Subgroups — #86902

Order 384.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#5709	C₂	1	1	yes	maximal, characteristic, complemented
3	#5706	C₂	1	1	yes	maximal, characteristic, complemented
4	#5704	C₂	1	1	yes	maximal, characteristic, complemented
5	#5702	C₂	1	1	yes	maximal, characteristic, complemented
6	#5700	C₂	1	1	yes	maximal, characteristic, complemented
7	#5696	C₂	1	1	yes	maximal, characteristic, complemented
8	#5666	C₂	1	1	yes	maximal, characteristic, complemented
9	#5660	C₂	1	1	yes	maximal, characteristic, complemented
10	#5654	C₂	1	1	yes	maximal, characteristic, complemented
11	#5648	C₂	1	1	yes	maximal, characteristic, complemented
12	#5621	C₂	1	1	yes	maximal, characteristic, complemented
13	#5620	C₂	1	1	yes	maximal, characteristic, complemented
14	#5615	C₂	1	1	yes	maximal, characteristic, complemented
15	#5615	C₂	1	1	yes	maximal, characteristic, complemented
16	#5613	C₂	1	1	yes	maximal, characteristic, complemented
17	#5610	C₂	1	1	yes	maximal, characteristic, complemented
18	#5607	C₂	1	1	yes	maximal, characteristic, complemented
19	#5599	C₂	1	1	yes	maximal, characteristic, complemented
20	#5562	C₂	1	1	yes	maximal, characteristic, complemented
21	#5560	C₂	1	1	yes	maximal, characteristic, complemented
22	#5560	C₂	1	1	yes	maximal, characteristic, complemented
23	#5559	C₂	1	1	yes	maximal, characteristic, complemented
24	#5556	C₂	1	1	yes	maximal, characteristic, complemented
25	#5552	C₂	1	1	yes	maximal, characteristic, complemented
26	#5552	C₂	1	1	yes	maximal, characteristic, complemented
27	#5548	C₂	1	1	yes	maximal, characteristic, complemented
28	#5528	C₂	1	1	yes	maximal, characteristic, complemented
29	#5527	C₂	1	1	yes	maximal, characteristic, complemented
30	#5515	C₂	1	1	yes	maximal, characteristic, complemented
31	#5507	C₂	1	1	yes	maximal, characteristic, complemented
32	#3562	—	3	1	no	maximal, Sylow
33	C₂×#237	C₂²	1	1	yes	characteristic
34	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
35	C₂×#235	C₂²	1	1	yes	characteristic
36	C₂×#235	C₂²	1	1	yes	characteristic
37	C₂×#235	C₂²	1	1	yes	characteristic, complemented
38	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×#126	C₂²	1	1	yes	characteristic, complemented
40	C₃×#126	C₂²	1	1	yes	characteristic, complemented
41	C₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₃×#123	C₂²	1	1	yes	characteristic
43	C₃×#123	C₂²	1	1	yes	characteristic, complemented
44	C₃×#121	C₂²	1	1	yes	characteristic
45	C₃×#121	C₂²	1	1	yes	characteristic
46	C₃×#121	C₂²	1	1	yes	characteristic, complemented
47	C₃×#121	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₃×#117	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	#940	C₂²	1	1	yes	characteristic
55	#940	C₂²	1	1	yes	characteristic
56	#940	C₂²	1	1	yes	characteristic, complemented
57	#940	C₂²	1	1	yes	characteristic, complemented
58	#939	C₂²	1	1	yes	characteristic
59	#939	C₂²	1	1	yes	characteristic
60	#939	C₂²	1	1	yes	characteristic
61	#939	C₂²	1	1	yes	characteristic, complemented
62	#939	C₂²	1	1	yes	characteristic, complemented
63	#939	C₂²	1	1	yes	characteristic, complemented
64	#939	C₂²	1	1	yes	characteristic, complemented
65	#938	C₂²	1	1	yes	characteristic
66	#938	C₂²	1	1	yes	characteristic, complemented
67	#938	C₂²	1	1	yes	characteristic, complemented
68	#937	C₂²	1	1	yes	characteristic
69	#937	C₂²	1	1	yes	characteristic
70	#937	C₂²	1	1	yes	characteristic
71	#937	C₂²	1	1	yes	characteristic
72	#936	C₂²	1	1	yes	characteristic, complemented
73	#935	C₂²	1	1	yes	characteristic
74	#935	C₂²	1	1	yes	characteristic, complemented
75	#935	C₂²	1	1	yes	characteristic, complemented
76	#930	C₂²	1	1	yes	characteristic
77	#930	C₂²	1	1	yes	characteristic
78	#930	C₂²	1	1	yes	characteristic
79	#930	C₂²	1	1	yes	characteristic, complemented
80	#929	C₂²	1	1	yes	characteristic
81	#929	C₂²	1	1	yes	characteristic, complemented
82	#929	C₂²	1	1	yes	characteristic, complemented
83	#929	C₂²	1	1	yes	characteristic, complemented
84	#929	C₂²	1	1	yes	characteristic, complemented
85	#929	C₂²	1	1	yes	characteristic, complemented
86	C₄×#67	C₂²	1	1	yes	characteristic
87	C₄×#67	C₂²	1	1	yes	characteristic, complemented
88	C₄×#67	C₂²	1	1	yes	characteristic, complemented
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	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
94	#924	C₂²	1	1	yes	characteristic, complemented
95	#924	C₂²	1	1	yes	characteristic, complemented
96	#898	C₂²	1	1	yes	characteristic
97	#898	C₂²	1	1	yes	characteristic
98	#898	C₂²	1	1	yes	characteristic
99	#898	C₂²	1	1	yes	characteristic, complemented
100	#898	C₂²	1	1	yes	characteristic, complemented
101	#898	C₂²	1	1	yes	characteristic, complemented
102	#896	C₂²	1	1	yes	characteristic
103	#896	C₂²	1	1	yes	characteristic
104	#896	C₂²	1	1	yes	characteristic, complemented
105	#896	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	#896	C₂²	1	1	yes	characteristic, complemented
110	#896	C₂²	1	1	yes	characteristic, complemented
111	#895	C₂²	1	1	yes	characteristic
112	#895	C₂²	1	1	yes	characteristic
113	#895	C₂²	1	1	yes	characteristic
114	#895	C₂²	1	1	yes	characteristic, complemented
115	#895	C₂²	1	1	yes	characteristic, complemented
116	#894	C₂²	1	1	yes	characteristic
117	#894	C₂²	1	1	yes	characteristic
118	#894	C₂²	1	1	yes	characteristic
119	#894	C₂²	1	1	yes	characteristic
120	#894	C₂²	1	1	yes	characteristic, complemented
121	#894	C₂²	1	1	yes	characteristic, complemented
122	#894	C₂²	1	1	yes	characteristic, complemented
123	#893	C₂²	1	1	yes	characteristic
124	#893	C₂²	1	1	yes	characteristic, complemented
125	#892	C₂²	1	1	yes	characteristic
126	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
127	#890	C₂²	1	1	yes	characteristic, complemented
128	#889	C₂²	1	1	yes	characteristic, complemented
129	#889	C₂²	1	1	yes	characteristic, complemented
130	#889	C₂²	1	1	yes	characteristic, complemented
131	#889	C₂²	1	1	yes	characteristic, complemented
132	#888	C₂²	1	1	yes	characteristic, complemented
133	#888	C₂²	1	1	yes	characteristic, complemented
134	#887	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic, complemented
137	#885	C₂²	1	1	yes	characteristic
138	#885	C₂²	1	1	yes	characteristic
139	#885	C₂²	1	1	yes	characteristic
140	#885	C₂²	1	1	yes	characteristic
141	#885	C₂²	1	1	yes	characteristic
142	#885	C₂²	1	1	yes	characteristic
143	#885	C₂²	1	1	yes	characteristic, complemented
144	#885	C₂²	1	1	yes	characteristic, complemented
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, complemented
149	#884	C₂²	1	1	yes	characteristic, complemented
150	#884	C₂²	1	1	yes	characteristic, complemented
151	#884	C₂²	1	1	yes	characteristic, complemented
152	#883	C₂²	1	1	yes	characteristic, complemented
153	#883	C₂²	1	1	yes	characteristic, complemented
154	#883	C₂²	1	1	yes	characteristic, complemented
155	#883	C₂²	1	1	yes	characteristic, complemented
156	#883	C₂²	1	1	yes	characteristic, complemented
157	#882	C₂²	1	1	yes	characteristic
158	#882	C₂²	1	1	yes	characteristic
159	#882	C₂²	1	1	yes	characteristic
160	#882	C₂²	1	1	yes	characteristic
161	#67⋊C₄	C₂²	1	1	yes	characteristic
162	#67⋊C₄	C₂²	1	1	yes	characteristic
163	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
168	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	#879	C₂²	1	1	yes	characteristic, complemented
170	#879	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	#877	C₂²	1	1	yes	characteristic, complemented
175	#877	C₂²	1	1	yes	characteristic, complemented
176	#876	C₂²	1	1	yes	characteristic
177	#876	C₂²	1	1	yes	characteristic
178	#875	C₂²	1	1	yes	characteristic
179	#875	C₂²	1	1	yes	characteristic, complemented
180	#875	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₁₂	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	#562	—	3	1	no	—
189	#562	—	3	1	no	—
190	#560	—	3	1	no	—
191	#560	—	3	1	no	—
192	#559	—	3	1	no	—
193	#556	—	3	1	no	—
194	#553	—	3	1	no	—
195	#553	D₃	1	1	yes	characteristic, complemented
196	#551	—	3	1	no	—
197	#551	—	3	1	no	—
198	#550	—	3	1	no	—
199	#548	—	3	1	no	—
200	#548	—	3	1	no	—
201	#547	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	—	3	1	no	—
204	#541	—	3	1	no	—
205	#540	—	3	1	no	—
206	#540	—	3	1	no	—
207	#540	—	3	1	no	—
208	#539	—	3	1	no	—
209	#539	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#538	—	3	1	no	—
213	#538	—	3	1	no	—
214	#536	—	3	1	no	—
215	#535	—	3	1	no	—
216	#532	—	3	1	no	—
217	#529	—	3	1	no	—
218	#529	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂³×D₃	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	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	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₃×C₄	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	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	C₂²×Dic₃	C₂³	1	1	yes	characteristic
250	C₂²×Dic₃	C₂³	1	1	yes	characteristic
251	C₂²×Dic₃	C₂³	1	1	yes	characteristic
252	C₂²×Dic₃	C₂³	1	1	yes	characteristic
253	#237	—	4	2	no	—
254	D₃×D₄	—	4	2	no	—
255	#235	—	4	2	no	—
256	#235	—	4	2	no	—
257	#235	—	4	2	no	—
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×C₄×D₃	C₂³	1	1	yes	characteristic
267	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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×Dic₆	—	4	2	no	—
278	C₂×Dic₆	C₂³	1	1	yes	characteristic
279	C₂×Dic₆	C₂³	1	1	yes	characteristic
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	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₃×C₄⋊C₄	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×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×C₄²	C₂³	1	1	yes	characteristic
305	C₃×C₄²	C₂³	1	1	yes	characteristic
306	C₃×C₄²	C₂³	1	1	yes	characteristic
307	#217	C₂³	1	1	yes	characteristic
308	#217	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	(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	(C₂×D₃)⋊C₄	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	Dic₃⋊C₄	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	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	C₂×#41	—	3	1	no	—
381	C₂×#41	—	3	1	no	—
382	C₂×#41	—	3	1	no	—
383	C₂×#41	—	3	1	no	—
384	C₂²×Q₈	—	3	1	no	—
385	C₂²×D₄	—	3	1	no	—
386	C₄⋊Q₈	—	3	1	no	—
387	C₄⋊Q₈	—	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, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
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	#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	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	—	3	1	no	—
441	#123	—	3	1	no	—
442	#123	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	C₂×D₃	1	1	yes	characteristic
445	#123	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
455	C₂²⋊Q₈	—	3	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	3	1	no	—
458	C₂²⋊Q₈	—	3	1	no	—
459	C₂²⋊Q₈	—	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	C₂×D₃	1	1	yes	characteristic
487	#121	C₂×D₃	1	1	yes	characteristic
488	#121	C₂×D₃	1	1	yes	characteristic, complemented
489	#121	C₂×D₃	1	1	yes	characteristic, complemented
490	#120	—	3	1	no	—
491	#120	—	3	1	no	—
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×Q₈	—	3	1	no	—
501	C₄×Q₈	—	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	C₂×D₃	1	1	yes	characteristic, complemented
519	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
520	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
528	C₂×C₄⋊C₄	—	3	1	no	—
529	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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×C₄²	—	3	1	no	—
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	C₂³×C₃	C₂⁴	1	1	yes	characteristic
539	C₂²×D₃	—	4	1	no	—
540	C₂²×D₃	—	4	1	no	—
541	C₂²×D₃	—	4	1	no	—
542	C₂²×D₃	—	4	1	no	—
543	C₂²×D₃	—	4	1	no	—
544	C₂²×D₃	—	4	1	no	—
545	C₂²×D₃	C₂⁴	1	1	yes	characteristic
546	C₂²×D₃	C₂⁴	1	1	yes	characteristic
547	C₂²×D₃	C₂⁴	1	1	yes	characteristic
548	C₂²×D₃	C₂⁴	1	1	yes	characteristic
549	C₂²×D₃	C₂⁴	1	1	yes	characteristic
550	C₃×D₄	—	4	1	no	—
551	C₃×D₄	—	4	1	no	—
552	C₃×D₄	—	4	1	no	—
553	C₃×D₄	—	4	1	no	—
554	C₃×D₄	—	4	1	no	—
555	C₃×D₄	—	4	1	no	—
556	C₂×C₃×C₄	—	4	1	no	—
557	C₂×C₃×C₄	—	4	1	no	—
558	C₂×C₃×C₄	—	4	1	no	—
559	C₂×C₃×C₄	—	4	1	no	—
560	C₂×C₃×C₄	—	4	1	no	—
561	C₂×C₃×C₄	—	4	1	no	—
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	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
571	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
572	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
573	#67	—	2	2	no	—
574	#67	—	2	2	no	—
575	#67	—	2	2	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	#67	—	4	1	no	—
585	#67	—	4	1	no	—
586	#67	—	4	1	no	—
587	#67	—	4	1	no	—
588	#67	—	4	1	no	—
589	C₂×Dic₃	—	2	2	no	—
590	C₂×Dic₃	—	4	1	no	—
591	C₂×Dic₃	—	4	1	no	—
592	C₂×Dic₃	—	4	1	no	—
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	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
598	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
599	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
600	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
601	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
602	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
603	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
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	D₁₂	—	4	1	no	—
612	C₄×D₃	—	2	2	no	—
613	C₄×D₃	—	2	2	no	—
614	C₄×D₃	—	4	1	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	Dic₆	—	2	2	no	—
624	Dic₆	—	2	2	no	—
625	Dic₆	—	2	2	no	—
626	Dic₆	—	4	1	no	—
627	Dic₆	—	4	1	no	—
628	Dic₆	—	4	1	no	—
629	C₂⁴	—	3	1	no	—
630	C₂⁴	—	3	1	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	—	3	1	no	—
638	C₂×Q₈	—	3	1	no	—
639	C₂×Q₈	—	3	1	no	—
640	C₂×Q₈	—	3	1	no	—
641	C₂×Q₈	—	12	2	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	—	12	2	no	—
667	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
672	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	C₂²×D₃	1	1	yes	characteristic
689	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
690	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄⋊C₄	—	3	1	no	—
695	C₄⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	3	1	no	—
731	C₂²⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
769	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄²	—	3	1	no	—
779	C₄²	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
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	—	2	1	no	—
800	C₂²×C₃	—	2	1	no	—
801	C₂²×C₃	—	2	1	no	—
802	C₂²×C₃	C₂⁵	1	1	yes	characteristic
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	—	8	2	no	—
819	C₂×D₃	—	8	2	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	—	2	1	no	—
841	Dic₃	H(5,𝔽₂)	1	2	yes	—
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	—	12	1	no	—
851	C₂³	—	12	1	no	—
852	C₂³	—	12	1	no	—
853	C₂³	C₂³×D₃	1	1	yes	characteristic
854	C₂³	C₂³×D₃	1	1	yes	characteristic
855	C₂³	C₂³×D₃	1	1	yes	characteristic
856	C₂³	C₂³×D₃	1	1	yes	characteristic
857	Q₈	—	6	2	no	—
858	Q₈	—	6	2	no	—
859	Q₈	—	6	2	no	—
860	Q₈	—	12	1	no	—
861	Q₈	—	12	1	no	—
862	Q₈	—	12	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	1	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	1	no	—
869	D₄	—	6	2	no	—
870	D₄	—	6	2	no	—
871	D₄	—	6	2	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	D₄	—	12	1	no	—
890	D₄	—	12	1	no	—
891	D₄	—	12	1	no	—
892	D₄	—	12	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	—	3	1	no	—
900	C₂×C₄	—	3	1	no	—
901	C₂×C₄	—	3	1	no	—
902	C₂×C₄	—	3	1	no	—
903	C₂×C₄	—	3	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	6	2	no	—
911	C₂×C₄	—	6	2	no	—
912	C₂×C₄	—	6	2	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	—	12	1	no	—
924	C₂×C₄	—	12	1	no	—
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×C₄	C₂³×D₃	1	1	yes	characteristic
936	C₂×C₃	—	4	1	no	—
937	C₂×C₃	—	4	1	no	—
938	C₂×C₃	—	4	1	no	—
939	C₂×C₃	—	4	1	no	—
940	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
941	C₂×C₃	#585	1	1	yes	characteristic
942	C₂×C₃	#585	1	1	yes	characteristic
943	D₃	—	4	1	no	—
944	D₃	—	4	1	no	—
945	D₃	—	4	1	no	—
946	D₃	—	4	1	no	—
947	D₃	—	4	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	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	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	—	6	1	no	—
975	C₂²	—	24	2	no	—
976	C₂²	—	24	2	no	—
977	C₂²	C₂⁴×D₃	1	1	yes	characteristic
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	—	2	1	no	—
989	C₄	—	3	2	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	C₄	—	6	1	no	—
999	C₄	—	6	1	no	—
1000	C₃	#3562	1	1	yes	characteristic, complemented, Sylow
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	12	1	no	—
1006	C₂	—	12	1	no	—
1007	C₂	—	12	1	no	—
1008	C₂	—	12	1	no	—
1009	C₂	—	12	1	no	—
1010	C₂	#5964	1	1	yes	characteristic
1011	C₂	#5964	1	1	yes	characteristic
1012	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#553	C₂
hypercenter	#553	D₃
hypocenter	C₃	#3562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₃×#553	C₂	semidirect
2. #5709	C₂	semidirect
3. #5706	C₂	semidirect
4. #5704	C₂	semidirect
5. #5702	C₂	semidirect
6. #5700	C₂	semidirect
7. #5696	C₂	semidirect
8. #5666	C₂	semidirect
9. #5660	C₂	semidirect
10. #5654	C₂	semidirect
11. #5648	C₂	semidirect
12. #5621	C₂	semidirect
13. #5620	C₂	semidirect
14. #5615	C₂	semidirect
15. #5615	C₂	semidirect
16. #5613	C₂	semidirect
17. #5610	C₂	semidirect
18. #5607	C₂	semidirect
19. #5599	C₂	semidirect
20. #5562	C₂	semidirect
21. #5560	C₂	semidirect
22. #5560	C₂	semidirect
23. #5559	C₂	semidirect
24. #5556	C₂	semidirect
25. #5552	C₂	semidirect
26. #5552	C₂	semidirect
27. #5548	C₂	semidirect
28. #5528	C₂	semidirect
29. #5527	C₂	semidirect
30. #5515	C₂	semidirect
31. #5507	C₂	semidirect
37. C₂×#235	C₂²	semidirect
38. C₂²×Dic₆	C₂²	semidirect
39. C₃×#126	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#125	C₂²	semidirect
43. C₃×#123	C₂²	semidirect
46. C₃×#121	C₂²	semidirect
47. C₃×#121	C₂²	semidirect
48. C₃×C₄×D₄	C₂²	semidirect
49. C₃×C₄×D₄	C₂²	semidirect
50. C₃×C₄×D₄	C₂²	semidirect
51. C₃×C₄×D₄	C₂²	semidirect
52. C₃×#117	C₂²	semidirect
53. C₂×C₃×C₄⋊C₄	C₂²	semidirect
56. #940	C₂²	semidirect
57. #940	C₂²	semidirect
61. #939	C₂²	semidirect
62. #939	C₂²	semidirect
63. #939	C₂²	semidirect
64. #939	C₂²	semidirect
66. #938	C₂²	semidirect
67. #938	C₂²	semidirect
72. #936	C₂²	semidirect
74. #935	C₂²	semidirect
75. #935	C₂²	semidirect
79. #930	C₂²	semidirect
81. #929	C₂²	semidirect
82. #929	C₂²	semidirect
83. #929	C₂²	semidirect
84. #929	C₂²	semidirect
85. #929	C₂²	semidirect
87. C₄×#67	C₂²	semidirect
88. C₄×#67	C₂²	semidirect
89. C₄×#67	C₂²	semidirect
90. C₄×#67	C₂²	semidirect
91. C₄×#67	C₂²	semidirect
94. #924	C₂²	semidirect
95. #924	C₂²	semidirect
99. #898	C₂²	semidirect
100. #898	C₂²	semidirect
101. #898	C₂²	semidirect
104. #896	C₂²	semidirect
105. #896	C₂²	semidirect
106. #896	C₂²	semidirect
107. #896	C₂²	semidirect
108. #896	C₂²	semidirect
109. #896	C₂²	semidirect
110. #896	C₂²	semidirect
114. #895	C₂²	semidirect
115. #895	C₂²	semidirect
120. #894	C₂²	semidirect
121. #894	C₂²	semidirect
122. #894	C₂²	semidirect
124. #893	C₂²	semidirect
126. D₃×C₄⋊C₄	C₂²	semidirect
127. #890	C₂²	semidirect
128. #889	C₂²	semidirect
129. #889	C₂²	semidirect
130. #889	C₂²	semidirect
131. #889	C₂²	semidirect
132. #888	C₂²	semidirect
133. #888	C₂²	semidirect
134. #887	C₂²	semidirect
135. #887	C₂²	semidirect
136. #886	C₂²	semidirect
143. #885	C₂²	semidirect
144. #885	C₂²	semidirect
148. #884	C₂²	semidirect
149. #884	C₂²	semidirect
150. #884	C₂²	semidirect
151. #884	C₂²	semidirect
152. #883	C₂²	semidirect
153. #883	C₂²	semidirect
154. #883	C₂²	semidirect
155. #883	C₂²	semidirect
156. #883	C₂²	semidirect
163. #67⋊C₄	C₂²	semidirect
164. #67⋊C₄	C₂²	semidirect
165. #67⋊C₄	C₂²	semidirect
166. #67⋊C₄	C₂²	semidirect
169. #879	C₂²	semidirect
170. #879	C₂²	semidirect
171. #878	C₂²	semidirect
172. #878	C₂²	semidirect
173. #878	C₂²	semidirect
174. #877	C₂²	semidirect
175. #877	C₂²	semidirect
179. #875	C₂²	semidirect
180. #875	C₂²	semidirect
181. C₄×D₁₂	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
195. #553	D₃	semidirect
402. #126	C₂×D₃	semidirect
403. #126	C₂×D₃	semidirect
409. #125	C₂×D₃	semidirect
445. #123	C₂×D₃	semidirect
488. #121	C₂×D₃	semidirect
489. #121	C₂×D₃	semidirect
518. C₄×D₄	C₂×D₃	semidirect
519. C₄×D₄	C₂×D₃	semidirect
520. C₄×D₄	C₂×D₃	semidirect
521. C₄×D₄	C₂×D₃	semidirect
527. #117	C₂×D₃	semidirect
529. C₂×C₄⋊C₄	C₂×D₃	semidirect
1000. C₃	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₃×#553	2
#5709	2
#5706	2
#5704	2
#5702	2
#5700	2
#5696	2
#5666	2
#5660	2
#5654	2
#5648	2
#5621	2
#5620	2
#5615	2
#5613	2
#5610	2
#5607	2
#5599	2
#5562	2
#5560	2
#5559	2
#5556	2
#5552	2
#5548	2
#5528	2
#5527	2
#5515	2
#5507	2
#3562	3