Subgroups — #86392

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#5710	C₂	1	1	yes	maximal, characteristic, complemented
3	#5706	C₂	1	1	yes	maximal, characteristic, complemented
4	#5705	C₂	1	1	yes	maximal, characteristic, complemented
5	#5702	C₂	1	1	yes	maximal, characteristic, complemented
6	#5677	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	#5670	C₂	1	1	yes	maximal, characteristic, complemented
9	#5669	C₂	1	1	yes	maximal, characteristic, complemented
10	#5664	C₂	1	1	yes	maximal, characteristic, complemented
11	#5658	C₂	1	1	yes	maximal, characteristic, complemented
12	#5657	C₂	1	1	yes	maximal, characteristic, complemented
13	#5649	C₂	1	1	yes	maximal, characteristic, complemented
14	#5637	C₂	1	1	yes	maximal, characteristic, complemented
15	#5632	C₂	1	1	yes	maximal, characteristic, complemented
16	#5616	C₂	1	1	yes	maximal, characteristic, complemented
17	#5613	C₂	1	1	yes	maximal, characteristic, complemented
18	#5610	C₂	1	1	yes	maximal, characteristic, complemented
19	#5610	C₂	1	1	yes	maximal, characteristic, complemented
20	#5598	C₂	1	1	yes	maximal, characteristic, complemented
21	#5596	C₂	1	1	yes	maximal, characteristic, complemented
22	#5591	C₂	1	1	yes	maximal, characteristic, complemented
23	#5591	C₂	1	1	yes	maximal, characteristic, complemented
24	#5590	C₂	1	1	yes	maximal, characteristic, complemented
25	#5587	C₂	1	1	yes	maximal, characteristic, complemented
26	#5560	C₂	1	1	yes	maximal, characteristic, complemented
27	#5545	C₂	1	1	yes	maximal, characteristic, complemented
28	#5538	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#885	C₂	1	1	yes	maximal, characteristic, complemented
31	#5486	C₂	1	1	yes	maximal, characteristic, complemented
32	#3514	—	3	1	no	maximal, Sylow
33	C₂²×#67	C₂²	1	1	yes	characteristic
34	C₂²×#67	C₂²	1	1	yes	characteristic
35	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×#237	C₂²	1	1	yes	characteristic
37	C₂×#237	C₂²	1	1	yes	characteristic, complemented
38	C₂×#237	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
40	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
41	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
42	C₃×#126	C₂²	1	1	yes	characteristic, complemented
43	C₃×#126	C₂²	1	1	yes	characteristic, complemented
44	C₃×#124	C₂²	1	1	yes	characteristic, complemented
45	C₃×#124	C₂²	1	1	yes	characteristic, complemented
46	C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₃×#123	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×#121	C₂²	1	1	yes	characteristic, complemented
50	C₃×#121	C₂²	1	1	yes	characteristic, complemented
51	C₃×#121	C₂²	1	1	yes	characteristic, complemented
52	C₃×#120	C₂²	1	1	yes	characteristic
53	C₃×#120	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×#217	C₂²	1	1	yes	characteristic, complemented
58	C₂×#217	C₂²	1	1	yes	characteristic, complemented
59	#947	C₂²	1	1	yes	characteristic, complemented
60	#946	C₂²	1	1	yes	characteristic, complemented
61	#944	C₂²	1	1	yes	characteristic, complemented
62	#940	C₂²	1	1	yes	characteristic
63	#939	C₂²	1	1	yes	characteristic
64	#939	C₂²	1	1	yes	characteristic
65	#939	C₂²	1	1	yes	characteristic
66	#939	C₂²	1	1	yes	characteristic, complemented
67	#939	C₂²	1	1	yes	characteristic, complemented
68	#939	C₂²	1	1	yes	characteristic, complemented
69	#939	C₂²	1	1	yes	characteristic, complemented
70	#938	C₂²	1	1	yes	characteristic, complemented
71	#938	C₂²	1	1	yes	characteristic, complemented
72	#937	C₂²	1	1	yes	characteristic
73	#937	C₂²	1	1	yes	characteristic, complemented
74	#937	C₂²	1	1	yes	characteristic, complemented
75	#937	C₂²	1	1	yes	characteristic, complemented
76	#936	C₂²	1	1	yes	characteristic, complemented
77	#936	C₂²	1	1	yes	characteristic, complemented
78	#935	C₂²	1	1	yes	characteristic, complemented
79	#935	C₂²	1	1	yes	characteristic, complemented
80	#935	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
85	#930	C₂²	1	1	yes	characteristic, complemented
86	#929	C₂²	1	1	yes	characteristic, complemented
87	C₄×#67	C₂²	1	1	yes	characteristic
88	C₄×#67	C₂²	1	1	yes	characteristic
89	C₄×#67	C₂²	1	1	yes	characteristic, complemented
90	C₄×#67	C₂²	1	1	yes	characteristic, complemented
91	C₄×#67	C₂²	1	1	yes	characteristic, complemented
92	C₄×#67	C₂²	1	1	yes	characteristic, complemented
93	C₄×#67	C₂²	1	1	yes	characteristic, complemented
94	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	#926	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
100	#898	C₂²	1	1	yes	characteristic, complemented
101	#898	C₂²	1	1	yes	characteristic, complemented
102	#898	C₂²	1	1	yes	characteristic, complemented
103	#898	C₂²	1	1	yes	characteristic, complemented
104	#897	C₂²	1	1	yes	characteristic, complemented
105	#897	C₂²	1	1	yes	characteristic, complemented
106	#896	C₂²	1	1	yes	characteristic, complemented
107	#896	C₂²	1	1	yes	characteristic, complemented
108	#896	C₂²	1	1	yes	characteristic, complemented
109	#894	C₂²	1	1	yes	characteristic, complemented
110	#894	C₂²	1	1	yes	characteristic, complemented
111	#894	C₂²	1	1	yes	characteristic, complemented
112	#894	C₂²	1	1	yes	characteristic, complemented
113	#893	C₂²	1	1	yes	characteristic, complemented
114	#893	C₂²	1	1	yes	characteristic, complemented
115	#892	C₂²	1	1	yes	characteristic, complemented
116	#892	C₂²	1	1	yes	characteristic, complemented
117	#892	C₂²	1	1	yes	characteristic, complemented
118	#889	C₂²	1	1	yes	characteristic, complemented
119	#888	C₂²	1	1	yes	characteristic, complemented
120	#888	C₂²	1	1	yes	characteristic, complemented
121	#887	C₂²	1	1	yes	characteristic, complemented
122	#887	C₂²	1	1	yes	characteristic, complemented
123	#887	C₂²	1	1	yes	characteristic, complemented
124	#886	C₂²	1	1	yes	characteristic, complemented
125	#886	C₂²	1	1	yes	characteristic, complemented
126	#885	C₂²	1	1	yes	characteristic
127	#885	C₂²	1	1	yes	characteristic
128	#885	C₂²	1	1	yes	characteristic
129	#885	C₂²	1	1	yes	characteristic, complemented
130	#885	C₂²	1	1	yes	characteristic, complemented
131	#885	C₂²	1	1	yes	characteristic, complemented
132	#885	C₂²	1	1	yes	characteristic, complemented
133	#885	C₂²	1	1	yes	characteristic, complemented
134	#885	C₂²	1	1	yes	characteristic, complemented
135	#885	C₂²	1	1	yes	characteristic, complemented
136	#885	C₂²	1	1	yes	characteristic, complemented
137	#885	C₂²	1	1	yes	characteristic, complemented
138	#885	C₂²	1	1	yes	characteristic, complemented
139	#885	C₂²	1	1	yes	characteristic, complemented
140	#885	C₂²	1	1	yes	characteristic, complemented
141	#884	C₂²	1	1	yes	characteristic
142	#884	C₂²	1	1	yes	characteristic
143	#884	C₂²	1	1	yes	characteristic, complemented
144	#884	C₂²	1	1	yes	characteristic, complemented
145	#883	C₂²	1	1	yes	characteristic, complemented
146	#883	C₂²	1	1	yes	characteristic, complemented
147	#882	C₂²	1	1	yes	characteristic
148	#882	C₂²	1	1	yes	characteristic
149	#67⋊C₄	C₂²	1	1	yes	characteristic
150	#67⋊C₄	C₂²	1	1	yes	characteristic
151	#67⋊C₄	C₂²	1	1	yes	characteristic
152	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	#879	C₂²	1	1	yes	characteristic, complemented
167	#879	C₂²	1	1	yes	characteristic, complemented
168	#879	C₂²	1	1	yes	characteristic, complemented
169	#878	C₂²	1	1	yes	characteristic, complemented
170	#878	C₂²	1	1	yes	characteristic, complemented
171	#878	C₂²	1	1	yes	characteristic, complemented
172	#878	C₂²	1	1	yes	characteristic, complemented
173	#878	C₂²	1	1	yes	characteristic, complemented
174	#878	C₂²	1	1	yes	characteristic, complemented
175	#877	C₂²	1	1	yes	characteristic, complemented
176	#877	C₂²	1	1	yes	characteristic, complemented
177	#877	C₂²	1	1	yes	characteristic, complemented
178	#877	C₂²	1	1	yes	characteristic, complemented
179	#877	C₂²	1	1	yes	characteristic, complemented
180	#876	C₂²	1	1	yes	characteristic, complemented
181	#875	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
183	#872	C₂²	1	1	yes	characteristic, complemented
184	#872	C₂²	1	1	yes	characteristic, complemented
185	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#559	—	3	1	no	—
189	#556	—	3	1	no	—
190	#555	—	3	1	no	—
191	#555	—	3	1	no	—
192	#551	—	3	1	no	—
193	#551	—	3	1	no	—
194	#551	—	3	1	no	—
195	#551	—	3	1	no	—
196	D₄×Q₈	—	3	1	no	—
197	#548	—	3	1	no	—
198	#548	—	3	1	no	—
199	#546	—	3	1	no	—
200	#546	—	3	1	no	—
201	#546	—	3	1	no	—
202	#546	—	3	1	no	—
203	D₄²	—	3	1	no	—
204	#542	—	3	1	no	—
205	#542	—	3	1	no	—
206	#538	—	3	1	no	—
207	#538	—	3	1	no	—
208	#538	—	3	1	no	—
209	#538	D₃	1	1	yes	characteristic, complemented
210	#532	—	3	1	no	—
211	#529	—	3	1	no	—
212	#529	—	3	1	no	—
213	#529	—	3	1	no	—
214	C₂×#124	—	3	1	no	—
215	C₂×#124	—	3	1	no	—
216	#518	—	3	1	no	—
217	#518	—	3	1	no	—
218	C₄×#41	—	3	1	no	—
219	C₂⁴×C₃	C₂³	1	1	yes	characteristic
220	C₂³×D₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₂³×D₃	C₂³	1	1	yes	characteristic
223	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
235	C₂×#67	—	2	4	no	—
236	C₂×#67	—	4	2	no	—
237	C₂×#67	C₂³	1	1	yes	characteristic
238	C₂×#67	C₂³	1	1	yes	characteristic
239	C₂×#67	C₂³	1	1	yes	characteristic
240	C₂×#67	C₂³	1	1	yes	characteristic
241	C₂×#67	C₂³	1	1	yes	characteristic
242	C₂×#67	C₂³	1	1	yes	characteristic
243	C₂×#67	C₂³	1	1	yes	characteristic
244	C₂×#67	C₂³	1	1	yes	characteristic
245	C₂×#67	C₂³	1	1	yes	characteristic
246	C₂×#67	C₂³	1	1	yes	characteristic
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂×#67	C₂³	1	1	yes	characteristic
249	C₂×#67	C₂³	1	1	yes	characteristic
250	C₂×#67	C₂³	1	1	yes	characteristic
251	C₂²×Dic₃	C₂³	1	1	yes	characteristic
252	C₂²×Dic₃	C₂³	1	1	yes	characteristic
253	C₂²×Dic₃	C₂³	1	1	yes	characteristic
254	C₂²×Dic₃	C₂³	1	1	yes	characteristic
255	C₂²×Dic₃	C₂³	1	1	yes	characteristic
256	C₂²×Dic₃	C₂³	1	1	yes	characteristic
257	C₂²×Dic₃	C₂³	1	1	yes	characteristic
258	C₂²×Dic₃	C₂³	1	1	yes	characteristic
259	C₂²×Dic₃	C₂³	1	1	yes	characteristic
260	D₃×Q₈	—	4	2	no	—
261	#237	—	2	4	no	—
262	#237	—	4	2	no	—
263	#237	—	4	2	no	—
264	D₃×D₄	—	2	4	no	—
265	D₃×D₄	—	4	2	no	—
266	C₂×D₁₂	C₂³	1	1	yes	characteristic
267	C₂×D₁₂	C₂³	1	1	yes	characteristic
268	C₂×D₁₂	C₂³	1	1	yes	characteristic
269	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
279	C₂×Dic₆	—	4	2	no	—
280	C₂×Dic₆	C₂³	1	1	yes	characteristic
281	C₂×Dic₆	C₂³	1	1	yes	characteristic
282	C₂×Dic₆	C₂³	1	1	yes	characteristic
283	C₂×Dic₆	C₂³	1	1	yes	characteristic
284	C₂×Dic₆	C₂³	1	1	yes	characteristic
285	C₂×Dic₆	C₂³	1	1	yes	characteristic
286	C₂×Dic₆	C₂³	1	1	yes	characteristic
287	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
299	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
300	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
302	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₃×C₄²	C₂³	1	1	yes	characteristic
308	C₃×C₄²	C₂³	1	1	yes	characteristic
309	#217	C₂³	1	1	yes	characteristic
310	#217	C₂³	1	1	yes	characteristic
311	#217	C₂³	1	1	yes	characteristic
312	#217	C₂³	1	1	yes	characteristic
313	#217	C₂³	1	1	yes	characteristic
314	#217	C₂³	1	1	yes	characteristic
315	#217	C₂³	1	1	yes	characteristic
316	#217	C₂³	1	1	yes	characteristic
317	#217	C₂³	1	1	yes	characteristic
318	#217	C₂³	1	1	yes	characteristic
319	#217	C₂³	1	1	yes	characteristic
320	#217	C₂³	1	1	yes	characteristic
321	#217	C₂³	1	1	yes	characteristic
322	#217	C₂³	1	1	yes	characteristic
323	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
324	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
325	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
326	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
327	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
328	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
329	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
342	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
343	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
344	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
347	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
348	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
349	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
350	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
351	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
352	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
353	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
354	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
369	C₄×Dic₃	C₂³	1	1	yes	characteristic
370	C₄×Dic₃	C₂³	1	1	yes	characteristic
371	C₄×Dic₃	C₂³	1	1	yes	characteristic
372	C₄×Dic₃	C₂³	1	1	yes	characteristic
373	C₄×Dic₃	C₂³	1	1	yes	characteristic
374	C₄×Dic₃	C₂³	1	1	yes	characteristic
375	C₄×Dic₃	C₂³	1	1	yes	characteristic
376	C₄×Dic₃	C₂³	1	1	yes	characteristic
377	C₄×Dic₃	C₂³	1	1	yes	characteristic
378	C₄×Dic₃	C₂³	1	1	yes	characteristic
379	C₄×Dic₃	C₂³	1	1	yes	characteristic
380	C₄×Dic₃	C₂³	1	1	yes	characteristic
381	C₄×Dic₃	C₂³	1	1	yes	characteristic
382	C₄×Dic₃	C₂³	1	1	yes	characteristic
383	C₂×#41	—	3	1	no	—
384	C₂×#41	—	3	1	no	—
385	C₂×#41	—	3	1	no	—
386	C₂²×Q₈	—	3	1	no	—
387	C₂²×Q₈	—	3	1	no	—
388	C₂²×D₄	—	3	1	no	—
389	C₂²×D₄	—	3	1	no	—
390	C₂²×D₄	—	3	1	no	—
391	C₂²×D₄	—	3	1	no	—
392	C₄⋊Q₈	—	3	1	no	—
393	C₄⋊Q₈	—	3	1	no	—
394	C₄⋊Q₈	—	3	1	no	—
395	#127	—	3	1	no	—
396	#126	—	3	1	no	—
397	#126	—	3	1	no	—
398	#126	—	3	1	no	—
399	#126	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	C₂×D₃	1	1	yes	characteristic, complemented
405	#126	C₂×D₃	1	1	yes	characteristic, complemented
406	#125	—	3	1	no	—
407	#124	—	3	1	no	—
408	#124	—	3	1	no	—
409	#124	—	3	1	no	—
410	#124	—	3	1	no	—
411	#124	—	3	1	no	—
412	#124	—	3	1	no	—
413	#124	—	3	1	no	—
414	#124	—	3	1	no	—
415	#124	—	3	1	no	—
416	#124	—	3	1	no	—
417	#124	—	3	1	no	—
418	#124	—	3	1	no	—
419	#124	—	3	1	no	—
420	#124	—	3	1	no	—
421	#124	—	3	1	no	—
422	#124	—	3	1	no	—
423	#124	—	3	1	no	—
424	#124	—	3	1	no	—
425	#124	—	3	1	no	—
426	#124	C₂×D₃	1	1	yes	characteristic, complemented
427	#124	C₂×D₃	1	1	yes	characteristic, complemented
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	3	1	no	—
434	#123	—	3	1	no	—
435	#123	—	3	1	no	—
436	#123	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	C₂×D₃	1	1	yes	characteristic, complemented
441	#123	C₂×D₃	1	1	yes	characteristic, complemented
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	C₂²⋊Q₈	—	3	1	no	—
447	C₂²⋊Q₈	—	3	1	no	—
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	—	3	1	no	—
452	C₂²⋊Q₈	—	3	1	no	—
453	C₂²⋊Q₈	—	3	1	no	—
454	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
455	#121	—	3	1	no	—
456	#121	—	3	1	no	—
457	#121	—	3	1	no	—
458	#121	—	3	1	no	—
459	#121	—	3	1	no	—
460	#121	—	3	1	no	—
461	#121	—	3	1	no	—
462	#121	—	3	1	no	—
463	#121	—	3	1	no	—
464	#121	—	3	1	no	—
465	#121	—	3	1	no	—
466	#121	—	3	1	no	—
467	#121	—	3	1	no	—
468	#121	—	3	1	no	—
469	#121	C₂×D₃	1	1	yes	characteristic, complemented
470	#121	C₂×D₃	1	1	yes	characteristic, complemented
471	#121	C₂×D₃	1	1	yes	characteristic, complemented
472	#120	—	3	1	no	—
473	#120	—	3	1	no	—
474	#120	—	3	1	no	—
475	#120	—	3	1	no	—
476	#120	—	3	1	no	—
477	#120	—	3	1	no	—
478	#120	C₂×D₃	1	1	yes	characteristic
479	#120	C₂×D₃	1	1	yes	characteristic, complemented
480	C₄×Q₈	—	3	1	no	—
481	C₄×Q₈	—	3	1	no	—
482	C₄×Q₈	—	3	1	no	—
483	C₄×Q₈	—	3	1	no	—
484	C₄×Q₈	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	—	3	1	no	—
487	C₄×D₄	—	3	1	no	—
488	C₄×D₄	—	3	1	no	—
489	C₄×D₄	—	3	1	no	—
490	C₄×D₄	—	3	1	no	—
491	C₄×D₄	—	3	1	no	—
492	C₄×D₄	—	3	1	no	—
493	C₄×D₄	—	3	1	no	—
494	C₄×D₄	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	—	3	1	no	—
507	C₄×D₄	—	3	1	no	—
508	C₄×D₄	—	3	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
511	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
512	#117	—	3	1	no	—
513	#117	—	3	1	no	—
514	#117	—	3	1	no	—
515	#117	—	3	1	no	—
516	#117	—	3	1	no	—
517	#117	—	3	1	no	—
518	#117	—	3	1	no	—
519	#117	—	3	1	no	—
520	#117	—	3	1	no	—
521	#117	—	3	1	no	—
522	#117	—	3	1	no	—
523	C₂×C₂²⋊C₄	—	3	1	no	—
524	C₂×C₂²⋊C₄	—	3	1	no	—
525	C₂×C₂²⋊C₄	—	3	1	no	—
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	—	3	1	no	—
528	C₂×C₂²⋊C₄	—	3	1	no	—
529	C₂×C₂²⋊C₄	—	3	1	no	—
530	C₂×C₂²⋊C₄	—	3	1	no	—
531	C₂×C₂²⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
535	C₂×C₄²	—	3	1	no	—
536	C₂×C₄²	—	3	1	no	—
537	C₂×C₄²	—	3	1	no	—
538	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	4	1	no	—
540	C₂³×C₃	—	4	1	no	—
541	C₂³×C₃	C₂⁴	1	1	yes	characteristic
542	C₂³×C₃	C₂⁴	1	1	yes	characteristic
543	C₂³×C₃	C₂⁴	1	1	yes	characteristic
544	C₂³×C₃	C₂⁴	1	1	yes	characteristic
545	C₂³×C₃	C₂⁴	1	1	yes	characteristic
546	C₂²×D₃	—	2	2	no	—
547	C₂²×D₃	—	2	2	no	—
548	C₂²×D₃	—	2	2	no	—
549	C₂²×D₃	—	4	1	no	—
550	C₂²×D₃	—	4	1	no	—
551	C₂²×D₃	—	4	1	no	—
552	C₂²×D₃	—	4	1	no	—
553	C₂²×D₃	—	4	1	no	—
554	C₂²×D₃	—	4	1	no	—
555	C₂²×D₃	C₂⁴	1	1	yes	characteristic
556	C₂²×D₃	C₂⁴	1	1	yes	characteristic
557	C₂²×D₃	C₂⁴	1	1	yes	characteristic
558	C₂²×D₃	C₂⁴	1	1	yes	characteristic
559	C₃×Q₈	—	4	1	no	—
560	C₃×D₄	—	2	2	no	—
561	C₃×D₄	—	2	2	no	—
562	C₃×D₄	—	4	1	no	—
563	C₃×D₄	—	4	1	no	—
564	C₃×D₄	—	4	1	no	—
565	C₃×D₄	—	4	1	no	—
566	C₃×D₄	—	4	1	no	—
567	C₂×C₃×C₄	—	4	1	no	—
568	C₂×C₃×C₄	—	4	1	no	—
569	C₂×C₃×C₄	—	4	1	no	—
570	C₂×C₃×C₄	—	4	1	no	—
571	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
572	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
581	#67	—	2	2	no	—
582	#67	—	2	2	no	—
583	#67	—	2	2	no	—
584	#67	—	2	2	no	—
585	#67	—	2	2	no	—
586	#67	—	2	2	no	—
587	#67	—	2	2	no	—
588	#67	—	2	2	no	—
589	#67	—	4	1	no	—
590	#67	—	4	1	no	—
591	#67	—	4	1	no	—
592	#67	—	4	1	no	—
593	#67	—	4	1	no	—
594	#67	#41	1	4	yes	complemented
595	C₂×Dic₃	—	2	2	no	—
596	C₂×Dic₃	—	2	2	no	—
597	C₂×Dic₃	—	2	2	no	—
598	C₂×Dic₃	—	2	2	no	—
599	C₂×Dic₃	—	2	2	no	—
600	C₂×Dic₃	—	4	1	no	—
601	C₂×Dic₃	—	4	1	no	—
602	C₂×Dic₃	—	4	1	no	—
603	C₂×Dic₃	—	4	1	no	—
604	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
605	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
606	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
607	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
608	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
609	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
610	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
611	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
612	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
613	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
614	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
615	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
616	D₁₂	—	2	2	no	—
617	D₁₂	—	4	1	no	—
618	D₁₂	—	4	1	no	—
619	C₄×D₃	—	2	2	no	—
620	C₄×D₃	—	2	2	no	—
621	C₄×D₃	—	2	2	no	—
622	C₄×D₃	—	4	1	no	—
623	C₄×D₃	—	4	1	no	—
624	C₄×D₃	—	4	1	no	—
625	C₄×D₃	—	4	1	no	—
626	C₄×D₃	—	4	1	no	—
627	C₄×D₃	—	4	1	no	—
628	C₄×D₃	—	4	1	no	—
629	Dic₆	—	2	2	no	—
630	Dic₆	—	2	2	no	—
631	Dic₆	—	2	2	no	—
632	Dic₆	—	2	2	no	—
633	Dic₆	—	4	1	no	—
634	Dic₆	—	4	1	no	—
635	Dic₆	—	4	1	no	—
636	C₂⁴	—	3	1	no	—
637	C₂⁴	—	3	1	no	—
638	C₂⁴	—	3	1	no	—
639	C₂⁴	C₂²×D₃	1	1	yes	characteristic
640	#41	—	6	4	no	—
641	#41	—	12	2	no	—
642	#41	—	12	2	no	—
643	C₂×Q₈	—	3	1	no	—
644	C₂×Q₈	—	3	1	no	—
645	C₂×Q₈	—	3	1	no	—
646	C₂×Q₈	—	3	1	no	—
647	C₂×Q₈	—	3	1	no	—
648	C₂×Q₈	—	3	1	no	—
649	C₂×Q₈	—	3	1	no	—
650	C₂×Q₈	—	12	2	no	—
651	C₂×Q₈	—	12	2	no	—
652	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	3	1	no	—
656	C₂×D₄	—	3	1	no	—
657	C₂×D₄	—	3	1	no	—
658	C₂×D₄	—	3	1	no	—
659	C₂×D₄	—	3	1	no	—
660	C₂×D₄	—	3	1	no	—
661	C₂×D₄	—	3	1	no	—
662	C₂×D₄	—	3	1	no	—
663	C₂×D₄	—	3	1	no	—
664	C₂×D₄	—	3	1	no	—
665	C₂×D₄	—	3	1	no	—
666	C₂×D₄	—	3	1	no	—
667	C₂×D₄	—	3	1	no	—
668	C₂×D₄	—	3	1	no	—
669	C₂×D₄	—	3	1	no	—
670	C₂×D₄	—	6	4	no	—
671	C₂×D₄	—	6	4	no	—
672	C₂×D₄	—	12	2	no	—
673	C₂×D₄	—	12	2	no	—
674	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
675	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
676	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
677	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
678	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
679	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
680	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
681	C₂²×C₄	—	3	1	no	—
682	C₂²×C₄	—	3	1	no	—
683	C₂²×C₄	—	3	1	no	—
684	C₂²×C₄	—	3	1	no	—
685	C₂²×C₄	—	3	1	no	—
686	C₂²×C₄	—	3	1	no	—
687	C₂²×C₄	—	3	1	no	—
688	C₂²×C₄	—	3	1	no	—
689	C₂²×C₄	—	3	1	no	—
690	C₂²×C₄	—	3	1	no	—
691	C₂²×C₄	—	3	1	no	—
692	C₂²×C₄	—	3	1	no	—
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	3	1	no	—
696	C₂²×C₄	—	3	1	no	—
697	C₂²×C₄	—	3	1	no	—
698	C₂²×C₄	—	3	1	no	—
699	C₂²×C₄	—	3	1	no	—
700	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
701	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
702	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
704	C₄⋊C₄	—	3	1	no	—
705	C₄⋊C₄	—	3	1	no	—
706	C₄⋊C₄	—	3	1	no	—
707	C₄⋊C₄	—	3	1	no	—
708	C₄⋊C₄	—	3	1	no	—
709	C₄⋊C₄	—	3	1	no	—
710	C₄⋊C₄	—	3	1	no	—
711	C₄⋊C₄	—	3	1	no	—
712	C₄⋊C₄	—	3	1	no	—
713	C₄⋊C₄	—	3	1	no	—
714	C₄⋊C₄	—	3	1	no	—
715	C₄⋊C₄	—	3	1	no	—
716	C₄⋊C₄	—	3	1	no	—
717	C₄⋊C₄	—	3	1	no	—
718	C₄⋊C₄	—	3	1	no	—
719	C₄⋊C₄	—	3	1	no	—
720	C₄⋊C₄	—	3	1	no	—
721	C₄⋊C₄	—	3	1	no	—
722	C₄⋊C₄	—	3	1	no	—
723	C₄⋊C₄	—	3	1	no	—
724	C₄⋊C₄	—	3	1	no	—
725	C₄⋊C₄	—	3	1	no	—
726	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
732	C₂²⋊C₄	—	3	1	no	—
733	C₂²⋊C₄	—	3	1	no	—
734	C₂²⋊C₄	—	3	1	no	—
735	C₂²⋊C₄	—	3	1	no	—
736	C₂²⋊C₄	—	3	1	no	—
737	C₂²⋊C₄	—	3	1	no	—
738	C₂²⋊C₄	—	3	1	no	—
739	C₂²⋊C₄	—	3	1	no	—
740	C₂²⋊C₄	—	3	1	no	—
741	C₂²⋊C₄	—	3	1	no	—
742	C₂²⋊C₄	—	3	1	no	—
743	C₂²⋊C₄	—	3	1	no	—
744	C₂²⋊C₄	—	3	1	no	—
745	C₂²⋊C₄	—	3	1	no	—
746	C₂²⋊C₄	—	3	1	no	—
747	C₂²⋊C₄	—	3	1	no	—
748	C₂²⋊C₄	—	3	1	no	—
749	C₂²⋊C₄	—	3	1	no	—
750	C₂²⋊C₄	—	3	1	no	—
751	C₂²⋊C₄	—	3	1	no	—
752	C₂²⋊C₄	—	3	1	no	—
753	C₂²⋊C₄	—	3	1	no	—
754	C₂²⋊C₄	—	3	1	no	—
755	C₂²⋊C₄	—	3	1	no	—
756	C₂²⋊C₄	—	3	1	no	—
757	C₂²⋊C₄	—	3	1	no	—
758	C₂²⋊C₄	—	3	1	no	—
759	C₂²⋊C₄	—	3	1	no	—
760	C₂²⋊C₄	—	3	1	no	—
761	C₂²⋊C₄	—	3	1	no	—
762	C₂²⋊C₄	—	3	1	no	—
763	C₂²⋊C₄	—	3	1	no	—
764	C₂²⋊C₄	—	3	1	no	—
765	C₂²⋊C₄	—	3	1	no	—
766	C₂²⋊C₄	—	3	1	no	—
767	C₂²⋊C₄	—	3	1	no	—
768	C₂²⋊C₄	—	3	1	no	—
769	C₂²⋊C₄	—	3	1	no	—
770	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
777	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
778	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
784	C₄²	—	3	1	no	—
785	C₄²	—	3	1	no	—
786	C₄²	—	3	1	no	—
787	C₄²	—	3	1	no	—
788	C₄²	—	3	1	no	—
789	C₄²	—	3	1	no	—
790	C₄²	—	3	1	no	—
791	C₄²	—	3	1	no	—
792	C₄²	—	3	1	no	—
793	C₄²	—	3	1	no	—
794	C₄²	—	3	1	no	—
795	C₄²	—	3	1	no	—
796	C₄²	—	3	1	no	—
797	C₄²	—	3	1	no	—
798	C₄²	C₂²×D₃	1	1	yes	characteristic
799	C₄²	C₂²×D₃	1	1	yes	characteristic
800	C₂²×C₃	—	2	1	no	—
801	C₂²×C₃	—	2	1	no	—
802	C₂²×C₃	—	2	1	no	—
803	C₂²×C₃	—	2	1	no	—
804	C₂²×C₃	—	2	1	no	—
805	C₂²×C₃	—	2	1	no	—
806	C₂²×C₃	—	2	1	no	—
807	C₂²×C₃	—	2	1	no	—
808	C₂²×C₃	—	2	1	no	—
809	C₂²×C₃	—	2	1	no	—
810	C₂²×C₃	—	2	1	no	—
811	C₂²×C₃	—	2	1	no	—
812	C₂²×C₃	—	2	1	no	—
813	C₂²×C₃	—	2	1	no	—
814	C₂²×C₃	—	8	2	no	—
815	C₂²×C₃	C₂×#41	1	2	yes	—
816	C₂²×C₃	C₂⁵	1	1	yes	characteristic
817	C₂×D₃	—	2	1	no	—
818	C₂×D₃	—	2	1	no	—
819	C₂×D₃	—	2	1	no	—
820	C₂×D₃	—	2	1	no	—
821	C₂×D₃	—	2	1	no	—
822	C₂×D₃	—	2	1	no	—
823	C₂×D₃	—	2	1	no	—
824	C₂×D₃	—	2	1	no	—
825	C₂×D₃	—	2	1	no	—
826	C₂×D₃	—	2	1	no	—
827	C₂×D₃	—	2	1	no	—
828	C₂×D₃	—	8	2	no	—
829	C₂×D₃	—	8	2	no	—
830	C₂×D₃	—	8	2	no	—
831	C₂×D₃	C₂×#41	1	2	yes	—
832	C₃×C₄	—	2	1	no	—
833	C₃×C₄	—	2	1	no	—
834	C₃×C₄	—	2	1	no	—
835	C₃×C₄	—	2	1	no	—
836	C₃×C₄	—	2	1	no	—
837	C₃×C₄	—	2	1	no	—
838	C₃×C₄	—	2	1	no	—
839	C₃×C₄	—	2	1	no	—
840	C₃×C₄	—	2	1	no	—
841	C₃×C₄	—	2	1	no	—
842	Dic₃	—	2	1	no	—
843	Dic₃	—	2	1	no	—
844	Dic₃	—	2	1	no	—
845	Dic₃	—	2	1	no	—
846	Dic₃	—	2	1	no	—
847	Dic₃	—	2	1	no	—
848	Dic₃	—	2	1	no	—
849	Dic₃	—	2	1	no	—
850	Dic₃	—	2	1	no	—
851	Dic₃	—	2	1	no	—
852	Dic₃	C₂×#41	1	2	yes	—
853	Dic₃	H(5,𝔽₂)	1	2	yes	—
854	C₂³	—	2	2	no	—
855	C₂³	—	3	1	no	—
856	C₂³	—	3	1	no	—
857	C₂³	—	3	1	no	—
858	C₂³	—	3	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	6	2	no	—
862	C₂³	—	6	2	no	—
863	C₂³	—	6	2	no	—
864	C₂³	—	12	1	no	—
865	C₂³	—	12	1	no	—
866	C₂³	—	12	1	no	—
867	C₂³	—	12	1	no	—
868	C₂³	—	12	1	no	—
869	C₂³	—	12	1	no	—
870	C₂³	C₂³×D₃	1	1	yes	characteristic
871	C₂³	C₂³×D₃	1	1	yes	characteristic
872	C₂³	C₂³×D₃	1	1	yes	characteristic
873	C₂³	C₂³×D₃	1	1	yes	characteristic
874	C₂³	C₂³×D₃	1	1	yes	characteristic
875	Q₈	—	4	1	no	—
876	Q₈	—	6	2	no	—
877	Q₈	—	6	2	no	—
878	Q₈	—	6	2	no	—
879	Q₈	—	6	2	no	—
880	Q₈	—	12	1	no	—
881	Q₈	—	12	1	no	—
882	Q₈	—	12	1	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	3	4	no	—
886	D₄	—	4	1	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	4	1	no	—
890	D₄	—	4	1	no	—
891	D₄	—	6	2	no	—
892	D₄	—	6	2	no	—
893	D₄	—	6	2	no	—
894	D₄	—	6	2	no	—
895	D₄	—	6	2	no	—
896	D₄	—	6	2	no	—
897	D₄	—	6	2	no	—
898	D₄	—	6	2	no	—
899	D₄	—	6	2	no	—
900	D₄	—	12	1	no	—
901	D₄	—	12	1	no	—
902	D₄	—	12	1	no	—
903	D₄	—	12	1	no	—
904	D₄	—	12	1	no	—
905	D₄	—	12	1	no	—
906	D₄	—	12	1	no	—
907	C₂×C₄	—	3	1	no	—
908	C₂×C₄	—	3	1	no	—
909	C₂×C₄	—	3	1	no	—
910	C₂×C₄	—	3	1	no	—
911	C₂×C₄	—	3	1	no	—
912	C₂×C₄	—	3	1	no	—
913	C₂×C₄	—	3	1	no	—
914	C₂×C₄	—	3	1	no	—
915	C₂×C₄	—	3	1	no	—
916	C₂×C₄	—	3	1	no	—
917	C₂×C₄	—	3	1	no	—
918	C₂×C₄	—	3	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	6	2	no	—
924	C₂×C₄	—	6	2	no	—
925	C₂×C₄	—	6	2	no	—
926	C₂×C₄	—	6	2	no	—
927	C₂×C₄	—	6	2	no	—
928	C₂×C₄	—	6	2	no	—
929	C₂×C₄	—	6	2	no	—
930	C₂×C₄	—	6	2	no	—
931	C₂×C₄	—	12	1	no	—
932	C₂×C₄	—	12	1	no	—
933	C₂×C₄	—	12	1	no	—
934	C₂×C₄	—	12	1	no	—
935	C₂×C₄	—	12	1	no	—
936	C₂×C₄	—	12	1	no	—
937	C₂×C₄	—	12	1	no	—
938	C₂×C₄	—	12	1	no	—
939	C₂×C₄	—	12	1	no	—
940	C₂×C₄	—	12	1	no	—
941	C₂×C₄	—	12	1	no	—
942	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
950	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
951	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
952	C₂×C₃	—	2	2	no	—
953	C₂×C₃	—	4	1	no	—
954	C₂×C₃	—	4	1	no	—
955	C₂×C₃	—	4	1	no	—
956	C₂×C₃	—	4	1	no	—
957	C₂×C₃	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂×C₃	#585	1	1	yes	characteristic
960	D₃	—	2	2	no	—
961	D₃	—	4	1	no	—
962	D₃	—	4	1	no	—
963	D₃	—	4	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	3	2	no	—
979	C₂²	—	6	1	no	—
980	C₂²	—	6	1	no	—
981	C₂²	—	6	1	no	—
982	C₂²	—	6	1	no	—
983	C₂²	—	6	1	no	—
984	C₂²	—	6	1	no	—
985	C₂²	—	6	1	no	—
986	C₂²	—	6	1	no	—
987	C₂²	—	6	1	no	—
988	C₂²	—	6	1	no	—
989	C₂²	—	6	1	no	—
990	C₂²	—	8	2	no	—
991	C₂²	—	24	2	no	—
992	C₂²	—	24	2	no	—
993	C₂²	—	24	2	no	—
994	C₂²	D₃×#41	1	2	yes	—
995	C₂²	C₂⁴×D₃	1	1	yes	characteristic
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	3	2	no	—
1007	C₄	—	3	2	no	—
1008	C₄	—	6	1	no	—
1009	C₄	—	6	1	no	—
1010	C₄	—	6	1	no	—
1011	C₄	—	6	1	no	—
1012	C₄	—	6	1	no	—
1013	C₄	—	6	1	no	—
1014	C₄	—	6	1	no	—
1015	C₄	—	6	1	no	—
1016	C₄	—	6	1	no	—
1017	C₄	—	6	1	no	—
1018	C₃	#3514	1	1	yes	characteristic, complemented, Sylow
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	6	2	no	—
1025	C₂	—	12	1	no	—
1026	C₂	—	12	1	no	—
1027	C₂	—	12	1	no	—
1028	C₂	C₂×D₃×#41	1	1	yes	characteristic
1029	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#538	C₂
hypercenter	#538	D₃
hypocenter	C₃	#3514
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₃×#538	C₂	semidirect
2. #5710	C₂	semidirect
3. #5706	C₂	semidirect
4. #5705	C₂	semidirect
5. #5702	C₂	semidirect
6. #5677	C₂	semidirect
7. D₃×#124	C₂	semidirect
8. #5670	C₂	semidirect
9. #5669	C₂	semidirect
10. #5664	C₂	semidirect
11. #5658	C₂	semidirect
12. #5657	C₂	semidirect
13. #5649	C₂	semidirect
14. #5637	C₂	semidirect
15. #5632	C₂	semidirect
16. #5616	C₂	semidirect
17. #5613	C₂	semidirect
18. #5610	C₂	semidirect
19. #5610	C₂	semidirect
20. #5598	C₂	semidirect
21. #5596	C₂	semidirect
22. #5591	C₂	semidirect
23. #5591	C₂	semidirect
24. #5590	C₂	semidirect
25. #5587	C₂	semidirect
26. #5560	C₂	semidirect
27. #5545	C₂	semidirect
28. #5538	C₂	semidirect
29. C₄×#237	C₂	semidirect
30. C₂×#885	C₂	semidirect
31. #5486	C₂	semidirect
35. C₂×D₃×Q₈	C₂²	semidirect
37. C₂×#237	C₂²	semidirect
38. C₂×#237	C₂²	semidirect
41. C₂²×Dic₆	C₂²	semidirect
42. C₃×#126	C₂²	semidirect
43. C₃×#126	C₂²	semidirect
44. C₃×#124	C₂²	semidirect
45. C₃×#124	C₂²	semidirect
46. C₃×#123	C₂²	semidirect
47. C₃×#123	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
53. C₃×#120	C₂²	semidirect
54. C₃×C₄×D₄	C₂²	semidirect
55. C₃×C₄×D₄	C₂²	semidirect
56. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
57. C₂×#217	C₂²	semidirect
58. C₂×#217	C₂²	semidirect
59. #947	C₂²	semidirect
60. #946	C₂²	semidirect
61. #944	C₂²	semidirect
66. #939	C₂²	semidirect
67. #939	C₂²	semidirect
68. #939	C₂²	semidirect
69. #939	C₂²	semidirect
70. #938	C₂²	semidirect
71. #938	C₂²	semidirect
73. #937	C₂²	semidirect
74. #937	C₂²	semidirect
75. #937	C₂²	semidirect
76. #936	C₂²	semidirect
77. #936	C₂²	semidirect
78. #935	C₂²	semidirect
79. #935	C₂²	semidirect
80. #935	C₂²	semidirect
81. D₄×Dic₃	C₂²	semidirect
82. D₄×Dic₃	C₂²	semidirect
83. D₄×Dic₃	C₂²	semidirect
84. D₄×Dic₃	C₂²	semidirect
85. #930	C₂²	semidirect
86. #929	C₂²	semidirect
89. C₄×#67	C₂²	semidirect
90. C₄×#67	C₂²	semidirect
91. C₄×#67	C₂²	semidirect
92. C₄×#67	C₂²	semidirect
93. C₄×#67	C₂²	semidirect
94. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
95. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
96. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
97. #926	C₂²	semidirect
98. C₂×C₄×Dic₃	C₂²	semidirect
99. C₂×C₄×Dic₃	C₂²	semidirect
100. #898	C₂²	semidirect
101. #898	C₂²	semidirect
102. #898	C₂²	semidirect
103. #898	C₂²	semidirect
104. #897	C₂²	semidirect
105. #897	C₂²	semidirect
106. #896	C₂²	semidirect
107. #896	C₂²	semidirect
108. #896	C₂²	semidirect
109. #894	C₂²	semidirect
110. #894	C₂²	semidirect
111. #894	C₂²	semidirect
112. #894	C₂²	semidirect
113. #893	C₂²	semidirect
114. #893	C₂²	semidirect
115. #892	C₂²	semidirect
116. #892	C₂²	semidirect
117. #892	C₂²	semidirect
118. #889	C₂²	semidirect
119. #888	C₂²	semidirect
120. #888	C₂²	semidirect
121. #887	C₂²	semidirect
122. #887	C₂²	semidirect
123. #887	C₂²	semidirect
124. #886	C₂²	semidirect
125. #886	C₂²	semidirect
129. #885	C₂²	semidirect
130. #885	C₂²	semidirect
131. #885	C₂²	semidirect
132. #885	C₂²	semidirect
133. #885	C₂²	semidirect
134. #885	C₂²	semidirect
135. #885	C₂²	semidirect
136. #885	C₂²	semidirect
137. #885	C₂²	semidirect
138. #885	C₂²	semidirect
139. #885	C₂²	semidirect
140. #885	C₂²	semidirect
143. #884	C₂²	semidirect
144. #884	C₂²	semidirect
145. #883	C₂²	semidirect
146. #883	C₂²	semidirect
152. #67⋊C₄	C₂²	semidirect
153. #67⋊C₄	C₂²	semidirect
154. #67⋊C₄	C₂²	semidirect
155. #67⋊C₄	C₂²	semidirect
156. #67⋊C₄	C₂²	semidirect
157. #67⋊C₄	C₂²	semidirect
158. #67⋊C₄	C₂²	semidirect
159. #67⋊C₄	C₂²	semidirect
160. D₃×C₂²⋊C₄	C₂²	semidirect
161. D₃×C₂²⋊C₄	C₂²	semidirect
162. D₃×C₂²⋊C₄	C₂²	semidirect
163. D₃×C₂²⋊C₄	C₂²	semidirect
164. D₃×C₂²⋊C₄	C₂²	semidirect
165. D₃×C₂²⋊C₄	C₂²	semidirect
166. #879	C₂²	semidirect
167. #879	C₂²	semidirect
168. #879	C₂²	semidirect
169. #878	C₂²	semidirect
170. #878	C₂²	semidirect
171. #878	C₂²	semidirect
172. #878	C₂²	semidirect
173. #878	C₂²	semidirect
174. #878	C₂²	semidirect
175. #877	C₂²	semidirect
176. #877	C₂²	semidirect
177. #877	C₂²	semidirect
178. #877	C₂²	semidirect
179. #877	C₂²	semidirect
180. #876	C₂²	semidirect
181. #875	C₂²	semidirect
182. C₄×D₁₂	C₂²	semidirect
183. #872	C₂²	semidirect
184. #872	C₂²	semidirect
185. C₄²×D₃	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
209. #538	D₃	semidirect
404. #126	C₂×D₃	semidirect
405. #126	C₂×D₃	semidirect
426. #124	C₂×D₃	semidirect
427. #124	C₂×D₃	semidirect
440. #123	C₂×D₃	semidirect
441. #123	C₂×D₃	semidirect
454. C₂²⋊Q₈	C₂×D₃	semidirect
469. #121	C₂×D₃	semidirect
470. #121	C₂×D₃	semidirect
471. #121	C₂×D₃	semidirect
479. #120	C₂×D₃	semidirect
510. C₄×D₄	C₂×D₃	semidirect
511. C₄×D₄	C₂×D₃	semidirect
534. C₂×C₂²⋊C₄	C₂×D₃	semidirect
594. #67	#41	semidirect
1018. C₃	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₃×#538	2
#5710	2
#5706	2
#5705	2
#5702	2
#5677	2
D₃×#124	2
#5670	2
#5669	2
#5664	2
#5658	2
#5657	2
#5649	2
#5637	2
#5632	2
#5616	2
#5613	2
#5610	2
#5598	2
#5596	2
#5591	2
#5590	2
#5587	2
#5560	2
#5545	2
#5538	2
C₄×#237	2
C₂×#885	2
#5486	2
#3514	3