Subgroups — C₃×#60525 #10679132

Order 768.

2234 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3488	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3099	C₂	1	6	yes	maximal, complemented
4	C₃×#3096	C₂	1	6	yes	maximal, complemented
5	C₃×#3094	C₂	1	3	yes	maximal, complemented
6	C₃×#3092	C₂	1	3	yes	maximal, complemented
7	C₃×#3091	C₂	1	3	yes	maximal, complemented
8	C₂×C₃×#481	C₂	1	3	yes	maximal, complemented
9	C₃×#2912	C₂	1	2	yes	maximal, complemented
10	C₃×#2897	C₂	1	2	yes	maximal, complemented
11	C₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	#60525	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×#131	C₂²	1	2	yes	—
16	C₃×#550	—	2	1	no	—
17	C₃×#548	—	2	1	no	—
18	C₃×#546	—	2	3	no	—
19	C₃×D₄²	—	2	3	no	—
20	C₃×#537	C₂²	1	3	yes	—
21	C₃×#535	C₂²	1	3	yes	—
22	C₃×#525	C₂²	1	3	yes	—
23	C₂×C₃×#121	C₂²	1	3	yes	—
24	C₃×#520	—	2	3	no	—
25	C₃×#520	—	2	1	no	—
26	C₃×#520	C₂²	1	2	yes	—
27	C₃×#520	C₂²	1	1	yes	characteristic
28	C₃×#520	C₂²	1	6	yes	complemented
29	C₂×C₃×C₄×Q₈	—	2	1	no	—
30	C₂×C₃×C₄×D₄	—	2	3	no	—
31	C₂×C₃×#117	C₂²	1	3	yes	complemented
32	C₂²×C₃×C₄⋊C₄	C₂²	1	3	yes	complemented
33	C₃×#485	C₂²	1	6	yes	complemented
34	C₃×#484	C₂²	1	3	yes	complemented
35	C₃×#483	C₂²	1	1	yes	characteristic, complemented
36	C₃×#483	C₂²	1	6	yes	complemented
37	C₃×#482	C₂²	1	6	yes	complemented
38	C₃×#482	C₂²	1	12	yes	complemented
39	C₃×#481	C₂²	1	3	yes	complemented
40	C₃×#481	C₂²	1	6	yes	complemented
41	C₃×#481	C₂²	1	12	yes	complemented
42	C₃×#480	C₂²	1	3	yes	complemented
43	C₃×#480	C₂²	1	6	yes	complemented
44	C₃×#428	C₂²	1	6	yes	complemented
45	C₃×#428	C₂²	1	6	yes	complemented
46	C₃×#427	C₂²	1	6	yes	complemented
47	C₂×C₃×#106	C₂²	1	6	yes	complemented
48	C₃×#418	C₂²	1	6	yes	complemented
49	C₃×#417	C₂²	1	6	yes	complemented
50	C₃×#416	C₂²	1	6	yes	complemented
51	C₂×C₃×#102	C₂²	1	6	yes	complemented
52	C₃×#408	C₂²	1	6	yes	complemented
53	C₃×#407	C₂²	1	3	yes	complemented
54	C₂×C₃×C₂²⋊C₈	C₂²	1	3	yes	complemented
55	#3488	C₂×C₃	1	1	yes	characteristic
56	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
57	#3099	C₂×C₃	1	6	yes	complemented
58	#3096	C₂×C₃	1	6	yes	complemented
59	#3094	C₂×C₃	1	3	yes	complemented
60	#3092	C₂×C₃	1	3	yes	complemented
61	#3091	C₂×C₃	1	3	yes	complemented
62	C₂×#481	C₂×C₃	1	3	yes	complemented
63	#2912	C₂×C₃	1	2	yes	complemented
64	#2897	C₂×C₃	1	2	yes	complemented
65	#2880	C₂×C₃	1	1	yes	characteristic, complemented
66	C₃×H(5,𝔽₂)	—	2	8	no	—
67	C₂×C₃×#41	—	2	8	no	—
68	C₂×C₃×#41	—	2	1	no	—
69	C₂×C₃×#41	D₄	1	3	yes	—
70	C₂×C₃×#41	D₄	1	1	yes	characteristic
71	C₂×C₃×#41	C₂³	1	3	yes	—
72	C₂×C₃×#41	C₂³	1	3	yes	—
73	C₂×C₃×#41	C₂³	1	1	yes	characteristic
74	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
75	C₂²×C₃×D₄	—	2	3	no	—
76	C₂²×C₃×D₄	—	2	3	no	—
77	C₂²×C₃×D₄	D₄	1	3	yes	—
78	C₂²×C₃×D₄	C₂³	1	3	yes	—
79	C₂³×C₃×C₄	—	2	3	no	—
80	C₂³×C₃×C₄	C₂³	1	3	yes	—
81	C₃×#131	—	2	8	no	—
82	C₂×C₃×M₁₆	C₂³	1	6	yes	—
83	C₂²×C₃×C₈	C₂³	1	6	yes	—
84	C₃×#127	—	2	3	no	—
85	C₃×#124	—	2	3	no	—
86	C₃×#123	—	2	3	no	—
87	C₃×C₂²⋊Q₈	—	2	3	no	—
88	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
89	C₃×C₂²⋊Q₈	C₂³	1	3	yes	—
90	C₃×#121	—	2	6	no	—
91	C₃×#121	—	2	3	no	—
92	C₃×#121	—	2	3	no	—
93	C₃×#121	—	2	3	no	—
94	C₃×#121	C₂³	1	3	yes	—
95	C₃×#121	C₂³	1	6	yes	—
96	C₃×#121	C₂³	1	3	yes	—
97	C₃×#120	—	2	3	no	—
98	C₃×#120	—	2	6	no	—
99	C₃×C₄×Q₈	—	2	2	no	—
100	C₃×C₄×Q₈	—	2	6	no	—
101	C₃×C₄×Q₈	—	2	1	no	—
102	C₃×C₄×D₄	—	2	6	no	—
103	C₃×C₄×D₄	—	2	12	no	—
104	C₃×C₄×D₄	—	2	6	no	—
105	C₃×C₄×D₄	—	2	3	no	—
106	C₃×C₄×D₄	—	2	3	no	—
107	C₃×C₄×D₄	—	2	3	no	—
108	C₃×#117	—	2	3	no	—
109	C₃×#117	—	2	3	no	—
110	C₃×#117	C₂³	1	6	yes	—
111	C₃×#117	C₂³	1	3	yes	—
112	C₃×#117	C₂³	1	6	yes	—
113	C₂×C₃×C₄⋊C₄	—	2	3	no	—
114	C₂×C₃×C₄⋊C₄	—	2	3	no	—
115	C₂×C₃×C₄⋊C₄	—	2	3	no	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
122	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
123	C₂×C₃×C₄²	—	2	3	no	—
124	C₃×#107	C₂³	1	6	yes	—
125	C₃×#107	C₂³	1	6	yes	—
126	C₃×#106	C₂³	1	6	yes	—
127	C₃×#106	C₂³	1	12	yes	—
128	C₃×#106	C₂³	1	2	yes	—
129	C₃×#103	C₂³	1	2	yes	—
130	C₃×#103	C₂³	1	6	yes	—
131	C₃×#102	C₂³	1	6	yes	—
132	C₃×#102	C₂³	1	12	yes	—
133	C₃×#102	C₂³	1	6	yes	—
134	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
135	C₃×C₂²⋊C₈	C₂³	1	3	yes	—
136	C₃×C₂²⋊C₈	C₂³	1	6	yes	—
137	C₃×C₂²⋊C₈	C₂³	1	6	yes	—
138	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
139	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
140	C₂×#131	C₂²×C₃	1	2	yes	—
141	#550	—	2	1	no	—
142	#548	—	2	1	no	—
143	#546	—	2	3	no	—
144	D₄²	—	2	3	no	—
145	#537	C₂²×C₃	1	3	yes	—
146	#535	C₂²×C₃	1	3	yes	—
147	#525	C₂²×C₃	1	3	yes	—
148	C₂×#121	C₂²×C₃	1	3	yes	—
149	#520	—	2	3	no	—
150	#520	—	2	1	no	—
151	#520	C₂²×C₃	1	2	yes	—
152	#520	C₂²×C₃	1	1	yes	characteristic
153	#520	C₂²×C₃	1	6	yes	complemented
154	C₂×C₄×Q₈	—	2	1	no	—
155	C₂×C₄×D₄	—	2	3	no	—
156	C₂×#117	C₂²×C₃	1	3	yes	complemented
157	C₂²×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
158	#485	C₂²×C₃	1	6	yes	complemented
159	#484	C₂²×C₃	1	3	yes	complemented
160	#483	C₂²×C₃	1	1	yes	characteristic, complemented
161	#483	C₂²×C₃	1	6	yes	complemented
162	#482	C₂²×C₃	1	6	yes	complemented
163	#482	C₂²×C₃	1	12	yes	complemented
164	#481	C₂²×C₃	1	3	yes	complemented
165	#481	C₂²×C₃	1	6	yes	complemented
166	#481	C₂²×C₃	1	12	yes	complemented
167	#480	C₂²×C₃	1	3	yes	complemented
168	#480	C₂²×C₃	1	6	yes	complemented
169	#428	C₂²×C₃	1	6	yes	complemented
170	#428	C₂²×C₃	1	6	yes	complemented
171	#427	C₂²×C₃	1	6	yes	complemented
172	C₂×#106	C₂²×C₃	1	6	yes	complemented
173	#418	C₂²×C₃	1	6	yes	complemented
174	#417	C₂²×C₃	1	6	yes	complemented
175	#416	C₂²×C₃	1	6	yes	complemented
176	C₂×#102	C₂²×C₃	1	6	yes	complemented
177	#408	C₂²×C₃	1	6	yes	complemented
178	#407	C₂²×C₃	1	3	yes	complemented
179	C₂×C₂²⋊C₈	C₂²×C₃	1	3	yes	complemented
180	C₂⁴×C₃	—	2	3	no	—
181	C₂⁴×C₃	C₂×D₄	1	3	yes	—
182	C₃×#41	—	2	4	no	—
183	C₃×#41	—	2	12	no	—
184	C₃×#41	—	2	12	no	—
185	C₃×#41	—	2	12	no	—
186	C₃×#41	—	4	4	no	—
187	C₃×#41	#41	1	8	yes	—
188	C₂×C₃×Q₈	—	2	4	no	—
189	C₂×C₃×Q₈	C₂×D₄	1	3	yes	—
190	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
192	C₂×C₃×D₄	—	2	12	no	—
193	C₂×C₃×D₄	—	2	3	no	—
194	C₂×C₃×D₄	—	2	3	no	—
195	C₂×C₃×D₄	—	2	3	no	—
196	C₂×C₃×D₄	—	2	6	no	—
197	C₂×C₃×D₄	—	2	3	no	—
198	C₂×C₃×D₄	—	2	12	no	—
199	C₂×C₃×D₄	—	4	12	no	—
200	C₂×C₃×D₄	—	8	6	no	—
201	C₂×C₃×D₄	C₂×D₄	1	6	yes	—
202	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
203	C₂×C₃×D₄	C₂×D₄	1	3	yes	—
204	C₂×C₃×D₄	C₂⁴	1	3	yes	—
205	C₂²×C₃×C₄	—	2	12	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	3	no	—
208	C₂²×C₃×C₄	—	2	3	no	—
209	C₂²×C₃×C₄	—	2	6	no	—
210	C₂²×C₃×C₄	—	2	6	no	—
211	C₂²×C₃×C₄	—	2	3	no	—
212	C₂²×C₃×C₄	—	8	6	no	—
213	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
214	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
215	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
216	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
218	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
219	C₃×M₁₆	—	2	12	no	—
220	C₂×C₃×C₈	—	2	12	no	—
221	C₂×C₃×C₈	C₂⁴	1	2	yes	—
222	C₂×C₃×C₈	C₂⁴	1	6	yes	—
223	C₃×C₄⋊C₄	—	2	3	no	—
224	C₃×C₄⋊C₄	—	2	6	no	—
225	C₃×C₄⋊C₄	—	2	6	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	2	3	no	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	2	3	no	—
230	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
231	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
233	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
234	C₃×C₂²⋊C₄	—	2	6	no	—
235	C₃×C₂²⋊C₄	—	2	6	no	—
236	C₃×C₂²⋊C₄	—	2	3	no	—
237	C₃×C₂²⋊C₄	—	2	1	no	—
238	C₃×C₂²⋊C₄	—	2	3	no	—
239	C₃×C₂²⋊C₄	—	2	3	no	—
240	C₃×C₂²⋊C₄	—	2	6	no	—
241	C₃×C₂²⋊C₄	—	2	3	no	—
242	C₃×C₄²	—	2	6	no	—
243	C₃×C₄²	—	2	6	no	—
244	C₃×C₄²	—	2	3	no	—
245	H(5,𝔽₂)	—	2	8	no	—
246	C₂×#41	—	2	8	no	—
247	C₂×#41	—	2	1	no	—
248	C₂×#41	C₃×D₄	1	3	yes	—
249	C₂×#41	C₃×D₄	1	1	yes	characteristic
250	C₂×#41	C₂³×C₃	1	3	yes	—
251	C₂×#41	C₂³×C₃	1	3	yes	—
252	C₂×#41	C₂³×C₃	1	1	yes	characteristic
253	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
254	C₂²×D₄	—	2	3	no	—
255	C₂²×D₄	—	2	3	no	—
256	C₂²×D₄	C₃×D₄	1	3	yes	—
257	C₂²×D₄	C₂³×C₃	1	3	yes	—
258	C₂³×C₄	—	2	3	no	—
259	C₂³×C₄	C₂³×C₃	1	3	yes	—
260	#131	—	2	8	no	—
261	C₂×M₁₆	C₂³×C₃	1	6	yes	—
262	C₂²×C₈	C₂³×C₃	1	6	yes	—
263	#127	—	2	3	no	—
264	#124	—	2	3	no	—
265	#123	—	2	3	no	—
266	C₂²⋊Q₈	—	2	3	no	—
267	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
268	C₂²⋊Q₈	C₂³×C₃	1	3	yes	—
269	#121	—	2	6	no	—
270	#121	—	2	3	no	—
271	#121	—	2	3	no	—
272	#121	—	2	3	no	—
273	#121	C₂³×C₃	1	3	yes	—
274	#121	C₂³×C₃	1	6	yes	—
275	#121	C₂³×C₃	1	3	yes	—
276	#120	—	2	3	no	—
277	#120	—	2	6	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	6	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×D₄	—	2	6	no	—
282	C₄×D₄	—	2	12	no	—
283	C₄×D₄	—	2	6	no	—
284	C₄×D₄	—	2	3	no	—
285	C₄×D₄	—	2	3	no	—
286	C₄×D₄	—	2	3	no	—
287	#117	—	2	3	no	—
288	#117	—	2	3	no	—
289	#117	C₂³×C₃	1	6	yes	—
290	#117	C₂³×C₃	1	6	yes	—
291	#117	C₂³×C₃	1	3	yes	—
292	C₂×C₄⋊C₄	—	2	3	no	—
293	C₂×C₄⋊C₄	—	2	3	no	—
294	C₂×C₄⋊C₄	—	2	3	no	—
295	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
296	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
297	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
298	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
300	C₂×C₂²⋊C₄	—	2	3	no	—
301	C₂×C₂²⋊C₄	—	2	3	no	—
302	C₂×C₄²	—	2	3	no	—
303	#107	C₂³×C₃	1	6	yes	—
304	#107	C₂³×C₃	1	6	yes	—
305	#106	C₂³×C₃	1	6	yes	—
306	#106	C₂³×C₃	1	12	yes	—
307	#106	C₂³×C₃	1	2	yes	—
308	#103	C₂³×C₃	1	2	yes	—
309	#103	C₂³×C₃	1	6	yes	—
310	#102	C₂³×C₃	1	6	yes	—
311	#102	C₂³×C₃	1	12	yes	—
312	#102	C₂³×C₃	1	6	yes	—
313	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
314	C₂²⋊C₈	C₂³×C₃	1	3	yes	—
315	C₂²⋊C₈	C₂³×C₃	1	6	yes	—
316	C₂²⋊C₈	C₂³×C₃	1	6	yes	—
317	C₂³×C₃	—	2	6	no	—
318	C₂³×C₃	—	2	6	no	—
319	C₂³×C₃	—	2	3	no	—
320	C₂³×C₃	—	4	3	no	—
321	C₂³×C₃	—	4	6	no	—
322	C₂³×C₃	—	8	3	no	—
323	C₂³×C₃	—	8	3	no	—
324	C₂³×C₃	C₂²×D₄	1	3	yes	—
325	C₂³×C₃	C₂²×D₄	1	3	yes	—
326	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
327	C₃×Q₈	—	2	6	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	#123	1	4	yes	—
330	C₃×D₄	—	2	12	no	—
331	C₃×D₄	—	2	6	no	—
332	C₃×D₄	—	2	6	no	—
333	C₃×D₄	—	4	6	no	—
334	C₃×D₄	—	4	6	no	—
335	C₃×D₄	—	4	6	no	—
336	C₃×D₄	—	8	3	no	—
337	C₃×D₄	—	8	6	no	—
338	C₃×D₄	#123	1	12	yes	—
339	C₂×C₃×C₄	—	2	6	no	—
340	C₂×C₃×C₄	—	2	6	no	—
341	C₂×C₃×C₄	—	2	6	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	6	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	6	no	—
347	C₂×C₃×C₄	—	2	3	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	4	6	no	—
350	C₂×C₃×C₄	—	4	2	no	—
351	C₂×C₃×C₄	—	4	6	no	—
352	C₂×C₃×C₄	—	8	6	no	—
353	C₂×C₃×C₄	—	8	6	no	—
354	C₂×C₃×C₄	—	8	3	no	—
355	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
356	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
358	C₂×C₃×C₄	C₂×#41	1	12	yes	—
359	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
360	C₃×C₈	—	2	2	no	—
361	C₃×C₈	—	2	6	no	—
362	C₂⁴	—	2	3	no	—
363	C₂⁴	C₂×C₃×D₄	1	3	yes	—
364	#41	—	2	4	no	—
365	#41	—	2	12	no	—
366	#41	—	2	12	no	—
367	#41	—	2	12	no	—
368	#41	—	4	4	no	—
369	#41	C₃×#41	1	8	yes	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	C₂×C₃×D₄	1	3	yes	—
372	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
374	C₂×D₄	—	2	12	no	—
375	C₂×D₄	—	2	3	no	—
376	C₂×D₄	—	2	3	no	—
377	C₂×D₄	—	2	3	no	—
378	C₂×D₄	—	2	6	no	—
379	C₂×D₄	—	2	3	no	—
380	C₂×D₄	—	2	12	no	—
381	C₂×D₄	—	4	12	no	—
382	C₂×D₄	—	8	6	no	—
383	C₂×D₄	C₂×C₃×D₄	1	6	yes	—
384	C₂×D₄	C₂×C₃×D₄	1	3	yes	—
385	C₂×D₄	C₂×C₃×D₄	1	3	yes	—
386	C₂×D₄	C₂⁴×C₃	1	3	yes	—
387	C₂²×C₄	—	2	12	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	3	no	—
390	C₂²×C₄	—	2	3	no	—
391	C₂²×C₄	—	2	6	no	—
392	C₂²×C₄	—	2	6	no	—
393	C₂²×C₄	—	2	3	no	—
394	C₂²×C₄	—	8	6	no	—
395	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
396	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
397	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
398	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
400	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
401	M₁₆	—	2	12	no	—
402	C₂×C₈	—	2	12	no	—
403	C₂×C₈	C₂⁴×C₃	1	2	yes	—
404	C₂×C₈	C₂⁴×C₃	1	6	yes	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
413	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
414	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
415	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	6	no	—
417	C₂²⋊C₄	—	2	6	no	—
418	C₂²⋊C₄	—	2	3	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	3	no	—
421	C₂²⋊C₄	—	2	3	no	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₄²	—	2	6	no	—
425	C₄²	—	2	6	no	—
426	C₄²	—	2	3	no	—
427	C₂²×C₃	—	2	1	no	—
428	C₂²×C₃	—	2	3	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	3	no	—
431	C₂²×C₃	—	2	3	no	—
432	C₂²×C₃	—	2	3	no	—
433	C₂²×C₃	—	2	3	no	—
434	C₂²×C₃	—	4	12	no	—
435	C₂²×C₃	—	4	3	no	—
436	C₂²×C₃	—	4	3	no	—
437	C₂²×C₃	—	4	3	no	—
438	C₂²×C₃	—	16	6	no	—
439	C₂²×C₃	C₂×#123	1	6	yes	—
440	C₂²×C₃	#577	1	2	yes	—
441	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	3	no	—
444	C₃×C₄	—	4	6	no	—
445	C₃×C₄	—	4	1	no	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	3	no	—
449	C₃×C₄	C₂×#123	1	6	yes	—
450	C₃×C₄	C₂²×#41	1	2	yes	—
451	C₂³	—	2	6	no	—
452	C₂³	—	2	6	no	—
453	C₂³	—	2	3	no	—
454	C₂³	—	4	3	no	—
455	C₂³	—	4	6	no	—
456	C₂³	—	8	3	no	—
457	C₂³	—	8	3	no	—
458	C₂³	C₂²×C₃×D₄	1	3	yes	—
459	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
460	C₂³	C₂²×C₃×D₄	1	3	yes	—
461	Q₈	—	2	6	no	—
462	Q₈	—	2	2	no	—
463	Q₈	C₃×#123	1	4	yes	—
464	D₄	—	2	12	no	—
465	D₄	—	2	6	no	—
466	D₄	—	2	6	no	—
467	D₄	—	4	6	no	—
468	D₄	—	4	6	no	—
469	D₄	—	4	6	no	—
470	D₄	—	8	6	no	—
471	D₄	—	8	3	no	—
472	D₄	C₃×#123	1	12	yes	—
473	C₂×C₄	—	2	6	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	6	no	—
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	2	6	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	6	no	—
481	C₂×C₄	—	2	3	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	6	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	6	no	—
486	C₂×C₄	—	8	6	no	—
487	C₂×C₄	—	8	6	no	—
488	C₂×C₄	—	8	3	no	—
489	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
490	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
492	C₂×C₄	C₂×C₃×#41	1	12	yes	—
493	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
494	C₈	—	2	2	no	—
495	C₈	—	2	6	no	—
496	C₂×C₃	—	2	2	no	—
497	C₂×C₃	—	2	6	no	—
498	C₂×C₃	—	4	3	no	—
499	C₂×C₃	—	8	3	no	—
500	C₂×C₃	C₂²×#123	1	1	yes	characteristic
501	C₂×C₃	C₂×#577	1	1	yes	characteristic
502	C₂×C₃	#3585	1	1	yes	characteristic
503	C₂²	—	2	1	no	—
504	C₂²	—	2	3	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	3	no	—
507	C₂²	—	2	3	no	—
508	C₂²	—	2	3	no	—
509	C₂²	—	2	3	no	—
510	C₂²	—	4	12	no	—
511	C₂²	—	4	3	no	—
512	C₂²	—	4	3	no	—
513	C₂²	—	4	3	no	—
514	C₂²	—	16	6	no	—
515	C₂²	C₂×C₃×#123	1	6	yes	—
516	C₂²	C₃×#577	1	2	yes	—
517	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	3	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	3	no	—
523	C₄	—	4	6	no	—
524	C₄	—	4	1	no	—
525	C₄	C₂×C₃×#123	1	6	yes	—
526	C₄	C₂²×C₃×#41	1	2	yes	—
527	C₃	#60525	1	1	yes	characteristic, direct product factor, Sylow
528	C₂	—	2	2	no	—
529	C₂	—	2	6	no	—
530	C₂	—	4	3	no	—
531	C₂	—	8	3	no	—
532	C₂	C₂²×C₃×#123	1	1	yes	characteristic
533	C₂	C₂×C₃×#577	1	1	yes	characteristic
534	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#520	C₂	semidirect
3. C₃×#3099	C₂	semidirect
4. C₃×#3096	C₂	semidirect
5. C₃×#3094	C₂	semidirect
6. C₃×#3092	C₂	semidirect
7. C₃×#3091	C₂	semidirect
8. C₂×C₃×#481	C₂	semidirect
9. C₃×#2912	C₂	semidirect
10. C₃×#2897	C₂	semidirect
11. C₃×#2880	C₂	semidirect
12. #60525	C₃	direct (N × H)
28. C₃×#520	C₂²	semidirect
31. C₂×C₃×#117	C₂²	semidirect
32. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
33. C₃×#485	C₂²	semidirect
34. C₃×#484	C₂²	semidirect
35. C₃×#483	C₂²	semidirect
36. C₃×#483	C₂²	semidirect
37. C₃×#482	C₂²	semidirect
38. C₃×#482	C₂²	semidirect
39. C₃×#481	C₂²	semidirect
40. C₃×#481	C₂²	semidirect
41. C₃×#481	C₂²	semidirect
42. C₃×#480	C₂²	semidirect
43. C₃×#480	C₂²	semidirect
44. C₃×#428	C₂²	semidirect
45. C₃×#428	C₂²	semidirect
46. C₃×#427	C₂²	semidirect
47. C₂×C₃×#106	C₂²	semidirect
48. C₃×#418	C₂²	semidirect
49. C₃×#417	C₂²	semidirect
50. C₃×#416	C₂²	semidirect
51. C₂×C₃×#102	C₂²	semidirect
52. C₃×#408	C₂²	semidirect
53. C₃×#407	C₂²	semidirect
54. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
56. C₂×#520	C₂×C₃	semidirect
57. #3099	C₂×C₃	semidirect
58. #3096	C₂×C₃	semidirect
59. #3094	C₂×C₃	semidirect
60. #3092	C₂×C₃	semidirect
61. #3091	C₂×C₃	semidirect
62. C₂×#481	C₂×C₃	semidirect
63. #2912	C₂×C₃	semidirect
64. #2897	C₂×C₃	semidirect
65. #2880	C₂×C₃	semidirect
153. #520	C₂²×C₃	semidirect
156. C₂×#117	C₂²×C₃	semidirect
157. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
158. #485	C₂²×C₃	semidirect
159. #484	C₂²×C₃	semidirect
160. #483	C₂²×C₃	semidirect
161. #483	C₂²×C₃	semidirect
162. #482	C₂²×C₃	semidirect
163. #482	C₂²×C₃	semidirect
164. #481	C₂²×C₃	semidirect
165. #481	C₂²×C₃	semidirect
166. #481	C₂²×C₃	semidirect
167. #480	C₂²×C₃	semidirect
168. #480	C₂²×C₃	semidirect
169. #428	C₂²×C₃	semidirect
170. #428	C₂²×C₃	semidirect
171. #427	C₂²×C₃	semidirect
172. C₂×#106	C₂²×C₃	semidirect
173. #418	C₂²×C₃	semidirect
174. #417	C₂²×C₃	semidirect
175. #416	C₂²×C₃	semidirect
176. C₂×#102	C₂²×C₃	semidirect
177. #408	C₂²×C₃	semidirect
178. #407	C₂²×C₃	semidirect
179. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
527. C₃	#60525	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×#3488	2
C₂×C₃×#520	2
C₃×#3099	2
C₃×#3096	2
C₃×#3094	2
C₃×#3092	2
C₃×#3091	2
C₂×C₃×#481	2
C₃×#2912	2
C₃×#2897	2
C₃×#2880	2
#60525	3

Subgroups — C3×#60525 #10679132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60525 #10679132