Subgroups — #86436

Order 384.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	#5711	C₂	1	1	yes	maximal, characteristic, complemented
3	#5709	C₂	1	1	yes	maximal, characteristic, complemented
4	#5709	C₂	1	1	yes	maximal, characteristic, complemented
5	#5708	C₂	1	1	yes	maximal, characteristic, complemented
6	#5697	C₂	1	1	yes	maximal, characteristic, complemented
7	#5696	C₂	1	1	yes	maximal, characteristic, complemented
8	#5695	C₂	1	1	yes	maximal, characteristic, complemented
9	#5693	C₂	1	1	yes	maximal, characteristic, complemented
10	#5666	C₂	1	1	yes	maximal, characteristic, complemented
11	#5666	C₂	1	1	yes	maximal, characteristic, complemented
12	#5663	C₂	1	1	yes	maximal, characteristic, complemented
13	#5663	C₂	1	1	yes	maximal, characteristic, complemented
14	#5663	C₂	1	1	yes	maximal, characteristic, complemented
15	#5661	C₂	1	1	yes	maximal, characteristic, complemented
16	#5656	C₂	1	1	yes	maximal, characteristic, complemented
17	#5655	C₂	1	1	yes	maximal, characteristic, complemented
18	#5645	C₂	1	1	yes	maximal, characteristic, complemented
19	#5638	C₂	1	1	yes	maximal, characteristic, complemented
20	#5638	C₂	1	1	yes	maximal, characteristic, complemented
21	#5629	C₂	1	1	yes	maximal, characteristic, complemented
22	#5629	C₂	1	1	yes	maximal, characteristic, complemented
23	#5627	C₂	1	1	yes	maximal, characteristic, complemented
24	#5620	C₂	1	1	yes	maximal, characteristic, complemented
25	#5599	C₂	1	1	yes	maximal, characteristic, complemented
26	#5562	C₂	1	1	yes	maximal, characteristic, complemented
27	#5553	C₂	1	1	yes	maximal, characteristic, complemented
28	#5547	C₂	1	1	yes	maximal, characteristic, complemented
29	#5540	C₂	1	1	yes	maximal, characteristic, complemented
30	#5514	C₂	1	1	yes	maximal, characteristic, complemented
31	#5507	C₂	1	1	yes	maximal, characteristic, complemented
32	#3539	—	3	1	no	maximal, Sylow
33	C₂×#239	C₂²	1	1	yes	characteristic
34	C₂×#237	C₂²	1	1	yes	characteristic
35	C₂×#235	C₂²	1	1	yes	characteristic
36	C₂×#235	C₂²	1	1	yes	characteristic, complemented
37	C₂×#235	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
39	C₃×#126	C₂²	1	1	yes	characteristic
40	C₃×#126	C₂²	1	1	yes	characteristic, complemented
41	C₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃×#123	C₂²	1	1	yes	characteristic
44	C₃×#123	C₂²	1	1	yes	characteristic
45	C₃×#123	C₂²	1	1	yes	characteristic
46	C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×#121	C₂²	1	1	yes	characteristic
51	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	#946	C₂²	1	1	yes	characteristic
55	#946	C₂²	1	1	yes	characteristic, complemented
56	#946	C₂²	1	1	yes	characteristic, complemented
57	#940	C₂²	1	1	yes	characteristic
58	#940	C₂²	1	1	yes	characteristic
59	#940	C₂²	1	1	yes	characteristic
60	#940	C₂²	1	1	yes	characteristic, complemented
61	#939	C₂²	1	1	yes	characteristic
62	#939	C₂²	1	1	yes	characteristic
63	#939	C₂²	1	1	yes	characteristic
64	#939	C₂²	1	1	yes	characteristic, complemented
65	#938	C₂²	1	1	yes	characteristic
66	#937	C₂²	1	1	yes	characteristic
67	#937	C₂²	1	1	yes	characteristic
68	#930	C₂²	1	1	yes	characteristic
69	#930	C₂²	1	1	yes	characteristic
70	#930	C₂²	1	1	yes	characteristic
71	#930	C₂²	1	1	yes	characteristic
72	#930	C₂²	1	1	yes	characteristic
73	#930	C₂²	1	1	yes	characteristic
74	#930	C₂²	1	1	yes	characteristic, complemented
75	#929	C₂²	1	1	yes	characteristic
76	#929	C₂²	1	1	yes	characteristic
77	#929	C₂²	1	1	yes	characteristic, complemented
78	C₄×#67	C₂²	1	1	yes	characteristic
79	C₄×#67	C₂²	1	1	yes	characteristic
80	C₄×#67	C₂²	1	1	yes	characteristic, complemented
81	C₄×#67	C₂²	1	1	yes	characteristic, complemented
82	C₄×#67	C₂²	1	1	yes	characteristic, complemented
83	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	#898	C₂²	1	1	yes	characteristic
85	#898	C₂²	1	1	yes	characteristic
86	#898	C₂²	1	1	yes	characteristic
87	#898	C₂²	1	1	yes	characteristic
88	#898	C₂²	1	1	yes	characteristic
89	#898	C₂²	1	1	yes	characteristic, complemented
90	#898	C₂²	1	1	yes	characteristic, complemented
91	#896	C₂²	1	1	yes	characteristic
92	#896	C₂²	1	1	yes	characteristic
93	#896	C₂²	1	1	yes	characteristic
94	#896	C₂²	1	1	yes	characteristic, complemented
95	#896	C₂²	1	1	yes	characteristic, complemented
96	#895	C₂²	1	1	yes	characteristic
97	#895	C₂²	1	1	yes	characteristic
98	#895	C₂²	1	1	yes	characteristic
99	#895	C₂²	1	1	yes	characteristic
100	#895	C₂²	1	1	yes	characteristic
101	#895	C₂²	1	1	yes	characteristic
102	#895	C₂²	1	1	yes	characteristic
103	#895	C₂²	1	1	yes	characteristic
104	#895	C₂²	1	1	yes	characteristic, complemented
105	#895	C₂²	1	1	yes	characteristic, complemented
106	#895	C₂²	1	1	yes	characteristic, complemented
107	#894	C₂²	1	1	yes	characteristic
108	#894	C₂²	1	1	yes	characteristic
109	#894	C₂²	1	1	yes	characteristic
110	#894	C₂²	1	1	yes	characteristic
111	#894	C₂²	1	1	yes	characteristic
112	#894	C₂²	1	1	yes	characteristic
113	#894	C₂²	1	1	yes	characteristic
114	#894	C₂²	1	1	yes	characteristic, complemented
115	#894	C₂²	1	1	yes	characteristic, complemented
116	#894	C₂²	1	1	yes	characteristic, complemented
117	#893	C₂²	1	1	yes	characteristic
118	#893	C₂²	1	1	yes	characteristic
119	#893	C₂²	1	1	yes	characteristic
120	#893	C₂²	1	1	yes	characteristic
121	#893	C₂²	1	1	yes	characteristic, complemented
122	#893	C₂²	1	1	yes	characteristic, complemented
123	#892	C₂²	1	1	yes	characteristic
124	#892	C₂²	1	1	yes	characteristic, complemented
125	#892	C₂²	1	1	yes	characteristic, complemented
126	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
127	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
129	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
130	#890	C₂²	1	1	yes	characteristic, complemented
131	#890	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#889	C₂²	1	1	yes	characteristic, complemented
134	#889	C₂²	1	1	yes	characteristic, complemented
135	#889	C₂²	1	1	yes	characteristic, complemented
136	#889	C₂²	1	1	yes	characteristic, complemented
137	#889	C₂²	1	1	yes	characteristic, complemented
138	#888	C₂²	1	1	yes	characteristic, complemented
139	#887	C₂²	1	1	yes	characteristic, complemented
140	#886	C₂²	1	1	yes	characteristic
141	#886	C₂²	1	1	yes	characteristic, complemented
142	#886	C₂²	1	1	yes	characteristic, complemented
143	#884	C₂²	1	1	yes	characteristic
144	#884	C₂²	1	1	yes	characteristic
145	#884	C₂²	1	1	yes	characteristic
146	#884	C₂²	1	1	yes	characteristic
147	#884	C₂²	1	1	yes	characteristic
148	#884	C₂²	1	1	yes	characteristic
149	#884	C₂²	1	1	yes	characteristic
150	#884	C₂²	1	1	yes	characteristic
151	#884	C₂²	1	1	yes	characteristic
152	#884	C₂²	1	1	yes	characteristic
153	#884	C₂²	1	1	yes	characteristic
154	#884	C₂²	1	1	yes	characteristic, complemented
155	#884	C₂²	1	1	yes	characteristic, complemented
156	#884	C₂²	1	1	yes	characteristic, complemented
157	#884	C₂²	1	1	yes	characteristic, complemented
158	#884	C₂²	1	1	yes	characteristic, complemented
159	#883	C₂²	1	1	yes	characteristic
160	#883	C₂²	1	1	yes	characteristic
161	#883	C₂²	1	1	yes	characteristic
162	#883	C₂²	1	1	yes	characteristic
163	#883	C₂²	1	1	yes	characteristic
164	#883	C₂²	1	1	yes	characteristic, complemented
165	#882	C₂²	1	1	yes	characteristic
166	#882	C₂²	1	1	yes	characteristic
167	#882	C₂²	1	1	yes	characteristic
168	#882	C₂²	1	1	yes	characteristic
169	#67⋊C₄	C₂²	1	1	yes	characteristic
170	#67⋊C₄	C₂²	1	1	yes	characteristic
171	#67⋊C₄	C₂²	1	1	yes	characteristic
172	#67⋊C₄	C₂²	1	1	yes	characteristic
173	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
174	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
176	#879	C₂²	1	1	yes	characteristic
177	#879	C₂²	1	1	yes	characteristic, complemented
178	#878	C₂²	1	1	yes	characteristic
179	#877	C₂²	1	1	yes	characteristic
180	#876	C₂²	1	1	yes	characteristic
181	#874	C₂²	1	1	yes	characteristic
182	C₄×D₁₂	C₂²	1	1	yes	characteristic
183	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
184	#872	C₂²	1	1	yes	characteristic
185	#872	C₂²	1	1	yes	characteristic, complemented
186	#872	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#560	—	3	1	no	—
189	#560	—	3	1	no	—
190	#560	—	3	1	no	—
191	#560	—	3	1	no	—
192	#553	—	3	1	no	—
193	#553	—	3	1	no	—
194	#553	—	3	1	no	—
195	#553	—	3	1	no	—
196	#553	—	3	1	no	—
197	#553	—	3	1	no	—
198	#552	—	3	1	no	—
199	#552	—	3	1	no	—
200	#550	—	3	1	no	—
201	#550	—	3	1	no	—
202	#547	—	3	1	no	—
203	#547	—	3	1	no	—
204	#541	—	3	1	no	—
205	#540	—	3	1	no	—
206	#540	—	3	1	no	—
207	#540	—	3	1	no	—
208	#540	—	3	1	no	—
209	#540	—	3	1	no	—
210	#539	—	3	1	no	—
211	#539	—	3	1	no	—
212	#539	—	3	1	no	—
213	#539	D₃	1	1	yes	characteristic, complemented
214	#537	—	3	1	no	—
215	#537	—	3	1	no	—
216	#525	—	3	1	no	—
217	#525	—	3	1	no	—
218	#525	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
229	C₂×#67	C₂³	1	1	yes	characteristic
230	C₂×#67	C₂³	1	1	yes	characteristic
231	C₂×#67	C₂³	1	1	yes	characteristic
232	C₂×#67	C₂³	1	1	yes	characteristic
233	C₂×#67	C₂³	1	1	yes	characteristic
234	C₂×#67	C₂³	1	1	yes	characteristic
235	C₂×#67	C₂³	1	1	yes	characteristic
236	C₂×#67	C₂³	1	1	yes	characteristic
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	C₂²×Dic₃	C₂³	1	1	yes	characteristic
246	C₂²×Dic₃	C₂³	1	1	yes	characteristic
247	C₂²×Dic₃	C₂³	1	1	yes	characteristic
248	#239	—	4	2	no	—
249	#237	—	4	2	no	—
250	#235	—	4	2	no	—
251	#235	—	4	2	no	—
252	#235	—	4	2	no	—
253	C₂×D₁₂	C₂³	1	1	yes	characteristic
254	C₂×D₁₂	C₂³	1	1	yes	characteristic
255	C₂×D₁₂	C₂³	1	1	yes	characteristic
256	C₂×D₁₂	C₂³	1	1	yes	characteristic
257	C₂×D₁₂	C₂³	1	1	yes	characteristic
258	C₂×D₁₂	C₂³	1	1	yes	characteristic
259	C₂×D₁₂	C₂³	1	1	yes	characteristic
260	C₂×D₁₂	C₂³	1	1	yes	characteristic
261	C₂×D₁₂	C₂³	1	1	yes	characteristic
262	C₂×D₁₂	C₂³	1	1	yes	characteristic
263	C₂×D₁₂	C₂³	1	1	yes	characteristic
264	C₂×D₁₂	C₂³	1	1	yes	characteristic
265	C₂×D₁₂	C₂³	1	1	yes	characteristic
266	C₂×D₁₂	C₂³	1	1	yes	characteristic
267	C₂×C₄×D₃	—	4	2	no	—
268	C₂×C₄×D₃	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×C₄×D₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
284	C₂×Dic₆	C₂³	1	1	yes	characteristic
285	C₂×Dic₆	C₂³	1	1	yes	characteristic
286	C₃×C₄⋊C₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₃×C₄⋊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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₃×C₄²	C₂³	1	1	yes	characteristic
311	C₃×C₄²	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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
317	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
318	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
319	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
320	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
321	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
322	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
345	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
346	C₄⋊Dic₃	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	Dic₃⋊C₄	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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
371	Dic₃⋊C₄	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	C₂×#41	—	3	1	no	—
381	C₂×#41	—	3	1	no	—
382	C₂×#41	—	3	1	no	—
383	C₂×#41	—	3	1	no	—
384	C₂×#41	—	3	1	no	—
385	C₂³×C₄	—	3	1	no	—
386	C₄⋊Q₈	—	3	1	no	—
387	#127	—	3	1	no	—
388	#127	—	3	1	no	—
389	#127	—	3	1	no	—
390	#127	—	3	1	no	—
391	#127	—	3	1	no	—
392	#126	—	3	1	no	—
393	#126	—	3	1	no	—
394	#126	—	3	1	no	—
395	#126	—	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	C₂×D₃	1	1	yes	characteristic
403	#126	C₂×D₃	1	1	yes	characteristic, complemented
404	#125	—	3	1	no	—
405	#125	—	3	1	no	—
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	3	1	no	—
412	#125	C₂×D₃	1	1	yes	characteristic, complemented
413	#125	C₂×D₃	1	1	yes	characteristic, complemented
414	#123	—	3	1	no	—
415	#123	—	3	1	no	—
416	#123	—	3	1	no	—
417	#123	—	3	1	no	—
418	#123	—	3	1	no	—
419	#123	—	3	1	no	—
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	#123	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
437	#123	C₂×D₃	1	1	yes	characteristic
438	#123	C₂×D₃	1	1	yes	characteristic
439	#123	C₂×D₃	1	1	yes	characteristic, complemented
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
450	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
451	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
452	#121	—	3	1	no	—
453	#121	—	3	1	no	—
454	#121	—	3	1	no	—
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	—	3	1	no	—
470	#121	—	3	1	no	—
471	#121	—	3	1	no	—
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	—	3	1	no	—
478	#121	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	#121	—	3	1	no	—
487	#121	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	—	3	1	no	—
491	#121	C₂×D₃	1	1	yes	characteristic
492	#120	—	3	1	no	—
493	#120	—	3	1	no	—
494	#120	—	3	1	no	—
495	#120	—	3	1	no	—
496	#120	—	3	1	no	—
497	#120	—	3	1	no	—
498	C₄×Q₈	—	3	1	no	—
499	C₄×Q₈	—	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	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	—	3	1	no	—
518	C₄×D₄	—	3	1	no	—
519	C₄×D₄	—	3	1	no	—
520	C₄×D₄	C₂×D₃	1	1	yes	characteristic
521	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
522	#117	—	3	1	no	—
523	#117	—	3	1	no	—
524	#117	—	3	1	no	—
525	#117	—	3	1	no	—
526	#117	—	3	1	no	—
527	#117	—	3	1	no	—
528	#117	—	3	1	no	—
529	C₂×C₄⋊C₄	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	—	3	1	no	—
533	C₂×C₄⋊C₄	—	3	1	no	—
534	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
535	C₂³×C₃	C₂⁴	1	1	yes	characteristic
536	C₂³×C₃	C₂⁴	1	1	yes	characteristic
537	C₂³×C₃	C₂⁴	1	1	yes	characteristic
538	C₂²×D₃	—	4	1	no	—
539	C₂²×D₃	—	4	1	no	—
540	C₂²×D₃	—	4	1	no	—
541	C₂²×D₃	C₂⁴	1	1	yes	characteristic
542	C₂²×D₃	C₂⁴	1	1	yes	characteristic
543	C₂²×D₃	C₂⁴	1	1	yes	characteristic
544	C₂²×D₃	C₂⁴	1	1	yes	characteristic
545	C₂²×D₃	C₂⁴	1	1	yes	characteristic
546	C₂²×D₃	C₂⁴	1	1	yes	characteristic
547	C₃×Q₈	—	4	1	no	—
548	C₃×D₄	—	4	1	no	—
549	C₃×D₄	—	4	1	no	—
550	C₃×D₄	—	4	1	no	—
551	C₂×C₃×C₄	—	4	1	no	—
552	C₂×C₃×C₄	—	4	1	no	—
553	C₂×C₃×C₄	—	4	1	no	—
554	C₂×C₃×C₄	—	4	1	no	—
555	C₂×C₃×C₄	—	4	1	no	—
556	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
557	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
558	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
568	#67	—	2	2	no	—
569	#67	—	2	2	no	—
570	#67	—	4	1	no	—
571	#67	—	4	1	no	—
572	#67	—	4	1	no	—
573	#67	—	4	1	no	—
574	#67	—	4	1	no	—
575	#67	—	4	1	no	—
576	#67	—	4	1	no	—
577	#67	—	4	1	no	—
578	#67	—	4	1	no	—
579	#67	—	4	1	no	—
580	#67	—	4	1	no	—
581	#67	—	4	1	no	—
582	#67	—	4	1	no	—
583	#67	—	4	1	no	—
584	C₂×Dic₃	—	2	2	no	—
585	C₂×Dic₃	—	4	1	no	—
586	C₂×Dic₃	—	4	1	no	—
587	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
588	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
589	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
590	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
591	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
592	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
593	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
594	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
595	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
596	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
597	D₁₂	—	4	1	no	—
598	D₁₂	—	4	1	no	—
599	D₁₂	—	4	1	no	—
600	D₁₂	—	4	1	no	—
601	D₁₂	—	4	1	no	—
602	D₁₂	—	4	1	no	—
603	D₁₂	—	4	1	no	—
604	D₁₂	—	4	1	no	—
605	D₁₂	—	4	1	no	—
606	D₁₂	—	4	1	no	—
607	D₁₂	—	4	1	no	—
608	D₁₂	—	4	1	no	—
609	D₁₂	—	4	1	no	—
610	D₁₂	—	4	1	no	—
611	C₄×D₃	—	2	2	no	—
612	C₄×D₃	—	2	2	no	—
613	C₄×D₃	—	2	2	no	—
614	C₄×D₃	—	2	2	no	—
615	C₄×D₃	—	4	1	no	—
616	C₄×D₃	—	4	1	no	—
617	C₄×D₃	—	4	1	no	—
618	C₄×D₃	—	4	1	no	—
619	C₄×D₃	—	4	1	no	—
620	C₄×D₃	—	4	1	no	—
621	C₄×D₃	—	4	1	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	Dic₆	—	2	2	no	—
628	Dic₆	—	2	2	no	—
629	C₂⁴	—	3	1	no	—
630	#41	—	12	2	no	—
631	#41	—	12	2	no	—
632	#41	—	12	2	no	—
633	#41	—	12	2	no	—
634	#41	—	12	2	no	—
635	C₂×Q₈	—	3	1	no	—
636	C₂×Q₈	—	3	1	no	—
637	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
638	C₂×D₄	—	3	1	no	—
639	C₂×D₄	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	3	1	no	—
642	C₂×D₄	—	3	1	no	—
643	C₂×D₄	—	3	1	no	—
644	C₂×D₄	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	3	1	no	—
649	C₂×D₄	—	3	1	no	—
650	C₂×D₄	—	3	1	no	—
651	C₂×D₄	—	3	1	no	—
652	C₂×D₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
669	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
670	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
671	C₂²×C₄	—	3	1	no	—
672	C₂²×C₄	—	3	1	no	—
673	C₂²×C₄	—	3	1	no	—
674	C₂²×C₄	—	3	1	no	—
675	C₂²×C₄	—	3	1	no	—
676	C₂²×C₄	—	3	1	no	—
677	C₂²×C₄	—	3	1	no	—
678	C₂²×C₄	—	3	1	no	—
679	C₂²×C₄	—	3	1	no	—
680	C₂²×C₄	—	3	1	no	—
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	—	12	2	no	—
691	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
692	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
693	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
694	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
695	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
696	C₄⋊C₄	—	3	1	no	—
697	C₄⋊C₄	—	3	1	no	—
698	C₄⋊C₄	—	3	1	no	—
699	C₄⋊C₄	—	3	1	no	—
700	C₄⋊C₄	—	3	1	no	—
701	C₄⋊C₄	—	3	1	no	—
702	C₄⋊C₄	—	3	1	no	—
703	C₄⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄²	—	3	1	no	—
781	C₄²	—	3	1	no	—
782	C₄²	—	3	1	no	—
783	C₄²	—	3	1	no	—
784	C₄²	—	3	1	no	—
785	C₄²	—	3	1	no	—
786	C₄²	—	3	1	no	—
787	C₄²	—	3	1	no	—
788	C₄²	C₂²×D₃	1	1	yes	characteristic
789	C₄²	C₂²×D₃	1	1	yes	characteristic
790	C₂²×C₃	—	2	1	no	—
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	—	2	1	no	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	1	no	—
795	C₂²×C₃	—	2	1	no	—
796	C₂²×C₃	—	2	1	no	—
797	C₂²×C₃	—	2	1	no	—
798	C₂²×C₃	—	2	1	no	—
799	C₂²×C₃	C₂⁵	1	1	yes	characteristic
800	C₂×D₃	—	2	1	no	—
801	C₂×D₃	—	2	1	no	—
802	C₂×D₃	—	2	1	no	—
803	C₂×D₃	—	2	1	no	—
804	C₂×D₃	—	2	1	no	—
805	C₂×D₃	—	2	1	no	—
806	C₂×D₃	—	2	1	no	—
807	C₂×D₃	—	2	1	no	—
808	C₂×D₃	—	2	1	no	—
809	C₂×D₃	—	2	1	no	—
810	C₂×D₃	—	2	1	no	—
811	C₂×D₃	—	2	1	no	—
812	C₂×D₃	—	2	1	no	—
813	C₂×D₃	—	2	1	no	—
814	C₂×D₃	—	2	1	no	—
815	C₂×D₃	—	2	1	no	—
816	C₂×D₃	—	2	1	no	—
817	C₂×D₃	—	2	1	no	—
818	C₂×D₃	—	4	4	no	—
819	C₃×C₄	—	2	1	no	—
820	C₃×C₄	—	2	1	no	—
821	C₃×C₄	—	2	1	no	—
822	C₃×C₄	—	2	1	no	—
823	C₃×C₄	—	2	1	no	—
824	C₃×C₄	—	2	1	no	—
825	C₃×C₄	—	2	1	no	—
826	C₃×C₄	—	2	1	no	—
827	C₃×C₄	—	2	1	no	—
828	C₃×C₄	—	2	1	no	—
829	C₃×C₄	—	2	1	no	—
830	C₃×C₄	—	2	1	no	—
831	Dic₃	—	2	1	no	—
832	Dic₃	—	2	1	no	—
833	Dic₃	—	2	1	no	—
834	Dic₃	—	2	1	no	—
835	Dic₃	—	2	1	no	—
836	Dic₃	—	2	1	no	—
837	Dic₃	—	2	1	no	—
838	Dic₃	—	2	1	no	—
839	Dic₃	—	2	1	no	—
840	Dic₃	H(5,𝔽₂)	1	2	yes	—
841	C₂³	—	3	1	no	—
842	C₂³	—	3	1	no	—
843	C₂³	—	3	1	no	—
844	C₂³	—	3	1	no	—
845	C₂³	—	3	1	no	—
846	C₂³	—	3	1	no	—
847	C₂³	—	12	1	no	—
848	C₂³	—	12	1	no	—
849	C₂³	—	12	1	no	—
850	C₂³	C₂³×D₃	1	1	yes	characteristic
851	C₂³	C₂³×D₃	1	1	yes	characteristic
852	C₂³	C₂³×D₃	1	1	yes	characteristic
853	Q₈	—	4	1	no	—
854	Q₈	—	6	2	no	—
855	Q₈	—	6	2	no	—
856	D₄	—	4	1	no	—
857	D₄	—	4	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	6	2	no	—
860	D₄	—	6	2	no	—
861	D₄	—	12	1	no	—
862	D₄	—	12	1	no	—
863	D₄	—	12	1	no	—
864	D₄	—	12	1	no	—
865	D₄	—	12	1	no	—
866	D₄	—	12	1	no	—
867	D₄	—	12	1	no	—
868	D₄	—	12	1	no	—
869	D₄	—	12	1	no	—
870	D₄	—	12	1	no	—
871	D₄	—	12	1	no	—
872	D₄	—	12	1	no	—
873	D₄	—	12	1	no	—
874	D₄	—	12	1	no	—
875	D₄	—	12	1	no	—
876	D₄	—	12	1	no	—
877	D₄	—	12	1	no	—
878	D₄	—	12	1	no	—
879	D₄	—	12	1	no	—
880	D₄	—	12	1	no	—
881	D₄	—	12	1	no	—
882	D₄	—	12	1	no	—
883	D₄	—	12	1	no	—
884	D₄	—	12	1	no	—
885	D₄	—	12	1	no	—
886	D₄	—	12	1	no	—
887	D₄	—	12	1	no	—
888	D₄	—	12	1	no	—
889	C₂×C₄	—	3	1	no	—
890	C₂×C₄	—	3	1	no	—
891	C₂×C₄	—	3	1	no	—
892	C₂×C₄	—	3	1	no	—
893	C₂×C₄	—	3	1	no	—
894	C₂×C₄	—	3	1	no	—
895	C₂×C₄	—	3	1	no	—
896	C₂×C₄	—	3	1	no	—
897	C₂×C₄	—	3	1	no	—
898	C₂×C₄	—	3	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	6	2	no	—
905	C₂×C₄	—	6	2	no	—
906	C₂×C₄	—	6	2	no	—
907	C₂×C₄	—	6	2	no	—
908	C₂×C₄	—	6	2	no	—
909	C₂×C₄	—	12	1	no	—
910	C₂×C₄	—	12	1	no	—
911	C₂×C₄	—	12	1	no	—
912	C₂×C₄	—	12	1	no	—
913	C₂×C₄	—	12	1	no	—
914	C₂×C₄	—	12	1	no	—
915	C₂×C₄	—	12	1	no	—
916	C₂×C₄	—	12	1	no	—
917	C₂×C₄	—	12	1	no	—
918	C₂×C₄	—	12	1	no	—
919	C₂×C₄	—	12	1	no	—
920	C₂×C₄	—	12	1	no	—
921	C₂×C₄	—	12	1	no	—
922	C₂×C₄	—	12	1	no	—
923	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
924	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
925	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
926	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
935	C₂×C₃	—	4	1	no	—
936	C₂×C₃	—	4	1	no	—
937	C₂×C₃	—	4	1	no	—
938	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
939	C₂×C₃	#585	1	1	yes	characteristic
940	C₂×C₃	#585	1	1	yes	characteristic
941	D₃	—	4	1	no	—
942	D₃	—	4	1	no	—
943	D₃	—	4	1	no	—
944	D₃	—	4	1	no	—
945	D₃	—	4	1	no	—
946	D₃	—	4	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	6	1	no	—
957	C₂²	—	6	1	no	—
958	C₂²	—	6	1	no	—
959	C₂²	—	6	1	no	—
960	C₂²	—	6	1	no	—
961	C₂²	—	6	1	no	—
962	C₂²	—	6	1	no	—
963	C₂²	—	6	1	no	—
964	C₂²	—	6	1	no	—
965	C₂²	—	6	1	no	—
966	C₂²	—	6	1	no	—
967	C₂²	—	6	1	no	—
968	C₂²	—	6	1	no	—
969	C₂²	—	6	1	no	—
970	C₂²	—	6	1	no	—
971	C₂²	—	6	1	no	—
972	C₂²	—	6	1	no	—
973	C₂²	—	6	1	no	—
974	C₂²	—	12	4	no	—
975	C₂²	C₂⁴×D₃	1	1	yes	characteristic
976	C₄	—	2	1	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	3	2	no	—
989	C₄	—	6	1	no	—
990	C₄	—	6	1	no	—
991	C₄	—	6	1	no	—
992	C₄	—	6	1	no	—
993	C₄	—	6	1	no	—
994	C₄	—	6	1	no	—
995	C₄	—	6	1	no	—
996	C₄	—	6	1	no	—
997	C₄	—	6	1	no	—
998	C₃	#3539	1	1	yes	characteristic, complemented, Sylow
999	C₂	—	4	1	no	—
1000	C₂	—	4	1	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	12	1	no	—
1003	C₂	—	12	1	no	—
1004	C₂	—	12	1	no	—
1005	C₂	—	12	1	no	—
1006	C₂	—	12	1	no	—
1007	C₂	—	12	1	no	—
1008	C₂	#5964	1	1	yes	characteristic
1009	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1010	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#539	C₂
hypercenter	#539	D₃
hypocenter	C₃	#3539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. C₃×#539	C₂	semidirect
2. #5711	C₂	semidirect
3. #5709	C₂	semidirect
4. #5709	C₂	semidirect
5. #5708	C₂	semidirect
6. #5697	C₂	semidirect
7. #5696	C₂	semidirect
8. #5695	C₂	semidirect
9. #5693	C₂	semidirect
10. #5666	C₂	semidirect
11. #5666	C₂	semidirect
12. #5663	C₂	semidirect
13. #5663	C₂	semidirect
14. #5663	C₂	semidirect
15. #5661	C₂	semidirect
16. #5656	C₂	semidirect
17. #5655	C₂	semidirect
18. #5645	C₂	semidirect
19. #5638	C₂	semidirect
20. #5638	C₂	semidirect
21. #5629	C₂	semidirect
22. #5629	C₂	semidirect
23. #5627	C₂	semidirect
24. #5620	C₂	semidirect
25. #5599	C₂	semidirect
26. #5562	C₂	semidirect
27. #5553	C₂	semidirect
28. #5547	C₂	semidirect
29. #5540	C₂	semidirect
30. #5514	C₂	semidirect
31. #5507	C₂	semidirect
36. C₂×#235	C₂²	semidirect
37. C₂×#235	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#125	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
46. C₃×#123	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₂²⋊Q₈	C₂²	semidirect
52. C₃×C₄×D₄	C₂²	semidirect
53. C₂×C₃×C₄⋊C₄	C₂²	semidirect
55. #946	C₂²	semidirect
56. #946	C₂²	semidirect
60. #940	C₂²	semidirect
64. #939	C₂²	semidirect
74. #930	C₂²	semidirect
77. #929	C₂²	semidirect
80. C₄×#67	C₂²	semidirect
81. C₄×#67	C₂²	semidirect
82. C₄×#67	C₂²	semidirect
83. C₂×Dic₃⋊C₄	C₂²	semidirect
89. #898	C₂²	semidirect
90. #898	C₂²	semidirect
94. #896	C₂²	semidirect
95. #896	C₂²	semidirect
104. #895	C₂²	semidirect
105. #895	C₂²	semidirect
106. #895	C₂²	semidirect
114. #894	C₂²	semidirect
115. #894	C₂²	semidirect
116. #894	C₂²	semidirect
121. #893	C₂²	semidirect
122. #893	C₂²	semidirect
124. #892	C₂²	semidirect
125. #892	C₂²	semidirect
126. D₃×C₄⋊C₄	C₂²	semidirect
127. D₃×C₄⋊C₄	C₂²	semidirect
128. D₃×C₄⋊C₄	C₂²	semidirect
129. D₃×C₄⋊C₄	C₂²	semidirect
130. #890	C₂²	semidirect
131. #890	C₂²	semidirect
132. #889	C₂²	semidirect
133. #889	C₂²	semidirect
134. #889	C₂²	semidirect
135. #889	C₂²	semidirect
136. #889	C₂²	semidirect
137. #889	C₂²	semidirect
138. #888	C₂²	semidirect
139. #887	C₂²	semidirect
141. #886	C₂²	semidirect
142. #886	C₂²	semidirect
154. #884	C₂²	semidirect
155. #884	C₂²	semidirect
156. #884	C₂²	semidirect
157. #884	C₂²	semidirect
158. #884	C₂²	semidirect
164. #883	C₂²	semidirect
173. #67⋊C₄	C₂²	semidirect
174. #67⋊C₄	C₂²	semidirect
175. #67⋊C₄	C₂²	semidirect
177. #879	C₂²	semidirect
183. C₄×D₁₂	C₂²	semidirect
185. #872	C₂²	semidirect
186. #872	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
213. #539	D₃	semidirect
403. #126	C₂×D₃	semidirect
412. #125	C₂×D₃	semidirect
413. #125	C₂×D₃	semidirect
439. #123	C₂×D₃	semidirect
450. C₂²⋊Q₈	C₂×D₃	semidirect
451. C₂²⋊Q₈	C₂×D₃	semidirect
521. C₄×D₄	C₂×D₃	semidirect
534. C₂×C₄⋊C₄	C₂×D₃	semidirect
998. C₃	#3539	semidirect

Maximal subgroups

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

subgroup	index
C₃×#539	2
#5711	2
#5709	2
#5708	2
#5697	2
#5696	2
#5695	2
#5693	2
#5666	2
#5663	2
#5661	2
#5656	2
#5655	2
#5645	2
#5638	2
#5629	2
#5627	2
#5620	2
#5599	2
#5562	2
#5553	2
#5547	2
#5540	2
#5514	2
#5507	2
#3539	3