Subgroups — C₃×#86076 #11906075

Order 1152.

3245 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1007	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5816	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5677	C₂	1	4	yes	maximal, complemented
7	C₃×#5676	C₂	1	4	yes	maximal, complemented
8	C₃×#5675	C₂	1	2	yes	maximal, complemented
9	C₃×#5674	C₂	1	2	yes	maximal, complemented
10	C₃×D₃×#124	C₂	1	2	yes	maximal, complemented
11	C₃×#5668	C₂	1	2	yes	maximal, complemented
12	C₃×#5490	C₂	1	8	yes	maximal, complemented
13	C₃×#5477	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3500	—	3	1	no	maximal
16	#86076	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#67	C₂²	1	4	yes	—
20	C₃×#1007	—	2	8	no	—
21	C₂×C₃×#239	C₂²	1	2	yes	complemented
22	C₂×C₃×#239	C₂²	1	2	yes	complemented
23	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
24	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
25	C₃×#1004	—	2	8	no	—
26	C₂×C₃×#237	C₂²	1	2	yes	—
27	C₂×C₃×#237	C₂²	1	2	yes	—
28	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
29	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
30	C₂×C₃×#235	C₂²	1	1	yes	characteristic
31	C₂×C₃×#235	C₂²	1	1	yes	characteristic
32	C₂×C₃×#235	C₂²	1	4	yes	complemented
33	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#124	C₂²	1	2	yes	complemented
35	C₃²×#124	C₂²	1	2	yes	complemented
36	C₃²×#124	C₂²	1	4	yes	complemented
37	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
38	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
39	C₃×#953	C₂²	1	4	yes	complemented
40	C₃×#947	C₂²	1	2	yes	complemented
41	C₃×#946	C₂²	1	4	yes	complemented
42	C₃×#944	C₂²	1	2	yes	complemented
43	C₃×#940	C₂²	1	2	yes	complemented
44	C₃×#938	C₂²	1	4	yes	complemented
45	C₃×#936	C₂²	1	2	yes	complemented
46	C₃×#930	C₂²	1	4	yes	complemented
47	C₃×#929	C₂²	1	4	yes	complemented
48	C₃×C₄×#67	C₂²	1	4	yes	complemented
49	C₃×#926	C₂²	1	1	yes	characteristic, complemented
50	C₃×#885	C₂²	1	8	yes	complemented
51	C₃×#884	C₂²	1	8	yes	complemented
52	C₃×#884	C₂²	1	8	yes	complemented
53	C₃×#883	C₂²	1	8	yes	complemented
54	C₃×#882	C₂²	1	8	yes	complemented
55	C₃×#67⋊C₄	C₂²	1	8	yes	complemented
56	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
57	C₃×#878	C₂²	1	8	yes	complemented
58	C₃×#875	C₂²	1	1	yes	characteristic, complemented
59	C₃×#875	C₂²	1	1	yes	characteristic, complemented
60	C₃×#874	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
62	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
63	C₃×#872	C₂²	1	2	yes	complemented
64	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
65	C₃×#869	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
67	C₂×C₃×2₋¹⁺⁴	—	3	1	no	—
68	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
69	C₂×#1007	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂×#1004	C₂×C₃	1	1	yes	characteristic, complemented
71	C₃×#548	—	3	4	no	—
72	C₃×#546	—	3	4	no	—
73	C₃×#546	—	3	8	no	—
74	C₃×#536	—	3	1	no	—
75	C₃×#536	—	3	2	no	—
76	C₃×#535	—	3	1	no	—
77	C₃×#535	—	3	2	no	—
78	C₃×#532	—	3	2	no	—
79	C₃×#532	—	3	1	no	—
80	C₂×C₃×#124	—	2	1	no	—
81	C₂×C₃×#124	—	3	2	no	—
82	C₂×C₃×#124	D₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic, complemented
84	C₃×C₄×#41	—	3	1	no	—
85	#5816	C₂×C₃	1	1	yes	characteristic, complemented
86	#5805	C₂×C₃	1	1	yes	characteristic, complemented
87	#5677	C₂×C₃	1	4	yes	complemented
88	#5676	C₂×C₃	1	4	yes	complemented
89	#5675	C₂×C₃	1	2	yes	complemented
90	#5674	C₂×C₃	1	2	yes	complemented
91	D₃×#124	C₂×C₃	1	2	yes	complemented
92	#5668	C₂×C₃	1	2	yes	complemented
93	#5490	C₂×C₃	1	8	yes	complemented
94	#5477	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂⁴×C₃²	C₂³	1	2	yes	—
97	C₂³×C₃×D₃	C₂³	1	4	yes	—
98	C₂×C₃²×Q₈	—	2	4	no	—
99	C₂×C₃²×Q₈	C₂³	1	2	yes	—
100	C₂×C₃²×Q₈	C₂³	1	2	yes	—
101	C₂×C₃²×D₄	—	2	4	no	—
102	C₂×C₃²×D₄	C₂³	1	2	yes	—
103	C₂×C₃²×D₄	C₂³	1	2	yes	—
104	C₂²×C₃²×C₄	C₂³	1	2	yes	—
105	C₂²×C₃²×C₄	C₂³	1	2	yes	—
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₂×C₃×#67	—	2	16	no	—
108	C₂×C₃×#67	C₂³	1	4	yes	—
109	C₂×C₃×#67	C₂³	1	4	yes	—
110	C₂×C₃×#67	C₂³	1	2	yes	—
111	C₂×C₃×#67	C₂³	1	2	yes	—
112	C₂×C₃×#67	C₂³	1	8	yes	—
113	C₂×C₃×#67	C₂³	1	2	yes	—
114	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
115	C₃×#239	—	2	8	no	—
116	C₃×#239	—	2	8	no	—
117	C₃×D₃×Q₈	—	2	8	no	—
118	C₃×D₃×Q₈	—	2	8	no	—
119	C₃×#237	—	2	8	no	—
120	C₃×#237	—	2	8	no	—
121	C₃×D₃×D₄	—	2	8	no	—
122	C₃×D₃×D₄	—	2	8	no	—
123	C₃×#235	—	2	4	no	—
124	C₃×#235	—	2	4	no	—
125	C₃×#235	—	2	16	no	—
126	C₃×#235	D₄	1	8	yes	complemented
127	C₂×C₃×D₁₂	C₂³	1	4	yes	—
128	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
129	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
130	C₂×C₃×D₁₂	C₂³	1	4	yes	—
131	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
133	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
135	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
136	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
137	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
138	C₂×C₃×Dic₆	C₂³	1	4	yes	—
139	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
140	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
141	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
142	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
143	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
144	C₃²×C₄²	C₂³	1	2	yes	—
145	C₃²×C₄²	C₂³	1	1	yes	characteristic
146	C₃²×C₄²	C₂³	1	1	yes	characteristic
147	C₃×#217	C₂³	1	8	yes	—
148	C₃×#217	C₂³	1	2	yes	—
149	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
154	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
155	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
156	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
157	C₃×C₄×Dic₃	C₂³	1	4	yes	—
158	C₃×C₄×Dic₃	C₂³	1	2	yes	—
159	#3500	—	3	1	no	Sylow
160	C₃×2₋¹⁺⁴	—	6	8	no	—
161	C₃×H(5,𝔽₂)	—	6	8	no	—
162	C₂×C₃×#41	—	3	2	no	—
163	C₂×C₃×#41	—	3	2	no	—
164	C₂×C₃×#41	—	3	2	no	—
165	C₂×C₃×#41	—	3	2	no	—
166	C₂×C₃×#41	—	3	1	no	—
167	C₂×C₃×#41	—	3	1	no	—
168	C₂×C₃×#41	—	3	1	no	—
169	C₂×C₃×#41	—	3	4	no	—
170	C₂²×C₃×Q₈	—	2	1	no	—
171	C₂²×C₃×Q₈	—	3	2	no	—
172	C₂²×C₃×Q₈	—	3	2	no	—
173	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
174	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂²×C₃×D₄	—	2	1	no	—
176	C₂²×C₃×D₄	—	3	4	no	—
177	C₂²×C₃×D₄	—	3	2	no	—
178	C₂²×C₃×D₄	—	3	2	no	—
179	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
181	C₂²×#67	C₂²×C₃	1	4	yes	—
182	#1007	—	2	8	no	—
183	C₂×#239	C₂²×C₃	1	2	yes	complemented
184	C₂×#239	C₂²×C₃	1	2	yes	complemented
185	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
186	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
187	#1004	—	2	8	no	—
188	C₂×#237	C₂²×C₃	1	2	yes	—
189	C₂×#237	C₂²×C₃	1	2	yes	—
190	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
191	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
192	C₂×#235	C₂²×C₃	1	1	yes	characteristic
193	C₂×#235	C₂²×C₃	1	1	yes	characteristic
194	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×#235	C₂²×C₃	1	4	yes	complemented
196	C₃×C₄⋊Q₈	—	3	2	no	—
197	C₃×C₄⋊Q₈	—	3	1	no	—
198	C₃×#127	—	3	2	no	—
199	C₃×#127	—	3	1	no	—
200	C₃×#124	—	2	2	no	—
201	C₃×#124	—	2	2	no	—
202	C₃×#124	—	2	4	no	—
203	C₃×#124	—	3	2	no	—
204	C₃×#124	—	3	2	no	—
205	C₃×#124	—	3	8	no	—
206	C₃×#124	—	3	1	no	—
207	C₃×#124	—	3	1	no	—
208	C₃×#124	C₂×D₃	1	2	yes	complemented
209	C₃×#124	C₂×D₃	1	2	yes	complemented
210	C₃×#124	C₂×D₃	1	4	yes	complemented
211	C₃×#124	C₂²×C₃	1	2	yes	complemented
212	C₃×#124	C₂²×C₃	1	2	yes	complemented
213	C₃×#124	C₂²×C₃	1	4	yes	complemented
214	C₃×#123	—	3	4	no	—
215	C₃×#123	—	3	8	no	—
216	C₃×C₂²⋊Q₈	—	3	4	no	—
217	C₃×C₂²⋊Q₈	—	3	8	no	—
218	C₃×#121	—	3	4	no	—
219	C₃×#121	—	3	4	no	—
220	C₃×#121	—	3	8	no	—
221	C₃×#121	—	3	8	no	—
222	C₃×#120	—	3	4	no	—
223	C₃×#120	—	3	8	no	—
224	C₃×C₄×Q₈	—	3	2	no	—
225	C₃×C₄×D₄	—	3	4	no	—
226	C₃×C₄×D₄	—	3	8	no	—
227	C₃×C₄×D₄	—	3	2	no	—
228	C₃×C₄×D₄	—	3	4	no	—
229	C₃×#117	—	3	1	no	—
230	C₃×#117	—	3	2	no	—
231	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
233	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
234	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
235	C₂×C₃×C₄²	—	2	1	no	—
236	C₂×C₃×C₄²	—	3	2	no	—
237	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
238	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
239	#953	C₂²×C₃	1	4	yes	complemented
240	#947	C₂²×C₃	1	2	yes	complemented
241	#946	C₂²×C₃	1	4	yes	complemented
242	#944	C₂²×C₃	1	2	yes	complemented
243	#940	C₂²×C₃	1	2	yes	complemented
244	#938	C₂²×C₃	1	4	yes	complemented
245	#936	C₂²×C₃	1	2	yes	complemented
246	#930	C₂²×C₃	1	4	yes	complemented
247	#929	C₂²×C₃	1	4	yes	complemented
248	C₄×#67	C₂²×C₃	1	4	yes	complemented
249	#926	C₂²×C₃	1	1	yes	characteristic, complemented
250	#885	C₂²×C₃	1	8	yes	complemented
251	#884	C₂²×C₃	1	8	yes	complemented
252	#884	C₂²×C₃	1	8	yes	complemented
253	#883	C₂²×C₃	1	8	yes	complemented
254	#882	C₂²×C₃	1	8	yes	complemented
255	#67⋊C₄	C₂²×C₃	1	8	yes	complemented
256	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
257	#878	C₂²×C₃	1	8	yes	complemented
258	#875	C₂²×C₃	1	1	yes	characteristic, complemented
259	#875	C₂²×C₃	1	1	yes	characteristic, complemented
260	#874	C₂²×C₃	1	1	yes	characteristic, complemented
261	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
262	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
263	#872	C₂²×C₃	1	2	yes	complemented
264	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
265	#869	C₂²×C₃	1	1	yes	characteristic, complemented
266	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
267	C₂³×C₃²	—	2	4	no	—
268	C₂³×C₃²	—	4	4	no	—
269	C₂³×C₃²	C₂⁴	1	4	yes	—
270	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
271	C₂²×C₃×D₃	—	2	8	no	—
272	C₂²×C₃×D₃	—	4	8	no	—
273	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
274	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
275	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
276	C₃²×Q₈	—	2	4	no	—
277	C₃²×Q₈	—	2	4	no	—
278	C₃²×D₄	—	2	4	no	—
279	C₃²×D₄	—	2	4	no	—
280	C₂×C₃²×C₄	—	2	4	no	—
281	C₂×C₃²×C₄	—	4	2	no	—
282	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
283	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
284	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
285	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
286	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
287	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
288	C₃×#67	—	2	4	no	—
289	C₃×#67	—	2	4	no	—
290	C₃×#67	—	2	8	no	—
291	C₃×#67	—	2	8	no	—
292	C₃×#67	—	4	8	no	—
293	C₃×#67	C₂×D₄	1	8	yes	—
294	C₂×C₃×Dic₃	—	2	8	no	—
295	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
296	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
297	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
298	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
299	C₃×D₁₂	—	2	8	no	—
300	C₃×D₁₂	—	2	2	no	—
301	C₃×D₁₂	—	2	2	no	—
302	C₃×D₁₂	—	4	4	no	—
303	C₃×D₁₂	C₂×D₄	1	4	yes	—
304	C₃×C₄×D₃	—	2	8	no	—
305	C₃×C₄×D₃	—	2	4	no	—
306	C₃×C₄×D₃	—	2	4	no	—
307	C₃×C₄×D₃	—	2	8	no	—
308	C₃×C₄×D₃	—	4	4	no	—
309	C₃×C₄×D₃	C₂×D₄	1	8	yes	—
310	C₃×Dic₆	—	2	2	no	—
311	C₃×Dic₆	—	2	2	no	—
312	C₃×Dic₆	—	2	8	no	—
313	C₃×Dic₆	C₂×D₄	1	4	yes	—
314	C₂×2₋¹⁺⁴	—	3	1	no	—
315	C₂×H(5,𝔽₂)	—	3	1	no	—
316	#548	—	3	4	no	—
317	#546	—	3	4	no	—
318	#546	—	3	8	no	—
319	#536	—	3	1	no	—
320	#536	—	3	2	no	—
321	#535	—	3	1	no	—
322	#535	—	3	2	no	—
323	#532	—	3	2	no	—
324	#532	—	3	1	no	—
325	C₂×#124	—	3	2	no	—
326	C₂×#124	C₃×D₃	1	1	yes	characteristic, complemented
327	C₄×#41	—	3	1	no	—
328	C₂⁴×C₃	—	2	2	no	—
329	C₂⁴×C₃	—	3	4	no	—
330	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
331	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
332	C₂³×D₃	C₂³×C₃	1	4	yes	—
333	C₃×#41	—	3	8	no	—
334	C₃×#41	—	6	16	no	—
335	C₃×#41	—	6	8	no	—
336	C₃×#41	—	6	8	no	—
337	C₃×#41	—	6	8	no	—
338	C₃×#41	—	6	8	no	—
339	C₃×#41	—	6	4	no	—
340	C₃×#41	—	6	4	no	—
341	C₂×C₃×Q₈	—	2	4	no	—
342	C₂×C₃×Q₈	—	2	4	no	—
343	C₂×C₃×Q₈	—	2	2	no	—
344	C₂×C₃×Q₈	—	2	2	no	—
345	C₂×C₃×Q₈	—	3	1	no	—
346	C₂×C₃×Q₈	—	3	4	no	—
347	C₂×C₃×Q₈	—	3	1	no	—
348	C₂×C₃×Q₈	—	3	1	no	—
349	C₂×C₃×Q₈	—	4	4	no	—
350	C₂×C₃×Q₈	—	6	8	no	—
351	C₂×C₃×Q₈	—	6	8	no	—
352	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
353	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
354	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
355	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
356	C₂×C₃×D₄	—	2	4	no	—
357	C₂×C₃×D₄	—	2	4	no	—
358	C₂×C₃×D₄	—	2	2	no	—
359	C₂×C₃×D₄	—	2	2	no	—
360	C₂×C₃×D₄	—	3	2	no	—
361	C₂×C₃×D₄	—	3	2	no	—
362	C₂×C₃×D₄	—	3	4	no	—
363	C₂×C₃×D₄	—	3	2	no	—
364	C₂×C₃×D₄	—	3	4	no	—
365	C₂×C₃×D₄	—	3	8	no	—
366	C₂×C₃×D₄	—	3	1	no	—
367	C₂×C₃×D₄	—	3	4	no	—
368	C₂×C₃×D₄	—	3	1	no	—
369	C₂×C₃×D₄	—	3	1	no	—
370	C₂×C₃×D₄	—	3	4	no	—
371	C₂×C₃×D₄	—	4	4	no	—
372	C₂×C₃×D₄	—	6	8	no	—
373	C₂×C₃×D₄	—	6	8	no	—
374	C₂×C₃×D₄	—	6	16	no	—
375	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
376	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
377	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
378	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
379	C₂²×C₃×C₄	—	2	1	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	2	no	—
382	C₂²×C₃×C₄	—	3	2	no	—
383	C₂²×C₃×C₄	—	3	4	no	—
384	C₂²×C₃×C₄	—	3	4	no	—
385	C₂²×C₃×C₄	—	3	4	no	—
386	C₂²×C₃×C₄	—	3	2	no	—
387	C₂²×C₃×C₄	—	3	2	no	—
388	C₂²×C₃×C₄	—	3	4	no	—
389	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
390	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
391	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
393	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
394	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
395	C₂×#67	—	2	16	no	—
396	C₂×#67	C₂³×C₃	1	4	yes	—
397	C₂×#67	C₂³×C₃	1	4	yes	—
398	C₂×#67	C₂³×C₃	1	2	yes	—
399	C₂×#67	C₂³×C₃	1	2	yes	—
400	C₂×#67	C₂³×C₃	1	8	yes	—
401	C₂×#67	C₂³×C₃	1	2	yes	—
402	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
403	#239	—	2	8	no	—
404	#239	—	2	8	no	—
405	D₃×Q₈	—	2	8	no	—
406	D₃×Q₈	—	2	8	no	—
407	#237	—	2	8	no	—
408	#237	—	2	8	no	—
409	D₃×D₄	—	2	8	no	—
410	D₃×D₄	—	2	8	no	—
411	#235	—	2	4	no	—
412	#235	—	2	4	no	—
413	#235	—	2	16	no	—
414	#235	C₃×D₄	1	8	yes	complemented
415	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
416	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
417	C₂×D₁₂	C₂³×C₃	1	4	yes	—
418	C₂×D₁₂	C₂³×C₃	1	4	yes	—
419	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
421	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
422	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
423	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
424	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
425	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
426	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
427	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
428	C₂×Dic₆	C₂³×C₃	1	4	yes	—
429	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
430	C₃×C₄⋊C₄	—	3	4	no	—
431	C₃×C₄⋊C₄	—	3	8	no	—
432	C₃×C₄⋊C₄	—	3	2	no	—
433	C₃×C₄⋊C₄	—	3	4	no	—
434	C₃×C₂²⋊C₄	—	2	8	no	—
435	C₃×C₂²⋊C₄	—	2	8	no	—
436	C₃×C₂²⋊C₄	—	3	8	no	—
437	C₃×C₂²⋊C₄	—	3	2	no	—
438	C₃×C₂²⋊C₄	—	3	4	no	—
439	C₃×C₂²⋊C₄	—	3	8	no	—
440	C₃×C₂²⋊C₄	—	3	4	no	—
441	C₃×C₂²⋊C₄	—	3	4	no	—
442	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
443	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
444	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
445	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
446	C₃×C₄²	—	2	1	no	—
447	C₃×C₄²	—	2	1	no	—
448	C₃×C₄²	—	2	2	no	—
449	C₃×C₄²	—	3	2	no	—
450	C₃×C₄²	—	3	4	no	—
451	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
452	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
453	C₃×C₄²	C₂²×D₃	1	2	yes	—
454	C₃×C₄²	C₂³×C₃	1	2	yes	—
455	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
456	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
457	#217	C₂³×C₃	1	8	yes	—
458	#217	C₂³×C₃	1	2	yes	—
459	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
460	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
461	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
462	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
463	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
464	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
465	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
466	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
467	C₄×Dic₃	C₂³×C₃	1	4	yes	—
468	C₄×Dic₃	C₂³×C₃	1	2	yes	—
469	C₂²×C₃²	—	2	2	no	—
470	C₂²×C₃²	—	2	4	no	—
471	C₂²×C₃²	—	2	8	no	—
472	C₂²×C₃²	—	8	4	no	—
473	C₂²×C₃²	C₂²×D₄	1	2	yes	—
474	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
475	C₂×C₃×D₃	—	2	4	no	—
476	C₂×C₃×D₃	—	2	2	no	—
477	C₂×C₃×D₃	—	2	2	no	—
478	C₂×C₃×D₃	—	2	4	no	—
479	C₂×C₃×D₃	—	2	4	no	—
480	C₂×C₃×D₃	—	8	8	no	—
481	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
482	C₃²×C₄	—	2	4	no	—
483	C₃²×C₄	—	2	2	no	—
484	C₃²×C₄	—	2	2	no	—
485	C₃²×C₄	C₂²×D₄	1	2	yes	—
486	C₃²×C₄	C₂²×D₄	1	2	yes	—
487	C₃×Dic₃	—	2	2	no	—
488	C₃×Dic₃	—	2	2	no	—
489	C₃×Dic₃	—	2	4	no	—
490	C₃×Dic₃	C₂²×D₄	1	4	yes	—
491	2₋¹⁺⁴	—	6	8	no	—
492	H(5,𝔽₂)	—	6	8	no	—
493	C₂×#41	—	3	2	no	—
494	C₂×#41	—	3	2	no	—
495	C₂×#41	—	3	2	no	—
496	C₂×#41	—	3	2	no	—
497	C₂×#41	—	3	1	no	—
498	C₂×#41	—	3	1	no	—
499	C₂×#41	—	3	1	no	—
500	C₂×#41	—	3	4	no	—
501	C₂²×Q₈	—	3	2	no	—
502	C₂²×Q₈	—	3	2	no	—
503	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
504	C₂²×D₄	—	3	4	no	—
505	C₂²×D₄	—	3	2	no	—
506	C₂²×D₄	—	3	2	no	—
507	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
508	C₄⋊Q₈	—	3	2	no	—
509	C₄⋊Q₈	—	3	1	no	—
510	#127	—	3	2	no	—
511	#127	—	3	1	no	—
512	#124	—	3	2	no	—
513	#124	—	3	2	no	—
514	#124	—	3	8	no	—
515	#124	—	3	1	no	—
516	#124	—	3	1	no	—
517	#124	C₂×C₃×D₃	1	2	yes	complemented
518	#124	C₂×C₃×D₃	1	2	yes	complemented
519	#124	C₂×C₃×D₃	1	4	yes	complemented
520	#123	—	3	4	no	—
521	#123	—	3	8	no	—
522	C₂²⋊Q₈	—	3	4	no	—
523	C₂²⋊Q₈	—	3	8	no	—
524	#121	—	3	4	no	—
525	#121	—	3	4	no	—
526	#121	—	3	8	no	—
527	#121	—	3	8	no	—
528	#120	—	3	4	no	—
529	#120	—	3	8	no	—
530	C₄×Q₈	—	3	2	no	—
531	C₄×D₄	—	3	4	no	—
532	C₄×D₄	—	3	8	no	—
533	C₄×D₄	—	3	2	no	—
534	C₄×D₄	—	3	4	no	—
535	#117	—	3	1	no	—
536	#117	—	3	2	no	—
537	C₂×C₂²⋊C₄	—	3	8	no	—
538	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
539	C₂×C₄²	—	3	2	no	—
540	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
541	C₂³×C₃	—	2	4	no	—
542	C₂³×C₃	—	2	4	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	4	no	—
545	C₂³×C₃	—	3	2	no	—
546	C₂³×C₃	—	3	2	no	—
547	C₂³×C₃	—	3	2	no	—
548	C₂³×C₃	—	4	4	no	—
549	C₂³×C₃	—	4	4	no	—
550	C₂³×C₃	—	4	4	no	—
551	C₂³×C₃	—	4	8	no	—
552	C₂³×C₃	—	6	8	no	—
553	C₂³×C₃	—	12	8	no	—
554	C₂³×C₃	C₂³×D₃	1	4	yes	—
555	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
556	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
557	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
558	C₂²×D₃	—	2	8	no	—
559	C₂²×D₃	—	4	8	no	—
560	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
561	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
562	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
563	C₃×Q₈	—	2	4	no	—
564	C₃×Q₈	—	2	4	no	—
565	C₃×Q₈	—	2	4	no	—
566	C₃×Q₈	—	2	4	no	—
567	C₃×Q₈	—	3	4	no	—
568	C₃×Q₈	—	4	4	no	—
569	C₃×Q₈	—	4	4	no	—
570	C₃×Q₈	—	6	8	no	—
571	C₃×Q₈	—	6	2	no	—
572	C₃×Q₈	—	6	2	no	—
573	C₃×D₄	—	2	4	no	—
574	C₃×D₄	—	2	4	no	—
575	C₃×D₄	—	2	4	no	—
576	C₃×D₄	—	2	4	no	—
577	C₃×D₄	—	3	8	no	—
578	C₃×D₄	—	3	4	no	—
579	C₃×D₄	—	4	4	no	—
580	C₃×D₄	—	4	4	no	—
581	C₃×D₄	—	6	8	no	—
582	C₃×D₄	—	6	8	no	—
583	C₃×D₄	—	6	8	no	—
584	C₃×D₄	—	6	4	no	—
585	C₃×D₄	—	6	4	no	—
586	C₃×D₄	—	6	2	no	—
587	C₃×D₄	—	6	2	no	—
588	C₃×D₄	—	12	4	no	—
589	C₃×D₄	—	12	8	no	—
590	C₂×C₃×C₄	—	2	4	no	—
591	C₂×C₃×C₄	—	2	4	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	4	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	3	2	no	—
599	C₂×C₃×C₄	—	3	8	no	—
600	C₂×C₃×C₄	—	3	4	no	—
601	C₂×C₃×C₄	—	3	2	no	—
602	C₂×C₃×C₄	—	3	2	no	—
603	C₂×C₃×C₄	—	4	4	no	—
604	C₂×C₃×C₄	—	4	2	no	—
605	C₂×C₃×C₄	—	4	2	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	—	6	8	no	—
608	C₂×C₃×C₄	—	6	8	no	—
609	C₂×C₃×C₄	—	6	8	no	—
610	C₂×C₃×C₄	—	6	4	no	—
611	C₂×C₃×C₄	—	6	4	no	—
612	C₂×C₃×C₄	—	12	4	no	—
613	C₂×C₃×C₄	D₃×D₄	1	4	yes	—
614	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
615	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
616	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
617	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
618	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
621	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
622	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
623	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
624	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
625	#67	—	2	4	no	—
626	#67	—	2	4	no	—
627	#67	—	2	8	no	—
628	#67	—	2	8	no	—
629	#67	—	4	8	no	—
630	#67	C₂×C₃×D₄	1	8	yes	—
631	C₂×Dic₃	—	2	8	no	—
632	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
633	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
634	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
635	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
636	D₁₂	—	2	8	no	—
637	D₁₂	—	2	2	no	—
638	D₁₂	—	2	2	no	—
639	D₁₂	—	4	4	no	—
640	D₁₂	C₂×C₃×D₄	1	4	yes	—
641	C₄×D₃	—	2	8	no	—
642	C₄×D₃	—	2	4	no	—
643	C₄×D₃	—	2	4	no	—
644	C₄×D₃	—	2	8	no	—
645	C₄×D₃	—	4	4	no	—
646	C₄×D₃	C₂×C₃×D₄	1	8	yes	—
647	Dic₆	—	2	2	no	—
648	Dic₆	—	2	2	no	—
649	Dic₆	—	2	8	no	—
650	Dic₆	C₂×C₃×D₄	1	4	yes	—
651	C₂×C₃²	—	2	2	no	—
652	C₂×C₃²	—	4	4	no	—
653	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
654	C₂×C₃²	#585	1	2	yes	—
655	C₃×D₃	—	2	4	no	—
656	C₃×D₃	—	4	2	no	—
657	C₃×D₃	—	4	2	no	—
658	C₂⁴	—	3	4	no	—
659	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
660	#41	—	3	8	no	—
661	#41	—	6	16	no	—
662	#41	—	6	8	no	—
663	#41	—	6	8	no	—
664	#41	—	6	8	no	—
665	#41	—	6	8	no	—
666	#41	—	6	4	no	—
667	#41	—	6	4	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	3	1	no	—
670	C₂×Q₈	—	3	4	no	—
671	C₂×Q₈	—	3	1	no	—
672	C₂×Q₈	—	3	1	no	—
673	C₂×Q₈	—	6	8	no	—
674	C₂×Q₈	—	6	8	no	—
675	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
676	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	3	2	no	—
679	C₂×D₄	—	3	2	no	—
680	C₂×D₄	—	3	4	no	—
681	C₂×D₄	—	3	2	no	—
682	C₂×D₄	—	3	4	no	—
683	C₂×D₄	—	3	8	no	—
684	C₂×D₄	—	3	1	no	—
685	C₂×D₄	—	3	4	no	—
686	C₂×D₄	—	3	1	no	—
687	C₂×D₄	—	3	1	no	—
688	C₂×D₄	—	3	4	no	—
689	C₂×D₄	—	6	8	no	—
690	C₂×D₄	—	6	8	no	—
691	C₂×D₄	—	6	16	no	—
692	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
693	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
694	C₂²×C₄	—	3	2	no	—
695	C₂²×C₄	—	3	4	no	—
696	C₂²×C₄	—	3	4	no	—
697	C₂²×C₄	—	3	4	no	—
698	C₂²×C₄	—	3	2	no	—
699	C₂²×C₄	—	3	2	no	—
700	C₂²×C₄	—	3	4	no	—
701	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
702	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
703	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
704	C₄⋊C₄	—	3	4	no	—
705	C₄⋊C₄	—	3	2	no	—
706	C₄⋊C₄	—	3	8	no	—
707	C₄⋊C₄	—	3	4	no	—
708	C₂²⋊C₄	—	3	8	no	—
709	C₂²⋊C₄	—	3	2	no	—
710	C₂²⋊C₄	—	3	4	no	—
711	C₂²⋊C₄	—	3	8	no	—
712	C₂²⋊C₄	—	3	4	no	—
713	C₂²⋊C₄	—	3	4	no	—
714	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
715	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
716	C₄²	—	3	2	no	—
717	C₄²	—	3	4	no	—
718	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
719	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
720	C₄²	C₂²×C₃×D₃	1	2	yes	—
721	C₂²×C₃	—	2	4	no	—
722	C₂²×C₃	—	2	2	no	—
723	C₂²×C₃	—	2	2	no	—
724	C₂²×C₃	—	2	4	no	—
725	C₂²×C₃	—	2	8	no	—
726	C₂²×C₃	—	2	4	no	—
727	C₂²×C₃	—	2	8	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	1	no	—
730	C₂²×C₃	—	3	4	no	—
731	C₂²×C₃	—	4	4	no	—
732	C₂²×C₃	—	4	8	no	—
733	C₂²×C₃	—	6	4	no	—
734	C₂²×C₃	—	6	2	no	—
735	C₂²×C₃	—	6	2	no	—
736	C₂²×C₃	—	6	4	no	—
737	C₂²×C₃	—	6	4	no	—
738	C₂²×C₃	—	8	4	no	—
739	C₂²×C₃	—	8	4	no	—
740	C₂²×C₃	—	8	8	no	—
741	C₂²×C₃	—	24	8	no	—
742	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
743	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
744	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
745	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
746	C₂×D₃	—	2	4	no	—
747	C₂×D₃	—	2	2	no	—
748	C₂×D₃	—	2	2	no	—
749	C₂×D₃	—	2	4	no	—
750	C₂×D₃	—	2	4	no	—
751	C₂×D₃	—	8	8	no	—
752	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
753	C₃×C₄	—	2	4	no	—
754	C₃×C₄	—	2	2	no	—
755	C₃×C₄	—	2	2	no	—
756	C₃×C₄	—	2	4	no	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	3	4	no	—
762	C₃×C₄	—	4	4	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	6	2	no	—
766	C₃×C₄	—	6	2	no	—
767	C₃×C₄	—	6	4	no	—
768	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
769	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
770	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
771	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
772	Dic₃	—	2	2	no	—
773	Dic₃	—	2	2	no	—
774	Dic₃	—	2	4	no	—
775	Dic₃	C₂²×C₃×D₄	1	4	yes	—
776	C₃²	#3500	1	1	yes	characteristic, complemented, Sylow
777	C₂³	—	2	4	no	—
778	C₂³	—	3	2	no	—
779	C₂³	—	3	2	no	—
780	C₂³	—	3	2	no	—
781	C₂³	—	4	4	no	—
782	C₂³	—	6	8	no	—
783	C₂³	—	12	8	no	—
784	C₂³	C₂³×C₃×D₃	1	4	yes	—
785	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
786	Q₈	—	2	4	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	3	4	no	—
789	Q₈	—	6	8	no	—
790	Q₈	—	6	2	no	—
791	Q₈	—	6	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	4	no	—
794	D₄	—	3	8	no	—
795	D₄	—	3	4	no	—
796	D₄	—	6	8	no	—
797	D₄	—	6	8	no	—
798	D₄	—	6	8	no	—
799	D₄	—	6	4	no	—
800	D₄	—	6	4	no	—
801	D₄	—	6	2	no	—
802	D₄	—	6	2	no	—
803	D₄	—	12	4	no	—
804	D₄	—	12	8	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	3	2	no	—
807	C₂×C₄	—	3	8	no	—
808	C₂×C₄	—	3	4	no	—
809	C₂×C₄	—	3	2	no	—
810	C₂×C₄	—	3	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	6	8	no	—
813	C₂×C₄	—	6	8	no	—
814	C₂×C₄	—	6	8	no	—
815	C₂×C₄	—	6	4	no	—
816	C₂×C₄	—	6	4	no	—
817	C₂×C₄	—	12	4	no	—
818	C₂×C₄	C₃×D₃×D₄	1	4	yes	—
819	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
820	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
821	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
822	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
823	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
824	C₂×C₃	—	2	4	no	—
825	C₂×C₃	—	2	2	no	—
826	C₂×C₃	—	2	2	no	—
827	C₂×C₃	—	2	1	no	—
828	C₂×C₃	—	2	2	no	—
829	C₂×C₃	—	4	4	no	—
830	C₂×C₃	—	4	4	no	—
831	C₂×C₃	—	6	4	no	—
832	C₂×C₃	—	8	4	no	—
833	C₂×C₃	—	12	2	no	—
834	C₂×C₃	—	12	2	no	—
835	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
836	C₂×C₃	#5964	1	2	yes	—
837	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
838	C₂×C₃	C₃×#585	1	2	yes	—
839	D₃	—	2	4	no	—
840	D₃	—	4	2	no	—
841	D₃	—	4	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	8	no	—
845	C₂²	—	3	4	no	—
846	C₂²	—	6	4	no	—
847	C₂²	—	6	2	no	—
848	C₂²	—	6	2	no	—
849	C₂²	—	6	4	no	—
850	C₂²	—	6	4	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	24	8	no	—
853	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
854	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	3	4	no	—
859	C₄	—	6	2	no	—
860	C₄	—	6	2	no	—
861	C₄	—	6	4	no	—
862	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
863	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
864	C₃	—	2	1	no	—
865	C₃	#86076	1	1	yes	characteristic, direct product factor
866	C₃	C₃×#3500	1	1	yes	characteristic, complemented
867	C₂	—	2	2	no	—
868	C₂	—	4	4	no	—
869	C₂	—	6	4	no	—
870	C₂	—	12	2	no	—
871	C₂	—	12	2	no	—
872	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
873	C₂	C₃×#5964	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#124	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×#124	D₃
hypocenter	C₃	C₃×#3500
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1007	C₂	semidirect
2. C₂×C₃×#1004	C₂	semidirect
3. C₂×C₃²×#124	C₂	semidirect
4. C₃×#5816	C₂	semidirect
5. C₃×#5805	C₂	semidirect
6. C₃×#5677	C₂	semidirect
7. C₃×#5676	C₂	semidirect
8. C₃×#5675	C₂	semidirect
9. C₃×#5674	C₂	semidirect
10. C₃×D₃×#124	C₂	semidirect
11. C₃×#5668	C₂	semidirect
12. C₃×#5490	C₂	semidirect
13. C₃×#5477	C₂	semidirect
14. C₃×C₄×#235	C₂	semidirect
16. #86076	C₃	direct (N × H)
17. C₂²×C₃²×Q₈	C₂²	semidirect
21. C₂×C₃×#239	C₂²	semidirect
22. C₂×C₃×#239	C₂²	semidirect
23. C₂×C₃×D₃×Q₈	C₂²	semidirect
24. C₂×C₃×D₃×Q₈	C₂²	semidirect
32. C₂×C₃×#235	C₂²	semidirect
33. C₂×C₃×#235	C₂²	semidirect
34. C₃²×#124	C₂²	semidirect
35. C₃²×#124	C₂²	semidirect
36. C₃²×#124	C₂²	semidirect
37. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₃²×C₄²	C₂²	semidirect
39. C₃×#953	C₂²	semidirect
40. C₃×#947	C₂²	semidirect
41. C₃×#946	C₂²	semidirect
42. C₃×#944	C₂²	semidirect
43. C₃×#940	C₂²	semidirect
44. C₃×#938	C₂²	semidirect
45. C₃×#936	C₂²	semidirect
46. C₃×#930	C₂²	semidirect
47. C₃×#929	C₂²	semidirect
48. C₃×C₄×#67	C₂²	semidirect
49. C₃×#926	C₂²	semidirect
50. C₃×#885	C₂²	semidirect
51. C₃×#884	C₂²	semidirect
52. C₃×#884	C₂²	semidirect
53. C₃×#883	C₂²	semidirect
54. C₃×#882	C₂²	semidirect
55. C₃×#67⋊C₄	C₂²	semidirect
56. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
57. C₃×#878	C₂²	semidirect
58. C₃×#875	C₂²	semidirect
59. C₃×#875	C₂²	semidirect
60. C₃×#874	C₂²	semidirect
61. C₃×C₄×D₁₂	C₂²	semidirect
62. C₃×C₄×D₁₂	C₂²	semidirect
63. C₃×#872	C₂²	semidirect
64. C₃×C₄²×D₃	C₂²	semidirect
65. C₃×#869	C₂²	semidirect
66. C₃×C₄×Dic₆	C₂²	semidirect
69. C₂×#1007	C₂×C₃	semidirect
70. C₂×#1004	C₂×C₃	semidirect
82. C₂×C₃×#124	D₃	semidirect
83. C₂×C₃×#124	C₂×C₃	semidirect
85. #5816	C₂×C₃	semidirect
86. #5805	C₂×C₃	semidirect
87. #5677	C₂×C₃	semidirect
88. #5676	C₂×C₃	semidirect
89. #5675	C₂×C₃	semidirect
90. #5674	C₂×C₃	semidirect
91. D₃×#124	C₂×C₃	semidirect
92. #5668	C₂×C₃	semidirect
93. #5490	C₂×C₃	semidirect
94. #5477	C₂×C₃	semidirect
95. C₄×#235	C₂×C₃	semidirect
126. C₃×#235	D₄	semidirect
173. C₂²×C₃×Q₈	C₂×D₃	semidirect
174. C₂²×C₃×Q₈	C₂²×C₃	semidirect
183. C₂×#239	C₂²×C₃	semidirect
184. C₂×#239	C₂²×C₃	semidirect
185. C₂×D₃×Q₈	C₂²×C₃	semidirect
186. C₂×D₃×Q₈	C₂²×C₃	semidirect
194. C₂×#235	C₂²×C₃	semidirect
195. C₂×#235	C₂²×C₃	semidirect
208. C₃×#124	C₂×D₃	semidirect
209. C₃×#124	C₂×D₃	semidirect
210. C₃×#124	C₂×D₃	semidirect
211. C₃×#124	C₂²×C₃	semidirect
212. C₃×#124	C₂²×C₃	semidirect
213. C₃×#124	C₂²×C₃	semidirect
233. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
234. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
237. C₂×C₃×C₄²	C₂×D₃	semidirect
238. C₂×C₃×C₄²	C₂²×C₃	semidirect
239. #953	C₂²×C₃	semidirect
240. #947	C₂²×C₃	semidirect
241. #946	C₂²×C₃	semidirect
242. #944	C₂²×C₃	semidirect
243. #940	C₂²×C₃	semidirect
244. #938	C₂²×C₃	semidirect
245. #936	C₂²×C₃	semidirect
246. #930	C₂²×C₃	semidirect
247. #929	C₂²×C₃	semidirect
248. C₄×#67	C₂²×C₃	semidirect
249. #926	C₂²×C₃	semidirect
250. #885	C₂²×C₃	semidirect
251. #884	C₂²×C₃	semidirect
252. #884	C₂²×C₃	semidirect
253. #883	C₂²×C₃	semidirect
254. #882	C₂²×C₃	semidirect
255. #67⋊C₄	C₂²×C₃	semidirect
256. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
257. #878	C₂²×C₃	semidirect
258. #875	C₂²×C₃	semidirect
259. #875	C₂²×C₃	semidirect
260. #874	C₂²×C₃	semidirect
261. C₄×D₁₂	C₂²×C₃	semidirect
262. C₄×D₁₂	C₂²×C₃	semidirect
263. #872	C₂²×C₃	semidirect
264. C₄²×D₃	C₂²×C₃	semidirect
265. #869	C₂²×C₃	semidirect
266. C₄×Dic₆	C₂²×C₃	semidirect
326. C₂×#124	C₃×D₃	semidirect
414. #235	C₃×D₄	semidirect
503. C₂²×Q₈	C₂×C₃×D₃	semidirect
517. #124	C₂×C₃×D₃	semidirect
518. #124	C₂×C₃×D₃	semidirect
519. #124	C₂×C₃×D₃	semidirect
538. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
540. C₂×C₄²	C₂×C₃×D₃	semidirect
776. C₃²	#3500	semidirect
865. C₃	#86076	direct (N × H)
866. C₃	C₃×#3500	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1007	2
C₂×C₃×#1004	2
C₂×C₃²×#124	2
C₃×#5816	2
C₃×#5805	2
C₃×#5677	2
C₃×#5676	2
C₃×#5675	2
C₃×#5674	2
C₃×D₃×#124	2
C₃×#5668	2
C₃×#5490	2
C₃×#5477	2
C₃×C₄×#235	2
C₃×#3500	3
#86076	3

Subgroups — C3×#86076 #11906075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86076 #11906075