Subgroups — C₃×#3540 #87424

Order 384.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
2	C₃×#560	C₂	1	2	yes	maximal, complemented
3	C₃×#559	C₂	1	2	yes	maximal, complemented
4	C₃×#556	C₂	1	2	yes	maximal, complemented
5	C₃×#555	C₂	1	2	yes	maximal, complemented
6	C₃×#551	C₂	1	2	yes	maximal, complemented
7	C₃×#548	C₂	1	2	yes	maximal, complemented
8	C₃×#546	C₂	1	2	yes	maximal, complemented
9	C₃×#542	C₂	1	2	yes	maximal, complemented
10	C₃×#542	C₂	1	4	yes	maximal, complemented
11	C₃×#538	C₂	1	4	yes	maximal, complemented
12	C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#525	C₂	1	2	yes	maximal, complemented
16	#3540	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×#41	C₂²	1	2	yes	—
19	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×#127	C₂²	1	2	yes	—
25	C₃×#126	C₂²	1	4	yes	complemented
26	C₃×#126	C₂²	1	4	yes	complemented
27	C₃×#126	C₂²	1	4	yes	complemented
28	C₃×#124	C₂²	1	2	yes	—
29	C₃×#124	C₂²	1	4	yes	—
30	C₃×#124	C₂²	1	4	yes	complemented
31	C₃×#124	C₂²	1	4	yes	complemented
32	C₃×#124	C₂²	1	4	yes	complemented
33	C₃×#124	C₂²	1	4	yes	complemented
34	C₃×#124	C₂²	1	2	yes	complemented
35	C₃×#124	C₂²	1	2	yes	complemented
36	C₃×#123	C₂²	1	1	yes	characteristic
37	C₃×#123	C₂²	1	1	yes	characteristic, complemented
38	C₃×#123	C₂²	1	2	yes	complemented
39	C₃×#123	C₂²	1	4	yes	complemented
40	C₃×#123	C₂²	1	4	yes	complemented
41	C₃×#123	C₂²	1	4	yes	complemented
42	C₃×#123	C₂²	1	2	yes	complemented
43	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
48	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
49	C₃×#121	C₂²	1	4	yes	—
50	C₃×#121	C₂²	1	2	yes	—
51	C₃×#121	C₂²	1	2	yes	—
52	C₃×#121	C₂²	1	2	yes	—
53	C₃×#121	C₂²	1	4	yes	complemented
54	C₃×#121	C₂²	1	4	yes	complemented
55	C₃×#121	C₂²	1	2	yes	complemented
56	C₃×#120	C₂²	1	1	yes	characteristic
57	C₃×#120	C₂²	1	2	yes	—
58	C₃×#120	C₂²	1	4	yes	—
59	C₃×#120	C₂²	1	1	yes	characteristic, complemented
60	C₃×#120	C₂²	1	4	yes	complemented
61	C₃×#120	C₂²	1	2	yes	complemented
62	C₃×C₄×Q₈	C₂²	1	4	yes	complemented
63	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
64	C₃×C₄×D₄	C₂²	1	2	yes	—
65	C₃×C₄×D₄	C₂²	1	4	yes	complemented
66	C₃×C₄×D₄	C₂²	1	4	yes	complemented
67	C₃×C₄×D₄	C₂²	1	4	yes	complemented
68	C₃×C₄×D₄	C₂²	1	2	yes	complemented
69	C₃×C₄×D₄	C₂²	1	2	yes	complemented
70	C₃×#117	C₂²	1	1	yes	characteristic, complemented
71	C₃×#117	C₂²	1	2	yes	complemented
72	C₃×#117	C₂²	1	1	yes	characteristic, complemented
73	C₃×#117	C₂²	1	1	yes	characteristic, complemented
74	C₃×#117	C₂²	1	4	yes	complemented
75	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	H(3,𝔽₄)	C₂×C₃	1	2	yes	complemented
77	#560	C₂×C₃	1	2	yes	complemented
78	#559	C₂×C₃	1	2	yes	complemented
79	#556	C₂×C₃	1	2	yes	complemented
80	#555	C₂×C₃	1	2	yes	complemented
81	#551	C₂×C₃	1	2	yes	complemented
82	#548	C₂×C₃	1	2	yes	complemented
83	#546	C₂×C₃	1	2	yes	complemented
84	#542	C₂×C₃	1	2	yes	complemented
85	#542	C₂×C₃	1	4	yes	complemented
86	#538	C₂×C₃	1	4	yes	complemented
87	#536	C₂×C₃	1	1	yes	characteristic, complemented
88	#535	C₂×C₃	1	1	yes	characteristic, complemented
89	#525	C₂×C₃	1	1	yes	characteristic, complemented
90	#525	C₂×C₃	1	2	yes	complemented
91	C₂⁴×C₃	C₂³	1	2	yes	—
92	C₂⁴×C₃	C₂³	1	1	yes	characteristic
93	C₃×#41	—	4	2	no	—
94	C₃×#41	—	4	4	no	—
95	C₂×C₃×Q₈	—	4	2	no	—
96	C₂×C₃×Q₈	C₂³	1	2	yes	—
97	C₂×C₃×Q₈	C₂³	1	4	yes	—
98	C₂×C₃×Q₈	C₂³	1	2	yes	—
99	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×D₄	—	4	2	no	—
101	C₂×C₃×D₄	C₂³	1	2	yes	—
102	C₂×C₃×D₄	C₂³	1	2	yes	—
103	C₂×C₃×D₄	C₂³	1	4	yes	—
104	C₂×C₃×D₄	C₂³	1	4	yes	—
105	C₂×C₃×D₄	C₂³	1	2	yes	—
106	C₂×C₃×D₄	C₂³	1	4	yes	—
107	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
108	C₂×C₃×D₄	C₂³	1	4	yes	—
109	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
110	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
111	C₂×C₃×D₄	C₂³	1	2	yes	—
112	C₂²×C₃×C₄	—	4	2	no	—
113	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂³	1	2	yes	—
115	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂³	1	4	yes	—
118	C₂²×C₃×C₄	C₂³	1	4	yes	—
119	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂³	1	2	yes	—
121	C₂²×C₃×C₄	C₂³	1	2	yes	—
122	C₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
139	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
141	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃×C₄²	C₂³	1	2	yes	—
151	C₃×C₄²	C₂³	1	4	yes	—
152	C₃×C₄²	C₂³	1	2	yes	—
153	C₃×C₄²	C₂³	1	2	yes	—
154	C₃×C₄²	C₂³	1	4	yes	—
155	C₂×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂×#41	C₂²×C₃	1	2	yes	—
157	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
161	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
162	#127	C₂²×C₃	1	2	yes	—
163	#126	C₂²×C₃	1	4	yes	complemented
164	#126	C₂²×C₃	1	4	yes	complemented
165	#126	C₂²×C₃	1	4	yes	complemented
166	#124	C₂²×C₃	1	2	yes	—
167	#124	C₂²×C₃	1	4	yes	—
168	#124	C₂²×C₃	1	2	yes	complemented
169	#124	C₂²×C₃	1	4	yes	complemented
170	#124	C₂²×C₃	1	2	yes	complemented
171	#124	C₂²×C₃	1	4	yes	complemented
172	#124	C₂²×C₃	1	4	yes	complemented
173	#124	C₂²×C₃	1	4	yes	complemented
174	#123	C₂²×C₃	1	1	yes	characteristic
175	#123	C₂²×C₃	1	4	yes	complemented
176	#123	C₂²×C₃	1	1	yes	characteristic, complemented
177	#123	C₂²×C₃	1	2	yes	complemented
178	#123	C₂²×C₃	1	2	yes	complemented
179	#123	C₂²×C₃	1	4	yes	complemented
180	#123	C₂²×C₃	1	4	yes	complemented
181	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
182	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
183	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
184	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
185	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
186	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
187	#121	C₂²×C₃	1	2	yes	—
188	#121	C₂²×C₃	1	2	yes	—
189	#121	C₂²×C₃	1	2	yes	—
190	#121	C₂²×C₃	1	4	yes	—
191	#121	C₂²×C₃	1	2	yes	complemented
192	#121	C₂²×C₃	1	4	yes	complemented
193	#121	C₂²×C₃	1	4	yes	complemented
194	#120	C₂²×C₃	1	1	yes	characteristic
195	#120	C₂²×C₃	1	2	yes	—
196	#120	C₂²×C₃	1	4	yes	—
197	#120	C₂²×C₃	1	1	yes	characteristic, complemented
198	#120	C₂²×C₃	1	4	yes	complemented
199	#120	C₂²×C₃	1	2	yes	complemented
200	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
201	C₄×Q₈	C₂²×C₃	1	4	yes	complemented
202	C₄×D₄	C₂²×C₃	1	2	yes	—
203	C₄×D₄	C₂²×C₃	1	4	yes	complemented
204	C₄×D₄	C₂²×C₃	1	2	yes	complemented
205	C₄×D₄	C₂²×C₃	1	4	yes	complemented
206	C₄×D₄	C₂²×C₃	1	4	yes	complemented
207	C₄×D₄	C₂²×C₃	1	2	yes	complemented
208	#117	C₂²×C₃	1	1	yes	characteristic, complemented
209	#117	C₂²×C₃	1	2	yes	complemented
210	#117	C₂²×C₃	1	1	yes	characteristic, complemented
211	#117	C₂²×C₃	1	1	yes	characteristic, complemented
212	#117	C₂²×C₃	1	4	yes	complemented
213	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
214	C₂³×C₃	—	4	1	no	—
215	C₂³×C₃	—	4	2	no	—
216	C₂³×C₃	—	4	2	no	—
217	C₂³×C₃	—	4	4	no	—
218	C₂³×C₃	C₂⁴	1	1	yes	characteristic
219	C₂³×C₃	C₂⁴	1	1	yes	characteristic
220	C₂³×C₃	C₂⁴	1	2	yes	—
221	C₂³×C₃	C₂⁴	1	4	yes	—
222	C₂³×C₃	C₂⁴	1	1	yes	characteristic
223	C₃×Q₈	—	2	4	no	—
224	C₃×Q₈	—	4	2	no	—
225	C₃×Q₈	—	4	4	no	—
226	C₃×Q₈	—	4	1	no	—
227	C₃×D₄	—	2	4	no	—
228	C₃×D₄	—	4	2	no	—
229	C₃×D₄	—	4	2	no	—
230	C₃×D₄	—	4	4	no	—
231	C₃×D₄	—	4	4	no	—
232	C₃×D₄	—	4	4	no	—
233	C₃×D₄	—	4	2	no	—
234	C₃×D₄	—	4	1	no	—
235	C₃×D₄	—	4	1	no	—
236	C₃×D₄	—	4	1	no	—
237	C₃×D₄	—	4	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	—	4	4	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	—	4	4	no	—
247	C₂×C₃×C₄	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄	C₂⁴	1	4	yes	—
249	C₂×C₃×C₄	C₂⁴	1	4	yes	—
250	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂⁴	1	2	yes	—
252	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂⁴	1	2	yes	—
254	C₂×C₃×C₄	C₂⁴	1	4	yes	—
255	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
257	C₂⁴	C₂³×C₃	1	2	yes	—
258	C₂⁴	C₂³×C₃	1	1	yes	characteristic
259	#41	—	4	2	no	—
260	#41	—	4	4	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	C₂³×C₃	1	2	yes	—
263	C₂×Q₈	C₂³×C₃	1	4	yes	—
264	C₂×Q₈	C₂³×C₃	1	2	yes	—
265	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	C₂³×C₃	1	2	yes	—
268	C₂×D₄	C₂³×C₃	1	2	yes	—
269	C₂×D₄	C₂³×C₃	1	4	yes	—
270	C₂×D₄	C₂³×C₃	1	4	yes	—
271	C₂×D₄	C₂³×C₃	1	2	yes	—
272	C₂×D₄	C₂³×C₃	1	4	yes	—
273	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
274	C₂×D₄	C₂³×C₃	1	4	yes	—
275	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
276	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
277	C₂×D₄	C₂³×C₃	1	2	yes	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₃	1	2	yes	—
281	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₃	1	4	yes	—
284	C₂²×C₄	C₂³×C₃	1	4	yes	—
285	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₃	1	2	yes	—
287	C₂²×C₄	C₂³×C₃	1	2	yes	—
288	C₄⋊C₄	C₂³×C₃	1	2	yes	—
289	C₄⋊C₄	C₂³×C₃	1	2	yes	—
290	C₄⋊C₄	C₂³×C₃	1	2	yes	—
291	C₄⋊C₄	C₂³×C₃	1	2	yes	—
292	C₄⋊C₄	C₂³×C₃	1	4	yes	—
293	C₄⋊C₄	C₂³×C₃	1	2	yes	—
294	C₄⋊C₄	C₂³×C₃	1	4	yes	—
295	C₄⋊C₄	C₂³×C₃	1	4	yes	—
296	C₄⋊C₄	C₂³×C₃	1	4	yes	—
297	C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
299	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
300	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
301	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
303	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
304	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
305	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
308	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
309	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
310	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
311	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
312	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
313	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
314	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
315	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
316	C₄²	C₂³×C₃	1	2	yes	—
317	C₄²	C₂³×C₃	1	4	yes	—
318	C₄²	C₂³×C₃	1	2	yes	—
319	C₄²	C₂³×C₃	1	2	yes	—
320	C₄²	C₂³×C₃	1	4	yes	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	—	8	4	no	—
335	C₂²×C₃	C₂⁵	1	1	yes	characteristic
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	4	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	C₂⁴×C₃	1	1	yes	characteristic
351	C₂³	C₂⁴×C₃	1	1	yes	characteristic
352	C₂³	C₂⁴×C₃	1	2	yes	—
353	C₂³	C₂⁴×C₃	1	4	yes	—
354	C₂³	C₂⁴×C₃	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	4	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂⁴×C₃	1	2	yes	—
380	C₂×C₄	C₂⁴×C₃	1	4	yes	—
381	C₂×C₄	C₂⁴×C₃	1	4	yes	—
382	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
383	C₂×C₄	C₂⁴×C₃	1	2	yes	—
384	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
385	C₂×C₄	C₂⁴×C₃	1	2	yes	—
386	C₂×C₄	C₂⁴×C₃	1	4	yes	—
387	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
388	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
389	C₂×C₃	—	4	1	no	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	4	4	no	—
393	C₂×C₃	—	4	1	no	—
394	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₃	#585	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	4	no	—
410	C₂²	C₂⁵×C₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
421	C₃	#3540	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	4	2	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	4	no	—
426	C₂	—	4	1	no	—
427	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂	C₃×#585	1	2	yes	—

	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×H(3,𝔽₄)	C₂	semidirect
2. C₃×#560	C₂	semidirect
3. C₃×#559	C₂	semidirect
4. C₃×#556	C₂	semidirect
5. C₃×#555	C₂	semidirect
6. C₃×#551	C₂	semidirect
7. C₃×#548	C₂	semidirect
8. C₃×#546	C₂	semidirect
9. C₃×#542	C₂	semidirect
10. C₃×#542	C₂	semidirect
11. C₃×#538	C₂	semidirect
12. C₃×#536	C₂	semidirect
13. C₃×#535	C₂	semidirect
14. C₃×#525	C₂	semidirect
15. C₃×#525	C₂	semidirect
16. #3540	C₃	direct (N × H)
19. C₂²×C₃×Q₈	C₂²	semidirect
20. C₂²×C₃×D₄	C₂²	semidirect
21. C₂³×C₃×C₄	C₂²	semidirect
22. C₃×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×#126	C₂²	semidirect
26. C₃×#126	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
30. C₃×#124	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#124	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
37. C₃×#123	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×#123	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×#123	C₂²	semidirect
43. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
54. C₃×#121	C₂²	semidirect
55. C₃×#121	C₂²	semidirect
59. C₃×#120	C₂²	semidirect
60. C₃×#120	C₂²	semidirect
61. C₃×#120	C₂²	semidirect
62. C₃×C₄×Q₈	C₂²	semidirect
63. C₃×C₄×Q₈	C₂²	semidirect
65. C₃×C₄×D₄	C₂²	semidirect
66. C₃×C₄×D₄	C₂²	semidirect
67. C₃×C₄×D₄	C₂²	semidirect
68. C₃×C₄×D₄	C₂²	semidirect
69. C₃×C₄×D₄	C₂²	semidirect
70. C₃×#117	C₂²	semidirect
71. C₃×#117	C₂²	semidirect
72. C₃×#117	C₂²	semidirect
73. C₃×#117	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
76. H(3,𝔽₄)	C₂×C₃	semidirect
77. #560	C₂×C₃	semidirect
78. #559	C₂×C₃	semidirect
79. #556	C₂×C₃	semidirect
80. #555	C₂×C₃	semidirect
81. #551	C₂×C₃	semidirect
82. #548	C₂×C₃	semidirect
83. #546	C₂×C₃	semidirect
84. #542	C₂×C₃	semidirect
85. #542	C₂×C₃	semidirect
86. #538	C₂×C₃	semidirect
87. #536	C₂×C₃	semidirect
88. #535	C₂×C₃	semidirect
89. #525	C₂×C₃	semidirect
90. #525	C₂×C₃	semidirect
157. C₂²×Q₈	C₂²×C₃	semidirect
158. C₂²×D₄	C₂²×C₃	semidirect
159. C₂³×C₄	C₂²×C₃	semidirect
160. C₄⋊Q₈	C₂²×C₃	semidirect
161. C₄⋊Q₈	C₂²×C₃	semidirect
163. #126	C₂²×C₃	semidirect
164. #126	C₂²×C₃	semidirect
165. #126	C₂²×C₃	semidirect
168. #124	C₂²×C₃	semidirect
169. #124	C₂²×C₃	semidirect
170. #124	C₂²×C₃	semidirect
171. #124	C₂²×C₃	semidirect
172. #124	C₂²×C₃	semidirect
173. #124	C₂²×C₃	semidirect
175. #123	C₂²×C₃	semidirect
176. #123	C₂²×C₃	semidirect
177. #123	C₂²×C₃	semidirect
178. #123	C₂²×C₃	semidirect
179. #123	C₂²×C₃	semidirect
180. #123	C₂²×C₃	semidirect
181. C₂²⋊Q₈	C₂²×C₃	semidirect
182. C₂²⋊Q₈	C₂²×C₃	semidirect
183. C₂²⋊Q₈	C₂²×C₃	semidirect
184. C₂²⋊Q₈	C₂²×C₃	semidirect
185. C₂²⋊Q₈	C₂²×C₃	semidirect
186. C₂²⋊Q₈	C₂²×C₃	semidirect
191. #121	C₂²×C₃	semidirect
192. #121	C₂²×C₃	semidirect
193. #121	C₂²×C₃	semidirect
197. #120	C₂²×C₃	semidirect
198. #120	C₂²×C₃	semidirect
199. #120	C₂²×C₃	semidirect
200. C₄×Q₈	C₂²×C₃	semidirect
201. C₄×Q₈	C₂²×C₃	semidirect
203. C₄×D₄	C₂²×C₃	semidirect
204. C₄×D₄	C₂²×C₃	semidirect
205. C₄×D₄	C₂²×C₃	semidirect
206. C₄×D₄	C₂²×C₃	semidirect
207. C₄×D₄	C₂²×C₃	semidirect
208. #117	C₂²×C₃	semidirect
209. #117	C₂²×C₃	semidirect
210. #117	C₂²×C₃	semidirect
211. #117	C₂²×C₃	semidirect
212. #117	C₂²×C₃	semidirect
213. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
421. C₃	#3540	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×H(3,𝔽₄)	2
C₃×#560	2
C₃×#559	2
C₃×#556	2
C₃×#555	2
C₃×#551	2
C₃×#548	2
C₃×#546	2
C₃×#542	2
C₃×#538	2
C₃×#536	2
C₃×#535	2
C₃×#525	2
#3540	3

Subgroups — C3×#3540 #87424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3540 #87424