Subgroups — C₃×D₃×#435 #11859190

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃²×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5127	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5111	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4836	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4730	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4728	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#435	—	3	1	no	maximal
17	D₃×#435	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₃×D₄	C₄	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
23	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
24	C₃×D₄×Dic₃	C₄	1	1	yes	characteristic
25	C₃×C₄×#67	C₂²	1	1	yes	characteristic
26	C₃×C₄×#67	C₂²	1	1	yes	characteristic
27	C₂×C₃×#208	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×D₃×M₁₆	—	2	4	no	—
30	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×D₃×C₈	—	2	4	no	—
33	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×#893	C₄	1	1	yes	characteristic
40	C₃×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
41	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
42	C₃×#67⋊C₄	C₄	1	1	yes	characteristic
43	C₃×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
44	C₃×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
45	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
46	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
47	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
51	C₃×#830	C₂²	1	1	yes	characteristic, complemented
52	C₃×#830	C₂²	1	1	yes	characteristic, complemented
53	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₃×#815	C₂²	1	1	yes	characteristic, complemented
58	C₃×#815	C₂²	1	1	yes	characteristic, complemented
59	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
62	C₃×#803	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₃×M₁₆	—	3	1	no	—
64	C₂³×C₃×C₈	—	3	1	no	—
65	C₂×C₃×C₄×D₄	—	3	1	no	—
66	C₂×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
68	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
69	C₃×#435	—	2	1	no	—
70	C₃×#435	—	3	1	no	—
71	C₃×#435	—	3	1	no	—
72	C₃×#435	—	3	1	no	—
73	C₃×#435	—	3	1	no	—
74	C₃×#435	—	3	1	no	—
75	C₃×#435	—	3	1	no	—
76	C₃×#435	—	3	1	no	—
77	C₃×#435	D₃	1	1	yes	characteristic, direct product factor
78	C₃×#435	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×C₃×C₄⋊C₈	—	3	1	no	—
80	C₂×C₃×C₂²⋊C₈	—	3	1	no	—
81	C₂×C₃×C₂²⋊C₈	—	3	1	no	—
82	C₂×C₃×#97	—	3	1	no	—
83	#5127	C₂×C₃	1	1	yes	characteristic, complemented
84	#5111	C₂×C₃	1	1	yes	characteristic, complemented
85	#5011	C₂×C₃	1	1	yes	characteristic, complemented
86	#4836	C₂×C₃	1	1	yes	characteristic, complemented
87	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
88	#4730	C₂×C₃	1	1	yes	characteristic, complemented
89	#4728	C₂×C₃	1	1	yes	characteristic, complemented
90	D₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
91	D₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
92	#4706	C₂×C₃	1	1	yes	characteristic, complemented
93	D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
99	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
101	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
103	C₃×D₃×D₄	—	2	4	no	—
104	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×D₃	—	2	2	no	—
106	C₂×C₃×C₄×D₃	—	2	2	no	—
107	C₂×C₃×C₄×D₃	—	2	2	no	—
108	C₂×C₃×C₄×D₃	—	2	2	no	—
109	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
118	C₃²×M₁₆	—	2	2	no	—
119	C₂×C₃²×C₈	—	2	2	no	—
120	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
122	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
123	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
124	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₃²×C₄²	C₂³	1	1	yes	characteristic
128	C₃×#217	C₂×C₄	1	1	yes	characteristic
129	C₃×#217	C₂×C₄	1	1	yes	characteristic
130	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
131	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
132	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
134	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
136	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
137	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
138	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
139	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
140	C₃×#208	—	2	2	no	—
141	C₂×C₃×C₃⋊C₈	—	2	2	no	—
142	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
146	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
147	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
148	C₃×D₃×C₈	—	2	2	no	—
149	C₃×D₃×C₈	—	2	2	no	—
150	C₃×D₃×C₈	—	2	2	no	—
151	C₃×D₃×C₈	—	2	2	no	—
152	C₃×D₃×C₈	—	2	2	no	—
153	C₃×D₃×C₈	D₄	1	4	yes	complemented
154	C₂×#435	—	3	1	no	Sylow
155	C₂²×C₃×D₄	—	3	1	no	—
156	C₂³×C₃×C₄	—	3	1	no	—
157	C₂³×C₃×C₄	—	3	1	no	—
158	C₂×D₃×D₄	C₃×C₄	1	1	yes	characteristic
159	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
160	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₃×M₁₆	—	2	1	no	—
162	C₂×C₃×M₁₆	—	3	1	no	—
163	C₂×C₃×M₁₆	—	3	1	no	—
164	C₂×C₃×M₁₆	—	3	1	no	—
165	C₂×C₃×M₁₆	—	6	4	no	—
166	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
167	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₈	—	2	1	no	—
169	C₂²×C₃×C₈	—	3	1	no	—
170	C₂²×C₃×C₈	—	3	1	no	—
171	C₂²×C₃×C₈	—	3	1	no	—
172	C₂²×C₃×C₈	—	3	1	no	—
173	C₂²×C₃×C₈	—	3	1	no	—
174	C₂²×C₃×C₈	—	3	1	no	—
175	C₂²×C₃×C₈	—	3	1	no	—
176	C₂²×C₃×C₈	—	6	4	no	—
177	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic, complemented
178	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	—	3	1	no	—
181	C₃×C₄×D₄	—	3	1	no	—
182	C₃×C₄×D₄	—	3	1	no	—
183	C₃×C₄×D₄	—	3	1	no	—
184	C₃×C₄×D₄	—	3	1	no	—
185	C₃×C₄×D₄	—	3	1	no	—
186	C₃×C₄×D₄	—	3	1	no	—
187	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
188	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	—	3	1	no	—
190	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
191	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
192	C₂×C₃×C₄²	—	3	1	no	—
193	D₄×Dic₃	C₃×C₄	1	1	yes	characteristic
194	C₄×#67	C₂²×C₃	1	1	yes	characteristic
195	C₄×#67	C₂²×C₃	1	1	yes	characteristic
196	C₂×#208	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
198	D₃×M₁₆	—	2	4	no	—
199	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₂×D₃×C₈	—	2	4	no	—
202	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
203	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
204	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
205	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
206	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
208	#893	C₃×C₄	1	1	yes	characteristic
209	D₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
210	#67⋊C₄	C₃×C₄	1	1	yes	characteristic
211	#67⋊C₄	C₃×C₄	1	1	yes	characteristic
212	D₃×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
213	D₃×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
214	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
215	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
216	C₃×C₄⋊C₈	—	2	1	no	—
217	C₃×C₄⋊C₈	—	3	1	no	—
218	C₃×C₄⋊C₈	—	3	1	no	—
219	C₃×C₄⋊C₈	—	3	1	no	—
220	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
221	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
222	C₃×C₂²⋊C₈	—	2	1	no	—
223	C₃×C₂²⋊C₈	—	2	1	no	—
224	C₃×C₂²⋊C₈	—	3	1	no	—
225	C₃×C₂²⋊C₈	—	3	1	no	—
226	C₃×C₂²⋊C₈	—	3	1	no	—
227	C₃×C₂²⋊C₈	—	3	1	no	—
228	C₃×C₂²⋊C₈	—	3	1	no	—
229	C₃×C₂²⋊C₈	—	3	1	no	—
230	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
231	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
232	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
234	C₃×#97	—	2	1	no	—
235	C₃×#97	—	3	1	no	—
236	C₃×#97	—	3	1	no	—
237	C₃×#97	—	3	1	no	—
238	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
239	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
240	#830	C₂²×C₃	1	1	yes	characteristic, complemented
241	#830	C₂²×C₃	1	1	yes	characteristic, complemented
242	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
243	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
244	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
245	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
246	#815	C₂²×C₃	1	1	yes	characteristic, complemented
247	#815	C₂²×C₃	1	1	yes	characteristic, complemented
248	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
249	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
251	#803	C₂²×C₃	1	1	yes	characteristic, complemented
252	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
253	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₃×D₃	—	2	2	no	—
255	C₂²×C₃×D₃	—	2	2	no	—
256	C₂²×C₃×D₃	—	2	2	no	—
257	C₂²×C₃×D₃	—	2	2	no	—
258	C₂²×C₃×D₃	—	2	2	no	—
259	C₂²×C₃×D₃	M₁₆	1	4	yes	complemented
260	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
261	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
262	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
263	C₃²×D₄	—	2	2	no	—
264	C₂×C₃²×C₄	—	2	1	no	—
265	C₂×C₃²×C₄	—	2	1	no	—
266	C₂×C₃²×C₄	—	2	1	no	—
267	C₂×C₃²×C₄	—	2	1	no	—
268	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
269	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
270	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
271	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
272	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
273	C₃×#67	—	2	2	no	—
274	C₃×#67	—	2	2	no	—
275	C₂×C₃×Dic₃	—	2	2	no	—
276	C₂×C₃×Dic₃	—	2	2	no	—
277	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
278	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
279	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
280	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
281	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
282	C₃×D₁₂	—	2	2	no	—
283	C₃×C₄×D₃	—	2	2	no	—
284	C₃×C₄×D₃	—	2	2	no	—
285	C₃×C₄×D₃	—	2	2	no	—
286	C₃×C₄×D₃	—	2	2	no	—
287	C₃×C₄×D₃	—	2	1	no	—
288	C₃×C₄×D₃	—	2	1	no	—
289	C₃×C₄×D₃	—	2	1	no	—
290	C₃×C₄×D₃	—	2	1	no	—
291	C₃×C₄×D₃	—	2	2	no	—
292	C₃×C₄×D₃	—	2	2	no	—
293	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
294	C₃×C₄×D₃	#41	1	2	yes	—
295	C₃²×C₈	—	2	1	no	—
296	C₃²×C₈	—	2	1	no	—
297	C₃²×C₈	—	2	1	no	—
298	C₃²×C₈	C₂×D₄	1	2	yes	complemented
299	C₃×C₃⋊C₈	—	2	1	no	—
300	C₃×C₃⋊C₈	—	2	1	no	—
301	C₃×C₃⋊C₈	—	2	1	no	—
302	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
303	C₂²×M₁₆	—	3	1	no	—
304	C₂³×C₈	—	3	1	no	—
305	C₂×C₄×D₄	—	3	1	no	—
306	#435	—	3	1	no	—
307	#435	—	3	1	no	—
308	#435	—	3	1	no	—
309	#435	—	3	1	no	—
310	#435	—	3	1	no	—
311	#435	—	3	1	no	—
312	#435	—	3	1	no	—
313	#435	C₃×D₃	1	1	yes	characteristic, direct product factor
314	C₂×C₄⋊C₈	—	3	1	no	—
315	C₂×C₂²⋊C₈	—	3	1	no	—
316	C₂×C₂²⋊C₈	—	3	1	no	—
317	C₂×#97	—	3	1	no	—
318	C₂⁴×C₃	—	3	1	no	—
319	C₂⁴×C₃	—	3	1	no	—
320	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
321	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
322	C₂×C₃×D₄	—	2	1	no	—
323	C₂×C₃×D₄	—	3	1	no	—
324	C₂×C₃×D₄	—	3	1	no	—
325	C₂×C₃×D₄	—	3	1	no	—
326	C₂×C₃×D₄	—	6	4	no	—
327	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
328	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
329	C₂²×C₃×C₄	—	2	1	no	—
330	C₂²×C₃×C₄	—	2	1	no	—
331	C₂²×C₃×C₄	—	3	1	no	—
332	C₂²×C₃×C₄	—	3	1	no	—
333	C₂²×C₃×C₄	—	3	1	no	—
334	C₂²×C₃×C₄	—	3	1	no	—
335	C₂²×C₃×C₄	—	3	1	no	—
336	C₂²×C₃×C₄	—	3	1	no	—
337	C₂²×C₃×C₄	—	3	1	no	—
338	C₂²×C₃×C₄	—	3	1	no	—
339	C₂²×C₃×C₄	—	3	1	no	—
340	C₂²×C₃×C₄	—	3	1	no	—
341	C₂²×C₃×C₄	—	3	1	no	—
342	C₂²×C₃×C₄	—	6	2	no	—
343	C₂²×C₃×C₄	—	6	2	no	—
344	C₂²×C₃×C₄	—	6	2	no	—
345	C₂²×C₃×C₄	—	6	2	no	—
346	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
350	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
351	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
352	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
353	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
354	D₃×D₄	—	2	4	no	—
355	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
356	C₂×C₄×D₃	—	2	2	no	—
357	C₂×C₄×D₃	—	2	2	no	—
358	C₂×C₄×D₃	—	2	2	no	—
359	C₂×C₄×D₃	—	2	2	no	—
360	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
361	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
362	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
363	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
364	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
365	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
366	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
369	C₃×M₁₆	—	2	2	no	—
370	C₃×M₁₆	—	2	2	no	—
371	C₃×M₁₆	—	4	2	no	—
372	C₃×M₁₆	—	6	2	no	—
373	C₃×M₁₆	—	6	2	no	—
374	C₃×M₁₆	—	6	2	no	—
375	C₂×C₃×C₈	—	2	2	no	—
376	C₂×C₃×C₈	—	2	2	no	—
377	C₂×C₃×C₈	—	2	1	no	—
378	C₂×C₃×C₈	—	2	1	no	—
379	C₂×C₃×C₈	—	2	1	no	—
380	C₂×C₃×C₈	—	2	1	no	—
381	C₂×C₃×C₈	—	3	1	no	—
382	C₂×C₃×C₈	—	3	4	no	—
383	C₂×C₃×C₈	—	3	1	no	—
384	C₂×C₃×C₈	—	3	1	no	—
385	C₂×C₃×C₈	—	3	1	no	—
386	C₂×C₃×C₈	—	4	2	no	—
387	C₂×C₃×C₈	—	6	2	no	—
388	C₂×C₃×C₈	—	6	2	no	—
389	C₂×C₃×C₈	—	6	2	no	—
390	C₂×C₃×C₈	—	6	2	no	—
391	C₂×C₃×C₈	—	6	2	no	—
392	C₂×C₃×C₈	—	6	2	no	—
393	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
394	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
395	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
396	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
397	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
398	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	3	1	no	—
403	C₃×C₄⋊C₄	—	3	1	no	—
404	C₃×C₄⋊C₄	—	3	1	no	—
405	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
406	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
407	C₃×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	C₃×C₂²⋊C₄	—	3	1	no	—
410	C₃×C₂²⋊C₄	—	3	1	no	—
411	C₃×C₂²⋊C₄	—	3	1	no	—
412	C₃×C₂²⋊C₄	—	3	1	no	—
413	C₃×C₂²⋊C₄	—	3	1	no	—
414	C₃×C₂²⋊C₄	—	3	1	no	—
415	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
416	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
418	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
419	C₃×C₄²	—	2	1	no	—
420	C₃×C₄²	—	3	1	no	—
421	C₃×C₄²	—	3	1	no	—
422	C₃×C₄²	—	3	1	no	—
423	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
424	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
425	#217	C₂×C₃×C₄	1	1	yes	characteristic
426	#217	C₂×C₃×C₄	1	1	yes	characteristic
427	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
428	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
429	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
430	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
431	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
432	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
433	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
434	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
435	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
436	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
437	#208	—	2	2	no	—
438	C₂×C₃⋊C₈	—	2	2	no	—
439	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
440	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
443	ΓL(1,𝔽₂₅)	—	2	2	no	—
444	ΓL(1,𝔽₂₅)	—	2	2	no	—
445	D₃×C₈	—	2	2	no	—
446	D₃×C₈	—	2	2	no	—
447	D₃×C₈	—	2	2	no	—
448	D₃×C₈	—	2	2	no	—
449	D₃×C₈	—	2	2	no	—
450	D₃×C₈	C₃×D₄	1	4	yes	complemented
451	C₂²×C₃²	—	2	1	no	—
452	C₂²×C₃²	—	2	1	no	—
453	C₂²×C₃²	—	2	1	no	—
454	C₂²×C₃²	—	2	1	no	—
455	C₂²×C₃²	—	2	1	no	—
456	C₂²×C₃²	C₂×M₁₆	1	2	yes	complemented
457	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₃×D₃	—	2	1	no	—
459	C₂×C₃×D₃	—	2	1	no	—
460	C₂×C₃×D₃	—	2	8	no	—
461	C₂×C₃×D₃	—	2	1	no	—
462	C₂×C₃×D₃	—	2	1	no	—
463	C₂×C₃×D₃	—	2	1	no	—
464	C₂×C₃×D₃	—	4	4	no	—
465	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
466	C₂×C₃×D₃	C₂×M₁₆	1	2	yes	—
467	C₂×C₃×D₃	C₂×M₁₆	1	2	yes	complemented
468	C₂×C₃×D₃	#131	1	2	yes	—
469	C₃²×C₄	—	2	1	no	—
470	C₃²×C₄	—	2	1	no	—
471	C₃²×C₄	—	2	1	no	—
472	C₃²×C₄	—	2	1	no	—
473	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
474	C₃²×C₄	C₂×#41	1	1	yes	characteristic
475	C₃×Dic₃	—	2	1	no	—
476	C₃×Dic₃	—	2	1	no	—
477	C₃×Dic₃	—	2	1	no	—
478	C₃×Dic₃	—	2	1	no	—
479	C₃×Dic₃	C₄×D₄	1	2	yes	—
480	C₂²×D₄	—	3	1	no	—
481	C₂³×C₄	—	3	1	no	—
482	C₂³×C₄	—	3	1	no	—
483	C₂×M₁₆	—	3	1	no	—
484	C₂×M₁₆	—	3	1	no	—
485	C₂×M₁₆	—	3	1	no	—
486	C₂×M₁₆	—	6	4	no	—
487	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
488	C₂²×C₈	—	3	1	no	—
489	C₂²×C₈	—	3	1	no	—
490	C₂²×C₈	—	3	1	no	—
491	C₂²×C₈	—	3	1	no	—
492	C₂²×C₈	—	3	1	no	—
493	C₂²×C₈	—	3	1	no	—
494	C₂²×C₈	—	3	1	no	—
495	C₂²×C₈	—	6	4	no	—
496	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	—	3	1	no	—
506	C₂×C₂²⋊C₄	—	3	1	no	—
507	C₂×C₂²⋊C₄	—	3	1	no	—
508	C₂×C₄²	—	3	1	no	—
509	C₄⋊C₈	—	3	1	no	—
510	C₄⋊C₈	—	3	1	no	—
511	C₄⋊C₈	—	3	1	no	—
512	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
513	C₂²⋊C₈	—	3	1	no	—
514	C₂²⋊C₈	—	3	1	no	—
515	C₂²⋊C₈	—	3	1	no	—
516	C₂²⋊C₈	—	3	1	no	—
517	C₂²⋊C₈	—	3	1	no	—
518	C₂²⋊C₈	—	3	1	no	—
519	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
520	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
521	#97	—	3	1	no	—
522	#97	—	3	1	no	—
523	#97	—	3	1	no	—
524	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	3	1	no	—
528	C₂³×C₃	—	3	4	no	—
529	C₂³×C₃	—	3	1	no	—
530	C₂³×C₃	—	3	1	no	—
531	C₂³×C₃	—	6	2	no	—
532	C₂³×C₃	—	6	2	no	—
533	C₂³×C₃	—	6	2	no	—
534	C₂³×C₃	—	6	2	no	—
535	C₂³×C₃	—	6	2	no	—
536	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
537	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
538	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
539	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
540	C₂²×D₃	—	2	2	no	—
541	C₂²×D₃	—	2	2	no	—
542	C₂²×D₃	—	2	2	no	—
543	C₂²×D₃	—	2	2	no	—
544	C₂²×D₃	—	2	2	no	—
545	C₂²×D₃	C₃×M₁₆	1	4	yes	complemented
546	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
547	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
548	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
549	C₃×D₄	—	2	2	no	—
550	C₃×D₄	—	2	2	no	—
551	C₃×D₄	—	4	2	no	—
552	C₃×D₄	—	6	2	no	—
553	C₃×D₄	—	6	2	no	—
554	C₃×D₄	—	6	2	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	3	1	no	—
569	C₂×C₃×C₄	—	3	2	no	—
570	C₂×C₃×C₄	—	3	2	no	—
571	C₂×C₃×C₄	—	3	1	no	—
572	C₂×C₃×C₄	—	3	1	no	—
573	C₂×C₃×C₄	—	3	1	no	—
574	C₂×C₃×C₄	—	3	1	no	—
575	C₂×C₃×C₄	—	4	1	no	—
576	C₂×C₃×C₄	—	4	1	no	—
577	C₂×C₃×C₄	—	4	1	no	—
578	C₂×C₃×C₄	—	4	1	no	—
579	C₂×C₃×C₄	—	6	2	no	—
580	C₂×C₃×C₄	—	6	2	no	—
581	C₂×C₃×C₄	—	6	2	no	—
582	C₂×C₃×C₄	—	6	2	no	—
583	C₂×C₃×C₄	—	6	2	no	—
584	C₂×C₃×C₄	—	6	2	no	—
585	C₂×C₃×C₄	—	6	2	no	—
586	C₂×C₃×C₄	—	6	2	no	—
587	C₂×C₃×C₄	—	6	1	no	—
588	C₂×C₃×C₄	—	6	1	no	—
589	C₂×C₃×C₄	—	6	1	no	—
590	C₂×C₃×C₄	—	6	1	no	—
591	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
592	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
594	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
596	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
597	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
598	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
600	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
601	#67	—	2	2	no	—
602	#67	—	2	2	no	—
603	C₂×Dic₃	—	2	2	no	—
604	C₂×Dic₃	—	2	2	no	—
605	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
606	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
607	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
608	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
609	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
610	D₁₂	—	2	2	no	—
611	C₄×D₃	—	2	2	no	—
612	C₄×D₃	—	2	2	no	—
613	C₄×D₃	—	2	2	no	—
614	C₄×D₃	—	2	2	no	—
615	C₄×D₃	—	2	1	no	—
616	C₄×D₃	—	2	1	no	—
617	C₄×D₃	—	2	1	no	—
618	C₄×D₃	—	2	1	no	—
619	C₄×D₃	—	2	2	no	—
620	C₄×D₃	—	2	2	no	—
621	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
622	C₄×D₃	C₃×#41	1	2	yes	—
623	C₃×C₈	—	2	1	no	—
624	C₃×C₈	—	2	1	no	—
625	C₃×C₈	—	2	1	no	—
626	C₃×C₈	—	2	1	no	—
627	C₃×C₈	—	2	1	no	—
628	C₃×C₈	—	2	1	no	—
629	C₃×C₈	—	2	2	no	—
630	C₃×C₈	—	3	2	no	—
631	C₃×C₈	—	4	1	no	—
632	C₃×C₈	—	4	1	no	—
633	C₃×C₈	—	4	1	no	—
634	C₃×C₈	—	6	1	no	—
635	C₃×C₈	—	6	1	no	—
636	C₃×C₈	—	6	1	no	—
637	C₃×C₈	D₃×D₄	1	2	yes	complemented
638	C₃×C₈	C₂×C₃×D₄	1	2	yes	complemented
639	C₃⋊C₈	—	2	1	no	—
640	C₃⋊C₈	—	2	1	no	—
641	C₃⋊C₈	—	2	1	no	—
642	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	complemented
643	C₂×C₃²	—	2	2	no	—
644	C₂×C₃²	—	4	1	no	—
645	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
646	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
647	C₂×C₃²	C₂×#131	1	1	yes	characteristic
648	C₃×D₃	—	2	2	no	—
649	C₃×D₃	—	4	1	no	—
650	C₃×D₃	#435	1	4	yes	direct product factor
651	C₂⁴	—	3	1	no	—
652	C₂⁴	—	3	1	no	—
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	3	1	no	—
656	C₂×D₄	—	6	4	no	—
657	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	3	1	no	—
666	C₂²×C₄	—	3	1	no	—
667	C₂²×C₄	—	3	1	no	—
668	C₂²×C₄	—	3	1	no	—
669	C₂²×C₄	—	6	2	no	—
670	C₂²×C₄	—	6	2	no	—
671	C₂²×C₄	—	6	2	no	—
672	C₂²×C₄	—	6	2	no	—
673	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
674	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
675	M₁₆	—	2	2	no	—
676	M₁₆	—	6	2	no	—
677	M₁₆	—	6	2	no	—
678	M₁₆	—	6	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	3	1	no	—
681	C₂×C₈	—	3	4	no	—
682	C₂×C₈	—	3	1	no	—
683	C₂×C₈	—	3	1	no	—
684	C₂×C₈	—	3	1	no	—
685	C₂×C₈	—	6	2	no	—
686	C₂×C₈	—	6	2	no	—
687	C₂×C₈	—	6	2	no	—
688	C₂×C₈	—	6	2	no	—
689	C₂×C₈	—	6	2	no	—
690	C₂×C₈	—	6	2	no	—
691	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
692	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
693	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
694	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
695	C₄⋊C₄	—	3	1	no	—
696	C₄⋊C₄	—	3	1	no	—
697	C₄⋊C₄	—	3	1	no	—
698	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
699	C₂²⋊C₄	—	3	1	no	—
700	C₂²⋊C₄	—	3	1	no	—
701	C₂²⋊C₄	—	3	1	no	—
702	C₂²⋊C₄	—	3	1	no	—
703	C₂²⋊C₄	—	3	1	no	—
704	C₂²⋊C₄	—	3	1	no	—
705	C₂²⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
706	C₂²⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
707	C₄²	—	3	1	no	—
708	C₄²	—	3	1	no	—
709	C₄²	—	3	1	no	—
710	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
711	C₂²×C₃	—	2	1	no	—
712	C₂²×C₃	—	2	1	no	—
713	C₂²×C₃	—	2	1	no	—
714	C₂²×C₃	—	2	1	no	—
715	C₂²×C₃	—	2	1	no	—
716	C₂²×C₃	—	2	1	no	—
717	C₂²×C₃	—	2	1	no	—
718	C₂²×C₃	—	2	1	no	—
719	C₂²×C₃	—	2	1	no	—
720	C₂²×C₃	—	2	1	no	—
721	C₂²×C₃	—	2	2	no	—
722	C₂²×C₃	—	2	1	no	—
723	C₂²×C₃	—	3	2	no	—
724	C₂²×C₃	—	3	2	no	—
725	C₂²×C₃	—	3	2	no	—
726	C₂²×C₃	—	3	2	no	—
727	C₂²×C₃	—	4	1	no	—
728	C₂²×C₃	—	4	1	no	—
729	C₂²×C₃	—	4	1	no	—
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	—	6	8	no	—
733	C₂²×C₃	—	6	1	no	—
734	C₂²×C₃	—	6	1	no	—
735	C₂²×C₃	—	6	1	no	—
736	C₂²×C₃	—	6	1	no	—
737	C₂²×C₃	—	6	1	no	—
738	C₂²×C₃	—	12	4	no	—
739	C₂²×C₃	D₃×M₁₆	1	2	yes	complemented
740	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	complemented
741	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
742	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
743	C₂×D₃	—	2	1	no	—
744	C₂×D₃	—	2	1	no	—
745	C₂×D₃	—	2	8	no	—
746	C₂×D₃	—	2	1	no	—
747	C₂×D₃	—	2	1	no	—
748	C₂×D₃	—	2	1	no	—
749	C₂×D₃	—	4	4	no	—
750	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
751	C₂×D₃	C₂×C₃×M₁₆	1	2	yes	—
752	C₂×D₃	C₂×C₃×M₁₆	1	2	yes	complemented
753	C₂×D₃	C₃×#131	1	2	yes	—
754	C₃×C₄	—	2	1	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	2	1	no	—
760	C₃×C₄	—	2	1	no	—
761	C₃×C₄	—	2	1	no	—
762	C₃×C₄	—	2	1	no	—
763	C₃×C₄	—	2	1	no	—
764	C₃×C₄	—	3	2	no	—
765	C₃×C₄	—	4	1	no	—
766	C₃×C₄	—	4	1	no	—
767	C₃×C₄	—	4	1	no	—
768	C₃×C₄	—	4	1	no	—
769	C₃×C₄	—	6	1	no	—
770	C₃×C₄	—	6	1	no	—
771	C₃×C₄	—	6	1	no	—
772	C₃×C₄	—	6	1	no	—
773	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
774	C₃×C₄	D₃×#41	1	1	yes	characteristic
775	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
776	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
777	Dic₃	—	2	1	no	—
778	Dic₃	—	2	1	no	—
779	Dic₃	—	2	1	no	—
780	Dic₃	—	2	1	no	—
781	Dic₃	C₃×C₄×D₄	1	2	yes	—
782	C₃²	C₂×#435	1	1	yes	characteristic, complemented, Sylow
783	C₂³	—	3	1	no	—
784	C₂³	—	3	4	no	—
785	C₂³	—	3	1	no	—
786	C₂³	—	3	1	no	—
787	C₂³	—	6	2	no	—
788	C₂³	—	6	2	no	—
789	C₂³	—	6	2	no	—
790	C₂³	—	6	2	no	—
791	C₂³	—	6	2	no	—
792	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
793	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
794	D₄	—	2	2	no	—
795	D₄	—	6	2	no	—
796	D₄	—	6	2	no	—
797	D₄	—	6	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	3	1	no	—
803	C₂×C₄	—	3	2	no	—
804	C₂×C₄	—	3	2	no	—
805	C₂×C₄	—	3	1	no	—
806	C₂×C₄	—	3	1	no	—
807	C₂×C₄	—	3	1	no	—
808	C₂×C₄	—	3	1	no	—
809	C₂×C₄	—	6	2	no	—
810	C₂×C₄	—	6	2	no	—
811	C₂×C₄	—	6	2	no	—
812	C₂×C₄	—	6	2	no	—
813	C₂×C₄	—	6	2	no	—
814	C₂×C₄	—	6	2	no	—
815	C₂×C₄	—	6	2	no	—
816	C₂×C₄	—	6	2	no	—
817	C₂×C₄	—	6	1	no	—
818	C₂×C₄	—	6	1	no	—
819	C₂×C₄	—	6	1	no	—
820	C₂×C₄	—	6	1	no	—
821	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
822	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
823	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
824	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
825	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
826	C₈	—	2	1	no	—
827	C₈	—	2	1	no	—
828	C₈	—	2	1	no	—
829	C₈	—	3	2	no	—
830	C₈	—	6	1	no	—
831	C₈	—	6	1	no	—
832	C₈	—	6	1	no	—
833	C₈	C₃×D₃×D₄	1	2	yes	complemented
834	C₂×C₃	—	2	2	no	—
835	C₂×C₃	—	2	2	no	—
836	C₂×C₃	—	2	1	no	—
837	C₂×C₃	—	2	1	no	—
838	C₂×C₃	—	2	1	no	—
839	C₂×C₃	—	3	4	no	—
840	C₂×C₃	—	4	2	no	—
841	C₂×C₃	—	4	1	no	—
842	C₂×C₃	—	4	1	no	—
843	C₂×C₃	—	6	2	no	—
844	C₂×C₃	—	8	1	no	—
845	C₂×C₃	—	12	1	no	—
846	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
847	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
848	C₂×C₃	D₃×#131	1	1	yes	characteristic
849	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
850	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
851	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
852	D₃	—	2	2	no	—
853	D₃	—	4	1	no	—
854	D₃	C₃×#435	1	4	yes	direct product factor
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	3	2	no	—
861	C₂²	—	3	2	no	—
862	C₂²	—	3	2	no	—
863	C₂²	—	3	2	no	—
864	C₂²	—	6	8	no	—
865	C₂²	—	6	1	no	—
866	C₂²	—	6	1	no	—
867	C₂²	—	6	1	no	—
868	C₂²	—	6	1	no	—
869	C₂²	—	6	1	no	—
870	C₂²	—	12	4	no	—
871	C₂²	C₃×D₃×M₁₆	1	2	yes	complemented
872	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	3	2	no	—
878	C₄	—	6	1	no	—
879	C₄	—	6	1	no	—
880	C₄	—	6	1	no	—
881	C₄	—	6	1	no	—
882	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
883	C₄	C₃×D₃×#41	1	1	yes	characteristic
884	C₃	—	2	1	no	—
885	C₃	D₃×#435	1	1	yes	characteristic, direct product factor
886	C₃	C₂×C₃×#435	1	1	yes	characteristic, complemented
887	C₂	—	2	2	no	—
888	C₂	—	3	4	no	—
889	C₂	—	4	1	no	—
890	C₂	—	6	2	no	—
891	C₂	—	12	1	no	—
892	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
893	C₂	C₂×C₃×D₃×M₁₆	1	1	yes	characteristic
894	C₂	C₃×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#435	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#435	D₃
hypocenter	C₃	C₂×C₃×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#435

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×M₁₆	C₂	semidirect
2. C₂²×C₃×D₃×C₈	C₂	semidirect
4. C₃²×#435	C₂	semidirect
5. C₃×#5127	C₂	semidirect
6. C₃×#5111	C₂	semidirect
7. C₃×#5011	C₂	semidirect
8. C₃×#4836	C₂	semidirect
9. C₃×D₃×C₄⋊C₈	C₂	semidirect
10. C₃×#4730	C₂	semidirect
11. C₃×#4728	C₂	semidirect
12. C₃×D₃×C₂²⋊C₈	C₂	semidirect
13. C₃×D₃×C₂²⋊C₈	C₂	semidirect
14. C₃×#4706	C₂	semidirect
15. C₃×D₃×#97	C₂	semidirect
17. D₃×#435	C₃	direct (N × H)
21. C₂×C₃²×M₁₆	C₂²	semidirect
22. C₂²×C₃²×C₈	C₂²	semidirect
27. C₂×C₃×#208	C₂²	semidirect
28. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
30. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
31. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
37. C₂×C₃×D₃×C₈	C₂²	semidirect
38. C₂×C₃×D₃×C₈	C₂²	semidirect
47. C₃²×C₄⋊C₈	C₂²	semidirect
48. C₃²×C₂²⋊C₈	C₂²	semidirect
49. C₃²×C₂²⋊C₈	C₂²	semidirect
50. C₃²×#97	C₂²	semidirect
51. C₃×#830	C₂²	semidirect
52. C₃×#830	C₂²	semidirect
53. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
54. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
55. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
56. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
57. C₃×#815	C₂²	semidirect
58. C₃×#815	C₂²	semidirect
59. C₃×Dic₃⋊C₈	C₂²	semidirect
60. C₃×Dic₃⋊C₈	C₂²	semidirect
61. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
62. C₃×#803	C₂²	semidirect
66. C₂×D₃×M₁₆	C₂×C₃	semidirect
67. C₂²×D₃×C₈	C₂×C₃	semidirect
77. C₃×#435	D₃	direct (N × H)
78. C₃×#435	C₂×C₃	semidirect
83. #5127	C₂×C₃	semidirect
84. #5111	C₂×C₃	semidirect
85. #5011	C₂×C₃	semidirect
86. #4836	C₂×C₃	semidirect
87. D₃×C₄⋊C₈	C₂×C₃	semidirect
88. #4730	C₂×C₃	semidirect
89. #4728	C₂×C₃	semidirect
90. D₃×C₂²⋊C₈	C₂×C₃	semidirect
91. D₃×C₂²⋊C₈	C₂×C₃	semidirect
92. #4706	C₂×C₃	semidirect
93. D₃×#97	C₂×C₃	semidirect
153. C₃×D₃×C₈	D₄	semidirect
166. C₂×C₃×M₁₆	C₂×D₃	semidirect
167. C₂×C₃×M₁₆	C₂²×C₃	semidirect
177. C₂²×C₃×C₈	C₂×D₃	semidirect
178. C₂²×C₃×C₈	C₂²×C₃	semidirect
196. C₂×#208	C₂²×C₃	semidirect
197. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
199. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
200. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
206. C₂×D₃×C₈	C₂²×C₃	semidirect
207. C₂×D₃×C₈	C₂²×C₃	semidirect
220. C₃×C₄⋊C₈	C₂×D₃	semidirect
221. C₃×C₄⋊C₈	C₂²×C₃	semidirect
230. C₃×C₂²⋊C₈	C₂×D₃	semidirect
231. C₃×C₂²⋊C₈	C₂×D₃	semidirect
232. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
233. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
238. C₃×#97	C₂×D₃	semidirect
239. C₃×#97	C₂²×C₃	semidirect
240. #830	C₂²×C₃	semidirect
241. #830	C₂²×C₃	semidirect
242. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
243. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
244. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
245. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
246. #815	C₂²×C₃	semidirect
247. #815	C₂²×C₃	semidirect
248. Dic₃⋊C₈	C₂²×C₃	semidirect
249. Dic₃⋊C₈	C₂²×C₃	semidirect
250. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
251. #803	C₂²×C₃	semidirect
259. C₂²×C₃×D₃	M₁₆	semidirect
298. C₃²×C₈	C₂×D₄	semidirect
302. C₃×C₃⋊C₈	C₂×D₄	semidirect
313. #435	C₃×D₃	direct (N × H)
450. D₃×C₈	C₃×D₄	semidirect
456. C₂²×C₃²	C₂×M₁₆	semidirect
467. C₂×C₃×D₃	C₂×M₁₆	semidirect
487. C₂×M₁₆	C₂×C₃×D₃	semidirect
496. C₂²×C₈	C₂×C₃×D₃	semidirect
512. C₄⋊C₈	C₂×C₃×D₃	semidirect
519. C₂²⋊C₈	C₂×C₃×D₃	semidirect
520. C₂²⋊C₈	C₂×C₃×D₃	semidirect
524. #97	C₂×C₃×D₃	semidirect
545. C₂²×D₃	C₃×M₁₆	semidirect
637. C₃×C₈	D₃×D₄	semidirect
638. C₃×C₈	C₂×C₃×D₄	semidirect
642. C₃⋊C₈	C₂×C₃×D₄	semidirect
650. C₃×D₃	#435	direct (N × H)
739. C₂²×C₃	D₃×M₁₆	semidirect
740. C₂²×C₃	C₂×C₃×M₁₆	semidirect
752. C₂×D₃	C₂×C₃×M₁₆	semidirect
782. C₃²	C₂×#435	semidirect
833. C₈	C₃×D₃×D₄	semidirect
854. D₃	C₃×#435	direct (N × H)
871. C₂²	C₃×D₃×M₁₆	semidirect
885. C₃	D₃×#435	direct (N × H)
886. C₃	C₂×C₃×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×M₁₆	2
C₂²×C₃×D₃×C₈	2
C₃×C₄×D₃×D₄	2
C₃²×#435	2
C₃×#5127	2
C₃×#5111	2
C₃×#5011	2
C₃×#4836	2
C₃×D₃×C₄⋊C₈	2
C₃×#4730	2
C₃×#4728	2
C₃×D₃×C₂²⋊C₈	2
C₃×#4706	2
C₃×D₃×#97	2
C₂×C₃×#435	3
D₃×#435	3

Subgroups — C3×D3×#435 #11859190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#435 #11859190