Subgroups — #86899

Order 384.

932 conjugacy classes of subgroups.

The subgroup lattice has 918 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	#5712	C₂	1	1	yes	maximal, characteristic, complemented
3	#5708	C₂	1	1	yes	maximal, characteristic, complemented
4	#5701	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	C₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	1	yes	maximal, characteristic, complemented
9	#5660	C₂	1	1	yes	maximal, characteristic, complemented
10	#5651	C₂	1	1	yes	maximal, characteristic, complemented
11	#5650	C₂	1	1	yes	maximal, characteristic, complemented
12	#5621	C₂	1	1	yes	maximal, characteristic, complemented
13	#5618	C₂	1	1	yes	maximal, characteristic, complemented
14	#5602	C₂	1	1	yes	maximal, characteristic, complemented
15	#5602	C₂	1	1	yes	maximal, characteristic, complemented
16	#5602	C₂	1	1	yes	maximal, characteristic, complemented
17	#5601	C₂	1	1	yes	maximal, characteristic, complemented
18	#5601	C₂	1	1	yes	maximal, characteristic, complemented
19	#5600	C₂	1	1	yes	maximal, characteristic, complemented
20	#5564	C₂	1	1	yes	maximal, characteristic, complemented
21	#5564	C₂	1	1	yes	maximal, characteristic, complemented
22	#5564	C₂	1	1	yes	maximal, characteristic, complemented
23	#5543	C₂	1	1	yes	maximal, characteristic, complemented
24	#5541	C₂	1	1	yes	maximal, characteristic, complemented
25	#5539	C₂	1	1	yes	maximal, characteristic, complemented
26	#5539	C₂	1	1	yes	maximal, characteristic, complemented
27	#5538	C₂	1	1	yes	maximal, characteristic, complemented
28	#5531	C₂	1	1	yes	maximal, characteristic, complemented
29	#5518	C₂	1	1	yes	maximal, characteristic, complemented
30	#5511	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#889	C₂	1	1	yes	maximal, characteristic, complemented
32	#3553	—	3	1	no	maximal, Sylow
33	C₃×#126	C₂²	1	1	yes	characteristic
34	C₃×#126	C₂²	1	1	yes	characteristic
35	C₃×#125	C₂²	1	1	yes	characteristic
36	C₃×#123	C₂²	1	1	yes	characteristic
37	C₃×#123	C₂²	1	1	yes	characteristic
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×#121	C₂²	1	1	yes	characteristic
40	C₃×#121	C₂²	1	1	yes	characteristic
41	C₃×#121	C₂²	1	1	yes	characteristic
42	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₃×#117	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	#939	C₂²	1	1	yes	characteristic
49	#939	C₂²	1	1	yes	characteristic
50	#939	C₂²	1	1	yes	characteristic
51	#939	C₂²	1	1	yes	characteristic
52	#939	C₂²	1	1	yes	characteristic
53	#938	C₂²	1	1	yes	characteristic
54	#936	C₂²	1	1	yes	characteristic
55	#935	C₂²	1	1	yes	characteristic
56	#935	C₂²	1	1	yes	characteristic
57	#935	C₂²	1	1	yes	characteristic
58	#935	C₂²	1	1	yes	characteristic
59	#935	C₂²	1	1	yes	characteristic
60	#935	C₂²	1	1	yes	characteristic
61	#935	C₂²	1	1	yes	characteristic
62	#935	C₂²	1	1	yes	characteristic
63	#935	C₂²	1	1	yes	characteristic
64	D₄×Dic₃	C₂²	1	1	yes	characteristic
65	D₄×Dic₃	C₂²	1	1	yes	characteristic
66	D₄×Dic₃	C₂²	1	1	yes	characteristic
67	D₄×Dic₃	C₂²	1	1	yes	characteristic
68	D₄×Dic₃	C₂²	1	1	yes	characteristic
69	D₄×Dic₃	C₂²	1	1	yes	characteristic
70	D₄×Dic₃	C₂²	1	1	yes	characteristic
71	D₄×Dic₃	C₂²	1	1	yes	characteristic
72	#929	C₂²	1	1	yes	characteristic
73	#929	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
77	C₄×#67	C₂²	1	1	yes	characteristic
78	#926	C₂²	1	1	yes	characteristic
79	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
81	#924	C₂²	1	1	yes	characteristic
82	#924	C₂²	1	1	yes	characteristic
83	#924	C₂²	1	1	yes	characteristic
84	#924	C₂²	1	1	yes	characteristic
85	#924	C₂²	1	1	yes	characteristic
86	#924	C₂²	1	1	yes	characteristic
87	#924	C₂²	1	1	yes	characteristic
88	#924	C₂²	1	1	yes	characteristic
89	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
92	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
96	#898	C₂²	1	1	yes	characteristic
97	#898	C₂²	1	1	yes	characteristic
98	#898	C₂²	1	1	yes	characteristic
99	#897	C₂²	1	1	yes	characteristic
100	#896	C₂²	1	1	yes	characteristic
101	#896	C₂²	1	1	yes	characteristic
102	#896	C₂²	1	1	yes	characteristic
103	#896	C₂²	1	1	yes	characteristic
104	#892	C₂²	1	1	yes	characteristic
105	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	#890	C₂²	1	1	yes	characteristic
107	#890	C₂²	1	1	yes	characteristic
108	#890	C₂²	1	1	yes	characteristic
109	#890	C₂²	1	1	yes	characteristic
110	#890	C₂²	1	1	yes	characteristic
111	#890	C₂²	1	1	yes	characteristic
112	#889	C₂²	1	1	yes	characteristic
113	#889	C₂²	1	1	yes	characteristic
114	#889	C₂²	1	1	yes	characteristic
115	#889	C₂²	1	1	yes	characteristic
116	#889	C₂²	1	1	yes	characteristic
117	#889	C₂²	1	1	yes	characteristic
118	#889	C₂²	1	1	yes	characteristic
119	#889	C₂²	1	1	yes	characteristic
120	#889	C₂²	1	1	yes	characteristic
121	#889	C₂²	1	1	yes	characteristic
122	#889	C₂²	1	1	yes	characteristic
123	#889	C₂²	1	1	yes	characteristic
124	#889	C₂²	1	1	yes	characteristic
125	#889	C₂²	1	1	yes	characteristic
126	#889	C₂²	1	1	yes	characteristic
127	#889	C₂²	1	1	yes	characteristic
128	#889	C₂²	1	1	yes	characteristic
129	#889	C₂²	1	1	yes	characteristic
130	#889	C₂²	1	1	yes	characteristic
131	#888	C₂²	1	1	yes	characteristic
132	#888	C₂²	1	1	yes	characteristic
133	#888	C₂²	1	1	yes	characteristic
134	#887	C₂²	1	1	yes	characteristic
135	#887	C₂²	1	1	yes	characteristic
136	#886	C₂²	1	1	yes	characteristic
137	#886	C₂²	1	1	yes	characteristic
138	#886	C₂²	1	1	yes	characteristic
139	#885	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
143	#883	C₂²	1	1	yes	characteristic
144	#67⋊C₄	C₂²	1	1	yes	characteristic
145	#67⋊C₄	C₂²	1	1	yes	characteristic
146	#879	C₂²	1	1	yes	characteristic
147	#879	C₂²	1	1	yes	characteristic
148	#879	C₂²	1	1	yes	characteristic
149	#879	C₂²	1	1	yes	characteristic
150	#879	C₂²	1	1	yes	characteristic
151	#879	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
156	#879	C₂²	1	1	yes	characteristic
157	#879	C₂²	1	1	yes	characteristic
158	#879	C₂²	1	1	yes	characteristic
159	#878	C₂²	1	1	yes	characteristic
160	#878	C₂²	1	1	yes	characteristic
161	#878	C₂²	1	1	yes	characteristic
162	#878	C₂²	1	1	yes	characteristic
163	#878	C₂²	1	1	yes	characteristic
164	#878	C₂²	1	1	yes	characteristic
165	#878	C₂²	1	1	yes	characteristic
166	#878	C₂²	1	1	yes	characteristic
167	#878	C₂²	1	1	yes	characteristic
168	#878	C₂²	1	1	yes	characteristic
169	#878	C₂²	1	1	yes	characteristic
170	#878	C₂²	1	1	yes	characteristic
171	#878	C₂²	1	1	yes	characteristic
172	#877	C₂²	1	1	yes	characteristic
173	#877	C₂²	1	1	yes	characteristic
174	#877	C₂²	1	1	yes	characteristic
175	#877	C₂²	1	1	yes	characteristic
176	#876	C₂²	1	1	yes	characteristic
177	#876	C₂²	1	1	yes	characteristic
178	#872	C₂²	1	1	yes	characteristic
179	#870	C₂²	1	1	yes	characteristic
180	#870	C₂²	1	1	yes	characteristic
181	#870	C₂²	1	1	yes	characteristic
182	#870	C₂²	1	1	yes	characteristic
183	#869	C₂²	1	1	yes	characteristic
184	C₄×Dic₆	C₂²	1	1	yes	characteristic
185	C₄×Dic₆	C₂²	1	1	yes	characteristic
186	C₄×Dic₆	C₂²	1	1	yes	characteristic
187	C₄×Dic₆	C₂²	1	1	yes	characteristic
188	#564	—	3	1	no	—
189	#563	—	3	1	no	—
190	#563	—	3	1	no	—
191	#562	—	3	1	no	—
192	#554	—	3	1	no	—
193	#554	—	3	1	no	—
194	#554	—	3	1	no	—
195	#554	—	3	1	no	—
196	#553	—	3	1	no	—
197	#553	—	3	1	no	—
198	#553	—	3	1	no	—
199	#553	D₃	1	1	yes	characteristic, complemented
200	#552	—	3	1	no	—
201	#552	—	3	1	no	—
202	#552	—	3	1	no	—
203	#552	—	3	1	no	—
204	#541	—	3	1	no	—
205	#541	—	3	1	no	—
206	#541	—	3	1	no	—
207	#541	—	3	1	no	—
208	#539	—	3	1	no	—
209	#539	—	3	1	no	—
210	#539	—	3	1	no	—
211	#539	—	3	1	no	—
212	#539	—	3	1	no	—
213	#539	—	3	1	no	—
214	#539	—	3	1	no	—
215	#539	—	3	1	no	—
216	#529	—	3	1	no	—
217	#529	—	3	1	no	—
218	C₂×#125	—	3	1	no	—
219	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×D₄	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	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	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₃×C₄	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	C₂²×Dic₃	C₂³	1	1	yes	characteristic
236	C₂²×Dic₃	C₂³	1	1	yes	characteristic
237	C₂²×Dic₃	C₂³	1	1	yes	characteristic
238	C₂²×Dic₃	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	C₂²×Dic₃	C₂³	1	1	yes	characteristic
243	C₂²×Dic₃	C₂³	1	1	yes	characteristic
244	C₂²×Dic₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
248	C₂×Dic₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₆	C₂³	1	1	yes	characteristic
250	C₂×Dic₆	C₂³	1	1	yes	characteristic
251	C₂×Dic₆	C₂³	1	1	yes	characteristic
252	C₂×Dic₆	C₂³	1	1	yes	characteristic
253	C₂×Dic₆	C₂³	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₃×C₄²	C₂³	1	1	yes	characteristic
275	C₃×C₄²	C₂³	1	1	yes	characteristic
276	C₃×C₄²	C₂³	1	1	yes	characteristic
277	#217	C₂³	1	1	yes	characteristic
278	#217	C₂³	1	1	yes	characteristic
279	#217	C₂³	1	1	yes	characteristic
280	#217	C₂³	1	1	yes	characteristic
281	#217	C₂³	1	1	yes	characteristic
282	#217	C₂³	1	1	yes	characteristic
283	#217	C₂³	1	1	yes	characteristic
284	#217	C₂³	1	1	yes	characteristic
285	#217	C₂³	1	1	yes	characteristic
286	#217	C₂³	1	1	yes	characteristic
287	#217	C₂³	1	1	yes	characteristic
288	#217	C₂³	1	1	yes	characteristic
289	#217	C₂³	1	1	yes	characteristic
290	#217	C₂³	1	1	yes	characteristic
291	#217	C₂³	1	1	yes	characteristic
292	#217	C₂³	1	1	yes	characteristic
293	#217	C₂³	1	1	yes	characteristic
294	#217	C₂³	1	1	yes	characteristic
295	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
321	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₃⋊C₄	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
362	C₄×Dic₃	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⋊Q₈	—	3	1	no	—
375	C₄⋊Q₈	—	3	1	no	—
376	C₄⋊Q₈	—	3	1	no	—
377	C₄⋊Q₈	—	3	1	no	—
378	#126	—	3	1	no	—
379	#126	—	3	1	no	—
380	#126	—	3	1	no	—
381	#126	—	3	1	no	—
382	#126	—	3	1	no	—
383	#126	—	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	C₂×D₃	1	1	yes	characteristic
397	#126	C₂×D₃	1	1	yes	characteristic
398	#125	—	3	1	no	—
399	#125	—	3	1	no	—
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	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	3	1	no	—
412	#125	—	3	1	no	—
413	#125	—	3	1	no	—
414	#125	—	3	1	no	—
415	#125	—	3	1	no	—
416	#125	—	3	1	no	—
417	#125	—	3	1	no	—
418	#125	—	3	1	no	—
419	#125	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	—	3	1	no	—
423	#125	—	3	1	no	—
424	#125	—	3	1	no	—
425	#125	—	3	1	no	—
426	#125	—	3	1	no	—
427	#125	C₂×D₃	1	1	yes	characteristic
428	#124	—	3	1	no	—
429	#124	—	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	—	3	1	no	—
445	#123	—	3	1	no	—
446	#123	—	3	1	no	—
447	#123	—	3	1	no	—
448	#123	C₂×D₃	1	1	yes	characteristic
449	#123	C₂×D₃	1	1	yes	characteristic
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	C₂²⋊Q₈	—	3	1	no	—
461	C₂²⋊Q₈	—	3	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	C₂²⋊Q₈	—	3	1	no	—
465	C₂²⋊Q₈	—	3	1	no	—
466	C₂²⋊Q₈	—	3	1	no	—
467	C₂²⋊Q₈	—	3	1	no	—
468	C₂²⋊Q₈	—	3	1	no	—
469	C₂²⋊Q₈	—	3	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	—	3	1	no	—
472	C₂²⋊Q₈	—	3	1	no	—
473	C₂²⋊Q₈	—	3	1	no	—
474	C₂²⋊Q₈	—	3	1	no	—
475	C₂²⋊Q₈	—	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	C₂×D₃	1	1	yes	characteristic
483	#121	C₂×D₃	1	1	yes	characteristic
484	#121	C₂×D₃	1	1	yes	characteristic
485	#121	C₂×D₃	1	1	yes	characteristic
486	C₄×Q₈	—	3	1	no	—
487	C₄×Q₈	—	3	1	no	—
488	C₄×Q₈	—	3	1	no	—
489	C₄×Q₈	—	3	1	no	—
490	C₄×Q₈	—	3	1	no	—
491	C₄×Q₈	—	3	1	no	—
492	C₄×D₄	—	3	1	no	—
493	C₄×D₄	—	3	1	no	—
494	C₄×D₄	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	C₂×D₃	1	1	yes	characteristic
507	C₄×D₄	C₂×D₃	1	1	yes	characteristic
508	C₄×D₄	C₂×D₃	1	1	yes	characteristic
509	C₄×D₄	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	—	3	1	no	—
519	C₂×C₄⋊C₄	—	3	1	no	—
520	C₂×C₄⋊C₄	—	3	1	no	—
521	C₂×C₄⋊C₄	—	3	1	no	—
522	C₂×C₄⋊C₄	—	3	1	no	—
523	C₂×C₄⋊C₄	—	3	1	no	—
524	C₂×C₄⋊C₄	—	3	1	no	—
525	C₂×C₄⋊C₄	—	3	1	no	—
526	C₂×C₄⋊C₄	—	3	1	no	—
527	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
528	C₂×C₄²	—	3	1	no	—
529	C₂³×C₃	C₂⁴	1	1	yes	characteristic
530	C₂³×C₃	C₂⁴	1	1	yes	characteristic
531	C₂³×C₃	C₂⁴	1	1	yes	characteristic
532	C₂³×C₃	C₂⁴	1	1	yes	characteristic
533	C₂²×D₃	C₂⁴	1	1	yes	characteristic
534	C₃×D₄	—	2	2	no	—
535	C₃×D₄	—	2	2	no	—
536	C₃×D₄	—	2	2	no	—
537	C₃×D₄	—	4	1	no	—
538	C₃×D₄	—	4	1	no	—
539	C₃×D₄	—	4	1	no	—
540	C₂×C₃×C₄	—	4	1	no	—
541	C₂×C₃×C₄	—	4	1	no	—
542	C₂×C₃×C₄	—	4	1	no	—
543	C₂×C₃×C₄	—	4	1	no	—
544	C₂×C₃×C₄	—	4	1	no	—
545	C₂×C₃×C₄	—	4	1	no	—
546	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
547	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
548	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
558	#67	—	4	1	no	—
559	#67	—	4	1	no	—
560	#67	—	4	1	no	—
561	C₂×Dic₃	—	2	2	no	—
562	C₂×Dic₃	—	4	1	no	—
563	C₂×Dic₃	—	4	1	no	—
564	C₂×Dic₃	—	4	1	no	—
565	C₂×Dic₃	—	4	1	no	—
566	C₂×Dic₃	—	4	1	no	—
567	C₂×Dic₃	—	4	1	no	—
568	C₂×Dic₃	—	4	1	no	—
569	C₂×Dic₃	—	4	1	no	—
570	C₂×Dic₃	—	4	1	no	—
571	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
572	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
573	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
574	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
575	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
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	C₄×D₃	—	4	1	no	—
587	C₄×D₃	—	4	1	no	—
588	C₄×D₃	—	4	1	no	—
589	Dic₆	—	4	1	no	—
590	Dic₆	—	4	1	no	—
591	Dic₆	—	4	1	no	—
592	Dic₆	—	4	1	no	—
593	Dic₆	—	4	1	no	—
594	Dic₆	—	4	1	no	—
595	C₂×Q₈	—	3	1	no	—
596	C₂×Q₈	—	3	1	no	—
597	C₂×Q₈	—	3	1	no	—
598	C₂×Q₈	—	3	1	no	—
599	C₂×Q₈	—	3	1	no	—
600	C₂×Q₈	—	3	1	no	—
601	C₂×D₄	—	3	1	no	—
602	C₂×D₄	—	3	1	no	—
603	C₂×D₄	—	3	1	no	—
604	C₂×D₄	—	3	1	no	—
605	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
606	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
607	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
608	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
609	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
610	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
611	C₂²×C₄	—	3	1	no	—
612	C₂²×C₄	—	3	1	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	1	no	—
615	C₂²×C₄	—	3	1	no	—
616	C₂²×C₄	—	3	1	no	—
617	C₂²×C₄	—	3	1	no	—
618	C₂²×C₄	—	3	1	no	—
619	C₂²×C₄	—	3	1	no	—
620	C₂²×C₄	—	3	1	no	—
621	C₂²×C₄	—	3	1	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
625	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
626	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
627	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
628	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
629	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
630	C₄⋊C₄	—	3	1	no	—
631	C₄⋊C₄	—	3	1	no	—
632	C₄⋊C₄	—	3	1	no	—
633	C₄⋊C₄	—	3	1	no	—
634	C₄⋊C₄	—	3	1	no	—
635	C₄⋊C₄	—	3	1	no	—
636	C₄⋊C₄	—	3	1	no	—
637	C₄⋊C₄	—	3	1	no	—
638	C₄⋊C₄	—	3	1	no	—
639	C₄⋊C₄	—	3	1	no	—
640	C₄⋊C₄	—	3	1	no	—
641	C₄⋊C₄	—	3	1	no	—
642	C₄⋊C₄	—	3	1	no	—
643	C₄⋊C₄	—	3	1	no	—
644	C₄⋊C₄	—	3	1	no	—
645	C₄⋊C₄	—	3	1	no	—
646	C₄⋊C₄	—	3	1	no	—
647	C₄⋊C₄	—	3	1	no	—
648	C₄⋊C₄	—	3	1	no	—
649	C₄⋊C₄	—	3	1	no	—
650	C₄⋊C₄	—	3	1	no	—
651	C₄⋊C₄	—	3	1	no	—
652	C₄⋊C₄	—	3	1	no	—
653	C₄⋊C₄	—	3	1	no	—
654	C₄⋊C₄	—	3	1	no	—
655	C₄⋊C₄	—	3	1	no	—
656	C₄⋊C₄	—	3	1	no	—
657	C₄⋊C₄	—	3	1	no	—
658	C₄⋊C₄	—	3	1	no	—
659	C₄⋊C₄	—	3	1	no	—
660	C₄⋊C₄	—	3	1	no	—
661	C₄⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
689	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
690	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
691	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
694	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
696	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
698	C₂²⋊C₄	—	3	1	no	—
699	C₂²⋊C₄	—	3	1	no	—
700	C₂²⋊C₄	—	3	1	no	—
701	C₂²⋊C₄	—	3	1	no	—
702	C₂²⋊C₄	—	3	1	no	—
703	C₂²⋊C₄	—	3	1	no	—
704	C₂²⋊C₄	—	3	1	no	—
705	C₂²⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
725	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
726	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
727	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
728	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
729	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
730	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
731	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
732	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
733	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
734	C₄²	—	3	1	no	—
735	C₄²	—	3	1	no	—
736	C₄²	—	3	1	no	—
737	C₄²	—	3	1	no	—
738	C₄²	—	3	1	no	—
739	C₄²	—	3	1	no	—
740	C₄²	—	3	1	no	—
741	C₄²	—	3	1	no	—
742	C₄²	—	3	1	no	—
743	C₄²	—	3	1	no	—
744	C₄²	—	3	1	no	—
745	C₄²	—	3	1	no	—
746	C₄²	—	3	1	no	—
747	C₄²	C₂²×D₃	1	1	yes	characteristic
748	C₄²	C₂²×D₃	1	1	yes	characteristic
749	C₄²	C₂²×D₃	1	1	yes	characteristic
750	C₂²×C₃	—	2	1	no	—
751	C₂²×C₃	—	2	1	no	—
752	C₂²×C₃	—	2	1	no	—
753	C₂²×C₃	—	2	1	no	—
754	C₂²×C₃	—	2	1	no	—
755	C₂²×C₃	—	2	1	no	—
756	C₂²×C₃	—	2	1	no	—
757	C₂²×C₃	—	2	1	no	—
758	C₂²×C₃	—	2	1	no	—
759	C₂²×C₃	—	2	1	no	—
760	C₂²×C₃	—	2	1	no	—
761	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
762	C₂²×C₃	C₂⁵	1	1	yes	characteristic
763	C₂×D₃	—	2	1	no	—
764	C₂×D₃	—	2	1	no	—
765	C₂×D₃	—	2	1	no	—
766	C₃×C₄	—	2	1	no	—
767	C₃×C₄	—	2	1	no	—
768	C₃×C₄	—	2	1	no	—
769	C₃×C₄	—	2	1	no	—
770	C₃×C₄	—	2	1	no	—
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	2	1	no	—
773	C₃×C₄	—	2	1	no	—
774	C₃×C₄	—	2	1	no	—
775	C₃×C₄	—	2	1	no	—
776	C₃×C₄	—	2	1	no	—
777	Dic₃	—	2	1	no	—
778	Dic₃	—	2	1	no	—
779	Dic₃	—	2	1	no	—
780	Dic₃	—	2	1	no	—
781	Dic₃	—	2	1	no	—
782	Dic₃	—	2	1	no	—
783	Dic₃	—	2	1	no	—
784	Dic₃	—	2	1	no	—
785	Dic₃	—	2	1	no	—
786	Dic₃	—	2	1	no	—
787	Dic₃	—	2	1	no	—
788	Dic₃	—	2	1	no	—
789	Dic₃	—	2	1	no	—
790	Dic₃	—	2	1	no	—
791	Dic₃	—	2	1	no	—
792	C₂³	—	3	1	no	—
793	C₂³	C₂³×D₃	1	1	yes	characteristic
794	C₂³	C₂³×D₃	1	1	yes	characteristic
795	C₂³	C₂³×D₃	1	1	yes	characteristic
796	C₂³	C₂³×D₃	1	1	yes	characteristic
797	Q₈	—	12	1	no	—
798	Q₈	—	12	1	no	—
799	Q₈	—	12	1	no	—
800	Q₈	—	12	1	no	—
801	Q₈	—	12	1	no	—
802	Q₈	—	12	1	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	1	no	—
807	D₄	—	4	1	no	—
808	D₄	—	4	1	no	—
809	D₄	—	6	2	no	—
810	D₄	—	12	1	no	—
811	D₄	—	12	1	no	—
812	D₄	—	12	1	no	—
813	C₂×C₄	—	3	1	no	—
814	C₂×C₄	—	3	1	no	—
815	C₂×C₄	—	3	1	no	—
816	C₂×C₄	—	3	1	no	—
817	C₂×C₄	—	3	1	no	—
818	C₂×C₄	—	3	1	no	—
819	C₂×C₄	—	3	1	no	—
820	C₂×C₄	—	3	1	no	—
821	C₂×C₄	—	3	1	no	—
822	C₂×C₄	—	3	1	no	—
823	C₂×C₄	—	3	1	no	—
824	C₂×C₄	—	3	1	no	—
825	C₂×C₄	—	3	1	no	—
826	C₂×C₄	—	3	1	no	—
827	C₂×C₄	—	3	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	6	2	no	—
835	C₂×C₄	—	12	1	no	—
836	C₂×C₄	—	12	1	no	—
837	C₂×C₄	—	12	1	no	—
838	C₂×C₄	—	12	1	no	—
839	C₂×C₄	—	12	1	no	—
840	C₂×C₄	—	12	1	no	—
841	C₂×C₄	—	12	1	no	—
842	C₂×C₄	—	12	1	no	—
843	C₂×C₄	—	12	1	no	—
844	C₂×C₄	—	12	1	no	—
845	C₂×C₄	—	12	1	no	—
846	C₂×C₄	—	12	1	no	—
847	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
848	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
849	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
850	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
851	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
852	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
853	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
854	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
858	C₂×C₃	—	2	2	no	—
859	C₂×C₃	—	4	1	no	—
860	C₂×C₃	—	4	1	no	—
861	C₂×C₃	—	4	1	no	—
862	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
863	C₂×C₃	#585	1	1	yes	characteristic
864	C₂×C₃	#585	1	1	yes	characteristic
865	D₃	—	4	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	6	1	no	—
878	C₂²	—	6	1	no	—
879	C₂²	—	6	1	no	—
880	C₂²	#1010	1	2	yes	—
881	C₂²	C₂⁴×D₃	1	1	yes	characteristic
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	6	1	no	—
894	C₄	—	6	1	no	—
895	C₄	—	6	1	no	—
896	C₄	—	6	1	no	—
897	C₄	—	6	1	no	—
898	C₄	—	6	1	no	—
899	C₄	—	6	1	no	—
900	C₄	—	6	1	no	—
901	C₄	—	6	1	no	—
902	C₄	—	6	1	no	—
903	C₄	—	6	1	no	—
904	C₄	—	6	1	no	—
905	C₄	—	6	1	no	—
906	C₄	—	6	1	no	—
907	C₄	—	6	1	no	—
908	C₃	#3553	1	1	yes	characteristic, complemented, Sylow
909	C₂	—	2	2	no	—
910	C₂	—	4	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	4	1	no	—
913	C₂	—	12	1	no	—
914	C₂	C₂×#1010	1	1	yes	characteristic
915	C₂	#5964	1	1	yes	characteristic
916	C₂	#5966	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	#3553
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. #5712	C₂	semidirect
3. #5708	C₂	semidirect
4. #5701	C₂	semidirect
5. #5701	C₂	semidirect
6. #5696	C₂	semidirect
7. C₃⋊#564	C₂	semidirect
8. #5665	C₂	semidirect
9. #5660	C₂	semidirect
10. #5651	C₂	semidirect
11. #5650	C₂	semidirect
12. #5621	C₂	semidirect
13. #5618	C₂	semidirect
14. #5602	C₂	semidirect
15. #5602	C₂	semidirect
16. #5602	C₂	semidirect
17. #5601	C₂	semidirect
18. #5601	C₂	semidirect
19. #5600	C₂	semidirect
20. #5564	C₂	semidirect
21. #5564	C₂	semidirect
22. #5564	C₂	semidirect
23. #5543	C₂	semidirect
24. #5541	C₂	semidirect
25. #5539	C₂	semidirect
26. #5539	C₂	semidirect
27. #5538	C₂	semidirect
28. #5531	C₂	semidirect
29. #5518	C₂	semidirect
30. #5511	C₂	semidirect
31. C₂×#889	C₂	semidirect
199. #553	D₃	semidirect
908. C₃	#3553	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
#5712	2
#5708	2
#5701	2
#5696	2
C₃⋊#564	2
#5665	2
#5660	2
#5651	2
#5650	2
#5621	2
#5618	2
#5602	2
#5601	2
#5600	2
#5564	2
#5543	2
#5541	2
#5539	2
#5538	2
#5531	2
#5518	2
#5511	2
C₂×#889	2
#3553	3