Subgroups — #86146

Order 384.

1040 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5710	C₂	1	1	yes	maximal, characteristic, complemented
3	#5707	C₂	1	1	yes	maximal, characteristic, complemented
4	#5704	C₂	1	1	yes	maximal, characteristic, complemented
5	#5701	C₂	1	1	yes	maximal, characteristic, complemented
6	#5696	C₂	1	1	yes	maximal, characteristic, complemented
7	#5692	C₂	1	1	yes	maximal, characteristic, complemented
8	#5678	C₂	1	1	yes	maximal, characteristic, complemented
9	#5669	C₂	1	1	yes	maximal, characteristic, complemented
10	#5663	C₂	1	1	yes	maximal, characteristic, complemented
11	#5662	C₂	1	1	yes	maximal, characteristic, complemented
12	#5660	C₂	1	1	yes	maximal, characteristic, complemented
13	#5657	C₂	1	1	yes	maximal, characteristic, complemented
14	#5640	C₂	1	1	yes	maximal, characteristic, complemented
15	#5638	C₂	1	1	yes	maximal, characteristic, complemented
16	#5615	C₂	1	1	yes	maximal, characteristic, complemented
17	#5613	C₂	1	1	yes	maximal, characteristic, complemented
18	#5580	C₂	1	1	yes	maximal, characteristic, complemented
19	#5578	C₂	1	1	yes	maximal, characteristic, complemented
20	#5557	C₂	1	1	yes	maximal, characteristic, complemented
21	#5548	C₂	1	1	yes	maximal, characteristic, complemented
22	#5547	C₂	1	1	yes	maximal, characteristic, complemented
23	#5547	C₂	1	1	yes	maximal, characteristic, complemented
24	#5538	C₂	1	1	yes	maximal, characteristic, complemented
25	#5538	C₂	1	1	yes	maximal, characteristic, complemented
26	#5528	C₂	1	1	yes	maximal, characteristic, complemented
27	#5528	C₂	1	1	yes	maximal, characteristic, complemented
28	#5522	C₂	1	1	yes	maximal, characteristic, complemented
29	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
30	#5479	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
32	#3455	—	3	1	no	maximal, Sylow
33	C₂×#235	C₂²	1	1	yes	characteristic
34	C₂×#235	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
36	C₃×#126	C₂²	1	1	yes	characteristic
37	C₃×#126	C₂²	1	1	yes	characteristic, complemented
38	C₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₃×#124	C₂²	1	1	yes	characteristic
40	C₃×#123	C₂²	1	1	yes	characteristic
41	C₃×#123	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×#121	C₂²	1	1	yes	characteristic
44	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×#117	C₂²	1	1	yes	characteristic
49	C₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
51	#947	C₂²	1	1	yes	characteristic
52	#946	C₂²	1	1	yes	characteristic
53	#946	C₂²	1	1	yes	characteristic, complemented
54	#944	C₂²	1	1	yes	characteristic, complemented
55	#940	C₂²	1	1	yes	characteristic, complemented
56	#939	C₂²	1	1	yes	characteristic
57	#939	C₂²	1	1	yes	characteristic
58	#939	C₂²	1	1	yes	characteristic
59	#939	C₂²	1	1	yes	characteristic
60	#938	C₂²	1	1	yes	characteristic
61	#938	C₂²	1	1	yes	characteristic
62	#937	C₂²	1	1	yes	characteristic
63	#937	C₂²	1	1	yes	characteristic
64	#936	C₂²	1	1	yes	characteristic
65	#935	C₂²	1	1	yes	characteristic
66	#935	C₂²	1	1	yes	characteristic, complemented
67	#930	C₂²	1	1	yes	characteristic
68	#929	C₂²	1	1	yes	characteristic
69	#929	C₂²	1	1	yes	characteristic, complemented
70	C₄×#67	C₂²	1	1	yes	characteristic
71	C₄×#67	C₂²	1	1	yes	characteristic
72	C₄×#67	C₂²	1	1	yes	characteristic
73	C₄×#67	C₂²	1	1	yes	characteristic
74	C₄×#67	C₂²	1	1	yes	characteristic
75	C₄×#67	C₂²	1	1	yes	characteristic
76	C₄×#67	C₂²	1	1	yes	characteristic, complemented
77	C₄×#67	C₂²	1	1	yes	characteristic, complemented
78	C₄×#67	C₂²	1	1	yes	characteristic, complemented
79	C₄×#67	C₂²	1	1	yes	characteristic, complemented
80	#926	C₂²	1	1	yes	characteristic
81	#926	C₂²	1	1	yes	characteristic, complemented
82	#924	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×Dic₃	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, complemented
88	#898	C₂²	1	1	yes	characteristic, complemented
89	#898	C₂²	1	1	yes	characteristic, complemented
90	#897	C₂²	1	1	yes	characteristic
91	#897	C₂²	1	1	yes	characteristic, complemented
92	#896	C₂²	1	1	yes	characteristic
93	#896	C₂²	1	1	yes	characteristic
94	#896	C₂²	1	1	yes	characteristic
95	#896	C₂²	1	1	yes	characteristic
96	#896	C₂²	1	1	yes	characteristic, complemented
97	#896	C₂²	1	1	yes	characteristic, complemented
98	#895	C₂²	1	1	yes	characteristic
99	#895	C₂²	1	1	yes	characteristic
100	#894	C₂²	1	1	yes	characteristic
101	#894	C₂²	1	1	yes	characteristic
102	#894	C₂²	1	1	yes	characteristic
103	#894	C₂²	1	1	yes	characteristic
104	#894	C₂²	1	1	yes	characteristic, complemented
105	#894	C₂²	1	1	yes	characteristic, complemented
106	#893	C₂²	1	1	yes	characteristic
107	#893	C₂²	1	1	yes	characteristic
108	#892	C₂²	1	1	yes	characteristic
109	#892	C₂²	1	1	yes	characteristic
110	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	#890	C₂²	1	1	yes	characteristic, complemented
113	#890	C₂²	1	1	yes	characteristic, complemented
114	#889	C₂²	1	1	yes	characteristic, complemented
115	#889	C₂²	1	1	yes	characteristic, complemented
116	#889	C₂²	1	1	yes	characteristic, complemented
117	#889	C₂²	1	1	yes	characteristic, complemented
118	#889	C₂²	1	1	yes	characteristic, complemented
119	#889	C₂²	1	1	yes	characteristic, complemented
120	#888	C₂²	1	1	yes	characteristic, complemented
121	#888	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
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
130	#885	C₂²	1	1	yes	characteristic, complemented
131	#885	C₂²	1	1	yes	characteristic, complemented
132	#884	C₂²	1	1	yes	characteristic
133	#884	C₂²	1	1	yes	characteristic
134	#884	C₂²	1	1	yes	characteristic
135	#884	C₂²	1	1	yes	characteristic
136	#884	C₂²	1	1	yes	characteristic
137	#884	C₂²	1	1	yes	characteristic
138	#883	C₂²	1	1	yes	characteristic
139	#883	C₂²	1	1	yes	characteristic
140	#883	C₂²	1	1	yes	characteristic
141	#883	C₂²	1	1	yes	characteristic
142	#883	C₂²	1	1	yes	characteristic, complemented
143	#883	C₂²	1	1	yes	characteristic, complemented
144	#882	C₂²	1	1	yes	characteristic
145	#882	C₂²	1	1	yes	characteristic
146	#67⋊C₄	C₂²	1	1	yes	characteristic
147	#67⋊C₄	C₂²	1	1	yes	characteristic
148	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
151	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
152	#879	C₂²	1	1	yes	characteristic
153	#879	C₂²	1	1	yes	characteristic
154	#879	C₂²	1	1	yes	characteristic
155	#879	C₂²	1	1	yes	characteristic, complemented
156	#879	C₂²	1	1	yes	characteristic, complemented
157	#879	C₂²	1	1	yes	characteristic, complemented
158	#878	C₂²	1	1	yes	characteristic
159	#878	C₂²	1	1	yes	characteristic
160	#878	C₂²	1	1	yes	characteristic, complemented
161	#878	C₂²	1	1	yes	characteristic, complemented
162	#877	C₂²	1	1	yes	characteristic
163	#877	C₂²	1	1	yes	characteristic
164	#876	C₂²	1	1	yes	characteristic
165	#876	C₂²	1	1	yes	characteristic, complemented
166	#875	C₂²	1	1	yes	characteristic
167	C₄×D₁₂	C₂²	1	1	yes	characteristic
168	C₄×D₁₂	C₂²	1	1	yes	characteristic
169	C₄×D₁₂	C₂²	1	1	yes	characteristic
170	C₄×D₁₂	C₂²	1	1	yes	characteristic
171	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
172	#872	C₂²	1	1	yes	characteristic
173	#872	C₂²	1	1	yes	characteristic
174	#872	C₂²	1	1	yes	characteristic
175	#872	C₂²	1	1	yes	characteristic
176	#872	C₂²	1	1	yes	characteristic, complemented
177	#872	C₂²	1	1	yes	characteristic, complemented
178	C₄²×D₃	C₂²	1	1	yes	characteristic
179	C₄²×D₃	C₂²	1	1	yes	characteristic
180	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
182	#870	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₆	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	#542	—	3	1	no	—
189	#542	—	3	1	no	—
190	#542	—	3	1	no	—
191	#542	—	3	1	no	—
192	#541	—	3	1	no	—
193	#541	—	3	1	no	—
194	#540	—	3	1	no	—
195	#540	—	3	1	no	—
196	#539	—	3	1	no	—
197	#539	—	3	1	no	—
198	#539	—	3	1	no	—
199	#539	—	3	1	no	—
200	#538	—	3	1	no	—
201	#538	—	3	1	no	—
202	#538	—	3	1	no	—
203	#538	—	3	1	no	—
204	#533	—	3	1	no	—
205	#532	—	3	1	no	—
206	#529	—	3	1	no	—
207	#529	—	3	1	no	—
208	#529	—	3	1	no	—
209	#529	—	3	1	no	—
210	#529	—	3	1	no	—
211	#529	—	3	1	no	—
212	#529	—	3	1	no	—
213	#529	D₃	1	1	yes	characteristic, complemented
214	#525	—	3	1	no	—
215	#525	—	3	1	no	—
216	C₄×#41	—	3	1	no	—
217	C₄×#41	—	3	1	no	—
218	C₂×#117	—	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	C₂²×Dic₃	C₂³	1	1	yes	characteristic
240	C₂²×Dic₃	C₂³	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³	1	1	yes	characteristic
242	#235	—	2	4	no	—
243	#235	—	2	4	no	—
244	C₂×D₁₂	C₂³	1	1	yes	characteristic
245	C₂×D₁₂	C₂³	1	1	yes	characteristic
246	C₂×D₁₂	C₂³	1	1	yes	characteristic
247	C₂×D₁₂	C₂³	1	1	yes	characteristic
248	C₂×D₁₂	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₃	—	2	4	no	—
250	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
264	C₂×Dic₆	C₂³	1	1	yes	characteristic
265	C₂×Dic₆	C₂³	1	1	yes	characteristic
266	C₂×Dic₆	C₂³	1	1	yes	characteristic
267	C₂×Dic₆	C₂³	1	1	yes	characteristic
268	C₂×Dic₆	C₂³	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₃×C₄²	C₂³	1	1	yes	characteristic
290	C₃×C₄²	C₂³	1	1	yes	characteristic
291	C₃×C₄²	C₂³	1	1	yes	characteristic
292	C₃×C₄²	C₂³	1	1	yes	characteristic
293	C₃×C₄²	C₂³	1	1	yes	characteristic
294	C₃×C₄²	C₂³	1	1	yes	characteristic
295	#217	C₂³	1	1	yes	characteristic
296	#217	C₂³	1	1	yes	characteristic
297	#217	C₂³	1	1	yes	characteristic
298	#217	C₂³	1	1	yes	characteristic
299	#217	C₂³	1	1	yes	characteristic
300	#217	C₂³	1	1	yes	characteristic
301	#217	C₂³	1	1	yes	characteristic
302	#217	C₂³	1	1	yes	characteristic
303	#217	C₂³	1	1	yes	characteristic
304	#217	C₂³	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
334	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
335	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
336	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
337	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
338	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
339	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
341	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
342	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
343	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
344	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
345	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
346	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
347	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
348	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
349	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
350	Dic₃⋊C₄	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
364	C₄×Dic₃	C₂³	1	1	yes	characteristic
365	C₄×Dic₃	C₂³	1	1	yes	characteristic
366	C₄×Dic₃	C₂³	1	1	yes	characteristic
367	C₄×Dic₃	C₂³	1	1	yes	characteristic
368	C₄×Dic₃	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	C₂×#41	—	3	1	no	—
378	C₂×#41	—	3	1	no	—
379	C₂³×C₄	—	3	1	no	—
380	C₄⋊Q₈	—	3	1	no	—
381	C₄⋊Q₈	—	3	1	no	—
382	C₄⋊Q₈	—	3	1	no	—
383	#127	—	3	1	no	—
384	#126	—	3	1	no	—
385	#126	—	3	1	no	—
386	#126	—	3	1	no	—
387	#126	—	3	1	no	—
388	#126	—	3	1	no	—
389	#126	—	3	1	no	—
390	#126	—	3	1	no	—
391	#126	—	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	C₂×D₃	1	1	yes	characteristic
399	#126	C₂×D₃	1	1	yes	characteristic, complemented
400	#125	—	3	1	no	—
401	#125	—	3	1	no	—
402	#125	—	3	1	no	—
403	#125	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
437	#123	—	3	1	no	—
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	—	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	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic
472	#120	—	3	1	no	—
473	#120	—	3	1	no	—
474	#120	—	3	1	no	—
475	#120	—	3	1	no	—
476	C₄×Q₈	—	3	1	no	—
477	C₄×Q₈	—	3	1	no	—
478	C₄×Q₈	—	3	1	no	—
479	C₄×Q₈	—	3	1	no	—
480	C₄×Q₈	—	3	1	no	—
481	C₄×Q₈	—	3	1	no	—
482	C₄×Q₈	—	3	1	no	—
483	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
484	C₄×D₄	—	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	C₂×D₃	1	1	yes	characteristic
506	C₄×D₄	C₂×D₃	1	1	yes	characteristic
507	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
508	#117	—	3	1	no	—
509	#117	—	3	1	no	—
510	#117	—	3	1	no	—
511	#117	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
521	#117	C₂×D₃	1	1	yes	characteristic, complemented
522	C₂×C₄⋊C₄	—	3	1	no	—
523	C₂×C₄⋊C₄	—	3	1	no	—
524	C₂×C₂²⋊C₄	—	3	1	no	—
525	C₂×C₂²⋊C₄	—	3	1	no	—
526	C₂×C₄²	—	3	1	no	—
527	C₂×C₄²	—	3	1	no	—
528	C₂×C₄²	—	3	1	no	—
529	C₂×C₄²	—	3	1	no	—
530	C₂×C₄²	—	3	1	no	—
531	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
532	C₂³×C₃	C₂⁴	1	1	yes	characteristic
533	C₂³×C₃	C₂⁴	1	1	yes	characteristic
534	C₂³×C₃	C₂⁴	1	1	yes	characteristic
535	C₂²×D₃	—	2	2	no	—
536	C₂²×D₃	—	4	1	no	—
537	C₂²×D₃	—	4	1	no	—
538	C₂²×D₃	C₂⁴	1	1	yes	characteristic
539	C₂²×D₃	C₂⁴	1	1	yes	characteristic
540	C₂²×D₃	C₂⁴	1	1	yes	characteristic
541	C₂²×D₃	C₂⁴	1	1	yes	characteristic
542	C₃×Q₈	—	4	1	no	—
543	C₃×D₄	—	4	1	no	—
544	C₃×D₄	—	4	1	no	—
545	C₃×D₄	—	4	1	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	4	1	no	—
550	C₂×C₃×C₄	—	4	1	no	—
551	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
554	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
564	#67	—	2	2	no	—
565	#67	—	2	2	no	—
566	#67	—	2	2	no	—
567	#67	—	4	1	no	—
568	#67	—	4	1	no	—
569	#67	—	4	1	no	—
570	#67	—	4	1	no	—
571	#67	—	4	1	no	—
572	#67	—	4	1	no	—
573	C₂×Dic₃	—	2	2	no	—
574	C₂×Dic₃	—	4	1	no	—
575	C₂×Dic₃	—	4	1	no	—
576	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
577	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
578	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
579	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
580	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
581	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
582	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
583	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
584	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
585	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
586	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
587	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
588	D₁₂	—	2	2	no	—
589	D₁₂	—	2	2	no	—
590	D₁₂	—	4	1	no	—
591	D₁₂	—	4	1	no	—
592	D₁₂	—	4	1	no	—
593	C₄×D₃	—	2	2	no	—
594	C₄×D₃	—	2	2	no	—
595	C₄×D₃	—	2	2	no	—
596	C₄×D₃	—	2	2	no	—
597	C₄×D₃	—	2	2	no	—
598	C₄×D₃	—	4	1	no	—
599	C₄×D₃	—	4	1	no	—
600	C₄×D₃	—	4	1	no	—
601	C₄×D₃	—	4	1	no	—
602	C₄×D₃	—	4	1	no	—
603	C₄×D₃	—	4	1	no	—
604	C₄×D₃	—	4	1	no	—
605	C₄×D₃	—	4	1	no	—
606	C₄×D₃	#41	1	4	yes	—
607	Dic₆	—	2	2	no	—
608	Dic₆	—	2	2	no	—
609	Dic₆	—	4	1	no	—
610	Dic₆	—	4	1	no	—
611	Dic₆	—	4	1	no	—
612	C₂⁴	—	3	1	no	—
613	#41	—	6	4	no	—
614	#41	—	6	4	no	—
615	C₂×Q₈	—	3	1	no	—
616	C₂×Q₈	—	3	1	no	—
617	C₂×Q₈	—	3	1	no	—
618	C₂×Q₈	—	3	1	no	—
619	C₂×Q₈	—	3	1	no	—
620	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
621	C₂×D₄	—	3	1	no	—
622	C₂×D₄	—	3	1	no	—
623	C₂×D₄	—	3	1	no	—
624	C₂×D₄	—	3	1	no	—
625	C₂×D₄	—	3	1	no	—
626	C₂×D₄	—	3	1	no	—
627	C₂×D₄	—	3	1	no	—
628	C₂×D₄	—	3	1	no	—
629	C₂×D₄	—	3	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	3	1	no	—
632	C₂×D₄	—	3	1	no	—
633	C₂×D₄	—	3	1	no	—
634	C₂×D₄	—	3	1	no	—
635	C₂×D₄	—	3	1	no	—
636	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
637	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
638	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	3	1	no	—
647	C₂²×C₄	—	3	1	no	—
648	C₂²×C₄	—	3	1	no	—
649	C₂²×C₄	—	3	1	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	6	4	no	—
657	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
658	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
659	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
660	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
661	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
662	C₄⋊C₄	—	3	1	no	—
663	C₄⋊C₄	—	3	1	no	—
664	C₄⋊C₄	—	3	1	no	—
665	C₄⋊C₄	—	3	1	no	—
666	C₄⋊C₄	—	3	1	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	—	3	1	no	—
671	C₄⋊C₄	—	3	1	no	—
672	C₄⋊C₄	—	3	1	no	—
673	C₄⋊C₄	—	3	1	no	—
674	C₄⋊C₄	—	3	1	no	—
675	C₄⋊C₄	—	3	1	no	—
676	C₄⋊C₄	—	3	1	no	—
677	C₄⋊C₄	—	3	1	no	—
678	C₄⋊C₄	—	3	1	no	—
679	C₄⋊C₄	—	3	1	no	—
680	C₄⋊C₄	—	3	1	no	—
681	C₄⋊C₄	—	3	1	no	—
682	C₄⋊C₄	—	3	1	no	—
683	C₄⋊C₄	—	3	1	no	—
684	C₄⋊C₄	—	3	1	no	—
685	C₄⋊C₄	—	3	1	no	—
686	C₄⋊C₄	—	3	1	no	—
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	3	1	no	—
689	C₄⋊C₄	—	3	1	no	—
690	C₄⋊C₄	—	3	1	no	—
691	C₄⋊C₄	—	3	1	no	—
692	C₄⋊C₄	—	3	1	no	—
693	C₄⋊C₄	—	3	1	no	—
694	C₄⋊C₄	—	3	1	no	—
695	C₄⋊C₄	—	3	1	no	—
696	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
700	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
701	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₂²⋊C₄	—	3	1	no	—
707	C₂²⋊C₄	—	3	1	no	—
708	C₂²⋊C₄	—	3	1	no	—
709	C₂²⋊C₄	—	3	1	no	—
710	C₂²⋊C₄	—	3	1	no	—
711	C₂²⋊C₄	—	3	1	no	—
712	C₂²⋊C₄	—	3	1	no	—
713	C₂²⋊C₄	—	3	1	no	—
714	C₂²⋊C₄	—	3	1	no	—
715	C₂²⋊C₄	—	3	1	no	—
716	C₂²⋊C₄	—	3	1	no	—
717	C₂²⋊C₄	—	3	1	no	—
718	C₂²⋊C₄	—	3	1	no	—
719	C₂²⋊C₄	—	3	1	no	—
720	C₂²⋊C₄	—	3	1	no	—
721	C₂²⋊C₄	—	3	1	no	—
722	C₂²⋊C₄	—	3	1	no	—
723	C₂²⋊C₄	—	3	1	no	—
724	C₂²⋊C₄	—	3	1	no	—
725	C₂²⋊C₄	—	3	1	no	—
726	C₂²⋊C₄	—	3	1	no	—
727	C₂²⋊C₄	—	3	1	no	—
728	C₂²⋊C₄	—	3	1	no	—
729	C₂²⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
741	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
742	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
743	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
744	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
745	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
746	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
747	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
748	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
749	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
750	C₄²	—	3	1	no	—
751	C₄²	—	3	1	no	—
752	C₄²	—	3	1	no	—
753	C₄²	—	3	1	no	—
754	C₄²	—	3	1	no	—
755	C₄²	—	3	1	no	—
756	C₄²	—	3	1	no	—
757	C₄²	—	3	1	no	—
758	C₄²	—	3	1	no	—
759	C₄²	—	3	1	no	—
760	C₄²	—	3	1	no	—
761	C₄²	—	3	1	no	—
762	C₄²	—	3	1	no	—
763	C₄²	—	3	1	no	—
764	C₄²	C₂²×D₃	1	1	yes	characteristic
765	C₄²	C₂²×D₃	1	1	yes	characteristic
766	C₄²	C₂²×D₃	1	1	yes	characteristic
767	C₄²	C₂²×D₃	1	1	yes	characteristic
768	C₄²	C₂²×D₃	1	1	yes	characteristic
769	C₄²	C₂²×D₃	1	1	yes	characteristic
770	C₂²×C₃	—	2	1	no	—
771	C₂²×C₃	—	2	1	no	—
772	C₂²×C₃	—	2	1	no	—
773	C₂²×C₃	—	2	1	no	—
774	C₂²×C₃	—	2	1	no	—
775	C₂²×C₃	—	2	1	no	—
776	C₂²×C₃	—	2	1	no	—
777	C₂²×C₃	—	2	1	no	—
778	C₂²×C₃	—	2	1	no	—
779	C₂²×C₃	C₂⁵	1	1	yes	characteristic
780	C₂×D₃	—	2	1	no	—
781	C₂×D₃	—	2	1	no	—
782	C₂×D₃	—	2	1	no	—
783	C₂×D₃	—	2	1	no	—
784	C₂×D₃	—	2	1	no	—
785	C₂×D₃	—	2	1	no	—
786	C₂×D₃	—	2	1	no	—
787	C₂×D₃	—	2	1	no	—
788	C₂×D₃	—	2	1	no	—
789	C₂×D₃	—	2	1	no	—
790	C₂×D₃	—	2	1	no	—
791	C₂×D₃	—	4	4	no	—
792	C₂×D₃	C₂×#41	1	2	yes	—
793	C₃×C₄	—	2	1	no	—
794	C₃×C₄	—	2	1	no	—
795	C₃×C₄	—	2	1	no	—
796	C₃×C₄	—	2	1	no	—
797	C₃×C₄	—	2	1	no	—
798	C₃×C₄	—	2	1	no	—
799	C₃×C₄	—	2	1	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	—	2	1	no	—
802	C₃×C₄	—	2	1	no	—
803	C₃×C₄	—	2	1	no	—
804	C₃×C₄	C₂×#41	1	2	yes	—
805	Dic₃	—	2	1	no	—
806	Dic₃	—	2	1	no	—
807	Dic₃	—	2	1	no	—
808	Dic₃	—	2	1	no	—
809	Dic₃	—	2	1	no	—
810	Dic₃	—	2	1	no	—
811	Dic₃	—	2	1	no	—
812	Dic₃	—	2	1	no	—
813	Dic₃	—	2	1	no	—
814	Dic₃	—	2	1	no	—
815	Dic₃	—	2	1	no	—
816	Dic₃	C₂×#41	1	2	yes	—
817	C₂³	—	3	1	no	—
818	C₂³	—	3	1	no	—
819	C₂³	—	3	1	no	—
820	C₂³	—	3	1	no	—
821	C₂³	—	6	2	no	—
822	C₂³	—	12	1	no	—
823	C₂³	—	12	1	no	—
824	C₂³	C₂³×D₃	1	1	yes	characteristic
825	C₂³	C₂³×D₃	1	1	yes	characteristic
826	C₂³	C₂³×D₃	1	1	yes	characteristic
827	Q₈	—	4	1	no	—
828	Q₈	—	6	2	no	—
829	Q₈	—	6	2	no	—
830	Q₈	—	12	1	no	—
831	Q₈	—	12	1	no	—
832	Q₈	—	12	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	6	2	no	—
837	D₄	—	6	2	no	—
838	D₄	—	6	2	no	—
839	D₄	—	6	2	no	—
840	D₄	—	6	2	no	—
841	D₄	—	6	2	no	—
842	D₄	—	12	1	no	—
843	D₄	—	12	1	no	—
844	D₄	—	12	1	no	—
845	D₄	—	12	1	no	—
846	D₄	—	12	1	no	—
847	D₄	—	12	1	no	—
848	D₄	—	12	1	no	—
849	D₄	—	12	1	no	—
850	D₄	—	12	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	3	1	no	—
855	C₂×C₄	—	3	4	no	—
856	C₂×C₄	—	3	1	no	—
857	C₂×C₄	—	3	1	no	—
858	C₂×C₄	—	3	1	no	—
859	C₂×C₄	—	3	1	no	—
860	C₂×C₄	—	3	1	no	—
861	C₂×C₄	—	3	1	no	—
862	C₂×C₄	—	3	1	no	—
863	C₂×C₄	—	3	1	no	—
864	C₂×C₄	—	3	1	no	—
865	C₂×C₄	—	3	1	no	—
866	C₂×C₄	—	3	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	6	2	no	—
870	C₂×C₄	—	6	2	no	—
871	C₂×C₄	—	6	2	no	—
872	C₂×C₄	—	6	2	no	—
873	C₂×C₄	—	6	2	no	—
874	C₂×C₄	—	6	2	no	—
875	C₂×C₄	—	12	1	no	—
876	C₂×C₄	—	12	1	no	—
877	C₂×C₄	—	12	1	no	—
878	C₂×C₄	—	12	1	no	—
879	C₂×C₄	—	12	1	no	—
880	C₂×C₄	—	12	1	no	—
881	C₂×C₄	—	12	1	no	—
882	C₂×C₄	—	12	1	no	—
883	C₂×C₄	—	12	1	no	—
884	C₂×C₄	—	12	1	no	—
885	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
895	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
896	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
897	C₂×C₃	—	4	1	no	—
898	C₂×C₃	—	4	1	no	—
899	C₂×C₃	—	4	1	no	—
900	C₂×C₃	C₂²×#41	1	1	yes	characteristic
901	C₂×C₃	#585	1	1	yes	characteristic
902	C₂×C₃	#585	1	1	yes	characteristic
903	D₃	—	2	2	no	—
904	D₃	—	4	1	no	—
905	D₃	—	4	1	no	—
906	D₃	—	4	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	3	2	no	—
917	C₂²	—	6	1	no	—
918	C₂²	—	6	1	no	—
919	C₂²	—	6	1	no	—
920	C₂²	—	6	1	no	—
921	C₂²	—	6	1	no	—
922	C₂²	—	6	1	no	—
923	C₂²	—	6	1	no	—
924	C₂²	—	6	1	no	—
925	C₂²	—	6	1	no	—
926	C₂²	—	6	1	no	—
927	C₂²	—	6	1	no	—
928	C₂²	—	12	4	no	—
929	C₂²	C₂⁴×D₃	1	1	yes	characteristic
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	3	2	no	—
942	C₄	—	6	1	no	—
943	C₄	—	6	1	no	—
944	C₄	—	6	1	no	—
945	C₄	—	6	1	no	—
946	C₄	—	6	1	no	—
947	C₄	—	6	1	no	—
948	C₄	—	6	1	no	—
949	C₄	—	6	1	no	—
950	C₄	—	6	1	no	—
951	C₄	—	6	1	no	—
952	C₄	—	6	1	no	—
953	C₄	D₃×#41	1	2	yes	—
954	C₃	#3455	1	1	yes	characteristic, complemented, Sylow
955	C₂	—	4	1	no	—
956	C₂	—	4	1	no	—
957	C₂	—	4	1	no	—
958	C₂	—	6	2	no	—
959	C₂	—	12	1	no	—
960	C₂	—	12	1	no	—
961	C₂	—	12	1	no	—
962	C₂	C₂×D₃×#41	1	1	yes	characteristic
963	C₂	#5964	1	1	yes	characteristic
964	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Frattini	C₂²	C₂⁴×D₃
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5710	C₂	semidirect
3. #5707	C₂	semidirect
4. #5704	C₂	semidirect
5. #5701	C₂	semidirect
6. #5696	C₂	semidirect
7. #5692	C₂	semidirect
8. #5678	C₂	semidirect
9. #5669	C₂	semidirect
10. #5663	C₂	semidirect
11. #5662	C₂	semidirect
12. #5660	C₂	semidirect
13. #5657	C₂	semidirect
14. #5640	C₂	semidirect
15. #5638	C₂	semidirect
16. #5615	C₂	semidirect
17. #5613	C₂	semidirect
18. #5580	C₂	semidirect
19. #5578	C₂	semidirect
20. #5557	C₂	semidirect
21. #5548	C₂	semidirect
22. #5547	C₂	semidirect
23. #5547	C₂	semidirect
24. #5538	C₂	semidirect
25. #5538	C₂	semidirect
26. #5528	C₂	semidirect
27. #5528	C₂	semidirect
28. #5522	C₂	semidirect
29. D₃×#117	C₂	semidirect
30. #5479	C₂	semidirect
31. C₄×#235	C₂	semidirect
37. C₃×#126	C₂²	semidirect
38. C₃×#125	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₄×Q₈	C₂²	semidirect
47. C₃×C₄×D₄	C₂²	semidirect
49. C₃×#117	C₂²	semidirect
50. C₂×C₃×C₄²	C₂²	semidirect
53. #946	C₂²	semidirect
54. #944	C₂²	semidirect
55. #940	C₂²	semidirect
66. #935	C₂²	semidirect
69. #929	C₂²	semidirect
76. C₄×#67	C₂²	semidirect
77. C₄×#67	C₂²	semidirect
78. C₄×#67	C₂²	semidirect
79. C₄×#67	C₂²	semidirect
81. #926	C₂²	semidirect
82. #924	C₂²	semidirect
83. C₂×C₄×Dic₃	C₂²	semidirect
87. #898	C₂²	semidirect
88. #898	C₂²	semidirect
89. #898	C₂²	semidirect
91. #897	C₂²	semidirect
96. #896	C₂²	semidirect
97. #896	C₂²	semidirect
104. #894	C₂²	semidirect
105. #894	C₂²	semidirect
112. #890	C₂²	semidirect
113. #890	C₂²	semidirect
114. #889	C₂²	semidirect
115. #889	C₂²	semidirect
116. #889	C₂²	semidirect
117. #889	C₂²	semidirect
118. #889	C₂²	semidirect
119. #889	C₂²	semidirect
120. #888	C₂²	semidirect
121. #888	C₂²	semidirect
122. #887	C₂²	semidirect
123. #887	C₂²	semidirect
125. #886	C₂²	semidirect
130. #885	C₂²	semidirect
131. #885	C₂²	semidirect
142. #883	C₂²	semidirect
143. #883	C₂²	semidirect
148. #67⋊C₄	C₂²	semidirect
149. #67⋊C₄	C₂²	semidirect
155. #879	C₂²	semidirect
156. #879	C₂²	semidirect
157. #879	C₂²	semidirect
160. #878	C₂²	semidirect
161. #878	C₂²	semidirect
165. #876	C₂²	semidirect
171. C₄×D₁₂	C₂²	semidirect
176. #872	C₂²	semidirect
177. #872	C₂²	semidirect
180. C₄²×D₃	C₂²	semidirect
181. C₄²×D₃	C₂²	semidirect
182. #870	C₂²	semidirect
183. C₄×Dic₆	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
213. #529	D₃	semidirect
399. #126	C₂×D₃	semidirect
409. #125	C₂×D₃	semidirect
439. #123	C₂×D₃	semidirect
455. C₂²⋊Q₈	C₂×D₃	semidirect
483. C₄×Q₈	C₂×D₃	semidirect
507. C₄×D₄	C₂×D₃	semidirect
521. #117	C₂×D₃	semidirect
531. C₂×C₄²	C₂×D₃	semidirect
954. C₃	#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5710	2
#5707	2
#5704	2
#5701	2
#5696	2
#5692	2
#5678	2
#5669	2
#5663	2
#5662	2
#5660	2
#5657	2
#5640	2
#5638	2
#5615	2
#5613	2
#5580	2
#5578	2
#5557	2
#5548	2
#5547	2
#5538	2
#5528	2
#5522	2
D₃×#117	2
#5479	2
C₄×#235	2
#3455	3