Subgroups — C₃×#86039 #11904284

Order 1152.

3965 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5791	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5653	C₂	1	4	yes	maximal, complemented
7	C₃×#5630	C₂	1	4	yes	maximal, complemented
8	C₃×#5609	C₂	1	4	yes	maximal, complemented
9	C₃×D₃×#120	C₂	1	4	yes	maximal, complemented
10	C₃×#5550	C₂	1	4	yes	maximal, complemented
11	C₃×D₄×D₁₂	C₂	1	4	yes	maximal, complemented
12	C₃×#5525	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5521	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3484	—	3	1	no	maximal
15	#86039	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
19	C₃×#1009	—	2	8	no	—
20	C₂×C₃×#239	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
22	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
23	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
24	C₂×C₃×#235	C₂²	1	2	yes	complemented
25	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×D₁₂	—	2	8	no	—
27	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
28	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₁₂	C₂²	1	4	yes	complemented
30	C₂²×C₃×D₁₂	C₂²	1	4	yes	complemented
31	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
32	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
33	C₃²×#123	C₂²	1	2	yes	complemented
34	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃²×#121	C₂²	1	2	yes	complemented
36	C₃²×#120	C₂²	1	2	yes	complemented
37	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
38	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
39	C₃×#953	C₂²	1	2	yes	complemented
40	C₃×#947	C₂²	1	2	yes	complemented
41	C₃×#940	C₂²	1	2	yes	complemented
42	C₃×#937	C₂²	1	8	yes	complemented
43	C₃×#937	C₂²	1	4	yes	complemented
44	C₃×#930	C₂²	1	4	yes	complemented
45	C₃×#930	C₂²	1	2	yes	complemented
46	C₃×#929	C₂²	1	2	yes	complemented
47	C₃×C₄×#67	C₂²	1	4	yes	complemented
48	C₃×#926	C₂²	1	1	yes	characteristic, complemented
49	C₃×#924	C₂²	1	2	yes	complemented
50	C₃×#895	C₂²	1	4	yes	complemented
51	C₃×#895	C₂²	1	8	yes	complemented
52	C₃×#894	C₂²	1	8	yes	complemented
53	C₃×#893	C₂²	1	4	yes	complemented
54	C₃×#884	C₂²	1	8	yes	complemented
55	C₃×#882	C₂²	1	4	yes	complemented
56	C₃×#882	C₂²	1	8	yes	complemented
57	C₃×#882	C₂²	1	8	yes	complemented
58	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
60	C₃×#875	C₂²	1	2	yes	complemented
61	C₃×#874	C₂²	1	2	yes	complemented
62	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
63	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
64	C₂³×C₃×D₄	—	3	1	no	—
65	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#546	—	3	4	no	—
68	C₃×#546	—	3	4	no	—
69	C₃×D₄²	—	3	4	no	—
70	C₃×D₄²	—	3	4	no	—
71	C₃×#535	—	3	1	no	—
72	C₃×#535	—	3	1	no	—
73	C₃×#534	—	3	4	no	—
74	C₃×#525	—	2	1	no	—
75	C₃×#525	—	3	1	no	—
76	C₃×#525	D₃	1	1	yes	characteristic, complemented
77	C₃×#525	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×#120	—	3	4	no	—
79	C₃×#518	—	3	1	no	—
80	#5830	C₂×C₃	1	1	yes	characteristic, complemented
81	#5791	C₂×C₃	1	1	yes	characteristic, complemented
82	#5653	C₂×C₃	1	4	yes	complemented
83	#5630	C₂×C₃	1	4	yes	complemented
84	#5609	C₂×C₃	1	4	yes	complemented
85	D₃×#120	C₂×C₃	1	4	yes	complemented
86	#5550	C₂×C₃	1	4	yes	complemented
87	D₄×D₁₂	C₂×C₃	1	4	yes	complemented
88	#5525	C₂×C₃	1	1	yes	characteristic, complemented
89	#5521	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
91	C₂³×C₃×D₃	—	2	8	no	—
92	C₂³×C₃×D₃	—	4	8	no	—
93	C₂³×C₃×D₃	C₂³	1	8	yes	—
94	C₂³×C₃×D₃	C₂³	1	2	yes	—
95	C₂³×C₃×D₃	C₂³	1	2	yes	—
96	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
97	C₃²×#41	—	2	4	no	—
98	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic, complemented
99	C₂×C₃²×D₄	C₂³	1	2	yes	—
100	C₂×C₃²×D₄	C₂³	1	4	yes	—
101	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic, complemented
102	C₂²×C₃²×C₄	—	2	4	no	—
103	C₂²×C₃²×C₄	C₂³	1	2	yes	—
104	C₂²×C₃²×C₄	C₂³	1	2	yes	—
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃²×C₄	C₂³	1	2	yes	complemented
108	C₂×C₃×#67	C₂³	1	4	yes	—
109	C₂×C₃×#67	C₂³	1	2	yes	—
110	C₂×C₃×#67	C₂³	1	4	yes	complemented
111	C₂×C₃×#67	C₂³	1	8	yes	complemented
112	C₃×#239	—	2	8	no	—
113	C₃×D₃×D₄	—	2	16	no	—
114	C₃×D₃×D₄	—	2	8	no	—
115	C₃×D₃×D₄	—	4	16	no	—
116	C₃×#235	—	2	4	no	—
117	C₃×#235	—	2	8	no	—
118	C₂×C₃×D₁₂	—	2	8	no	—
119	C₂×C₃×D₁₂	—	2	4	no	—
120	C₂×C₃×D₁₂	—	2	16	no	—
121	C₂×C₃×D₁₂	—	2	16	no	—
122	C₂×C₃×D₁₂	—	2	8	no	—
123	C₂×C₃×D₁₂	D₄	1	8	yes	complemented
124	C₂×C₃×D₁₂	C₂³	1	8	yes	—
125	C₂×C₃×D₁₂	C₂³	1	2	yes	—
126	C₂×C₃×D₁₂	C₂³	1	2	yes	—
127	C₂×C₃×D₁₂	C₂³	1	2	yes	—
128	C₂×C₃×D₁₂	C₂³	1	2	yes	—
129	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
130	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic, complemented
131	C₂×C₃×D₁₂	C₂³	1	8	yes	complemented
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
133	C₂×C₃×C₄×D₃	C₂³	1	2	yes	complemented
134	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
135	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic, complemented
136	C₃²×C₄⋊C₄	C₂³	1	2	yes	complemented
137	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
138	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
141	C₃²×C₄²	C₂³	1	2	yes	complemented
142	C₃×#217	C₂³	1	4	yes	—
143	C₃×#217	C₂³	1	2	yes	—
144	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
145	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
146	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
147	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
148	C₃×C₄⋊Dic₃	C₂³	1	2	yes	complemented
149	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
150	C₃×C₄×Dic₃	C₂³	1	2	yes	complemented
151	#3484	—	3	1	no	Sylow
152	C₂⁵×C₃	—	3	2	no	—
153	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
154	C₃×H(5,𝔽₂)	—	6	8	no	—
155	C₂×C₃×#41	—	2	1	no	—
156	C₂×C₃×#41	—	3	2	no	—
157	C₂×C₃×#41	—	3	1	no	—
158	C₂×C₃×#41	—	3	2	no	—
159	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂²×C₃×D₄	—	3	4	no	—
162	C₂²×C₃×D₄	—	3	2	no	—
163	C₂²×C₃×D₄	—	3	8	no	—
164	C₂²×C₃×D₄	—	3	1	no	—
165	C₂²×C₃×D₄	—	3	2	no	—
166	C₂²×C₃×D₄	—	3	1	no	—
167	C₂²×C₃×D₄	—	3	4	no	—
168	C₂²×C₃×D₄	—	3	4	no	—
169	C₂²×C₃×D₄	—	3	2	no	—
170	C₂²×C₃×D₄	—	6	8	no	—
171	C₂³×C₃×C₄	—	2	1	no	—
172	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
173	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
174	#1009	—	2	8	no	—
175	C₂×#239	C₂²×C₃	1	2	yes	complemented
176	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
177	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
178	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
179	C₂×#235	C₂²×C₃	1	2	yes	complemented
180	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂²×D₁₂	—	2	8	no	—
182	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
183	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
184	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₂²×D₁₂	C₂²×C₃	1	4	yes	complemented
186	C₂²×D₁₂	C₂²×C₃	1	4	yes	complemented
187	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
188	C₃×#127	—	3	2	no	—
189	C₃×#127	—	3	2	no	—
190	C₃×#124	—	3	2	no	—
191	C₃×#124	—	3	2	no	—
192	C₃×#123	—	2	2	no	—
193	C₃×#123	—	3	2	no	—
194	C₃×#123	—	3	8	no	—
195	C₃×#123	C₂×D₃	1	2	yes	complemented
196	C₃×#123	C₂²×C₃	1	2	yes	complemented
197	C₃×C₂²⋊Q₈	—	2	2	no	—
198	C₃×C₂²⋊Q₈	—	3	2	no	—
199	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
200	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
201	C₃×#121	—	2	2	no	—
202	C₃×#121	—	3	2	no	—
203	C₃×#121	—	3	4	no	—
204	C₃×#121	—	3	8	no	—
205	C₃×#121	—	3	4	no	—
206	C₃×#121	—	3	8	no	—
207	C₃×#121	C₂×D₃	1	2	yes	complemented
208	C₃×#121	C₂²×C₃	1	2	yes	complemented
209	C₃×#120	—	2	2	no	—
210	C₃×#120	—	3	2	no	—
211	C₃×#120	—	3	4	no	—
212	C₃×#120	—	3	8	no	—
213	C₃×#120	—	3	4	no	—
214	C₃×#120	—	3	8	no	—
215	C₃×#120	—	3	8	no	—
216	C₃×#120	C₂×D₃	1	2	yes	complemented
217	C₃×#120	C₂²×C₃	1	2	yes	complemented
218	C₃×C₄×D₄	—	2	4	no	—
219	C₃×C₄×D₄	—	3	4	no	—
220	C₃×C₄×D₄	—	3	4	no	—
221	C₃×C₄×D₄	—	3	4	no	—
222	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
223	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
224	C₃×#117	—	2	1	no	—
225	C₃×#117	—	3	1	no	—
226	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
227	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
229	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
230	#953	C₂²×C₃	1	2	yes	complemented
231	#947	C₂²×C₃	1	2	yes	complemented
232	#940	C₂²×C₃	1	2	yes	complemented
233	#937	C₂²×C₃	1	4	yes	complemented
234	#937	C₂²×C₃	1	8	yes	complemented
235	#930	C₂²×C₃	1	4	yes	complemented
236	#930	C₂²×C₃	1	2	yes	complemented
237	#929	C₂²×C₃	1	2	yes	complemented
238	C₄×#67	C₂²×C₃	1	4	yes	complemented
239	#926	C₂²×C₃	1	1	yes	characteristic, complemented
240	#924	C₂²×C₃	1	2	yes	complemented
241	#895	C₂²×C₃	1	8	yes	complemented
242	#895	C₂²×C₃	1	4	yes	complemented
243	#894	C₂²×C₃	1	8	yes	complemented
244	#893	C₂²×C₃	1	4	yes	complemented
245	#884	C₂²×C₃	1	8	yes	complemented
246	#882	C₂²×C₃	1	4	yes	complemented
247	#882	C₂²×C₃	1	8	yes	complemented
248	#882	C₂²×C₃	1	8	yes	complemented
249	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
250	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
251	#875	C₂²×C₃	1	2	yes	complemented
252	#874	C₂²×C₃	1	2	yes	complemented
253	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
254	C₂³×C₃²	—	2	2	no	—
255	C₂³×C₃²	—	2	4	no	—
256	C₂³×C₃²	C₂⁴	1	2	yes	—
257	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
258	C₂³×C₃²	C₂⁴	1	2	yes	—
259	C₂²×C₃×D₃	—	2	4	no	—
260	C₂²×C₃×D₃	—	2	16	no	—
261	C₂²×C₃×D₃	—	2	16	no	—
262	C₂²×C₃×D₃	—	2	8	no	—
263	C₂²×C₃×D₃	—	4	4	no	—
264	C₂²×C₃×D₃	—	4	8	no	—
265	C₂²×C₃×D₃	—	4	4	no	—
266	C₂²×C₃×D₃	—	4	8	no	—
267	C₂²×C₃×D₃	—	4	32	no	—
268	C₂²×C₃×D₃	C₂×D₄	1	8	yes	complemented
269	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
270	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
271	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
272	C₃²×Q₈	—	2	2	no	—
273	C₃²×D₄	—	2	4	no	—
274	C₃²×D₄	—	2	8	no	—
275	C₃²×D₄	—	2	2	no	—
276	C₂×C₃²×C₄	—	2	2	no	—
277	C₂×C₃²×C₄	—	2	4	no	—
278	C₂×C₃²×C₄	—	2	4	no	—
279	C₂×C₃²×C₄	—	2	4	no	—
280	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
281	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
282	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
283	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
284	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
285	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
286	C₃×#67	—	2	4	no	—
287	C₃×#67	—	2	8	no	—
288	C₃×#67	—	2	8	no	—
289	C₃×#67	—	4	8	no	—
290	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
291	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
292	C₃×D₁₂	—	2	16	no	—
293	C₃×D₁₂	—	2	8	no	—
294	C₃×D₁₂	—	2	4	no	—
295	C₃×D₁₂	—	2	4	no	—
296	C₃×D₁₂	—	2	2	no	—
297	C₃×D₁₂	—	4	8	no	—
298	C₃×D₁₂	C₂×D₄	1	8	yes	complemented
299	C₃×D₁₂	C₂×D₄	1	8	yes	complemented
300	C₃×C₄×D₃	—	2	8	no	—
301	C₃×C₄×D₃	—	2	4	no	—
302	C₃×C₄×D₃	—	4	8	no	—
303	C₃×Dic₆	—	2	2	no	—
304	C₂×H(5,𝔽₂)	—	3	1	no	—
305	C₂³×D₄	—	3	1	no	—
306	#546	—	3	4	no	—
307	#546	—	3	4	no	—
308	D₄²	—	3	4	no	—
309	D₄²	—	3	4	no	—
310	#535	—	3	1	no	—
311	#535	—	3	1	no	—
312	#534	—	3	4	no	—
313	#525	—	3	1	no	—
314	#525	C₃×D₃	1	1	yes	characteristic, complemented
315	C₂×#120	—	3	4	no	—
316	#518	—	3	1	no	—
317	C₂⁴×C₃	—	2	1	no	—
318	C₂⁴×C₃	—	3	2	no	—
319	C₂⁴×C₃	—	3	8	no	—
320	C₂⁴×C₃	—	3	2	no	—
321	C₂⁴×C₃	—	3	4	no	—
322	C₂⁴×C₃	—	6	8	no	—
323	C₂⁴×C₃	—	12	8	no	—
324	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
325	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
326	C₂³×D₃	—	2	8	no	—
327	C₂³×D₃	—	4	8	no	—
328	C₂³×D₃	C₂³×C₃	1	8	yes	—
329	C₂³×D₃	C₂³×C₃	1	2	yes	—
330	C₂³×D₃	C₂³×C₃	1	2	yes	—
331	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
332	C₃×#41	—	2	4	no	—
333	C₃×#41	—	2	4	no	—
334	C₃×#41	—	4	4	no	—
335	C₃×#41	—	6	8	no	—
336	C₃×#41	—	6	8	no	—
337	C₃×#41	—	6	4	no	—
338	C₂×C₃×Q₈	—	2	1	no	—
339	C₂×C₃×Q₈	—	3	1	no	—
340	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
341	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
342	C₂×C₃×D₄	—	2	4	no	—
343	C₂×C₃×D₄	—	2	2	no	—
344	C₂×C₃×D₄	—	2	1	no	—
345	C₂×C₃×D₄	—	3	4	no	—
346	C₂×C₃×D₄	—	3	2	no	—
347	C₂×C₃×D₄	—	3	4	no	—
348	C₂×C₃×D₄	—	3	8	no	—
349	C₂×C₃×D₄	—	3	8	no	—
350	C₂×C₃×D₄	—	3	2	no	—
351	C₂×C₃×D₄	—	3	2	no	—
352	C₂×C₃×D₄	—	3	4	no	—
353	C₂×C₃×D₄	—	3	8	no	—
354	C₂×C₃×D₄	—	3	2	no	—
355	C₂×C₃×D₄	—	3	2	no	—
356	C₂×C₃×D₄	—	3	1	no	—
357	C₂×C₃×D₄	—	3	8	no	—
358	C₂×C₃×D₄	—	6	16	no	—
359	C₂×C₃×D₄	—	6	16	no	—
360	C₂×C₃×D₄	—	6	8	no	—
361	C₂×C₃×D₄	—	6	8	no	—
362	C₂×C₃×D₄	—	6	8	no	—
363	C₂×C₃×D₄	—	6	16	no	—
364	C₂×C₃×D₄	—	6	4	no	—
365	C₂×C₃×D₄	—	12	16	no	—
366	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
367	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
368	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic, complemented
369	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
370	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
371	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
372	C₂²×C₃×C₄	—	2	4	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	1	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	3	4	no	—
380	C₂²×C₃×C₄	—	3	2	no	—
381	C₂²×C₃×C₄	—	3	8	no	—
382	C₂²×C₃×C₄	—	4	4	no	—
383	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
384	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
385	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	complemented
388	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
389	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
390	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	complemented
393	C₂×#67	C₂³×C₃	1	4	yes	—
394	C₂×#67	C₂³×C₃	1	2	yes	—
395	C₂×#67	C₂³×C₃	1	4	yes	complemented
396	C₂×#67	C₂³×C₃	1	8	yes	complemented
397	#239	—	2	8	no	—
398	D₃×D₄	—	2	16	no	—
399	D₃×D₄	—	2	8	no	—
400	D₃×D₄	—	4	16	no	—
401	#235	—	2	4	no	—
402	#235	—	2	8	no	—
403	C₂×D₁₂	—	2	8	no	—
404	C₂×D₁₂	—	2	4	no	—
405	C₂×D₁₂	—	2	16	no	—
406	C₂×D₁₂	—	2	16	no	—
407	C₂×D₁₂	—	2	8	no	—
408	C₂×D₁₂	C₃×D₄	1	8	yes	complemented
409	C₂×D₁₂	C₂³×C₃	1	2	yes	—
410	C₂×D₁₂	C₂³×C₃	1	8	yes	—
411	C₂×D₁₂	C₂³×C₃	1	2	yes	—
412	C₂×D₁₂	C₂³×C₃	1	2	yes	—
413	C₂×D₁₂	C₂³×C₃	1	2	yes	—
414	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic, complemented
415	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
416	C₂×D₁₂	C₂³×C₃	1	8	yes	complemented
417	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
418	C₂×C₄×D₃	C₂³×C₃	1	2	yes	complemented
419	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
420	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic, complemented
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	3	4	no	—
424	C₃×C₄⋊C₄	—	3	2	no	—
425	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
426	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
427	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
428	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
429	C₃×C₂²⋊C₄	—	2	2	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
431	C₃×C₂²⋊C₄	—	2	4	no	—
432	C₃×C₂²⋊C₄	—	3	2	no	—
433	C₃×C₂²⋊C₄	—	3	4	no	—
434	C₃×C₂²⋊C₄	—	3	8	no	—
435	C₃×C₂²⋊C₄	—	3	8	no	—
436	C₃×C₂²⋊C₄	—	3	8	no	—
437	C₃×C₂²⋊C₄	—	3	4	no	—
438	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
439	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
440	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
441	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
443	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
444	C₃×C₄²	—	2	2	no	—
445	C₃×C₄²	—	3	2	no	—
446	C₃×C₄²	C₂²×D₃	1	2	yes	complemented
447	C₃×C₄²	C₂³×C₃	1	2	yes	complemented
448	#217	C₂³×C₃	1	4	yes	—
449	#217	C₂³×C₃	1	2	yes	—
450	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
451	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
452	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
453	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
454	C₄⋊Dic₃	C₂³×C₃	1	2	yes	complemented
455	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
456	C₄×Dic₃	C₂³×C₃	1	2	yes	complemented
457	C₂²×C₃²	—	2	8	no	—
458	C₂²×C₃²	—	2	2	no	—
459	C₂²×C₃²	—	2	2	no	—
460	C₂²×C₃²	—	2	2	no	—
461	C₂²×C₃²	—	2	2	no	—
462	C₂²×C₃²	—	2	4	no	—
463	C₂²×C₃²	C₂²×D₄	1	2	yes	—
464	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	complemented
465	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
466	C₂×C₃×D₃	—	2	8	no	—
467	C₂×C₃×D₃	—	2	2	no	—
468	C₂×C₃×D₃	—	2	4	no	—
469	C₂×C₃×D₃	—	2	4	no	—
470	C₂×C₃×D₃	—	2	8	no	—
471	C₂×C₃×D₃	—	4	8	no	—
472	C₂×C₃×D₃	—	4	32	no	—
473	C₂×C₃×D₃	—	4	8	no	—
474	C₂×C₃×D₃	—	8	8	no	—
475	C₂×C₃×D₃	C₂²×D₄	1	8	yes	—
476	C₃²×C₄	—	2	2	no	—
477	C₃²×C₄	—	2	2	no	—
478	C₃²×C₄	—	2	4	no	—
479	C₃²×C₄	C₂²×D₄	1	2	yes	—
480	C₃²×C₄	C₂²×D₄	1	2	yes	—
481	C₃×Dic₃	—	2	2	no	—
482	C₃×Dic₃	—	2	4	no	—
483	C₂⁵	—	3	2	no	—
484	H(5,𝔽₂)	—	6	8	no	—
485	C₂×#41	—	3	2	no	—
486	C₂×#41	—	3	1	no	—
487	C₂×#41	—	3	2	no	—
488	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
489	C₂²×D₄	—	3	4	no	—
490	C₂²×D₄	—	3	2	no	—
491	C₂²×D₄	—	3	8	no	—
492	C₂²×D₄	—	3	1	no	—
493	C₂²×D₄	—	3	2	no	—
494	C₂²×D₄	—	3	1	no	—
495	C₂²×D₄	—	3	4	no	—
496	C₂²×D₄	—	3	4	no	—
497	C₂²×D₄	—	3	2	no	—
498	C₂²×D₄	—	6	8	no	—
499	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
500	#127	—	3	2	no	—
501	#127	—	3	2	no	—
502	#124	—	3	2	no	—
503	#124	—	3	2	no	—
504	#123	—	3	2	no	—
505	#123	—	3	8	no	—
506	#123	C₂×C₃×D₃	1	2	yes	complemented
507	C₂²⋊Q₈	—	3	2	no	—
508	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
509	#121	—	3	2	no	—
510	#121	—	3	4	no	—
511	#121	—	3	8	no	—
512	#121	—	3	4	no	—
513	#121	—	3	8	no	—
514	#121	C₂×C₃×D₃	1	2	yes	complemented
515	#120	—	3	2	no	—
516	#120	—	3	4	no	—
517	#120	—	3	8	no	—
518	#120	—	3	4	no	—
519	#120	—	3	8	no	—
520	#120	—	3	8	no	—
521	#120	C₂×C₃×D₃	1	2	yes	complemented
522	C₄×D₄	—	3	4	no	—
523	C₄×D₄	—	3	4	no	—
524	C₄×D₄	—	3	4	no	—
525	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
526	#117	—	3	1	no	—
527	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
528	C₂×C₂²⋊C₄	—	3	4	no	—
529	C₂×C₂²⋊C₄	—	3	8	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	2	4	no	—
532	C₂³×C₃	—	2	2	no	—
533	C₂³×C₃	—	2	4	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	—	2	2	no	—
536	C₂³×C₃	—	2	2	no	—
537	C₂³×C₃	—	3	4	no	—
538	C₂³×C₃	—	3	8	no	—
539	C₂³×C₃	—	3	4	no	—
540	C₂³×C₃	—	3	2	no	—
541	C₂³×C₃	—	4	2	no	—
542	C₂³×C₃	—	4	4	no	—
543	C₂³×C₃	—	6	16	no	—
544	C₂³×C₃	—	6	8	no	—
545	C₂³×C₃	—	6	4	no	—
546	C₂³×C₃	—	6	16	no	—
547	C₂³×C₃	—	12	4	no	—
548	C₂³×C₃	—	12	8	no	—
549	C₂³×C₃	—	12	4	no	—
550	C₂³×C₃	—	12	8	no	—
551	C₂³×C₃	—	12	32	no	—
552	C₂³×C₃	C₂³×D₃	1	2	yes	—
553	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
554	C₂³×C₃	C₂³×D₃	1	2	yes	—
555	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
556	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
557	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
558	C₂²×D₃	—	2	4	no	—
559	C₂²×D₃	—	2	16	no	—
560	C₂²×D₃	—	2	16	no	—
561	C₂²×D₃	—	2	8	no	—
562	C₂²×D₃	—	4	4	no	—
563	C₂²×D₃	—	4	8	no	—
564	C₂²×D₃	—	4	4	no	—
565	C₂²×D₃	—	4	8	no	—
566	C₂²×D₃	—	4	32	no	—
567	C₂²×D₃	C₂×C₃×D₄	1	8	yes	complemented
568	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
569	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
570	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
571	C₃×Q₈	—	2	2	no	—
572	C₃×Q₈	—	2	2	no	—
573	C₃×Q₈	—	4	2	no	—
574	C₃×Q₈	—	6	2	no	—
575	C₃×D₄	—	2	4	no	—
576	C₃×D₄	—	2	8	no	—
577	C₃×D₄	—	2	4	no	—
578	C₃×D₄	—	2	8	no	—
579	C₃×D₄	—	2	2	no	—
580	C₃×D₄	—	2	2	no	—
581	C₃×D₄	—	3	8	no	—
582	C₃×D₄	—	3	8	no	—
583	C₃×D₄	—	4	2	no	—
584	C₃×D₄	—	4	8	no	—
585	C₃×D₄	—	4	4	no	—
586	C₃×D₄	—	6	16	no	—
587	C₃×D₄	—	6	8	no	—
588	C₃×D₄	—	6	8	no	—
589	C₃×D₄	—	6	4	no	—
590	C₃×D₄	—	6	8	no	—
591	C₃×D₄	—	6	4	no	—
592	C₃×D₄	—	6	4	no	—
593	C₃×D₄	—	6	2	no	—
594	C₃×D₄	—	12	8	no	—
595	C₃×D₄	—	12	8	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	4	no	—
599	C₂×C₃×C₄	—	2	4	no	—
600	C₂×C₃×C₄	—	2	4	no	—
601	C₂×C₃×C₄	—	2	4	no	—
602	C₂×C₃×C₄	—	2	4	no	—
603	C₂×C₃×C₄	—	2	4	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	4	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	4	no	—
610	C₂×C₃×C₄	—	3	4	no	—
611	C₂×C₃×C₄	—	3	2	no	—
612	C₂×C₃×C₄	—	4	4	no	—
613	C₂×C₃×C₄	—	4	4	no	—
614	C₂×C₃×C₄	—	4	4	no	—
615	C₂×C₃×C₄	—	4	2	no	—
616	C₂×C₃×C₄	—	6	8	no	—
617	C₂×C₃×C₄	—	6	4	no	—
618	C₂×C₃×C₄	—	12	8	no	—
619	C₂×C₃×C₄	D₃×D₄	1	4	yes	complemented
620	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
621	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
622	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
623	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
624	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
625	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
626	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
627	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
628	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
629	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
630	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
631	#67	—	2	4	no	—
632	#67	—	2	8	no	—
633	#67	—	2	8	no	—
634	#67	—	4	8	no	—
635	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
636	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
637	D₁₂	—	2	16	no	—
638	D₁₂	—	2	8	no	—
639	D₁₂	—	2	4	no	—
640	D₁₂	—	2	4	no	—
641	D₁₂	—	2	2	no	—
642	D₁₂	—	4	8	no	—
643	D₁₂	C₂×C₃×D₄	1	8	yes	complemented
644	D₁₂	C₂×C₃×D₄	1	8	yes	complemented
645	C₄×D₃	—	2	8	no	—
646	C₄×D₃	—	2	4	no	—
647	C₄×D₃	—	4	8	no	—
648	Dic₆	—	2	2	no	—
649	C₂×C₃²	—	2	2	no	—
650	C₂×C₃²	—	2	4	no	—
651	C₂×C₃²	—	4	2	no	—
652	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
653	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
654	C₃×D₃	—	2	8	no	—
655	C₃×D₃	—	4	4	no	—
656	C₃×D₃	—	4	2	no	—
657	C₂⁴	—	3	2	no	—
658	C₂⁴	—	3	8	no	—
659	C₂⁴	—	3	2	no	—
660	C₂⁴	—	3	4	no	—
661	C₂⁴	—	6	8	no	—
662	C₂⁴	—	12	8	no	—
663	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
664	#41	—	2	4	no	—
665	#41	—	6	8	no	—
666	#41	—	6	8	no	—
667	#41	—	6	4	no	—
668	C₂×Q₈	—	3	1	no	—
669	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
670	C₂×D₄	—	3	4	no	—
671	C₂×D₄	—	3	2	no	—
672	C₂×D₄	—	3	4	no	—
673	C₂×D₄	—	3	8	no	—
674	C₂×D₄	—	3	2	no	—
675	C₂×D₄	—	3	2	no	—
676	C₂×D₄	—	3	4	no	—
677	C₂×D₄	—	3	8	no	—
678	C₂×D₄	—	3	2	no	—
679	C₂×D₄	—	3	2	no	—
680	C₂×D₄	—	3	1	no	—
681	C₂×D₄	—	3	8	no	—
682	C₂×D₄	—	3	8	no	—
683	C₂×D₄	—	6	16	no	—
684	C₂×D₄	—	6	16	no	—
685	C₂×D₄	—	6	8	no	—
686	C₂×D₄	—	6	8	no	—
687	C₂×D₄	—	6	8	no	—
688	C₂×D₄	—	6	16	no	—
689	C₂×D₄	—	6	4	no	—
690	C₂×D₄	—	12	16	no	—
691	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
692	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
693	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	3	4	no	—
696	C₂²×C₄	—	3	2	no	—
697	C₂²×C₄	—	3	8	no	—
698	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
699	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
700	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
701	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
702	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	complemented
703	C₄⋊C₄	—	3	2	no	—
704	C₄⋊C₄	—	3	4	no	—
705	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	complemented
706	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
707	C₂²⋊C₄	—	3	2	no	—
708	C₂²⋊C₄	—	3	4	no	—
709	C₂²⋊C₄	—	3	8	no	—
710	C₂²⋊C₄	—	3	8	no	—
711	C₂²⋊C₄	—	3	8	no	—
712	C₂²⋊C₄	—	3	4	no	—
713	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
714	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
715	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
716	C₄²	—	3	2	no	—
717	C₄²	C₂²×C₃×D₃	1	2	yes	complemented
718	C₂²×C₃	—	2	8	no	—
719	C₂²×C₃	—	2	8	no	—
720	C₂²×C₃	—	2	2	no	—
721	C₂²×C₃	—	2	2	no	—
722	C₂²×C₃	—	2	2	no	—
723	C₂²×C₃	—	2	2	no	—
724	C₂²×C₃	—	2	2	no	—
725	C₂²×C₃	—	2	2	no	—
726	C₂²×C₃	—	2	2	no	—
727	C₂²×C₃	—	2	4	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	4	no	—
730	C₂²×C₃	—	2	2	no	—
731	C₂²×C₃	—	2	4	no	—
732	C₂²×C₃	—	2	1	no	—
733	C₂²×C₃	—	3	8	no	—
734	C₂²×C₃	—	4	2	no	—
735	C₂²×C₃	—	4	2	no	—
736	C₂²×C₃	—	4	2	no	—
737	C₂²×C₃	—	4	2	no	—
738	C₂²×C₃	—	4	4	no	—
739	C₂²×C₃	—	4	8	no	—
740	C₂²×C₃	—	6	8	no	—
741	C₂²×C₃	—	6	2	no	—
742	C₂²×C₃	—	6	4	no	—
743	C₂²×C₃	—	6	4	no	—
744	C₂²×C₃	—	6	8	no	—
745	C₂²×C₃	—	12	8	no	—
746	C₂²×C₃	—	12	32	no	—
747	C₂²×C₃	—	12	8	no	—
748	C₂²×C₃	—	24	8	no	—
749	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
750	C₂²×C₃	#1009	1	4	yes	complemented
751	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
752	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
753	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
754	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
755	C₂×D₃	—	2	8	no	—
756	C₂×D₃	—	2	2	no	—
757	C₂×D₃	—	2	4	no	—
758	C₂×D₃	—	2	4	no	—
759	C₂×D₃	—	2	8	no	—
760	C₂×D₃	—	4	8	no	—
761	C₂×D₃	—	4	32	no	—
762	C₂×D₃	—	4	8	no	—
763	C₂×D₃	—	8	8	no	—
764	C₂×D₃	C₂²×C₃×D₄	1	8	yes	—
765	C₃×C₄	—	2	2	no	—
766	C₃×C₄	—	2	2	no	—
767	C₃×C₄	—	2	4	no	—
768	C₃×C₄	—	2	2	no	—
769	C₃×C₄	—	2	2	no	—
770	C₃×C₄	—	2	4	no	—
771	C₃×C₄	—	2	2	no	—
772	C₃×C₄	—	2	2	no	—
773	C₃×C₄	—	4	2	no	—
774	C₃×C₄	—	4	2	no	—
775	C₃×C₄	—	4	4	no	—
776	C₃×C₄	—	6	2	no	—
777	C₃×C₄	—	6	4	no	—
778	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
779	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
780	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
781	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
782	Dic₃	—	2	2	no	—
783	Dic₃	—	2	4	no	—
784	C₃²	#3484	1	1	yes	characteristic, complemented, Sylow
785	C₂³	—	2	2	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	3	4	no	—
788	C₂³	—	3	8	no	—
789	C₂³	—	3	4	no	—
790	C₂³	—	3	2	no	—
791	C₂³	—	6	16	no	—
792	C₂³	—	6	8	no	—
793	C₂³	—	6	4	no	—
794	C₂³	—	6	16	no	—
795	C₂³	—	12	4	no	—
796	C₂³	—	12	8	no	—
797	C₂³	—	12	4	no	—
798	C₂³	—	12	8	no	—
799	C₂³	—	12	32	no	—
800	C₂³	C₂³×C₃×D₃	1	2	yes	—
801	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
802	C₂³	C₂³×C₃×D₃	1	2	yes	—
803	Q₈	—	2	2	no	—
804	Q₈	—	6	2	no	—
805	D₄	—	2	4	no	—
806	D₄	—	2	8	no	—
807	D₄	—	2	2	no	—
808	D₄	—	3	8	no	—
809	D₄	—	3	8	no	—
810	D₄	—	6	16	no	—
811	D₄	—	6	8	no	—
812	D₄	—	6	8	no	—
813	D₄	—	6	4	no	—
814	D₄	—	6	8	no	—
815	D₄	—	6	4	no	—
816	D₄	—	6	4	no	—
817	D₄	—	6	2	no	—
818	D₄	—	12	8	no	—
819	D₄	—	12	8	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	3	4	no	—
825	C₂×C₄	—	3	2	no	—
826	C₂×C₄	—	6	8	no	—
827	C₂×C₄	—	6	4	no	—
828	C₂×C₄	—	12	8	no	—
829	C₂×C₄	C₃×D₃×D₄	1	4	yes	complemented
830	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
831	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
832	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
833	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
834	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
835	C₂×C₃	—	2	2	no	—
836	C₂×C₃	—	2	4	no	—
837	C₂×C₃	—	2	2	no	—
838	C₂×C₃	—	2	4	no	—
839	C₂×C₃	—	2	1	no	—
840	C₂×C₃	—	2	2	no	—
841	C₂×C₃	—	4	2	no	—
842	C₂×C₃	—	4	4	no	—
843	C₂×C₃	—	4	2	no	—
844	C₂×C₃	—	4	2	no	—
845	C₂×C₃	—	6	8	no	—
846	C₂×C₃	—	8	2	no	—
847	C₂×C₃	—	12	4	no	—
848	C₂×C₃	—	12	2	no	—
849	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
850	C₂×C₃	C₂×#1009	1	2	yes	—
851	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
852	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
853	D₃	—	2	8	no	—
854	D₃	—	4	4	no	—
855	D₃	—	4	2	no	—
856	C₂²	—	2	8	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	3	8	no	—
863	C₂²	—	6	8	no	—
864	C₂²	—	6	2	no	—
865	C₂²	—	6	4	no	—
866	C₂²	—	6	4	no	—
867	C₂²	—	6	8	no	—
868	C₂²	—	12	8	no	—
869	C₂²	—	12	32	no	—
870	C₂²	—	12	8	no	—
871	C₂²	—	24	8	no	—
872	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
873	C₂²	C₃×#1009	1	4	yes	complemented
874	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
875	C₄	—	2	2	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	4	no	—
878	C₄	—	6	2	no	—
879	C₄	—	6	4	no	—
880	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
881	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
882	C₃	—	2	1	no	—
883	C₃	#86039	1	1	yes	characteristic, direct product factor
884	C₃	C₃×#3484	1	1	yes	characteristic, complemented
885	C₂	—	2	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	6	8	no	—
889	C₂	—	12	4	no	—
890	C₂	—	12	2	no	—
891	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
892	C₂	C₂×C₃×#1009	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#525	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#525	D₃
hypocenter	C₃	C₃×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1009	C₂	semidirect
2. C₂³×C₃×D₁₂	C₂	semidirect
3. C₃²×#525	C₂	semidirect
4. C₃×#5830	C₂	semidirect
5. C₃×#5791	C₂	semidirect
6. C₃×#5653	C₂	semidirect
7. C₃×#5630	C₂	semidirect
8. C₃×#5609	C₂	semidirect
9. C₃×D₃×#120	C₂	semidirect
10. C₃×#5550	C₂	semidirect
11. C₃×D₄×D₁₂	C₂	semidirect
12. C₃×#5525	C₂	semidirect
13. C₃×#5521	C₂	semidirect
15. #86039	C₃	direct (N × H)
16. C₂⁴×C₃×D₃	C₂²	semidirect
17. C₂×C₃²×#41	C₂²	semidirect
18. C₂³×C₃²×C₄	C₂²	semidirect
20. C₂×C₃×#239	C₂²	semidirect
21. C₂×C₃×D₃×D₄	C₂²	semidirect
22. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂×C₃×D₃×D₄	C₂²	semidirect
24. C₂×C₃×#235	C₂²	semidirect
25. C₂×C₃×#235	C₂²	semidirect
28. C₂²×C₃×D₁₂	C₂²	semidirect
29. C₂²×C₃×D₁₂	C₂²	semidirect
30. C₂²×C₃×D₁₂	C₂²	semidirect
31. C₂²×C₃×D₁₂	C₂²	semidirect
32. C₂²×C₃×D₁₂	C₂²	semidirect
33. C₃²×#123	C₂²	semidirect
34. C₃²×C₂²⋊Q₈	C₂²	semidirect
35. C₃²×#121	C₂²	semidirect
36. C₃²×#120	C₂²	semidirect
37. C₃²×C₄×D₄	C₂²	semidirect
38. C₃²×#117	C₂²	semidirect
39. C₃×#953	C₂²	semidirect
40. C₃×#947	C₂²	semidirect
41. C₃×#940	C₂²	semidirect
42. C₃×#937	C₂²	semidirect
43. C₃×#937	C₂²	semidirect
44. C₃×#930	C₂²	semidirect
45. C₃×#930	C₂²	semidirect
46. C₃×#929	C₂²	semidirect
47. C₃×C₄×#67	C₂²	semidirect
48. C₃×#926	C₂²	semidirect
49. C₃×#924	C₂²	semidirect
50. C₃×#895	C₂²	semidirect
51. C₃×#895	C₂²	semidirect
52. C₃×#894	C₂²	semidirect
53. C₃×#893	C₂²	semidirect
54. C₃×#884	C₂²	semidirect
55. C₃×#882	C₂²	semidirect
56. C₃×#882	C₂²	semidirect
57. C₃×#882	C₂²	semidirect
58. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
60. C₃×#875	C₂²	semidirect
61. C₃×#874	C₂²	semidirect
62. C₃×C₄×D₁₂	C₂²	semidirect
65. C₂×#1009	C₂×C₃	semidirect
66. C₂³×D₁₂	C₂×C₃	semidirect
76. C₃×#525	D₃	semidirect
77. C₃×#525	C₂×C₃	semidirect
80. #5830	C₂×C₃	semidirect
81. #5791	C₂×C₃	semidirect
82. #5653	C₂×C₃	semidirect
83. #5630	C₂×C₃	semidirect
84. #5609	C₂×C₃	semidirect
85. D₃×#120	C₂×C₃	semidirect
86. #5550	C₂×C₃	semidirect
87. D₄×D₁₂	C₂×C₃	semidirect
88. #5525	C₂×C₃	semidirect
89. #5521	C₂×C₃	semidirect
96. C₂³×C₃×D₃	C₂³	semidirect
98. C₂×C₃²×Q₈	C₂³	semidirect
101. C₂×C₃²×D₄	C₂³	semidirect
107. C₂²×C₃²×C₄	C₂³	semidirect
110. C₂×C₃×#67	C₂³	semidirect
111. C₂×C₃×#67	C₂³	semidirect
123. C₂×C₃×D₁₂	D₄	semidirect
129. C₂×C₃×D₁₂	C₂³	semidirect
130. C₂×C₃×D₁₂	C₂³	semidirect
131. C₂×C₃×D₁₂	C₂³	semidirect
132. C₂×C₃×C₄×D₃	C₂³	semidirect
133. C₂×C₃×C₄×D₃	C₂³	semidirect
134. C₂×C₃×C₄×D₃	C₂³	semidirect
135. C₂×C₃×Dic₆	C₂³	semidirect
136. C₃²×C₄⋊C₄	C₂³	semidirect
137. C₃²×C₄⋊C₄	C₂³	semidirect
140. C₃²×C₂²⋊C₄	C₂³	semidirect
141. C₃²×C₄²	C₂³	semidirect
144. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
145. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
146. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
147. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
148. C₃×C₄⋊Dic₃	C₂³	semidirect
149. C₃×Dic₃⋊C₄	C₂³	semidirect
150. C₃×C₄×Dic₃	C₂³	semidirect
153. C₂⁴×D₃	C₂²×C₃	semidirect
159. C₂×C₃×#41	C₂×D₃	semidirect
160. C₂×C₃×#41	C₂²×C₃	semidirect
172. C₂³×C₃×C₄	C₂×D₃	semidirect
173. C₂³×C₃×C₄	C₂²×C₃	semidirect
175. C₂×#239	C₂²×C₃	semidirect
176. C₂×D₃×D₄	C₂²×C₃	semidirect
177. C₂×D₃×D₄	C₂²×C₃	semidirect
178. C₂×D₃×D₄	C₂²×C₃	semidirect
179. C₂×#235	C₂²×C₃	semidirect
180. C₂×#235	C₂²×C₃	semidirect
183. C₂²×D₁₂	C₂²×C₃	semidirect
184. C₂²×D₁₂	C₂²×C₃	semidirect
185. C₂²×D₁₂	C₂²×C₃	semidirect
186. C₂²×D₁₂	C₂²×C₃	semidirect
187. C₂²×D₁₂	C₂²×C₃	semidirect
195. C₃×#123	C₂×D₃	semidirect
196. C₃×#123	C₂²×C₃	semidirect
199. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
200. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
207. C₃×#121	C₂×D₃	semidirect
208. C₃×#121	C₂²×C₃	semidirect
216. C₃×#120	C₂×D₃	semidirect
217. C₃×#120	C₂²×C₃	semidirect
222. C₃×C₄×D₄	C₂×D₃	semidirect
223. C₃×C₄×D₄	C₂²×C₃	semidirect
226. C₃×#117	C₂×D₃	semidirect
227. C₃×#117	C₂²×C₃	semidirect
230. #953	C₂²×C₃	semidirect
231. #947	C₂²×C₃	semidirect
232. #940	C₂²×C₃	semidirect
233. #937	C₂²×C₃	semidirect
234. #937	C₂²×C₃	semidirect
235. #930	C₂²×C₃	semidirect
236. #930	C₂²×C₃	semidirect
237. #929	C₂²×C₃	semidirect
238. C₄×#67	C₂²×C₃	semidirect
239. #926	C₂²×C₃	semidirect
240. #924	C₂²×C₃	semidirect
241. #895	C₂²×C₃	semidirect
242. #895	C₂²×C₃	semidirect
243. #894	C₂²×C₃	semidirect
244. #893	C₂²×C₃	semidirect
245. #884	C₂²×C₃	semidirect
246. #882	C₂²×C₃	semidirect
247. #882	C₂²×C₃	semidirect
248. #882	C₂²×C₃	semidirect
249. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
250. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
251. #875	C₂²×C₃	semidirect
252. #874	C₂²×C₃	semidirect
253. C₄×D₁₂	C₂²×C₃	semidirect
268. C₂²×C₃×D₃	C₂×D₄	semidirect
280. C₂×C₃²×C₄	C₂×D₄	semidirect
298. C₃×D₁₂	C₂×D₄	semidirect
299. C₃×D₁₂	C₂×D₄	semidirect
314. #525	C₃×D₃	semidirect
331. C₂³×D₃	C₂³×C₃	semidirect
340. C₂×C₃×Q₈	C₂²×D₃	semidirect
341. C₂×C₃×Q₈	C₂³×C₃	semidirect
368. C₂×C₃×D₄	C₂²×D₃	semidirect
371. C₂×C₃×D₄	C₂³×C₃	semidirect
387. C₂²×C₃×C₄	C₂²×D₃	semidirect
392. C₂²×C₃×C₄	C₂³×C₃	semidirect
395. C₂×#67	C₂³×C₃	semidirect
396. C₂×#67	C₂³×C₃	semidirect
408. C₂×D₁₂	C₃×D₄	semidirect
414. C₂×D₁₂	C₂³×C₃	semidirect
415. C₂×D₁₂	C₂³×C₃	semidirect
416. C₂×D₁₂	C₂³×C₃	semidirect
417. C₂×C₄×D₃	C₂³×C₃	semidirect
418. C₂×C₄×D₃	C₂³×C₃	semidirect
419. C₂×C₄×D₃	C₂³×C₃	semidirect
420. C₂×Dic₆	C₂³×C₃	semidirect
425. C₃×C₄⋊C₄	C₂²×D₃	semidirect
426. C₃×C₄⋊C₄	C₂²×D₃	semidirect
427. C₃×C₄⋊C₄	C₂³×C₃	semidirect
428. C₃×C₄⋊C₄	C₂³×C₃	semidirect
440. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
443. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
446. C₃×C₄²	C₂²×D₃	semidirect
447. C₃×C₄²	C₂³×C₃	semidirect
450. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
451. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
452. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
453. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
454. C₄⋊Dic₃	C₂³×C₃	semidirect
455. Dic₃⋊C₄	C₂³×C₃	semidirect
456. C₄×Dic₃	C₂³×C₃	semidirect
464. C₂²×C₃²	H(5,𝔽₂)	semidirect
488. C₂×#41	C₂×C₃×D₃	semidirect
499. C₂³×C₄	C₂×C₃×D₃	semidirect
506. #123	C₂×C₃×D₃	semidirect
508. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
514. #121	C₂×C₃×D₃	semidirect
521. #120	C₂×C₃×D₃	semidirect
525. C₄×D₄	C₂×C₃×D₃	semidirect
527. #117	C₂×C₃×D₃	semidirect
567. C₂²×D₃	C₂×C₃×D₄	semidirect
619. C₂×C₃×C₄	D₃×D₄	semidirect
620. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
643. D₁₂	C₂×C₃×D₄	semidirect
644. D₁₂	C₂×C₃×D₄	semidirect
669. C₂×Q₈	C₂²×C₃×D₃	semidirect
693. C₂×D₄	C₂²×C₃×D₃	semidirect
702. C₂²×C₄	C₂²×C₃×D₃	semidirect
705. C₄⋊C₄	C₂²×C₃×D₃	semidirect
706. C₄⋊C₄	C₂²×C₃×D₃	semidirect
715. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
717. C₄²	C₂²×C₃×D₃	semidirect
750. C₂²×C₃	#1009	semidirect
752. C₂²×C₃	C₃×H(5,𝔽₂)	semidirect
784. C₃²	#3484	semidirect
829. C₂×C₄	C₃×D₃×D₄	semidirect
873. C₂²	C₃×#1009	semidirect
883. C₃	#86039	direct (N × H)
884. C₃	C₃×#3484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1009	2
C₂³×C₃×D₁₂	2
C₃²×#525	2
C₃×#5830	2
C₃×#5791	2
C₃×#5653	2
C₃×#5630	2
C₃×#5609	2
C₃×D₃×#120	2
C₃×#5550	2
C₃×D₄×D₁₂	2
C₃×#5525	2
C₃×#5521	2
C₃×#3484	3
#86039	3

Subgroups — C3×#86039 #11904284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86039 #11904284