Subgroups — C₃×#87268 #11901181

Order 1152.

3557 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5833	C₂	1	4	yes	maximal, complemented
4	C₃×#5832	C₂	1	4	yes	maximal, complemented
5	C₃×#5830	C₂	1	2	yes	maximal, complemented
6	C₃×#5828	C₂	1	4	yes	maximal, complemented
7	C₃×#5825	C₂	1	2	yes	maximal, complemented
8	C₃×#5816	C₂	1	2	yes	maximal, complemented
9	C₃×#5805	C₂	1	2	yes	maximal, complemented
10	C₃×#5804	C₂	1	4	yes	maximal, complemented
11	C₃×#5791	C₂	1	4	yes	maximal, complemented
12	C₂×C₃×#926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3449	—	3	1	no	maximal
14	#87268	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂×C₃²×#41	—	2	8	no	—
16	C₂×C₃²×#41	C₂²	1	2	yes	—
17	C₂×C₃²×#41	C₂²	1	2	yes	—
18	C₂×C₃²×#41	C₂²	1	2	yes	complemented
19	C₂×C₃²×#41	C₂²	1	2	yes	complemented
20	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃²×D₄	C₂²	1	2	yes	—
22	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
24	C₂³×C₃²×C₄	C₂²	1	2	yes	complemented
25	C₂²×C₃×#67	C₂²	1	2	yes	—
26	C₂×C₃×#235	—	2	8	no	—
27	C₂×C₃×#235	C₂²	1	2	yes	—
28	C₂×C₃×#235	C₂²	1	2	yes	—
29	C₂×C₃×#235	C₂²	1	2	yes	complemented
30	C₂×C₃×#235	C₂²	1	2	yes	complemented
31	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
33	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
34	C₃×#953	C₂²	1	8	yes	complemented
35	C₂×C₃×#217	C₂²	1	2	yes	—
36	C₃×#947	C₂²	1	4	yes	complemented
37	C₃×#946	C₂²	1	8	yes	complemented
38	C₃×#944	C₂²	1	4	yes	complemented
39	C₃×#940	C₂²	1	4	yes	complemented
40	C₃×#939	C₂²	1	16	yes	complemented
41	C₃×#938	C₂²	1	8	yes	complemented
42	C₃×#937	C₂²	1	8	yes	complemented
43	C₃×#936	C₂²	1	4	yes	complemented
44	C₃×#935	C₂²	1	8	yes	complemented
45	C₃×#930	C₂²	1	8	yes	complemented
46	C₃×#929	C₂²	1	8	yes	complemented
47	C₃×C₄×#67	C₂²	1	16	yes	complemented
48	C₃×#926	C₂²	1	2	yes	complemented
49	C₃×#926	C₂²	1	2	yes	complemented
50	C₃×#926	C₂²	1	2	yes	complemented
51	C₃×#926	C₂²	1	2	yes	complemented
52	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
53	C₃×#924	C₂²	1	8	yes	complemented
54	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
55	C₂²×C₃×#41	—	2	1	no	—
56	C₂²×C₃×#41	—	3	1	no	—
57	C₂²×C₃×#41	D₃	1	1	yes	characteristic, complemented
58	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂²×#235	C₂×C₃	1	1	yes	characteristic, complemented
60	C₃×#537	—	3	4	no	—
61	C₃×#536	—	3	2	no	—
62	C₃×#536	—	3	2	no	—
63	C₃×#535	—	3	2	no	—
64	C₃×#535	—	3	2	no	—
65	C₃×#534	—	3	4	no	—
66	C₃×#532	—	3	4	no	—
67	C₃×#525	—	3	4	no	—
68	C₃×#525	—	3	4	no	—
69	C₂×C₃×#117	—	3	1	no	—
70	#5833	C₂×C₃	1	4	yes	complemented
71	#5832	C₂×C₃	1	4	yes	complemented
72	#5830	C₂×C₃	1	2	yes	complemented
73	#5828	C₂×C₃	1	4	yes	complemented
74	#5825	C₂×C₃	1	2	yes	complemented
75	#5816	C₂×C₃	1	2	yes	complemented
76	#5805	C₂×C₃	1	2	yes	complemented
77	#5804	C₂×C₃	1	4	yes	complemented
78	#5791	C₂×C₃	1	4	yes	complemented
79	C₂×#926	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂⁴×C₃²	C₂³	1	2	yes	—
81	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
82	C₂³×C₃×D₃	C₂³	1	2	yes	—
83	C₃²×#41	—	2	8	no	—
84	C₃²×#41	—	2	8	no	—
85	C₃²×#41	—	2	8	no	—
86	C₃²×#41	—	2	8	no	—
87	C₂×C₃²×Q₈	—	2	4	no	—
88	C₂×C₃²×Q₈	C₂³	1	2	yes	—
89	C₂×C₃²×Q₈	C₂³	1	2	yes	—
90	C₂×C₃²×D₄	—	2	8	no	—
91	C₂×C₃²×D₄	—	2	4	no	—
92	C₂×C₃²×D₄	C₂³	1	4	yes	—
93	C₂×C₃²×D₄	C₂³	1	2	yes	—
94	C₂×C₃²×D₄	C₂³	1	2	yes	—
95	C₂×C₃²×D₄	C₂³	1	4	yes	—
96	C₂²×C₃²×C₄	—	2	8	no	—
97	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
98	C₂²×C₃²×C₄	C₂³	1	4	yes	—
99	C₂²×C₃²×C₄	C₂³	1	4	yes	—
100	C₂²×C₃²×C₄	C₂³	1	2	yes	—
101	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
103	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
104	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₂×C₃×#67	—	2	8	no	—
108	C₂×C₃×#67	C₂³	1	4	yes	—
109	C₂×C₃×#67	C₂³	1	4	yes	—
110	C₂×C₃×#67	C₂³	1	16	yes	—
111	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
112	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
113	C₃×#235	—	2	8	no	—
114	C₃×#235	—	2	8	no	—
115	C₃×#235	—	2	8	no	—
116	C₃×#235	—	2	8	no	—
117	C₂×C₃×D₁₂	—	2	4	no	—
118	C₂×C₃×D₁₂	C₂³	1	2	yes	—
119	C₂×C₃×D₁₂	C₂³	1	2	yes	—
120	C₂×C₃×C₄×D₃	—	2	8	no	—
121	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
122	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
123	C₂×C₃×Dic₆	—	2	4	no	—
124	C₂×C₃×Dic₆	C₂³	1	2	yes	—
125	C₂×C₃×Dic₆	C₂³	1	2	yes	—
126	C₃×#217	C₂³	1	16	yes	—
127	C₃×#217	C₂³	1	4	yes	—
128	C₃×#217	C₂³	1	4	yes	—
129	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
130	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
131	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
132	C₃×Dic₃⋊C₄	C₂³	1	16	yes	—
133	C₃×C₄×Dic₃	C₂³	1	4	yes	—
134	C₃×C₄×Dic₃	C₂³	1	4	yes	—
135	#3449	—	3	1	no	Sylow
136	C₂×C₃×#41	—	2	16	no	—
137	C₂×C₃×#41	—	2	8	no	—
138	C₂×C₃×#41	—	2	8	no	—
139	C₂×C₃×#41	—	2	2	no	—
140	C₂×C₃×#41	—	2	2	no	—
141	C₂×C₃×#41	—	2	2	no	—
142	C₂×C₃×#41	—	2	2	no	—
143	C₂×C₃×#41	—	3	2	no	—
144	C₂×C₃×#41	—	3	2	no	—
145	C₂×C₃×#41	—	3	2	no	—
146	C₂×C₃×#41	—	3	2	no	—
147	C₂×C₃×#41	—	6	8	no	—
148	C₂×C₃×#41	C₂×D₃	1	2	yes	—
149	C₂×C₃×#41	C₂×D₃	1	2	yes	—
150	C₂×C₃×#41	C₂×D₃	1	2	yes	complemented
151	C₂×C₃×#41	C₂×D₃	1	2	yes	complemented
152	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
153	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
154	C₂×C₃×#41	C₂²×C₃	1	2	yes	complemented
155	C₂×C₃×#41	C₂²×C₃	1	2	yes	complemented
156	C₂²×C₃×Q₈	—	2	1	no	—
157	C₂²×C₃×Q₈	—	3	1	no	—
158	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₂²×C₃×D₄	—	2	2	no	—
161	C₂²×C₃×D₄	—	2	1	no	—
162	C₂²×C₃×D₄	—	3	2	no	—
163	C₂²×C₃×D₄	—	3	1	no	—
164	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
165	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
166	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
167	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂³×C₃×C₄	—	2	1	no	—
169	C₂³×C₃×C₄	—	2	2	no	—
170	C₂³×C₃×C₄	—	3	2	no	—
171	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂×D₃	1	2	yes	complemented
173	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	complemented
175	C₂²×#67	C₂²×C₃	1	2	yes	—
176	C₂×#235	—	2	8	no	—
177	C₂×#235	C₂²×C₃	1	2	yes	—
178	C₂×#235	C₂²×C₃	1	2	yes	—
179	C₂×#235	C₂²×C₃	1	2	yes	complemented
180	C₂×#235	C₂²×C₃	1	2	yes	complemented
181	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
183	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₃×C₄⋊Q₈	—	3	4	no	—
185	C₃×#127	—	3	4	no	—
186	C₃×#124	—	3	4	no	—
187	C₃×#124	—	3	4	no	—
188	C₃×#123	—	3	8	no	—
189	C₃×#123	—	3	8	no	—
190	C₃×C₂²⋊Q₈	—	3	8	no	—
191	C₃×C₂²⋊Q₈	—	3	8	no	—
192	C₃×#121	—	3	8	no	—
193	C₃×#121	—	3	16	no	—
194	C₃×#121	—	3	8	no	—
195	C₃×#120	—	3	8	no	—
196	C₃×#120	—	3	8	no	—
197	C₃×C₄×D₄	—	3	16	no	—
198	C₃×#117	—	3	2	no	—
199	C₃×#117	—	3	2	no	—
200	C₃×#117	—	3	2	no	—
201	C₃×#117	—	3	2	no	—
202	C₂×C₃×C₄⋊C₄	—	3	2	no	—
203	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
204	C₂×C₃×C₄²	—	3	2	no	—
205	#953	C₂²×C₃	1	8	yes	complemented
206	C₂×#217	C₂²×C₃	1	2	yes	—
207	#947	C₂²×C₃	1	4	yes	complemented
208	#946	C₂²×C₃	1	8	yes	complemented
209	#944	C₂²×C₃	1	4	yes	complemented
210	#940	C₂²×C₃	1	4	yes	complemented
211	#939	C₂²×C₃	1	16	yes	complemented
212	#938	C₂²×C₃	1	8	yes	complemented
213	#937	C₂²×C₃	1	8	yes	complemented
214	#936	C₂²×C₃	1	4	yes	complemented
215	#935	C₂²×C₃	1	8	yes	complemented
216	#930	C₂²×C₃	1	8	yes	complemented
217	#929	C₂²×C₃	1	8	yes	complemented
218	C₄×#67	C₂²×C₃	1	16	yes	complemented
219	#926	C₂²×C₃	1	2	yes	complemented
220	#926	C₂²×C₃	1	2	yes	complemented
221	#926	C₂²×C₃	1	2	yes	complemented
222	#926	C₂²×C₃	1	2	yes	complemented
223	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
224	#924	C₂²×C₃	1	8	yes	complemented
225	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
226	C₂³×C₃²	—	2	4	no	—
227	C₂³×C₃²	—	4	2	no	—
228	C₂³×C₃²	—	4	4	no	—
229	C₂³×C₃²	C₂×D₄	1	4	yes	—
230	C₂³×C₃²	C₂⁴	1	4	yes	—
231	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
232	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
233	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
234	C₂²×C₃×D₃	—	2	4	no	—
235	C₂²×C₃×D₃	—	4	4	no	—
236	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
237	C₃²×Q₈	—	2	4	no	—
238	C₃²×Q₈	—	2	4	no	—
239	C₃²×D₄	—	2	8	no	—
240	C₃²×D₄	—	2	8	no	—
241	C₃²×D₄	—	2	4	no	—
242	C₃²×D₄	—	2	4	no	—
243	C₂×C₃²×C₄	—	2	4	no	—
244	C₂×C₃²×C₄	—	2	8	no	—
245	C₂×C₃²×C₄	—	2	8	no	—
246	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
247	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
248	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
249	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
250	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
251	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
252	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
253	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
254	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
256	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
257	C₃×#67	—	2	8	no	—
258	C₃×#67	—	2	8	no	—
259	C₃×#67	—	4	16	no	—
260	C₂×C₃×Dic₃	—	2	4	no	—
261	C₂×C₃×Dic₃	—	4	4	no	—
262	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
263	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
264	C₃×D₁₂	—	2	4	no	—
265	C₃×D₁₂	—	2	4	no	—
266	C₃×C₄×D₃	—	2	8	no	—
267	C₃×C₄×D₃	—	2	8	no	—
268	C₃×Dic₆	—	2	4	no	—
269	C₃×Dic₆	—	2	4	no	—
270	C₂²×#41	—	3	1	no	—
271	C₂²×#41	C₃×D₃	1	1	yes	characteristic, complemented
272	#537	—	3	4	no	—
273	#536	—	3	2	no	—
274	#536	—	3	2	no	—
275	#535	—	3	2	no	—
276	#535	—	3	2	no	—
277	#534	—	3	4	no	—
278	#532	—	3	4	no	—
279	#525	—	3	4	no	—
280	#525	—	3	4	no	—
281	C₂×#117	—	3	1	no	—
282	C₂⁴×C₃	—	2	2	no	—
283	C₂⁴×C₃	—	2	1	no	—
284	C₂⁴×C₃	—	3	2	no	—
285	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
286	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
287	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
288	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
289	C₂³×D₃	C₂³×C₃	1	2	yes	—
290	C₃×#41	—	2	16	no	—
291	C₃×#41	—	2	16	no	—
292	C₃×#41	—	2	16	no	—
293	C₃×#41	—	2	16	no	—
294	C₃×#41	—	2	8	no	—
295	C₃×#41	—	2	8	no	—
296	C₃×#41	—	2	8	no	—
297	C₃×#41	—	2	8	no	—
298	C₃×#41	—	2	8	no	—
299	C₃×#41	—	2	8	no	—
300	C₃×#41	—	2	8	no	—
301	C₃×#41	—	2	8	no	—
302	C₃×#41	—	6	8	no	—
303	C₃×#41	—	6	8	no	—
304	C₃×#41	—	6	8	no	—
305	C₃×#41	—	6	8	no	—
306	C₂×C₃×Q₈	—	2	8	no	—
307	C₂×C₃×Q₈	—	2	4	no	—
308	C₂×C₃×Q₈	—	2	4	no	—
309	C₂×C₃×Q₈	—	2	2	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	3	2	no	—
312	C₂×C₃×Q₈	—	3	2	no	—
313	C₂×C₃×Q₈	—	6	4	no	—
314	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
315	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
316	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
317	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
318	C₂×C₃×D₄	—	2	16	no	—
319	C₂×C₃×D₄	—	2	8	no	—
320	C₂×C₃×D₄	—	2	8	no	—
321	C₂×C₃×D₄	—	2	8	no	—
322	C₂×C₃×D₄	—	2	4	no	—
323	C₂×C₃×D₄	—	2	4	no	—
324	C₂×C₃×D₄	—	2	4	no	—
325	C₂×C₃×D₄	—	2	4	no	—
326	C₂×C₃×D₄	—	2	2	no	—
327	C₂×C₃×D₄	—	2	2	no	—
328	C₂×C₃×D₄	—	3	4	no	—
329	C₂×C₃×D₄	—	3	4	no	—
330	C₂×C₃×D₄	—	3	16	no	—
331	C₂×C₃×D₄	—	3	2	no	—
332	C₂×C₃×D₄	—	3	2	no	—
333	C₂×C₃×D₄	—	6	8	no	—
334	C₂×C₃×D₄	—	6	4	no	—
335	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
336	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
337	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
338	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
339	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
340	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
341	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
342	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
343	C₂²×C₃×C₄	—	2	16	no	—
344	C₂²×C₃×C₄	—	2	8	no	—
345	C₂²×C₃×C₄	—	2	8	no	—
346	C₂²×C₃×C₄	—	2	8	no	—
347	C₂²×C₃×C₄	—	2	1	no	—
348	C₂²×C₃×C₄	—	2	2	no	—
349	C₂²×C₃×C₄	—	2	1	no	—
350	C₂²×C₃×C₄	—	2	4	no	—
351	C₂²×C₃×C₄	—	2	4	no	—
352	C₂²×C₃×C₄	—	2	1	no	—
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂²×C₃×C₄	—	2	1	no	—
355	C₂²×C₃×C₄	—	2	1	no	—
356	C₂²×C₃×C₄	—	3	2	no	—
357	C₂²×C₃×C₄	—	3	4	no	—
358	C₂²×C₃×C₄	—	3	4	no	—
359	C₂²×C₃×C₄	—	3	4	no	—
360	C₂²×C₃×C₄	—	6	8	no	—
361	C₂²×C₃×C₄	#67	1	8	yes	complemented
362	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
363	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
364	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
365	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
366	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
368	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
373	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
374	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
375	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
381	C₂×#67	—	2	8	no	—
382	C₂×#67	C₂³×C₃	1	4	yes	—
383	C₂×#67	C₂³×C₃	1	4	yes	—
384	C₂×#67	C₂³×C₃	1	16	yes	—
385	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
386	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
387	#235	—	2	8	no	—
388	#235	—	2	8	no	—
389	#235	—	2	8	no	—
390	#235	—	2	8	no	—
391	C₂×D₁₂	—	2	4	no	—
392	C₂×D₁₂	C₂³×C₃	1	2	yes	—
393	C₂×D₁₂	C₂³×C₃	1	2	yes	—
394	C₂×C₄×D₃	—	2	8	no	—
395	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
396	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
397	C₂×Dic₆	—	2	4	no	—
398	C₂×Dic₆	C₂³×C₃	1	2	yes	—
399	C₂×Dic₆	C₂³×C₃	1	2	yes	—
400	C₃×C₄⋊C₄	—	3	16	no	—
401	C₃×C₄⋊C₄	—	3	4	no	—
402	C₃×C₄⋊C₄	—	3	4	no	—
403	C₃×C₂²⋊C₄	—	3	4	no	—
404	C₃×C₂²⋊C₄	—	3	4	no	—
405	C₃×C₂²⋊C₄	—	3	16	no	—
406	C₃×C₂²⋊C₄	—	3	16	no	—
407	C₃×C₄²	—	3	4	no	—
408	C₃×C₄²	—	3	4	no	—
409	#217	C₂³×C₃	1	16	yes	—
410	#217	C₂³×C₃	1	4	yes	—
411	#217	C₂³×C₃	1	4	yes	—
412	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	—
413	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
414	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
415	Dic₃⋊C₄	C₂³×C₃	1	16	yes	—
416	C₄×Dic₃	C₂³×C₃	1	4	yes	—
417	C₄×Dic₃	C₂³×C₃	1	4	yes	—
418	C₂²×C₃²	—	2	2	no	—
419	C₂²×C₃²	—	2	4	no	—
420	C₂²×C₃²	—	2	2	no	—
421	C₂²×C₃²	—	2	2	no	—
422	C₂²×C₃²	—	2	8	no	—
423	C₂²×C₃²	—	4	4	no	—
424	C₂²×C₃²	—	4	8	no	—
425	C₂²×C₃²	C₂²×D₄	1	2	yes	—
426	C₂²×C₃²	C₂²×D₄	1	2	yes	—
427	C₂²×C₃²	C₂²×D₄	1	2	yes	—
428	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
429	C₂×C₃×D₃	—	2	4	no	—
430	C₂×C₃×D₃	—	2	8	no	—
431	C₂×C₃×D₃	—	4	8	no	—
432	C₃²×C₄	—	2	4	no	—
433	C₃²×C₄	C₂²×D₄	1	2	yes	—
434	C₃²×C₄	C₂²×D₄	1	2	yes	—
435	C₃²×C₄	C₂²×D₄	1	2	yes	—
436	C₃²×C₄	C₂²×D₄	1	2	yes	—
437	C₃×Dic₃	—	2	4	no	—
438	C₃×Dic₃	—	2	8	no	—
439	C₂×#41	—	2	8	no	—
440	C₂×#41	—	3	2	no	—
441	C₂×#41	—	3	2	no	—
442	C₂×#41	—	3	2	no	—
443	C₂×#41	—	3	2	no	—
444	C₂×#41	—	6	8	no	—
445	C₂×#41	C₂×C₃×D₃	1	2	yes	—
446	C₂×#41	C₂×C₃×D₃	1	2	yes	—
447	C₂×#41	C₂×C₃×D₃	1	2	yes	complemented
448	C₂×#41	C₂×C₃×D₃	1	2	yes	complemented
449	C₂²×Q₈	—	3	1	no	—
450	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
451	C₂²×D₄	—	3	2	no	—
452	C₂²×D₄	—	3	1	no	—
453	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
454	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
455	C₂³×C₄	—	3	2	no	—
456	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
457	C₂³×C₄	C₂×C₃×D₃	1	2	yes	complemented
458	C₄⋊Q₈	—	3	4	no	—
459	#127	—	3	4	no	—
460	#124	—	3	4	no	—
461	#124	—	3	4	no	—
462	#123	—	3	8	no	—
463	#123	—	3	8	no	—
464	C₂²⋊Q₈	—	3	8	no	—
465	C₂²⋊Q₈	—	3	8	no	—
466	#121	—	3	8	no	—
467	#121	—	3	16	no	—
468	#121	—	3	8	no	—
469	#120	—	3	8	no	—
470	#120	—	3	8	no	—
471	C₄×D₄	—	3	16	no	—
472	#117	—	3	2	no	—
473	#117	—	3	2	no	—
474	#117	—	3	2	no	—
475	#117	—	3	2	no	—
476	C₂×C₄⋊C₄	—	3	2	no	—
477	C₂×C₂²⋊C₄	—	3	2	no	—
478	C₂×C₄²	—	3	2	no	—
479	C₂³×C₃	—	2	8	no	—
480	C₂³×C₃	—	2	4	no	—
481	C₂³×C₃	—	2	4	no	—
482	C₂³×C₃	—	2	1	no	—
483	C₂³×C₃	—	2	4	no	—
484	C₂³×C₃	—	2	1	no	—
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	2	4	no	—
487	C₂³×C₃	—	3	4	no	—
488	C₂³×C₃	—	4	2	no	—
489	C₂³×C₃	—	4	4	no	—
490	C₂³×C₃	—	4	2	no	—
491	C₂³×C₃	—	4	4	no	—
492	C₂³×C₃	—	4	4	no	—
493	C₂³×C₃	—	4	8	no	—
494	C₂³×C₃	—	6	4	no	—
495	C₂³×C₃	—	12	4	no	—
496	C₂³×C₃	C₂×#67	1	4	yes	—
497	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
498	C₂³×C₃	C₂³×D₃	1	4	yes	—
499	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
500	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
501	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
502	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
503	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
504	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
505	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
506	C₂²×D₃	—	2	4	no	—
507	C₂²×D₃	—	4	4	no	—
508	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
509	C₃×Q₈	—	2	8	no	—
510	C₃×Q₈	—	2	8	no	—
511	C₃×Q₈	—	2	4	no	—
512	C₃×Q₈	—	2	4	no	—
513	C₃×Q₈	—	2	4	no	—
514	C₃×Q₈	—	2	4	no	—
515	C₃×Q₈	—	6	4	no	—
516	C₃×Q₈	—	6	4	no	—
517	C₃×D₄	—	2	16	no	—
518	C₃×D₄	—	2	16	no	—
519	C₃×D₄	—	2	8	no	—
520	C₃×D₄	—	2	8	no	—
521	C₃×D₄	—	2	8	no	—
522	C₃×D₄	—	2	8	no	—
523	C₃×D₄	—	2	8	no	—
524	C₃×D₄	—	2	8	no	—
525	C₃×D₄	—	2	4	no	—
526	C₃×D₄	—	2	4	no	—
527	C₃×D₄	—	2	4	no	—
528	C₃×D₄	—	2	4	no	—
529	C₃×D₄	—	6	8	no	—
530	C₃×D₄	—	6	8	no	—
531	C₃×D₄	—	6	4	no	—
532	C₃×D₄	—	6	4	no	—
533	C₃×D₄	—	12	16	no	—
534	C₂×C₃×C₄	—	2	8	no	—
535	C₂×C₃×C₄	—	2	16	no	—
536	C₂×C₃×C₄	—	2	16	no	—
537	C₂×C₃×C₄	—	2	4	no	—
538	C₂×C₃×C₄	—	2	4	no	—
539	C₂×C₃×C₄	—	2	8	no	—
540	C₂×C₃×C₄	—	2	8	no	—
541	C₂×C₃×C₄	—	2	8	no	—
542	C₂×C₃×C₄	—	2	8	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	4	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	4	no	—
549	C₂×C₃×C₄	—	2	4	no	—
550	C₂×C₃×C₄	—	2	4	no	—
551	C₂×C₃×C₄	—	2	4	no	—
552	C₂×C₃×C₄	—	2	4	no	—
553	C₂×C₃×C₄	—	2	4	no	—
554	C₂×C₃×C₄	—	3	8	no	—
555	C₂×C₃×C₄	—	3	4	no	—
556	C₂×C₃×C₄	—	6	4	no	—
557	C₂×C₃×C₄	—	6	8	no	—
558	C₂×C₃×C₄	—	6	8	no	—
559	C₂×C₃×C₄	—	12	4	no	—
560	C₂×C₃×C₄	C₂×#67	1	4	yes	—
561	C₂×C₃×C₄	C₂×#67	1	4	yes	—
562	C₂×C₃×C₄	C₂×#67	1	4	yes	—
563	C₂×C₃×C₄	C₂×#67	1	4	yes	—
564	C₂×C₃×C₄	C₂×#67	1	4	yes	—
565	C₂×C₃×C₄	C₂×#67	1	4	yes	—
566	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
567	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
568	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
569	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
570	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
571	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
572	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
573	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
578	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
582	#67	—	2	8	no	—
583	#67	—	2	8	no	—
584	#67	—	4	16	no	—
585	C₂×Dic₃	—	2	4	no	—
586	C₂×Dic₃	—	4	4	no	—
587	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
588	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
589	D₁₂	—	2	4	no	—
590	D₁₂	—	2	4	no	—
591	C₄×D₃	—	2	8	no	—
592	C₄×D₃	—	2	8	no	—
593	Dic₆	—	2	4	no	—
594	Dic₆	—	2	4	no	—
595	C₂×C₃²	—	2	2	no	—
596	C₂×C₃²	—	2	2	no	—
597	C₂×C₃²	—	2	2	no	—
598	C₂×C₃²	—	4	4	no	—
599	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
600	C₂×C₃²	#585	1	2	yes	—
601	C₃×D₃	—	4	4	no	—
602	C₂⁴	—	3	2	no	—
603	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
604	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
605	#41	—	2	8	no	—
606	#41	—	2	8	no	—
607	#41	—	2	8	no	—
608	#41	—	2	8	no	—
609	#41	—	6	8	no	—
610	#41	—	6	8	no	—
611	#41	—	6	8	no	—
612	#41	—	6	8	no	—
613	C₂×Q₈	—	2	4	no	—
614	C₂×Q₈	—	3	2	no	—
615	C₂×Q₈	—	3	2	no	—
616	C₂×Q₈	—	6	4	no	—
617	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
618	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	3	4	no	—
622	C₂×D₄	—	3	4	no	—
623	C₂×D₄	—	3	16	no	—
624	C₂×D₄	—	3	2	no	—
625	C₂×D₄	—	3	2	no	—
626	C₂×D₄	—	6	8	no	—
627	C₂×D₄	—	6	4	no	—
628	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
629	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
630	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
631	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	3	2	no	—
634	C₂²×C₄	—	3	4	no	—
635	C₂²×C₄	—	3	4	no	—
636	C₂²×C₄	—	3	4	no	—
637	C₂²×C₄	—	6	8	no	—
638	C₂²×C₄	C₃×#67	1	8	yes	complemented
639	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
640	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
641	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
642	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
643	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
644	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
647	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
648	C₄⋊C₄	—	3	4	no	—
649	C₄⋊C₄	—	3	4	no	—
650	C₄⋊C₄	—	3	16	no	—
651	C₂²⋊C₄	—	3	4	no	—
652	C₂²⋊C₄	—	3	4	no	—
653	C₂²⋊C₄	—	3	16	no	—
654	C₂²⋊C₄	—	3	16	no	—
655	C₄²	—	3	4	no	—
656	C₄²	—	3	4	no	—
657	C₂²×C₃	—	2	4	no	—
658	C₂²×C₃	—	2	2	no	—
659	C₂²×C₃	—	2	2	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	2	2	no	—
662	C₂²×C₃	—	2	2	no	—
663	C₂²×C₃	—	2	2	no	—
664	C₂²×C₃	—	2	8	no	—
665	C₂²×C₃	—	2	8	no	—
666	C₂²×C₃	—	2	4	no	—
667	C₂²×C₃	—	2	4	no	—
668	C₂²×C₃	—	2	8	no	—
669	C₂²×C₃	—	2	2	no	—
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	—	2	2	no	—
672	C₂²×C₃	—	2	1	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	—	4	2	no	—
675	C₂²×C₃	—	4	8	no	—
676	C₂²×C₃	—	4	4	no	—
677	C₂²×C₃	—	4	4	no	—
678	C₂²×C₃	—	4	8	no	—
679	C₂²×C₃	—	4	16	no	—
680	C₂²×C₃	—	4	8	no	—
681	C₂²×C₃	—	4	8	no	—
682	C₂²×C₃	—	6	8	no	—
683	C₂²×C₃	—	6	4	no	—
684	C₂²×C₃	—	12	8	no	—
685	C₂²×C₃	C₂²×#67	1	2	yes	—
686	C₂²×C₃	C₂²×#67	1	2	yes	—
687	C₂²×C₃	C₂²×#67	1	2	yes	—
688	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
689	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
690	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
691	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
692	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
693	C₂×D₃	—	2	4	no	—
694	C₂×D₃	—	2	8	no	—
695	C₂×D₃	—	4	8	no	—
696	C₃×C₄	—	2	8	no	—
697	C₃×C₄	—	2	4	no	—
698	C₃×C₄	—	2	4	no	—
699	C₃×C₄	—	2	2	no	—
700	C₃×C₄	—	2	2	no	—
701	C₃×C₄	—	2	2	no	—
702	C₃×C₄	—	2	2	no	—
703	C₃×C₄	—	6	8	no	—
704	C₃×C₄	—	6	4	no	—
705	C₃×C₄	C₂²×#67	1	2	yes	—
706	C₃×C₄	C₂²×#67	1	2	yes	—
707	C₃×C₄	C₂²×#67	1	2	yes	—
708	C₃×C₄	C₂²×#67	1	2	yes	—
709	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
710	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
711	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
712	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
713	Dic₃	—	2	4	no	—
714	Dic₃	—	2	8	no	—
715	C₃²	#3449	1	1	yes	characteristic, complemented, Sylow
716	C₂³	—	2	4	no	—
717	C₂³	—	3	4	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	4	no	—
720	C₂³	—	6	4	no	—
721	C₂³	—	12	4	no	—
722	C₂³	C₂×C₃×#67	1	4	yes	—
723	C₂³	C₂³×C₃×D₃	1	4	yes	—
724	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
725	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
726	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
727	Q₈	—	2	4	no	—
728	Q₈	—	2	4	no	—
729	Q₈	—	6	4	no	—
730	Q₈	—	6	4	no	—
731	D₄	—	2	8	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	4	no	—
735	D₄	—	6	8	no	—
736	D₄	—	6	8	no	—
737	D₄	—	6	4	no	—
738	D₄	—	6	4	no	—
739	D₄	—	12	16	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	3	8	no	—
744	C₂×C₄	—	3	4	no	—
745	C₂×C₄	—	6	4	no	—
746	C₂×C₄	—	6	8	no	—
747	C₂×C₄	—	6	8	no	—
748	C₂×C₄	—	12	4	no	—
749	C₂×C₄	C₂×C₃×#67	1	4	yes	—
750	C₂×C₄	C₂×C₃×#67	1	4	yes	—
751	C₂×C₄	C₂×C₃×#67	1	4	yes	—
752	C₂×C₄	C₂×C₃×#67	1	4	yes	—
753	C₂×C₄	C₂×C₃×#67	1	4	yes	—
754	C₂×C₄	C₂×C₃×#67	1	4	yes	—
755	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
756	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
757	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
758	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
759	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
760	C₂×C₃	—	2	4	no	—
761	C₂×C₃	—	2	2	no	—
762	C₂×C₃	—	2	2	no	—
763	C₂×C₃	—	2	2	no	—
764	C₂×C₃	—	2	2	no	—
765	C₂×C₃	—	2	2	no	—
766	C₂×C₃	—	2	2	no	—
767	C₂×C₃	—	2	2	no	—
768	C₂×C₃	—	2	1	no	—
769	C₂×C₃	—	4	2	no	—
770	C₂×C₃	—	4	2	no	—
771	C₂×C₃	—	4	8	no	—
772	C₂×C₃	—	4	4	no	—
773	C₂×C₃	—	4	4	no	—
774	C₂×C₃	—	12	4	no	—
775	C₂×C₃	#5964	1	2	yes	—
776	C₂×C₃	C₂³×#67	1	1	yes	characteristic
777	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
778	C₂×C₃	C₃×#585	1	2	yes	—
779	D₃	—	4	4	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	8	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	8	no	—
787	C₂²	—	6	8	no	—
788	C₂²	—	6	4	no	—
789	C₂²	—	12	8	no	—
790	C₂²	C₂²×C₃×#67	1	2	yes	—
791	C₂²	C₂²×C₃×#67	1	2	yes	—
792	C₂²	C₂²×C₃×#67	1	2	yes	—
793	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
794	C₄	—	2	4	no	—
795	C₄	—	6	8	no	—
796	C₄	—	6	4	no	—
797	C₄	C₂²×C₃×#67	1	2	yes	—
798	C₄	C₂²×C₃×#67	1	2	yes	—
799	C₄	C₂²×C₃×#67	1	2	yes	—
800	C₄	C₂²×C₃×#67	1	2	yes	—
801	C₃	—	2	1	no	—
802	C₃	#87268	1	1	yes	characteristic, direct product factor
803	C₃	C₃×#3449	1	1	yes	characteristic, complemented
804	C₂	—	2	2	no	—
805	C₂	—	2	2	no	—
806	C₂	—	2	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	12	4	no	—
809	C₂	C₃×#5964	1	2	yes	—
810	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×#41	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂²×C₃×#41	D₃
hypocenter	C₃	C₃×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×#41	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₃×#5833	C₂	semidirect
4. C₃×#5832	C₂	semidirect
5. C₃×#5830	C₂	semidirect
6. C₃×#5828	C₂	semidirect
7. C₃×#5825	C₂	semidirect
8. C₃×#5816	C₂	semidirect
9. C₃×#5805	C₂	semidirect
10. C₃×#5804	C₂	semidirect
11. C₃×#5791	C₂	semidirect
12. C₂×C₃×#926	C₂	semidirect
14. #87268	C₃	direct (N × H)
18. C₂×C₃²×#41	C₂²	semidirect
19. C₂×C₃²×#41	C₂²	semidirect
20. C₂²×C₃²×Q₈	C₂²	semidirect
22. C₂²×C₃²×D₄	C₂²	semidirect
24. C₂³×C₃²×C₄	C₂²	semidirect
29. C₂×C₃×#235	C₂²	semidirect
30. C₂×C₃×#235	C₂²	semidirect
31. C₂²×C₃×D₁₂	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₂²×C₃×Dic₆	C₂²	semidirect
34. C₃×#953	C₂²	semidirect
36. C₃×#947	C₂²	semidirect
37. C₃×#946	C₂²	semidirect
38. C₃×#944	C₂²	semidirect
39. C₃×#940	C₂²	semidirect
40. C₃×#939	C₂²	semidirect
41. C₃×#938	C₂²	semidirect
42. C₃×#937	C₂²	semidirect
43. C₃×#936	C₂²	semidirect
44. C₃×#935	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×#926	C₂²	semidirect
50. C₃×#926	C₂²	semidirect
51. C₃×#926	C₂²	semidirect
52. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
53. C₃×#924	C₂²	semidirect
54. C₂×C₃×C₄×Dic₃	C₂²	semidirect
57. C₂²×C₃×#41	D₃	semidirect
58. C₂²×C₃×#41	C₂×C₃	semidirect
59. C₂²×#235	C₂×C₃	semidirect
70. #5833	C₂×C₃	semidirect
71. #5832	C₂×C₃	semidirect
72. #5830	C₂×C₃	semidirect
73. #5828	C₂×C₃	semidirect
74. #5825	C₂×C₃	semidirect
75. #5816	C₂×C₃	semidirect
76. #5805	C₂×C₃	semidirect
77. #5804	C₂×C₃	semidirect
78. #5791	C₂×C₃	semidirect
79. C₂×#926	C₂×C₃	semidirect
97. C₂²×C₃²×C₄	D₄	semidirect
150. C₂×C₃×#41	C₂×D₃	semidirect
151. C₂×C₃×#41	C₂×D₃	semidirect
154. C₂×C₃×#41	C₂²×C₃	semidirect
155. C₂×C₃×#41	C₂²×C₃	semidirect
158. C₂²×C₃×Q₈	C₂×D₃	semidirect
159. C₂²×C₃×Q₈	C₂²×C₃	semidirect
165. C₂²×C₃×D₄	C₂×D₃	semidirect
167. C₂²×C₃×D₄	C₂²×C₃	semidirect
172. C₂³×C₃×C₄	C₂×D₃	semidirect
174. C₂³×C₃×C₄	C₂²×C₃	semidirect
179. C₂×#235	C₂²×C₃	semidirect
180. C₂×#235	C₂²×C₃	semidirect
181. C₂²×D₁₂	C₂²×C₃	semidirect
182. C₂²×C₄×D₃	C₂²×C₃	semidirect
183. C₂²×Dic₆	C₂²×C₃	semidirect
205. #953	C₂²×C₃	semidirect
207. #947	C₂²×C₃	semidirect
208. #946	C₂²×C₃	semidirect
209. #944	C₂²×C₃	semidirect
210. #940	C₂²×C₃	semidirect
211. #939	C₂²×C₃	semidirect
212. #938	C₂²×C₃	semidirect
213. #937	C₂²×C₃	semidirect
214. #936	C₂²×C₃	semidirect
215. #935	C₂²×C₃	semidirect
216. #930	C₂²×C₃	semidirect
217. #929	C₂²×C₃	semidirect
218. C₄×#67	C₂²×C₃	semidirect
219. #926	C₂²×C₃	semidirect
220. #926	C₂²×C₃	semidirect
221. #926	C₂²×C₃	semidirect
222. #926	C₂²×C₃	semidirect
223. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
224. #924	C₂²×C₃	semidirect
225. C₂×C₄×Dic₃	C₂²×C₃	semidirect
271. C₂²×#41	C₃×D₃	semidirect
361. C₂²×C₃×C₄	#67	semidirect
362. C₂²×C₃×C₄	C₃×D₄	semidirect
447. C₂×#41	C₂×C₃×D₃	semidirect
448. C₂×#41	C₂×C₃×D₃	semidirect
450. C₂²×Q₈	C₂×C₃×D₃	semidirect
454. C₂²×D₄	C₂×C₃×D₃	semidirect
457. C₂³×C₄	C₂×C₃×D₃	semidirect
638. C₂²×C₄	C₃×#67	semidirect
715. C₃²	#3449	semidirect
802. C₃	#87268	direct (N × H)
803. C₃	C₃×#3449	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×#41	2
C₂²×C₃×#235	2
C₃×#5833	2
C₃×#5832	2
C₃×#5830	2
C₃×#5828	2
C₃×#5825	2
C₃×#5816	2
C₃×#5805	2
C₃×#5804	2
C₃×#5791	2
C₂×C₃×#926	2
C₃×#3449	3
#87268	3

Subgroups — C3×#87268 #11901181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87268 #11901181