Subgroups — C₃×#85764 #11903454

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5806	C₂	1	2	yes	maximal, complemented
3	C₃×#5791	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#926	C₂	1	2	yes	maximal, complemented
5	C₃×#5565	C₂	1	2	yes	maximal, complemented
6	C₃×#5563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5557	C₂	1	2	yes	maximal, complemented
8	C₃×#5555	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5543	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5541	C₂	1	2	yes	maximal, complemented
12	C₃×#5538	C₂	1	4	yes	maximal, complemented
13	C₃×C₄×#237	C₂	1	2	yes	maximal, complemented
14	C₃×#5513	C₂	1	2	yes	maximal, complemented
15	C₃×#5495	C₂	1	4	yes	maximal, complemented
16	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3475	—	3	1	no	maximal
19	#85764	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₃²×C₄	C₂²	1	2	yes	—
22	C₂×C₃×#237	C₂²	1	2	yes	—
23	C₂×C₃×#235	C₂²	1	1	yes	characteristic
24	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
25	C₃²×C₄×D₄	C₂²	1	2	yes	—
26	C₃²×C₄×D₄	C₂²	1	2	yes	—
27	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
33	C₃×#953	C₂²	1	4	yes	—
34	C₂×C₃×#217	C₂²	1	4	yes	—
35	C₃×#939	C₂²	1	4	yes	—
36	C₃×#938	C₂²	1	2	yes	—
37	C₃×#936	C₂²	1	2	yes	—
38	C₃×#935	C₂²	1	4	yes	—
39	C₃×D₄×Dic₃	C₂²	1	2	yes	—
40	C₃×#930	C₂²	1	2	yes	complemented
41	C₃×#930	C₂²	1	2	yes	complemented
42	C₃×#929	C₂²	1	4	yes	—
43	C₃×C₄×#67	C₂²	1	2	yes	—
44	C₃×C₄×#67	C₂²	1	2	yes	—
45	C₃×C₄×#67	C₂²	1	4	yes	complemented
46	C₃×C₄×#67	C₂²	1	4	yes	complemented
47	C₃×#926	C₂²	1	4	yes	—
48	C₃×#926	C₂²	1	1	yes	characteristic
49	C₃×#926	C₂²	1	2	yes	—
50	C₃×#926	C₂²	1	4	yes	complemented
51	C₃×#926	C₂²	1	2	yes	complemented
52	C₃×#926	C₂²	1	2	yes	complemented
53	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
54	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
55	C₃×#924	C₂²	1	2	yes	—
56	C₃×#924	C₂²	1	2	yes	—
57	C₃×#924	C₂²	1	2	yes	complemented
58	C₃×#924	C₂²	1	2	yes	complemented
59	C₂×C₃×C₄×Dic₃	C₂²	1	4	yes	complemented
60	C₃×#898	C₂²	1	4	yes	complemented
61	C₃×#897	C₂²	1	2	yes	complemented
62	C₃×#892	C₂²	1	2	yes	complemented
63	C₃×#890	C₂²	1	2	yes	complemented
64	C₃×#889	C₂²	1	4	yes	complemented
65	C₃×#887	C₂²	1	2	yes	complemented
66	C₃×#886	C₂²	1	4	yes	complemented
67	C₃×#885	C₂²	1	4	yes	complemented
68	C₃×#883	C₂²	1	4	yes	complemented
69	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
70	C₃×#879	C₂²	1	4	yes	complemented
71	C₃×#879	C₂²	1	4	yes	complemented
72	C₃×#878	C₂²	1	4	yes	complemented
73	C₃×#877	C₂²	1	4	yes	complemented
74	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
75	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
76	C₃×#872	C₂²	1	2	yes	complemented
77	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
78	C₃×#870	C₂²	1	2	yes	complemented
79	C₃×#869	C₂²	1	1	yes	characteristic, complemented
80	C₃×#869	C₂²	1	1	yes	characteristic, complemented
81	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
82	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
85	C₃×#556	—	3	1	no	—
86	C₃×#555	—	3	1	no	—
87	C₃×#554	—	3	1	no	—
88	C₃×#553	—	3	2	no	—
89	C₃×#552	—	3	2	no	—
90	C₃×#552	—	3	2	no	—
91	C₃×#551	—	3	4	no	—
92	C₃×#547	—	3	1	no	—
93	C₃×#546	—	3	2	no	—
94	C₃×#533	—	3	1	no	—
95	C₃×#529	—	3	4	no	—
96	C₃×#529	—	3	2	no	—
97	C₃×#525	—	3	2	no	—
98	C₃×C₄×#41	—	3	2	no	—
99	C₃×C₄×#41	—	3	1	no	—
100	C₂×C₃×C₄×D₄	—	2	1	no	—
101	C₂×C₃×C₄×D₄	D₃	1	1	yes	characteristic, complemented
102	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂×C₃×#117	—	3	2	no	—
104	#5806	C₂×C₃	1	2	yes	complemented
105	#5791	C₂×C₃	1	2	yes	complemented
106	C₂×#926	C₂×C₃	1	2	yes	complemented
107	#5565	C₂×C₃	1	2	yes	complemented
108	#5563	C₂×C₃	1	1	yes	characteristic, complemented
109	#5557	C₂×C₃	1	2	yes	complemented
110	#5555	C₂×C₃	1	1	yes	characteristic, complemented
111	#5543	C₂×C₃	1	1	yes	characteristic, complemented
112	#5542	C₂×C₃	1	1	yes	characteristic, complemented
113	#5541	C₂×C₃	1	2	yes	complemented
114	#5538	C₂×C₃	1	4	yes	complemented
115	C₄×#237	C₂×C₃	1	2	yes	complemented
116	#5513	C₂×C₃	1	2	yes	complemented
117	#5495	C₂×C₃	1	4	yes	complemented
118	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
119	#5470	C₂×C₃	1	1	yes	characteristic, complemented
120	C₂⁴×C₃²	C₂³	1	2	yes	—
121	C₂×C₃²×D₄	—	2	4	no	—
122	C₂×C₃²×D₄	C₂³	1	2	yes	—
123	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
124	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	—	2	8	no	—
126	C₂²×C₃²×C₄	C₂³	1	2	yes	—
127	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
128	C₂²×C₃²×C₄	C₂³	1	2	yes	—
129	C₂²×C₃²×C₄	C₂³	1	2	yes	—
130	C₂²×C₃²×C₄	C₂³	1	2	yes	—
131	C₂²×C₃²×C₄	C₂³	1	2	yes	—
132	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
133	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
134	C₂×C₃×#67	C₂³	1	4	yes	—
135	C₂×C₃×#67	C₂³	1	2	yes	—
136	C₂×C₃×#67	C₂³	1	4	yes	—
137	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
138	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
139	C₃×#237	—	2	8	no	—
140	C₃×#235	—	2	4	no	—
141	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
145	C₂×C₃×Dic₆	C₂³	1	2	yes	—
146	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
147	C₂×C₃×Dic₆	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₄²	C₂³	1	1	yes	characteristic
156	C₃²×C₄²	C₂³	1	1	yes	characteristic
157	C₃²×C₄²	C₂³	1	1	yes	characteristic
158	C₃²×C₄²	C₂³	1	1	yes	characteristic
159	C₃×#217	C₂³	1	4	yes	—
160	C₃×#217	C₂³	1	4	yes	—
161	C₃×#217	C₂³	1	4	yes	—
162	C₃×#217	C₂³	1	4	yes	—
163	C₃×#217	C₂³	1	4	yes	—
164	C₃×#217	C₂³	1	2	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
166	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
167	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
168	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
169	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
170	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
171	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
172	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
174	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
175	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
176	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
180	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
183	C₃×C₄×Dic₃	C₂³	1	2	yes	—
184	C₃×C₄×Dic₃	C₂³	1	4	yes	—
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	2	yes	—
187	C₃×C₄×Dic₃	C₂³	1	2	yes	—
188	C₃×C₄×Dic₃	C₂³	1	4	yes	—
189	#3475	—	3	1	no	Sylow
190	C₂×C₃×#41	—	3	2	no	—
191	C₂×C₃×#41	—	3	1	no	—
192	C₂²×C₃×D₄	—	2	1	no	—
193	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
194	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
195	C₂³×C₃×C₄	—	2	2	no	—
196	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
197	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
198	C₂×#237	C₂²×C₃	1	2	yes	—
199	C₂×#235	C₂²×C₃	1	1	yes	characteristic
200	C₃×C₄⋊Q₈	—	3	1	no	—
201	C₃×C₄⋊Q₈	—	3	1	no	—
202	C₃×#126	—	3	4	no	—
203	C₃×#126	—	3	4	no	—
204	C₃×#126	—	3	4	no	—
205	C₃×#125	—	3	4	no	—
206	C₃×#125	—	3	2	no	—
207	C₃×#125	—	3	2	no	—
208	C₃×#124	—	3	2	no	—
209	C₃×#124	—	3	4	no	—
210	C₃×#123	—	3	4	no	—
211	C₃×#123	—	3	4	no	—
212	C₃×#123	—	3	4	no	—
213	C₃×#123	—	3	4	no	—
214	C₃×C₂²⋊Q₈	—	3	2	no	—
215	C₃×C₂²⋊Q₈	—	3	2	no	—
216	C₃×C₂²⋊Q₈	—	3	2	no	—
217	C₃×C₂²⋊Q₈	—	3	2	no	—
218	C₃×C₂²⋊Q₈	—	3	2	no	—
219	C₃×C₂²⋊Q₈	—	3	4	no	—
220	C₃×#121	—	3	2	no	—
221	C₃×#121	—	3	4	no	—
222	C₃×#121	—	3	2	no	—
223	C₃×#121	—	3	2	no	—
224	C₃×#120	—	3	4	no	—
225	C₃×C₄×Q₈	—	3	2	no	—
226	C₃×C₄×Q₈	—	3	2	no	—
227	C₃×C₄×Q₈	—	3	1	no	—
228	C₃×C₄×Q₈	—	3	1	no	—
229	C₃×C₄×Q₈	—	3	2	no	—
230	C₃×C₄×D₄	—	2	1	no	—
231	C₃×C₄×D₄	—	2	2	no	—
232	C₃×C₄×D₄	—	2	1	no	—
233	C₃×C₄×D₄	—	2	1	no	—
234	C₃×C₄×D₄	—	2	2	no	—
235	C₃×C₄×D₄	—	2	1	no	—
236	C₃×C₄×D₄	—	3	2	no	—
237	C₃×C₄×D₄	—	3	2	no	—
238	C₃×C₄×D₄	—	3	2	no	—
239	C₃×C₄×D₄	—	3	4	no	—
240	C₃×C₄×D₄	—	3	4	no	—
241	C₃×C₄×D₄	—	3	4	no	—
242	C₃×C₄×D₄	—	3	1	no	—
243	C₃×C₄×D₄	—	3	1	no	—
244	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
245	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
246	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
247	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
248	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
249	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
250	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
251	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
252	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
253	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
254	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
255	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
256	C₃×#117	—	3	1	no	—
257	C₃×#117	—	3	2	no	—
258	C₃×#117	—	3	4	no	—
259	C₃×#117	—	3	4	no	—
260	C₃×#117	—	3	2	no	—
261	C₃×#117	—	3	2	no	—
262	C₃×#117	—	3	2	no	—
263	C₃×#117	—	3	4	no	—
264	C₃×#117	—	3	2	no	—
265	C₂×C₃×C₄⋊C₄	—	2	1	no	—
266	C₂×C₃×C₄⋊C₄	—	3	2	no	—
267	C₂×C₃×C₄⋊C₄	—	3	2	no	—
268	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
272	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
273	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
274	C₂×C₃×C₄²	—	2	1	no	—
275	C₂×C₃×C₄²	—	3	4	no	—
276	C₂×C₃×C₄²	—	3	2	no	—
277	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
278	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
279	#953	C₂²×C₃	1	4	yes	—
280	C₂×#217	C₂²×C₃	1	4	yes	—
281	#939	C₂²×C₃	1	4	yes	—
282	#938	C₂²×C₃	1	2	yes	—
283	#936	C₂²×C₃	1	2	yes	—
284	#935	C₂²×C₃	1	4	yes	—
285	D₄×Dic₃	C₂²×C₃	1	2	yes	—
286	#930	C₂²×C₃	1	2	yes	complemented
287	#930	C₂²×C₃	1	2	yes	complemented
288	#929	C₂²×C₃	1	4	yes	—
289	C₄×#67	C₂²×C₃	1	2	yes	—
290	C₄×#67	C₂²×C₃	1	2	yes	—
291	C₄×#67	C₂²×C₃	1	4	yes	complemented
292	C₄×#67	C₂²×C₃	1	4	yes	complemented
293	#926	C₂²×C₃	1	2	yes	—
294	#926	C₂²×C₃	1	1	yes	characteristic
295	#926	C₂²×C₃	1	4	yes	—
296	#926	C₂²×C₃	1	4	yes	complemented
297	#926	C₂²×C₃	1	2	yes	complemented
298	#926	C₂²×C₃	1	2	yes	complemented
299	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
300	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
301	#924	C₂²×C₃	1	2	yes	—
302	#924	C₂²×C₃	1	2	yes	—
303	#924	C₂²×C₃	1	2	yes	complemented
304	#924	C₂²×C₃	1	2	yes	complemented
305	C₂×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
306	#898	C₂²×C₃	1	4	yes	complemented
307	#897	C₂²×C₃	1	2	yes	complemented
308	#892	C₂²×C₃	1	2	yes	complemented
309	#890	C₂²×C₃	1	2	yes	complemented
310	#889	C₂²×C₃	1	4	yes	complemented
311	#887	C₂²×C₃	1	2	yes	complemented
312	#886	C₂²×C₃	1	4	yes	complemented
313	#885	C₂²×C₃	1	4	yes	complemented
314	#883	C₂²×C₃	1	4	yes	complemented
315	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
316	#879	C₂²×C₃	1	4	yes	complemented
317	#879	C₂²×C₃	1	4	yes	complemented
318	#878	C₂²×C₃	1	4	yes	complemented
319	#877	C₂²×C₃	1	4	yes	complemented
320	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
321	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
322	#872	C₂²×C₃	1	2	yes	complemented
323	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
324	#870	C₂²×C₃	1	2	yes	complemented
325	#869	C₂²×C₃	1	1	yes	characteristic, complemented
326	#869	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
328	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
329	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
330	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
331	C₂³×C₃²	—	2	4	no	—
332	C₂³×C₃²	—	2	4	no	—
333	C₂³×C₃²	—	4	2	no	—
334	C₂³×C₃²	C₂⁴	1	2	yes	—
335	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
336	C₂³×C₃²	C₂⁴	1	2	yes	—
337	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
338	C₃²×D₄	—	2	4	no	—
339	C₃²×D₄	—	2	2	no	—
340	C₃²×D₄	#41	1	4	yes	complemented
341	C₂×C₃²×C₄	—	2	2	no	—
342	C₂×C₃²×C₄	—	2	4	no	—
343	C₂×C₃²×C₄	—	2	4	no	—
344	C₂×C₃²×C₄	—	2	4	no	—
345	C₂×C₃²×C₄	—	2	4	no	—
346	C₂×C₃²×C₄	—	2	4	no	—
347	C₂×C₃²×C₄	—	4	1	no	—
348	C₂×C₃²×C₄	#41	1	4	yes	complemented
349	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
350	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
351	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
352	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
353	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
354	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
355	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
356	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
357	C₃×#67	—	2	4	no	—
358	C₃×#67	—	2	8	no	—
359	C₃×#67	—	4	4	no	—
360	C₂×C₃×Dic₃	—	2	8	no	—
361	C₂×C₃×Dic₃	—	4	4	no	—
362	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
363	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
364	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
365	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
366	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
367	C₃×D₁₂	—	2	2	no	—
368	C₃×C₄×D₃	—	2	4	no	—
369	C₃×C₄×D₃	—	2	4	no	—
370	C₃×C₄×D₃	—	4	2	no	—
371	C₃×Dic₆	—	2	2	no	—
372	C₃×Dic₆	—	2	4	no	—
373	C₃×Dic₆	—	4	2	no	—
374	#556	—	3	1	no	—
375	#555	—	3	1	no	—
376	#554	—	3	1	no	—
377	#553	—	3	2	no	—
378	#552	—	3	2	no	—
379	#552	—	3	2	no	—
380	#551	—	3	4	no	—
381	#547	—	3	1	no	—
382	#546	—	3	2	no	—
383	#533	—	3	1	no	—
384	#529	—	3	4	no	—
385	#529	—	3	2	no	—
386	#525	—	3	2	no	—
387	C₄×#41	—	3	2	no	—
388	C₄×#41	—	3	1	no	—
389	C₂×C₄×D₄	C₃×D₃	1	1	yes	characteristic, complemented
390	C₂×#117	—	3	2	no	—
391	C₂⁴×C₃	—	2	2	no	—
392	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
393	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
394	C₃×#41	—	6	8	no	—
395	C₃×#41	—	6	4	no	—
396	C₂×C₃×Q₈	—	3	1	no	—
397	C₂×C₃×Q₈	—	3	2	no	—
398	C₂×C₃×Q₈	—	3	2	no	—
399	C₂×C₃×D₄	—	2	8	no	—
400	C₂×C₃×D₄	—	2	4	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	2	2	no	—
403	C₂×C₃×D₄	—	2	1	no	—
404	C₂×C₃×D₄	—	2	1	no	—
405	C₂×C₃×D₄	—	3	2	no	—
406	C₂×C₃×D₄	—	3	4	no	—
407	C₂×C₃×D₄	—	3	4	no	—
408	C₂×C₃×D₄	—	3	1	no	—
409	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
410	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
411	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
412	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
413	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
415	C₂²×C₃×C₄	—	2	8	no	—
416	C₂²×C₃×C₄	—	2	8	no	—
417	C₂²×C₃×C₄	—	2	1	no	—
418	C₂²×C₃×C₄	—	2	1	no	—
419	C₂²×C₃×C₄	—	2	1	no	—
420	C₂²×C₃×C₄	—	2	2	no	—
421	C₂²×C₃×C₄	—	2	2	no	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	2	no	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	3	4	no	—
426	C₂²×C₃×C₄	—	3	4	no	—
427	C₂²×C₃×C₄	—	3	2	no	—
428	C₂²×C₃×C₄	—	3	2	no	—
429	C₂²×C₃×C₄	—	3	2	no	—
430	C₂²×C₃×C₄	—	4	8	no	—
431	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
433	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
434	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
435	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
436	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
437	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
440	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
442	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
443	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
444	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
445	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
446	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂×#67	C₂³×C₃	1	4	yes	—
448	C₂×#67	C₂³×C₃	1	2	yes	—
449	C₂×#67	C₂³×C₃	1	4	yes	—
450	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
451	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
452	#237	—	2	8	no	—
453	#235	—	2	4	no	—
454	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
455	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
456	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
457	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
458	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
459	C₂×Dic₆	C₂³×C₃	1	2	yes	—
460	C₂×Dic₆	C₂³×C₃	1	2	yes	—
461	C₃×C₄⋊C₄	—	2	1	no	—
462	C₃×C₄⋊C₄	—	2	1	no	—
463	C₃×C₄⋊C₄	—	2	2	no	—
464	C₃×C₄⋊C₄	—	3	2	no	—
465	C₃×C₄⋊C₄	—	3	4	no	—
466	C₃×C₄⋊C₄	—	3	4	no	—
467	C₃×C₄⋊C₄	—	3	2	no	—
468	C₃×C₄⋊C₄	—	3	4	no	—
469	C₃×C₄⋊C₄	—	3	4	no	—
470	C₃×C₄⋊C₄	—	3	1	no	—
471	C₃×C₄⋊C₄	—	3	1	no	—
472	C₃×C₄⋊C₄	—	3	2	no	—
473	C₃×C₄⋊C₄	—	3	2	no	—
474	C₃×C₄⋊C₄	—	3	4	no	—
475	C₃×C₄⋊C₄	—	3	4	no	—
476	C₃×C₄⋊C₄	—	3	2	no	—
477	C₃×C₄⋊C₄	—	3	2	no	—
478	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
481	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
482	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	2	2	no	—
486	C₃×C₂²⋊C₄	—	2	2	no	—
487	C₃×C₂²⋊C₄	—	2	2	no	—
488	C₃×C₂²⋊C₄	—	3	2	no	—
489	C₃×C₂²⋊C₄	—	3	4	no	—
490	C₃×C₂²⋊C₄	—	3	4	no	—
491	C₃×C₂²⋊C₄	—	3	4	no	—
492	C₃×C₂²⋊C₄	—	3	4	no	—
493	C₃×C₂²⋊C₄	—	3	4	no	—
494	C₃×C₂²⋊C₄	—	3	2	no	—
495	C₃×C₂²⋊C₄	—	3	4	no	—
496	C₃×C₂²⋊C₄	—	3	2	no	—
497	C₃×C₂²⋊C₄	—	3	4	no	—
498	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₃×C₄²	—	2	1	no	—
507	C₃×C₄²	—	2	1	no	—
508	C₃×C₄²	—	2	1	no	—
509	C₃×C₄²	—	2	1	no	—
510	C₃×C₄²	—	3	4	no	—
511	C₃×C₄²	—	3	4	no	—
512	C₃×C₄²	—	3	2	no	—
513	C₃×C₄²	—	3	2	no	—
514	C₃×C₄²	—	3	2	no	—
515	C₃×C₄²	—	3	4	no	—
516	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
517	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
520	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
521	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
522	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
523	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
524	#217	C₂³×C₃	1	4	yes	—
525	#217	C₂³×C₃	1	4	yes	—
526	#217	C₂³×C₃	1	4	yes	—
527	#217	C₂³×C₃	1	4	yes	—
528	#217	C₂³×C₃	1	4	yes	—
529	#217	C₂³×C₃	1	2	yes	—
530	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
531	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
532	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
533	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
534	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
535	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
536	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
537	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
539	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
540	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
541	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
542	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
543	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
544	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
545	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
546	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
547	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
548	C₄×Dic₃	C₂³×C₃	1	4	yes	—
549	C₄×Dic₃	C₂³×C₃	1	2	yes	—
550	C₄×Dic₃	C₂³×C₃	1	2	yes	—
551	C₄×Dic₃	C₂³×C₃	1	2	yes	—
552	C₄×Dic₃	C₂³×C₃	1	4	yes	—
553	C₄×Dic₃	C₂³×C₃	1	4	yes	—
554	C₂²×C₃²	—	2	1	no	—
555	C₂²×C₃²	—	2	1	no	—
556	C₂²×C₃²	—	2	2	no	—
557	C₂²×C₃²	—	2	2	no	—
558	C₂²×C₃²	—	2	2	no	—
559	C₂²×C₃²	—	2	2	no	—
560	C₂²×C₃²	—	2	2	no	—
561	C₂²×C₃²	—	4	8	no	—
562	C₂²×C₃²	C₂×#41	1	4	yes	—
563	C₂²×C₃²	C₂×#41	1	2	yes	—
564	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
565	C₂×C₃×D₃	—	2	2	no	—
566	C₂×C₃×D₃	—	2	2	no	—
567	C₂×C₃×D₃	—	2	2	no	—
568	C₃²×C₄	—	2	1	no	—
569	C₃²×C₄	—	2	2	no	—
570	C₃²×C₄	—	2	2	no	—
571	C₃²×C₄	—	2	1	no	—
572	C₃²×C₄	—	2	1	no	—
573	C₃²×C₄	C₂×#41	1	2	yes	—
574	C₃²×C₄	C₂×#41	1	2	yes	—
575	C₃²×C₄	C₂×#41	1	2	yes	—
576	C₃×Dic₃	—	2	2	no	—
577	C₃×Dic₃	—	2	4	no	—
578	C₃×Dic₃	—	2	2	no	—
579	C₃×Dic₃	—	2	4	no	—
580	C₃×Dic₃	—	2	2	no	—
581	C₂×#41	—	3	2	no	—
582	C₂×#41	—	3	1	no	—
583	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
584	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
585	C₄⋊Q₈	—	3	1	no	—
586	C₄⋊Q₈	—	3	1	no	—
587	#126	—	3	4	no	—
588	#126	—	3	4	no	—
589	#126	—	3	4	no	—
590	#125	—	3	4	no	—
591	#125	—	3	2	no	—
592	#125	—	3	2	no	—
593	#124	—	3	2	no	—
594	#124	—	3	4	no	—
595	#123	—	3	4	no	—
596	#123	—	3	4	no	—
597	#123	—	3	4	no	—
598	#123	—	3	4	no	—
599	C₂²⋊Q₈	—	3	2	no	—
600	C₂²⋊Q₈	—	3	2	no	—
601	C₂²⋊Q₈	—	3	2	no	—
602	C₂²⋊Q₈	—	3	2	no	—
603	C₂²⋊Q₈	—	3	2	no	—
604	C₂²⋊Q₈	—	3	4	no	—
605	#121	—	3	4	no	—
606	#121	—	3	2	no	—
607	#121	—	3	2	no	—
608	#121	—	3	2	no	—
609	#120	—	3	4	no	—
610	C₄×Q₈	—	3	2	no	—
611	C₄×Q₈	—	3	2	no	—
612	C₄×Q₈	—	3	1	no	—
613	C₄×Q₈	—	3	1	no	—
614	C₄×Q₈	—	3	2	no	—
615	C₄×D₄	—	3	2	no	—
616	C₄×D₄	—	3	4	no	—
617	C₄×D₄	—	3	2	no	—
618	C₄×D₄	—	3	2	no	—
619	C₄×D₄	—	3	4	no	—
620	C₄×D₄	—	3	4	no	—
621	C₄×D₄	—	3	1	no	—
622	C₄×D₄	—	3	1	no	—
623	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
624	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
625	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
626	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
627	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
628	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
629	#117	—	3	1	no	—
630	#117	—	3	2	no	—
631	#117	—	3	4	no	—
632	#117	—	3	4	no	—
633	#117	—	3	2	no	—
634	#117	—	3	2	no	—
635	#117	—	3	2	no	—
636	#117	—	3	4	no	—
637	#117	—	3	2	no	—
638	C₂×C₄⋊C₄	—	3	2	no	—
639	C₂×C₄⋊C₄	—	3	2	no	—
640	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	—	3	4	no	—
642	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
643	C₂×C₄²	—	3	4	no	—
644	C₂×C₄²	—	3	2	no	—
645	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
646	C₂³×C₃	—	2	8	no	—
647	C₂³×C₃	—	2	4	no	—
648	C₂³×C₃	—	2	4	no	—
649	C₂³×C₃	—	2	4	no	—
650	C₂³×C₃	—	2	4	no	—
651	C₂³×C₃	—	2	1	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	2	no	—
654	C₂³×C₃	—	3	2	no	—
655	C₂³×C₃	—	4	4	no	—
656	C₂³×C₃	—	4	2	no	—
657	C₂³×C₃	—	4	2	no	—
658	C₂³×C₃	—	4	4	no	—
659	C₂³×C₃	C₂³×D₃	1	2	yes	—
660	C₂³×C₃	C₂³×D₃	1	2	yes	—
661	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
662	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
663	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
664	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
665	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
666	C₃×Q₈	—	6	4	no	—
667	C₃×Q₈	—	6	2	no	—
668	C₃×Q₈	—	12	2	no	—
669	C₃×D₄	—	2	8	no	—
670	C₃×D₄	—	2	4	no	—
671	C₃×D₄	—	2	4	no	—
672	C₃×D₄	—	2	4	no	—
673	C₃×D₄	—	2	2	no	—
674	C₃×D₄	—	2	2	no	—
675	C₃×D₄	—	2	4	no	—
676	C₃×D₄	—	6	8	no	—
677	C₃×D₄	—	6	4	no	—
678	C₃×D₄	—	6	2	no	—
679	C₃×D₄	—	12	4	no	—
680	C₃×D₄	#235	1	4	yes	complemented
681	C₃×D₄	C₃×#41	1	4	yes	complemented
682	C₂×C₃×C₄	—	2	4	no	—
683	C₂×C₃×C₄	—	2	4	no	—
684	C₂×C₃×C₄	—	2	4	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	4	no	—
687	C₂×C₃×C₄	—	2	4	no	—
688	C₂×C₃×C₄	—	2	4	no	—
689	C₂×C₃×C₄	—	2	4	no	—
690	C₂×C₃×C₄	—	2	4	no	—
691	C₂×C₃×C₄	—	2	4	no	—
692	C₂×C₃×C₄	—	2	4	no	—
693	C₂×C₃×C₄	—	2	4	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	2	no	—
702	C₂×C₃×C₄	—	2	2	no	—
703	C₂×C₃×C₄	—	2	4	no	—
704	C₂×C₃×C₄	—	3	2	no	—
705	C₂×C₃×C₄	—	3	2	no	—
706	C₂×C₃×C₄	—	3	4	no	—
707	C₂×C₃×C₄	—	3	2	no	—
708	C₂×C₃×C₄	—	3	4	no	—
709	C₂×C₃×C₄	—	4	4	no	—
710	C₂×C₃×C₄	—	4	4	no	—
711	C₂×C₃×C₄	—	4	4	no	—
712	C₂×C₃×C₄	—	4	4	no	—
713	C₂×C₃×C₄	—	4	4	no	—
714	C₂×C₃×C₄	—	4	1	no	—
715	C₂×C₃×C₄	—	4	1	no	—
716	C₂×C₃×C₄	—	4	2	no	—
717	C₂×C₃×C₄	—	6	8	no	—
718	C₂×C₃×C₄	—	6	4	no	—
719	C₂×C₃×C₄	—	6	4	no	—
720	C₂×C₃×C₄	—	12	2	no	—
721	C₂×C₃×C₄	—	12	4	no	—
722	C₂×C₃×C₄	#237	1	4	yes	complemented
723	C₂×C₃×C₄	C₃×#41	1	4	yes	complemented
724	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
725	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
726	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
727	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
728	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
729	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
730	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
731	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
732	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
733	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
734	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
735	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
736	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
738	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
739	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
740	#67	—	2	4	no	—
741	#67	—	2	8	no	—
742	#67	—	4	4	no	—
743	C₂×Dic₃	—	2	8	no	—
744	C₂×Dic₃	—	4	4	no	—
745	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
746	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
747	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
748	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
749	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
750	D₁₂	—	2	2	no	—
751	C₄×D₃	—	2	4	no	—
752	C₄×D₃	—	2	4	no	—
753	C₄×D₃	—	4	2	no	—
754	Dic₆	—	2	2	no	—
755	Dic₆	—	2	4	no	—
756	Dic₆	—	4	2	no	—
757	C₂×C₃²	—	2	2	no	—
758	C₂×C₃²	—	2	4	no	—
759	C₂×C₃²	—	4	2	no	—
760	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
761	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
762	C₂×C₃²	#585	1	1	yes	characteristic
763	C₃×D₃	—	4	2	no	—
764	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
765	#41	—	6	8	no	—
766	#41	—	6	4	no	—
767	C₂×Q₈	—	3	1	no	—
768	C₂×Q₈	—	3	2	no	—
769	C₂×Q₈	—	3	2	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	3	2	no	—
772	C₂×D₄	—	3	4	no	—
773	C₂×D₄	—	3	4	no	—
774	C₂×D₄	—	3	1	no	—
775	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
776	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
777	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
778	C₂²×C₄	—	2	8	no	—
779	C₂²×C₄	—	3	4	no	—
780	C₂²×C₄	—	3	4	no	—
781	C₂²×C₄	—	3	2	no	—
782	C₂²×C₄	—	3	2	no	—
783	C₂²×C₄	—	3	2	no	—
784	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
785	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
786	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
787	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
788	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
789	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
790	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
791	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
792	C₄⋊C₄	—	3	1	no	—
793	C₄⋊C₄	—	3	1	no	—
794	C₄⋊C₄	—	3	2	no	—
795	C₄⋊C₄	—	3	2	no	—
796	C₄⋊C₄	—	3	4	no	—
797	C₄⋊C₄	—	3	4	no	—
798	C₄⋊C₄	—	3	2	no	—
799	C₄⋊C₄	—	3	2	no	—
800	C₄⋊C₄	—	3	4	no	—
801	C₄⋊C₄	—	3	4	no	—
802	C₄⋊C₄	—	3	2	no	—
803	C₄⋊C₄	—	3	4	no	—
804	C₄⋊C₄	—	3	4	no	—
805	C₄⋊C₄	—	3	2	no	—
806	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
807	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
808	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
809	C₂²⋊C₄	—	3	2	no	—
810	C₂²⋊C₄	—	3	4	no	—
811	C₂²⋊C₄	—	3	4	no	—
812	C₂²⋊C₄	—	3	4	no	—
813	C₂²⋊C₄	—	3	4	no	—
814	C₂²⋊C₄	—	3	4	no	—
815	C₂²⋊C₄	—	3	2	no	—
816	C₂²⋊C₄	—	3	4	no	—
817	C₂²⋊C₄	—	3	2	no	—
818	C₂²⋊C₄	—	3	4	no	—
819	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
823	C₄²	—	3	2	no	—
824	C₄²	—	3	4	no	—
825	C₄²	—	3	4	no	—
826	C₄²	—	3	4	no	—
827	C₄²	—	3	2	no	—
828	C₄²	—	3	2	no	—
829	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
830	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
831	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
832	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
833	C₂²×C₃	—	2	2	no	—
834	C₂²×C₃	—	2	2	no	—
835	C₂²×C₃	—	2	1	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	1	no	—
838	C₂²×C₃	—	2	2	no	—
839	C₂²×C₃	—	2	2	no	—
840	C₂²×C₃	—	2	1	no	—
841	C₂²×C₃	—	2	2	no	—
842	C₂²×C₃	—	2	1	no	—
843	C₂²×C₃	—	2	4	no	—
844	C₂²×C₃	—	2	2	no	—
845	C₂²×C₃	—	2	2	no	—
846	C₂²×C₃	—	2	2	no	—
847	C₂²×C₃	—	2	2	no	—
848	C₂²×C₃	—	2	2	no	—
849	C₂²×C₃	—	2	2	no	—
850	C₂²×C₃	—	2	4	no	—
851	C₂²×C₃	—	2	2	no	—
852	C₂²×C₃	—	2	1	no	—
853	C₂²×C₃	—	4	2	no	—
854	C₂²×C₃	—	4	2	no	—
855	C₂²×C₃	—	4	2	no	—
856	C₂²×C₃	—	4	2	no	—
857	C₂²×C₃	—	4	8	no	—
858	C₂²×C₃	—	4	8	no	—
859	C₂²×C₃	—	4	16	no	—
860	C₂²×C₃	—	6	2	no	—
861	C₂²×C₃	—	6	2	no	—
862	C₂²×C₃	—	6	2	no	—
863	C₂²×C₃	C₂×#235	1	4	yes	—
864	C₂²×C₃	C₂×#237	1	2	yes	—
865	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
866	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
867	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
868	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
869	C₂×D₃	—	2	2	no	—
870	C₂×D₃	—	2	2	no	—
871	C₂×D₃	—	2	2	no	—
872	C₃×C₄	—	2	2	no	—
873	C₃×C₄	—	2	1	no	—
874	C₃×C₄	—	2	2	no	—
875	C₃×C₄	—	2	2	no	—
876	C₃×C₄	—	2	1	no	—
877	C₃×C₄	—	2	1	no	—
878	C₃×C₄	—	2	2	no	—
879	C₃×C₄	—	2	2	no	—
880	C₃×C₄	—	2	1	no	—
881	C₃×C₄	—	2	1	no	—
882	C₃×C₄	—	2	1	no	—
883	C₃×C₄	—	2	2	no	—
884	C₃×C₄	—	2	2	no	—
885	C₃×C₄	—	2	2	no	—
886	C₃×C₄	—	4	2	no	—
887	C₃×C₄	—	4	2	no	—
888	C₃×C₄	—	4	1	no	—
889	C₃×C₄	—	4	1	no	—
890	C₃×C₄	—	6	2	no	—
891	C₃×C₄	—	6	4	no	—
892	C₃×C₄	—	6	2	no	—
893	C₃×C₄	—	6	2	no	—
894	C₃×C₄	—	6	4	no	—
895	C₃×C₄	C₂×#235	1	2	yes	—
896	C₃×C₄	C₂×#237	1	2	yes	—
897	C₃×C₄	C₂×#237	1	2	yes	—
898	C₃×C₄	C₂×C₃×#41	1	2	yes	—
899	C₃×C₄	C₂×C₃×#41	1	2	yes	—
900	C₃×C₄	C₂×C₃×#41	1	2	yes	—
901	Dic₃	—	2	2	no	—
902	Dic₃	—	2	4	no	—
903	Dic₃	—	2	2	no	—
904	Dic₃	—	2	4	no	—
905	Dic₃	—	2	2	no	—
906	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
907	C₂³	—	2	4	no	—
908	C₂³	—	2	4	no	—
909	C₂³	—	3	2	no	—
910	C₂³	—	4	2	no	—
911	C₂³	C₂³×C₃×D₃	1	2	yes	—
912	C₂³	C₂³×C₃×D₃	1	2	yes	—
913	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
914	Q₈	—	6	4	no	—
915	Q₈	—	6	2	no	—
916	Q₈	—	12	2	no	—
917	D₄	—	2	4	no	—
918	D₄	—	2	2	no	—
919	D₄	—	6	8	no	—
920	D₄	—	6	4	no	—
921	D₄	—	6	2	no	—
922	D₄	—	12	4	no	—
923	D₄	C₃×#235	1	4	yes	complemented
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	4	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	3	2	no	—
931	C₂×C₄	—	3	2	no	—
932	C₂×C₄	—	3	4	no	—
933	C₂×C₄	—	3	2	no	—
934	C₂×C₄	—	3	4	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	6	8	no	—
937	C₂×C₄	—	6	4	no	—
938	C₂×C₄	—	6	4	no	—
939	C₂×C₄	—	12	2	no	—
940	C₂×C₄	—	12	4	no	—
941	C₂×C₄	C₃×#237	1	4	yes	complemented
942	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
943	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
944	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
945	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
946	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
947	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
948	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
949	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
950	C₂×C₃	—	2	4	no	—
951	C₂×C₃	—	2	2	no	—
952	C₂×C₃	—	2	4	no	—
953	C₂×C₃	—	2	2	no	—
954	C₂×C₃	—	2	4	no	—
955	C₂×C₃	—	2	1	no	—
956	C₂×C₃	—	2	1	no	—
957	C₂×C₃	—	2	1	no	—
958	C₂×C₃	—	4	4	no	—
959	C₂×C₃	—	4	4	no	—
960	C₂×C₃	—	4	2	no	—
961	C₂×C₃	—	4	2	no	—
962	C₂×C₃	—	12	2	no	—
963	C₂×C₃	C₂²×#235	1	1	yes	characteristic
964	C₂×C₃	C₂²×#237	1	1	yes	characteristic
965	C₂×C₃	#5964	1	1	yes	characteristic
966	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
967	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
968	C₂×C₃	C₃×#585	1	1	yes	characteristic
969	D₃	—	4	2	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	4	8	no	—
978	C₂²	—	6	2	no	—
979	C₂²	—	6	2	no	—
980	C₂²	—	6	2	no	—
981	C₂²	C₂×C₃×#235	1	4	yes	—
982	C₂²	C₂×C₃×#237	1	2	yes	—
983	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
984	C₄	—	2	1	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	6	2	no	—
990	C₄	—	6	4	no	—
991	C₄	—	6	2	no	—
992	C₄	—	6	2	no	—
993	C₄	—	6	4	no	—
994	C₄	C₂×C₃×#235	1	2	yes	—
995	C₄	C₂×C₃×#237	1	2	yes	—
996	C₄	C₂×C₃×#237	1	2	yes	—
997	C₃	—	2	1	no	—
998	C₃	#85764	1	1	yes	characteristic, direct product factor
999	C₃	C₃×#3475	1	1	yes	characteristic, complemented
1000	C₂	—	2	2	no	—
1001	C₂	—	2	4	no	—
1002	C₂	—	4	2	no	—
1003	C₂	—	12	2	no	—
1004	C₂	C₂²×C₃×#235	1	1	yes	characteristic
1005	C₂	C₂²×C₃×#237	1	1	yes	characteristic
1006	C₂	C₃×#5964	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	C₂×C₃²×C₄×D₄	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×C₄×D₄	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄×D₄	C₂	semidirect
2. C₃×#5806	C₂	semidirect
3. C₃×#5791	C₂	semidirect
4. C₂×C₃×#926	C₂	semidirect
5. C₃×#5565	C₂	semidirect
6. C₃×#5563	C₂	semidirect
7. C₃×#5557	C₂	semidirect
8. C₃×#5555	C₂	semidirect
9. C₃×#5543	C₂	semidirect
10. C₃×#5542	C₂	semidirect
11. C₃×#5541	C₂	semidirect
12. C₃×#5538	C₂	semidirect
13. C₃×C₄×#237	C₂	semidirect
14. C₃×#5513	C₂	semidirect
15. C₃×#5495	C₂	semidirect
16. C₃×C₄×#235	C₂	semidirect
17. C₃×#5470	C₂	semidirect
19. #85764	C₃	direct (N × H)
40. C₃×#930	C₂²	semidirect
41. C₃×#930	C₂²	semidirect
45. C₃×C₄×#67	C₂²	semidirect
46. C₃×C₄×#67	C₂²	semidirect
50. C₃×#926	C₂²	semidirect
51. C₃×#926	C₂²	semidirect
52. C₃×#926	C₂²	semidirect
53. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
54. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
57. C₃×#924	C₂²	semidirect
58. C₃×#924	C₂²	semidirect
59. C₂×C₃×C₄×Dic₃	C₂²	semidirect
60. C₃×#898	C₂²	semidirect
61. C₃×#897	C₂²	semidirect
62. C₃×#892	C₂²	semidirect
63. C₃×#890	C₂²	semidirect
64. C₃×#889	C₂²	semidirect
65. C₃×#887	C₂²	semidirect
66. C₃×#886	C₂²	semidirect
67. C₃×#885	C₂²	semidirect
68. C₃×#883	C₂²	semidirect
69. C₃×#67⋊C₄	C₂²	semidirect
70. C₃×#879	C₂²	semidirect
71. C₃×#879	C₂²	semidirect
72. C₃×#878	C₂²	semidirect
73. C₃×#877	C₂²	semidirect
74. C₃×C₄×D₁₂	C₂²	semidirect
75. C₃×C₄×D₁₂	C₂²	semidirect
76. C₃×#872	C₂²	semidirect
77. C₃×C₄²×D₃	C₂²	semidirect
78. C₃×#870	C₂²	semidirect
79. C₃×#869	C₂²	semidirect
80. C₃×#869	C₂²	semidirect
81. C₃×C₄×Dic₆	C₂²	semidirect
82. C₃×C₄×Dic₆	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
101. C₂×C₃×C₄×D₄	D₃	semidirect
102. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
104. #5806	C₂×C₃	semidirect
105. #5791	C₂×C₃	semidirect
106. C₂×#926	C₂×C₃	semidirect
107. #5565	C₂×C₃	semidirect
108. #5563	C₂×C₃	semidirect
109. #5557	C₂×C₃	semidirect
110. #5555	C₂×C₃	semidirect
111. #5543	C₂×C₃	semidirect
112. #5542	C₂×C₃	semidirect
113. #5541	C₂×C₃	semidirect
114. #5538	C₂×C₃	semidirect
115. C₄×#237	C₂×C₃	semidirect
116. #5513	C₂×C₃	semidirect
117. #5495	C₂×C₃	semidirect
118. C₄×#235	C₂×C₃	semidirect
119. #5470	C₂×C₃	semidirect
286. #930	C₂²×C₃	semidirect
287. #930	C₂²×C₃	semidirect
291. C₄×#67	C₂²×C₃	semidirect
292. C₄×#67	C₂²×C₃	semidirect
296. #926	C₂²×C₃	semidirect
297. #926	C₂²×C₃	semidirect
298. #926	C₂²×C₃	semidirect
299. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
300. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
303. #924	C₂²×C₃	semidirect
304. #924	C₂²×C₃	semidirect
305. C₂×C₄×Dic₃	C₂²×C₃	semidirect
306. #898	C₂²×C₃	semidirect
307. #897	C₂²×C₃	semidirect
308. #892	C₂²×C₃	semidirect
309. #890	C₂²×C₃	semidirect
310. #889	C₂²×C₃	semidirect
311. #887	C₂²×C₃	semidirect
312. #886	C₂²×C₃	semidirect
313. #885	C₂²×C₃	semidirect
314. #883	C₂²×C₃	semidirect
315. #67⋊C₄	C₂²×C₃	semidirect
316. #879	C₂²×C₃	semidirect
317. #879	C₂²×C₃	semidirect
318. #878	C₂²×C₃	semidirect
319. #877	C₂²×C₃	semidirect
320. C₄×D₁₂	C₂²×C₃	semidirect
321. C₄×D₁₂	C₂²×C₃	semidirect
322. #872	C₂²×C₃	semidirect
323. C₄²×D₃	C₂²×C₃	semidirect
324. #870	C₂²×C₃	semidirect
325. #869	C₂²×C₃	semidirect
326. #869	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
328. C₄×Dic₆	C₂²×C₃	semidirect
329. C₄×Dic₆	C₂²×C₃	semidirect
330. C₄×Dic₆	C₂²×C₃	semidirect
340. C₃²×D₄	#41	semidirect
348. C₂×C₃²×C₄	#41	semidirect
389. C₂×C₄×D₄	C₃×D₃	semidirect
680. C₃×D₄	#235	semidirect
681. C₃×D₄	C₃×#41	semidirect
722. C₂×C₃×C₄	#237	semidirect
723. C₂×C₃×C₄	C₃×#41	semidirect
906. C₃²	#3475	semidirect
923. D₄	C₃×#235	semidirect
941. C₂×C₄	C₃×#237	semidirect
998. C₃	#85764	direct (N × H)
999. C₃	C₃×#3475	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×D₄	2
C₃×#5806	2
C₃×#5791	2
C₂×C₃×#926	2
C₃×#5565	2
C₃×#5563	2
C₃×#5557	2
C₃×#5555	2
C₃×#5543	2
C₃×#5542	2
C₃×#5541	2
C₃×#5538	2
C₃×C₄×#237	2
C₃×#5513	2
C₃×#5495	2
C₃×C₄×#235	2
C₃×#5470	2
C₃×#3475	3
#85764	3

Subgroups — C3×#85764 #11903454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85764 #11903454