C₃	semidirect
82. #547	C₂×C₃	semidirect
83. #544	C₂×C₃	semidirect
84. #540	C₂×C₃	semidirect
85. #539	C₂×C₃	semidirect
86. #539	C₂×C₃	semidirect
87. #537	C₂×C₃	semidirect
88. #532	C₂×C₃	semidirect
89. #529	C₂×C₃	semidirect
90. C₂×#125	C₂×C₃	semidirect
394. C₃	#3559	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#563	2
C₃×#562	2
C₃×#554	2
C₃×#553	2
C₃×#547	2
C₃×#544	2
C₃×#540	2
C₃×#539	2
C₃×#537	2
C₃×#532	2
C₃×#529	2
C₂×C₃×#125	2
#3559	3

Subgroups — C3×#3559 #87443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3559 #87443