Subgroups — C₂×C₃×#3215 #10679391

Order 768.

2242 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×#3215	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#451	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#450	C₂	1	2	yes	maximal
9	C₂×C₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#3215	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Q₁₆	C₂²	1	4	yes	complemented
14	C₂²×C₃×SD₁₆	C₂²	1	4	yes	—
15	C₃×#533	—	2	4	no	—
16	C₃×#533	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#125	—	2	1	no	—
20	C₂×C₃×#124	—	2	1	no	—
21	C₂×C₃×#124	—	2	1	no	—
22	C₂×C₃×#124	—	2	4	no	—
23	C₂×C₃×#124	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	8	yes	—
25	C₂×C₃×#124	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Q₈	—	2	1	no	—
29	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
30	C₂×C₃×#117	—	2	1	no	—
31	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
32	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
33	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₃×#497	C₂²	1	16	yes	complemented
35	C₃×#489	C₂²	1	16	yes	complemented
36	C₃×#464	C₂²	1	32	yes	complemented
37	C₃×#451	C₂²	1	16	yes	complemented
38	C₃×#450	C₂²	1	16	yes	—
39	C₃×#432	C₂²	1	8	yes	complemented
40	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
41	C₂×C₃×#103	C₂²	1	4	yes	complemented
42	C₂×C₃×#102	C₂²	1	4	yes	—
43	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂×C₃×#97	C₂²	1	2	yes	complemented
45	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂²×#124	C₂×C₃	1	1	yes	characteristic
47	#3215	C₂×C₃	1	16	yes	direct product factor
48	C₂×#497	C₂×C₃	1	2	yes	complemented
49	C₂×#489	C₂×C₃	1	2	yes	complemented
50	C₂×#464	C₂×C₃	1	4	yes	complemented
51	C₂×#451	C₂×C₃	1	2	yes	complemented
52	C₂×#450	C₂×C₃	1	2	yes	—
53	C₂×#432	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁵×C₃	—	2	1	no	—
55	C₂²×C₃×Q₈	—	2	2	no	—
56	C₂²×C₃×Q₈	—	2	1	no	—
57	C₂²×C₃×Q₈	—	2	1	no	—
58	C₂²×C₃×Q₈	—	4	4	no	—
59	C₂²×C₃×Q₈	C₂³	1	2	yes	—
60	C₂²×C₃×Q₈	C₂³	1	2	yes	—
61	C₂²×C₃×Q₈	C₂³	1	4	yes	—
62	C₂²×C₃×D₄	—	2	2	no	—
63	C₂²×C₃×D₄	—	2	1	no	—
64	C₂²×C₃×D₄	—	4	4	no	—
65	C₂²×C₃×D₄	C₂³	1	2	yes	—
66	C₂²×C₃×D₄	C₂³	1	4	yes	—
67	C₂³×C₃×C₄	—	2	1	no	—
68	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
69	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
70	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
71	C₂×C₃×Q₁₆	—	4	8	no	—
72	C₂×C₃×Q₁₆	C₂³	1	16	yes	complemented
73	C₂×C₃×SD₁₆	—	4	8	no	—
74	C₂×C₃×SD₁₆	C₂³	1	16	yes	—
75	C₂²×C₃×C₈	C₂³	1	4	yes	—
76	C₃×C₄⋊Q₈	—	2	2	no	—
77	C₃×C₄⋊Q₈	—	2	2	no	—
78	C₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
79	C₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
80	C₃×#125	—	2	8	no	—
81	C₃×#124	—	2	8	no	—
82	C₃×#124	—	2	4	no	—
83	C₃×#124	—	2	8	no	—
84	C₃×#124	—	2	4	no	—
85	C₃×#124	C₂³	1	8	yes	—
86	C₃×#124	C₂³	1	8	yes	—
87	C₃×C₂²⋊Q₈	—	2	8	no	—
88	C₃×C₂²⋊Q₈	—	2	4	no	—
89	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
90	C₃×C₄×Q₈	—	2	8	no	—
91	C₃×C₄×Q₈	—	2	4	no	—
92	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
93	C₃×#117	—	2	8	no	—
94	C₂×C₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
102	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
103	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₃×C₄²	—	2	2	no	—
108	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
109	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
110	C₂×C₃×C₄²	D₄	1	4	yes	—
111	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₄²	C₂³	1	4	yes	—
114	C₃×C₄⋊C₈	C₂³	1	8	yes	complemented
115	C₃×#103	C₂³	1	16	yes	complemented
116	C₃×#102	C₂³	1	16	yes	—
117	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
118	C₃×#97	C₂³	1	8	yes	complemented
119	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
120	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂²×Q₁₆	C₂²×C₃	1	4	yes	complemented
122	C₂²×SD₁₆	C₂²×C₃	1	4	yes	—
123	#533	—	2	4	no	—
124	#533	C₂²×C₃	1	8	yes	complemented
125	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×#125	—	2	1	no	—
128	C₂×#124	—	2	1	no	—
129	C₂×#124	—	2	1	no	—
130	C₂×#124	—	2	4	no	—
131	C₂×#124	C₂²×C₃	1	2	yes	—
132	C₂×#124	C₂²×C₃	1	8	yes	—
133	C₂×#124	C₂²×C₃	1	2	yes	—
134	C₂×C₂²⋊Q₈	—	2	1	no	—
135	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
136	C₂×C₄×Q₈	—	2	1	no	—
137	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
138	C₂×#117	—	2	1	no	—
139	C₂²×C₂²⋊C₄	—	2	1	no	—
140	C₂²×C₂²⋊C₄	—	2	1	no	—
141	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
142	#497	C₂²×C₃	1	16	yes	complemented
143	#489	C₂²×C₃	1	16	yes	complemented
144	#464	C₂²×C₃	1	32	yes	complemented
145	#451	C₂²×C₃	1	16	yes	complemented
146	#450	C₂²×C₃	1	16	yes	—
147	#432	C₂²×C₃	1	8	yes	complemented
148	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
149	C₂×#103	C₂²×C₃	1	4	yes	complemented
150	C₂×#102	C₂²×C₃	1	4	yes	—
151	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
152	C₂×#97	C₂²×C₃	1	2	yes	complemented
153	C₂⁴×C₃	—	2	4	no	—
154	C₂⁴×C₃	—	2	2	no	—
155	C₂⁴×C₃	—	4	4	no	—
156	C₂⁴×C₃	—	4	4	no	—
157	C₂⁴×C₃	—	4	4	no	—
158	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×Q₈	—	2	4	no	—
161	C₂×C₃×Q₈	—	2	4	no	—
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	—	2	8	no	—
164	C₂×C₃×Q₈	—	2	8	no	—
165	C₂×C₃×Q₈	—	4	8	no	—
166	C₂×C₃×Q₈	—	4	4	no	—
167	C₂×C₃×Q₈	—	4	4	no	—
168	C₂×C₃×Q₈	—	4	8	no	—
169	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
170	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	8	no	—
174	C₂×C₃×D₄	—	4	8	no	—
175	C₂×C₃×D₄	—	4	4	no	—
176	C₂×C₃×D₄	—	4	8	no	—
177	C₂×C₃×D₄	C₂⁴	1	4	yes	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	—	2	2	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	4	2	no	—
185	C₂²×C₃×C₄	—	4	4	no	—
186	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
187	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
188	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
194	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
195	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
196	C₃×Q₁₆	—	4	16	no	—
197	C₃×SD₁₆	—	4	16	no	—
198	C₂×C₃×C₈	—	2	8	no	—
199	C₂×C₃×C₈	C₂⁴	1	8	yes	—
200	C₃×C₄⋊C₄	—	2	4	no	—
201	C₃×C₄⋊C₄	—	2	4	no	—
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	2	8	no	—
204	C₃×C₄⋊C₄	—	2	8	no	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
207	C₃×C₂²⋊C₄	—	2	8	no	—
208	C₃×C₂²⋊C₄	—	2	8	no	—
209	C₃×C₂²⋊C₄	—	2	8	no	—
210	C₃×C₂²⋊C₄	—	2	8	no	—
211	C₃×C₂²⋊C₄	—	2	8	no	—
212	C₃×C₄²	—	2	8	no	—
213	C₃×C₄²	C₂×D₄	1	4	yes	—
214	C₃×C₄²	C₂×D₄	1	2	yes	—
215	C₃×C₄²	C₂×D₄	1	4	yes	—
216	C₃×C₄²	C₂×D₄	1	2	yes	—
217	C₃×C₄²	C₂⁴	1	2	yes	—
218	C₃×C₄²	C₂⁴	1	2	yes	—
219	C₂⁵	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	4	4	no	—
224	C₂²×Q₈	C₂³×C₃	1	2	yes	—
225	C₂²×Q₈	C₂³×C₃	1	2	yes	—
226	C₂²×Q₈	C₂³×C₃	1	4	yes	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	4	4	no	—
230	C₂²×D₄	C₂³×C₃	1	2	yes	—
231	C₂²×D₄	C₂³×C₃	1	4	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
234	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂×Q₁₆	—	4	8	no	—
237	C₂×Q₁₆	C₂³×C₃	1	16	yes	complemented
238	C₂×SD₁₆	—	4	8	no	—
239	C₂×SD₁₆	C₂³×C₃	1	16	yes	—
240	C₂²×C₈	C₂³×C₃	1	4	yes	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	C₂³×C₃	1	4	yes	complemented
244	C₄⋊Q₈	C₂³×C₃	1	4	yes	complemented
245	#125	—	2	8	no	—
246	#124	—	2	8	no	—
247	#124	—	2	4	no	—
248	#124	—	2	8	no	—
249	#124	—	2	4	no	—
250	#124	C₂³×C₃	1	8	yes	—
251	#124	C₂³×C₃	1	8	yes	—
252	C₂²⋊Q₈	—	2	8	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
255	C₄×Q₈	—	2	8	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
258	#117	—	2	8	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
274	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
275	C₂×C₄²	C₃×D₄	1	4	yes	—
276	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₃	1	4	yes	—
279	C₄⋊C₈	C₂³×C₃	1	8	yes	complemented
280	#103	C₂³×C₃	1	16	yes	complemented
281	#102	C₂³×C₃	1	16	yes	—
282	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
283	#97	C₂³×C₃	1	8	yes	complemented
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	4	no	—
287	C₂³×C₃	—	4	8	no	—
288	C₂³×C₃	—	4	8	no	—
289	C₂³×C₃	—	4	4	no	—
290	C₂³×C₃	—	4	8	no	—
291	C₂³×C₃	—	4	4	no	—
292	C₂³×C₃	—	4	4	no	—
293	C₂³×C₃	—	8	16	no	—
294	C₂³×C₃	#137	1	4	yes	—
295	C₂³×C₃	C₂²×D₄	1	2	yes	—
296	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
297	C₃×Q₈	—	2	8	no	—
298	C₃×Q₈	—	2	8	no	—
299	C₃×Q₈	—	4	8	no	—
300	C₃×Q₈	—	4	8	no	—
301	C₃×Q₈	—	4	4	no	—
302	C₃×Q₈	—	4	4	no	—
303	C₃×D₄	—	2	8	no	—
304	C₃×D₄	—	4	8	no	—
305	C₃×D₄	—	4	4	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	8	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	4	4	no	—
318	C₂×C₃×C₄	—	4	8	no	—
319	C₂×C₃×C₄	—	4	4	no	—
320	C₂×C₃×C₄	—	4	4	no	—
321	C₂×C₃×C₄	—	4	4	no	—
322	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
325	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
329	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
330	C₃×C₈	—	2	8	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	4	4	no	—
334	C₂⁴	—	4	4	no	—
335	C₂⁴	—	4	4	no	—
336	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	8	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
348	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	C₂⁴×C₃	1	4	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
367	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
371	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
374	Q₁₆	—	4	16	no	—
375	SD₁₆	—	4	16	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	C₂⁴×C₃	1	8	yes	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₄²	—	2	8	no	—
391	C₄²	C₂×C₃×D₄	1	4	yes	—
392	C₄²	C₂×C₃×D₄	1	2	yes	—
393	C₄²	C₂×C₃×D₄	1	4	yes	—
394	C₄²	C₂×C₃×D₄	1	2	yes	—
395	C₄²	C₂⁴×C₃	1	2	yes	—
396	C₄²	C₂⁴×C₃	1	2	yes	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	8	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	4	4	no	—
401	C₂²×C₃	—	4	4	no	—
402	C₂²×C₃	—	4	4	no	—
403	C₂²×C₃	—	8	16	no	—
404	C₂²×C₃	—	8	8	no	—
405	C₂²×C₃	#535	1	2	yes	—
406	C₂²×C₃	C₂×#137	1	4	yes	—
407	C₂²×C₃	C₂×#137	1	2	yes	—
408	C₂²×C₃	#575	1	2	yes	—
409	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	4	4	no	—
416	C₃×C₄	—	4	4	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	#535	1	2	yes	—
419	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	8	16	no	—
430	C₂³	C₃×#137	1	4	yes	—
431	C₂³	C₂²×C₃×D₄	1	2	yes	—
432	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
433	Q₈	—	2	8	no	—
434	Q₈	—	2	8	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	8	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	4	no	—
439	D₄	—	2	8	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
459	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
460	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
461	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
462	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
463	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
464	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
465	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
466	C₈	—	2	8	no	—
467	C₂×C₃	—	2	4	no	—
468	C₂×C₃	—	8	4	no	—
469	C₂×C₃	#3215	1	4	yes	direct product factor
470	C₂×C₃	C₂×#535	1	1	yes	characteristic
471	C₂×C₃	C₂²×#137	1	1	yes	characteristic
472	C₂×C₃	C₂×#575	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	16	no	—
480	C₂²	—	8	8	no	—
481	C₂²	C₃×#535	1	2	yes	—
482	C₂²	C₂×C₃×#137	1	4	yes	—
483	C₂²	C₂×C₃×#137	1	2	yes	—
484	C₂²	C₃×#575	1	2	yes	—
485	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	4	no	—
494	C₄	C₃×#535	1	2	yes	—
495	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
496	C₃	C₂×#3215	1	1	yes	characteristic, direct product factor, Sylow
497	C₂	—	2	4	no	—
498	C₂	—	8	4	no	—
499	C₂	C₃×#3215	1	4	yes	direct product factor
500	C₂	C₂×C₃×#535	1	1	yes	characteristic
501	C₂	C₂²×C₃×#137	1	1	yes	characteristic
502	C₂	C₂×C₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3215	C₂	direct (N × H)
4. C₂×C₃×#497	C₂	semidirect
5. C₂×C₃×#489	C₂	semidirect
6. C₂×C₃×#464	C₂	semidirect
7. C₂×C₃×#451	C₂	semidirect
9. C₂×C₃×#432	C₂	semidirect
10. C₂×#3215	C₃	direct (N × H)
13. C₂²×C₃×Q₁₆	C₂²	semidirect
16. C₃×#533	C₂²	semidirect
17. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₃×C₄×Q₈	C₂²	semidirect
34. C₃×#497	C₂²	semidirect
35. C₃×#489	C₂²	semidirect
36. C₃×#464	C₂²	semidirect
37. C₃×#451	C₂²	semidirect
39. C₃×#432	C₂²	semidirect
40. C₂×C₃×C₄⋊C₈	C₂²	semidirect
41. C₂×C₃×#103	C₂²	semidirect
44. C₂×C₃×#97	C₂²	semidirect
45. C₂×#533	C₂×C₃	semidirect
47. #3215	C₂×C₃	direct (N × H)
48. C₂×#497	C₂×C₃	semidirect
49. C₂×#489	C₂×C₃	semidirect
50. C₂×#464	C₂×C₃	semidirect
51. C₂×#451	C₂×C₃	semidirect
53. C₂×#432	C₂×C₃	semidirect
72. C₂×C₃×Q₁₆	C₂³	semidirect
78. C₃×C₄⋊Q₈	C₂³	semidirect
79. C₃×C₄⋊Q₈	C₂³	semidirect
92. C₃×C₄×Q₈	C₂³	semidirect
114. C₃×C₄⋊C₈	C₂³	semidirect
115. C₃×#103	C₂³	semidirect
118. C₃×#97	C₂³	semidirect
121. C₂²×Q₁₆	C₂²×C₃	semidirect
124. #533	C₂²×C₃	semidirect
125. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
126. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
137. C₂×C₄×Q₈	C₂²×C₃	semidirect
142. #497	C₂²×C₃	semidirect
143. #489	C₂²×C₃	semidirect
144. #464	C₂²×C₃	semidirect
145. #451	C₂²×C₃	semidirect
147. #432	C₂²×C₃	semidirect
148. C₂×C₄⋊C₈	C₂²×C₃	semidirect
149. C₂×#103	C₂²×C₃	semidirect
152. C₂×#97	C₂²×C₃	semidirect
237. C₂×Q₁₆	C₂³×C₃	semidirect
243. C₄⋊Q₈	C₂³×C₃	semidirect
244. C₄⋊Q₈	C₂³×C₃	semidirect
257. C₄×Q₈	C₂³×C₃	semidirect
279. C₄⋊C₈	C₂³×C₃	semidirect
280. #103	C₂³×C₃	semidirect
283. #97	C₂³×C₃	semidirect
469. C₂×C₃	#3215	direct (N × H)
496. C₃	C₂×#3215	direct (N × H)
499. C₂	C₃×#3215	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×#533	2
C₂²×C₃×#124	2
C₃×#3215	2
C₂×C₃×#497	2
C₂×C₃×#489	2
C₂×C₃×#464	2
C₂×C₃×#451	2
C₂×C₃×#450	2
C₂×C₃×#432	2
C₂×#3215	3

Subgroups — C2×C3×#3215 #10679391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3215 #10679391