Subgroups — #86801

Order 384.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#5711	C₂	1	1	yes	maximal, characteristic, complemented
3	#5709	C₂	1	1	yes	maximal, characteristic, complemented
4	#5707	C₂	1	1	yes	maximal, characteristic, complemented
5	#5704	C₂	1	1	yes	maximal, characteristic, complemented
6	#5678	C₂	1	1	yes	maximal, characteristic, complemented
7	#5676	C₂	1	1	yes	maximal, characteristic, complemented
8	#5667	C₂	1	1	yes	maximal, characteristic, complemented
9	#5666	C₂	1	1	yes	maximal, characteristic, complemented
10	#5657	C₂	1	1	yes	maximal, characteristic, complemented
11	#5654	C₂	1	1	yes	maximal, characteristic, complemented
12	#5653	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
14	#5647	C₂	1	1	yes	maximal, characteristic, complemented
15	#5645	C₂	1	1	yes	maximal, characteristic, complemented
16	#5630	C₂	1	1	yes	maximal, characteristic, complemented
17	#5629	C₂	1	1	yes	maximal, characteristic, complemented
18	#5590	C₂	1	1	yes	maximal, characteristic, complemented
19	#5589	C₂	1	1	yes	maximal, characteristic, complemented
20	#5564	C₂	1	1	yes	maximal, characteristic, complemented
21	#5562	C₂	1	1	yes	maximal, characteristic, complemented
22	#5550	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
24	#5535	C₂	1	1	yes	maximal, characteristic, complemented
25	#5530	C₂	1	1	yes	maximal, characteristic, complemented
26	#5527	C₂	1	1	yes	maximal, characteristic, complemented
27	#5524	C₂	1	1	yes	maximal, characteristic, complemented
28	#5493	C₂	1	1	yes	maximal, characteristic, complemented
29	#5490	C₂	1	1	yes	maximal, characteristic, complemented
30	#5490	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#884	C₂	1	1	yes	maximal, characteristic, complemented
32	#3534	—	3	1	no	maximal, Sylow
33	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
36	C₂×#239	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
38	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×#235	C₂²	1	1	yes	characteristic, complemented
41	C₂×#235	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₁₂	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₁₂	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
45	C₃×#126	C₂²	1	1	yes	characteristic, complemented
46	C₃×#126	C₂²	1	1	yes	characteristic, complemented
47	C₃×#124	C₂²	1	1	yes	characteristic, complemented
48	C₃×#123	C₂²	1	1	yes	characteristic, complemented
49	C₃×#123	C₂²	1	1	yes	characteristic, complemented
50	C₃×#123	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×#120	C₂²	1	1	yes	characteristic
54	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
56	C₃×#117	C₂²	1	1	yes	characteristic, complemented
57	C₃×#117	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	#953	C₂²	1	1	yes	characteristic, complemented
61	#947	C₂²	1	1	yes	characteristic, complemented
62	#946	C₂²	1	1	yes	characteristic, complemented
63	#946	C₂²	1	1	yes	characteristic, complemented
64	#940	C₂²	1	1	yes	characteristic, complemented
65	#939	C₂²	1	1	yes	characteristic
66	#939	C₂²	1	1	yes	characteristic, complemented
67	#938	C₂²	1	1	yes	characteristic, complemented
68	#938	C₂²	1	1	yes	characteristic, complemented
69	#937	C₂²	1	1	yes	characteristic, complemented
70	#937	C₂²	1	1	yes	characteristic, complemented
71	#937	C₂²	1	1	yes	characteristic, complemented
72	#935	C₂²	1	1	yes	characteristic, complemented
73	#930	C₂²	1	1	yes	characteristic
74	#930	C₂²	1	1	yes	characteristic, complemented
75	#930	C₂²	1	1	yes	characteristic, complemented
76	#930	C₂²	1	1	yes	characteristic, complemented
77	#930	C₂²	1	1	yes	characteristic, complemented
78	#930	C₂²	1	1	yes	characteristic, complemented
79	#930	C₂²	1	1	yes	characteristic, complemented
80	#929	C₂²	1	1	yes	characteristic, complemented
81	#929	C₂²	1	1	yes	characteristic, complemented
82	#929	C₂²	1	1	yes	characteristic, complemented
83	C₄×#67	C₂²	1	1	yes	characteristic, complemented
84	C₄×#67	C₂²	1	1	yes	characteristic, complemented
85	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	#924	C₂²	1	1	yes	characteristic, complemented
87	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	#898	C₂²	1	1	yes	characteristic, complemented
89	#898	C₂²	1	1	yes	characteristic, complemented
90	#898	C₂²	1	1	yes	characteristic, complemented
91	#897	C₂²	1	1	yes	characteristic, complemented
92	#897	C₂²	1	1	yes	characteristic, complemented
93	#896	C₂²	1	1	yes	characteristic, complemented
94	#896	C₂²	1	1	yes	characteristic, complemented
95	#896	C₂²	1	1	yes	characteristic, complemented
96	#895	C₂²	1	1	yes	characteristic, complemented
97	#895	C₂²	1	1	yes	characteristic, complemented
98	#895	C₂²	1	1	yes	characteristic, complemented
99	#895	C₂²	1	1	yes	characteristic, complemented
100	#895	C₂²	1	1	yes	characteristic, complemented
101	#895	C₂²	1	1	yes	characteristic, complemented
102	#895	C₂²	1	1	yes	characteristic, complemented
103	#895	C₂²	1	1	yes	characteristic, complemented
104	#894	C₂²	1	1	yes	characteristic, complemented
105	#894	C₂²	1	1	yes	characteristic, complemented
106	#894	C₂²	1	1	yes	characteristic, complemented
107	#894	C₂²	1	1	yes	characteristic, complemented
108	#894	C₂²	1	1	yes	characteristic, complemented
109	#894	C₂²	1	1	yes	characteristic, complemented
110	#894	C₂²	1	1	yes	characteristic, complemented
111	#894	C₂²	1	1	yes	characteristic, complemented
112	#894	C₂²	1	1	yes	characteristic, complemented
113	#893	C₂²	1	1	yes	characteristic, complemented
114	#893	C₂²	1	1	yes	characteristic, complemented
115	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	#890	C₂²	1	1	yes	characteristic, complemented
118	#890	C₂²	1	1	yes	characteristic, complemented
119	#889	C₂²	1	1	yes	characteristic, complemented
120	#886	C₂²	1	1	yes	characteristic, complemented
121	#886	C₂²	1	1	yes	characteristic, complemented
122	#886	C₂²	1	1	yes	characteristic, complemented
123	#886	C₂²	1	1	yes	characteristic, complemented
124	#886	C₂²	1	1	yes	characteristic, complemented
125	#885	C₂²	1	1	yes	characteristic, complemented
126	#885	C₂²	1	1	yes	characteristic, complemented
127	#885	C₂²	1	1	yes	characteristic, complemented
128	#884	C₂²	1	1	yes	characteristic
129	#884	C₂²	1	1	yes	characteristic, complemented
130	#884	C₂²	1	1	yes	characteristic, complemented
131	#884	C₂²	1	1	yes	characteristic, complemented
132	#884	C₂²	1	1	yes	characteristic, complemented
133	#884	C₂²	1	1	yes	characteristic, complemented
134	#884	C₂²	1	1	yes	characteristic, complemented
135	#884	C₂²	1	1	yes	characteristic, complemented
136	#884	C₂²	1	1	yes	characteristic, complemented
137	#884	C₂²	1	1	yes	characteristic, complemented
138	#884	C₂²	1	1	yes	characteristic, complemented
139	#884	C₂²	1	1	yes	characteristic, complemented
140	#884	C₂²	1	1	yes	characteristic, complemented
141	#884	C₂²	1	1	yes	characteristic, complemented
142	#884	C₂²	1	1	yes	characteristic, complemented
143	#884	C₂²	1	1	yes	characteristic, complemented
144	#884	C₂²	1	1	yes	characteristic, complemented
145	#883	C₂²	1	1	yes	characteristic, complemented
146	#883	C₂²	1	1	yes	characteristic, complemented
147	#883	C₂²	1	1	yes	characteristic, complemented
148	#883	C₂²	1	1	yes	characteristic, complemented
149	#883	C₂²	1	1	yes	characteristic, complemented
150	#883	C₂²	1	1	yes	characteristic, complemented
151	#883	C₂²	1	1	yes	characteristic, complemented
152	#882	C₂²	1	1	yes	characteristic
153	#882	C₂²	1	1	yes	characteristic, complemented
154	#882	C₂²	1	1	yes	characteristic, complemented
155	#882	C₂²	1	1	yes	characteristic, complemented
156	#882	C₂²	1	1	yes	characteristic, complemented
157	#882	C₂²	1	1	yes	characteristic, complemented
158	#882	C₂²	1	1	yes	characteristic, complemented
159	#882	C₂²	1	1	yes	characteristic, complemented
160	#882	C₂²	1	1	yes	characteristic, complemented
161	#882	C₂²	1	1	yes	characteristic, complemented
162	#882	C₂²	1	1	yes	characteristic, complemented
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, complemented
168	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
173	#879	C₂²	1	1	yes	characteristic, complemented
174	#878	C₂²	1	1	yes	characteristic, complemented
175	#878	C₂²	1	1	yes	characteristic, complemented
176	#876	C₂²	1	1	yes	characteristic, complemented
177	#876	C₂²	1	1	yes	characteristic, complemented
178	#875	C₂²	1	1	yes	characteristic, complemented
179	#874	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₁₂	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	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
186	#872	C₂²	1	1	yes	characteristic, complemented
187	#870	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	#553	—	3	1	no	—
193	#553	—	3	1	no	—
194	#551	—	3	1	no	—
195	#551	D₃	1	1	yes	characteristic, complemented
196	#546	—	3	1	no	—
197	#546	—	3	1	no	—
198	#546	—	3	1	no	—
199	#546	—	3	1	no	—
200	#546	—	3	1	no	—
201	#546	—	3	1	no	—
202	D₄²	—	3	1	no	—
203	D₄²	—	3	1	no	—
204	#540	—	3	1	no	—
205	#540	—	3	1	no	—
206	#539	—	3	1	no	—
207	#539	—	3	1	no	—
208	#539	—	3	1	no	—
209	#538	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#537	—	3	1	no	—
213	#534	—	3	1	no	—
214	#534	—	3	1	no	—
215	#534	—	3	1	no	—
216	#525	—	3	1	no	—
217	C₂×#123	—	3	1	no	—
218	C₂×#121	—	3	1	no	—
219	C₂⁴×C₃	C₂³	1	1	yes	characteristic
220	C₂³×D₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₂³×D₃	C₂³	1	1	yes	characteristic
223	C₂³×D₃	C₂³	1	1	yes	characteristic
224	C₂³×D₃	C₂³	1	1	yes	characteristic
225	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	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	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
234	C₂×#67	—	4	2	no	—
235	C₂×#67	—	4	2	no	—
236	C₂×#67	—	4	2	no	—
237	C₂×#67	C₂³	1	1	yes	characteristic
238	C₂×#67	C₂³	1	1	yes	characteristic
239	C₂×#67	C₂³	1	1	yes	characteristic
240	C₂×#67	C₂³	1	1	yes	characteristic
241	C₂×#67	C₂³	1	1	yes	characteristic
242	C₂×#67	C₂³	1	1	yes	characteristic
243	C₂×#67	C₂³	1	1	yes	characteristic
244	C₂×#67	C₂³	1	1	yes	characteristic
245	C₂×#67	C₂³	1	1	yes	characteristic
246	C₂×#67	C₂³	1	1	yes	characteristic
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂×#67	C₂³	1	1	yes	characteristic
249	C₂×#67	C₂³	1	1	yes	characteristic
250	C₂×#67	C₂³	1	1	yes	characteristic
251	C₂×#67	C₂³	1	1	yes	characteristic
252	C₂×#67	C₂³	1	1	yes	characteristic
253	C₂×#67	C₂³	1	1	yes	characteristic
254	C₂×#67	C₂³	1	1	yes	characteristic
255	C₂²×Dic₃	C₂³	1	1	yes	characteristic
256	C₂²×Dic₃	C₂³	1	1	yes	characteristic
257	C₂²×Dic₃	C₂³	1	1	yes	characteristic
258	#239	—	4	2	no	—
259	D₃×D₄	—	4	2	no	—
260	D₃×D₄	—	4	2	no	—
261	D₃×D₄	—	4	2	no	—
262	#235	—	4	2	no	—
263	#235	—	4	2	no	—
264	C₂×D₁₂	—	4	2	no	—
265	C₂×D₁₂	—	4	2	no	—
266	C₂×D₁₂	C₂³	1	1	yes	characteristic
267	C₂×D₁₂	C₂³	1	1	yes	characteristic
268	C₂×D₁₂	C₂³	1	1	yes	characteristic
269	C₂×D₁₂	C₂³	1	1	yes	characteristic
270	C₂×D₁₂	C₂³	1	1	yes	characteristic
271	C₂×D₁₂	C₂³	1	1	yes	characteristic
272	C₂×D₁₂	C₂³	1	1	yes	characteristic
273	C₂×D₁₂	C₂³	1	1	yes	characteristic
274	C₂×D₁₂	C₂³	1	1	yes	characteristic
275	C₂×D₁₂	C₂³	1	1	yes	characteristic
276	C₂×D₁₂	C₂³	1	1	yes	characteristic
277	C₂×D₁₂	C₂³	1	1	yes	characteristic
278	C₂×D₁₂	C₂³	1	1	yes	characteristic
279	C₂×D₁₂	C₂³	1	1	yes	characteristic
280	C₂×D₁₂	C₂³	1	1	yes	characteristic
281	C₂×D₁₂	C₂³	1	1	yes	characteristic
282	C₂×C₄×D₃	—	4	2	no	—
283	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
298	C₂×Dic₆	C₂³	1	1	yes	characteristic
299	C₂×Dic₆	C₂³	1	1	yes	characteristic
300	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
301	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
304	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
321	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₃×C₄²	C₂³	1	1	yes	characteristic
323	C₃×C₄²	C₂³	1	1	yes	characteristic
324	C₃×C₄²	C₂³	1	1	yes	characteristic
325	#217	C₂³	1	1	yes	characteristic
326	#217	C₂³	1	1	yes	characteristic
327	#217	C₂³	1	1	yes	characteristic
328	#217	C₂³	1	1	yes	characteristic
329	#217	C₂³	1	1	yes	characteristic
330	#217	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
342	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
343	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
344	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
351	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
353	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
355	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
356	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
357	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
358	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
359	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
360	(C₂×D₃)⋊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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
371	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
378	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
379	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
380	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
381	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
382	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
383	C₄×Dic₃	C₂³	1	1	yes	characteristic
384	C₄×Dic₃	C₂³	1	1	yes	characteristic
385	C₄×Dic₃	C₂³	1	1	yes	characteristic
386	C₂×#41	—	3	1	no	—
387	C₂×#41	—	3	1	no	—
388	C₂×#41	—	3	1	no	—
389	C₂²×D₄	—	3	1	no	—
390	C₂²×D₄	—	3	1	no	—
391	C₂²×D₄	—	3	1	no	—
392	C₂²×D₄	—	3	1	no	—
393	C₂²×D₄	—	3	1	no	—
394	C₂²×D₄	—	3	1	no	—
395	C₂²×D₄	—	3	1	no	—
396	C₂²×D₄	—	3	1	no	—
397	C₂³×C₄	—	3	1	no	—
398	#127	—	3	1	no	—
399	#127	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	—	3	1	no	—
405	#126	—	3	1	no	—
406	#126	C₂×D₃	1	1	yes	characteristic, complemented
407	#126	C₂×D₃	1	1	yes	characteristic, complemented
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	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	C₂×D₃	1	1	yes	characteristic, complemented
418	#123	—	3	1	no	—
419	#123	—	3	1	no	—
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	#123	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	3	1	no	—
434	#123	—	3	1	no	—
435	#123	—	3	1	no	—
436	#123	—	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	C₂×D₃	1	1	yes	characteristic, complemented
444	#123	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
457	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
458	#121	—	3	1	no	—
459	#121	—	3	1	no	—
460	#121	—	3	1	no	—
461	#121	—	3	1	no	—
462	#121	—	3	1	no	—
463	#121	—	3	1	no	—
464	#121	—	3	1	no	—
465	#121	—	3	1	no	—
466	#121	—	3	1	no	—
467	#121	—	3	1	no	—
468	#121	—	3	1	no	—
469	#121	—	3	1	no	—
470	#121	—	3	1	no	—
471	#121	—	3	1	no	—
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	—	3	1	no	—
478	#121	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	#121	—	3	1	no	—
487	#121	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	—	3	1	no	—
491	#121	—	3	1	no	—
492	#121	—	3	1	no	—
493	#121	—	3	1	no	—
494	#120	—	3	1	no	—
495	#120	—	3	1	no	—
496	#120	—	3	1	no	—
497	#120	—	3	1	no	—
498	#120	—	3	1	no	—
499	#120	—	3	1	no	—
500	#120	—	3	1	no	—
501	#120	—	3	1	no	—
502	#120	—	3	1	no	—
503	#120	—	3	1	no	—
504	#120	—	3	1	no	—
505	#120	—	3	1	no	—
506	#120	—	3	1	no	—
507	#120	—	3	1	no	—
508	#120	—	3	1	no	—
509	#120	C₂×D₃	1	1	yes	characteristic
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	—	3	1	no	—
518	C₄×D₄	—	3	1	no	—
519	C₄×D₄	—	3	1	no	—
520	C₄×D₄	—	3	1	no	—
521	C₄×D₄	—	3	1	no	—
522	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	3	1	no	—
524	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
525	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
526	#117	—	3	1	no	—
527	#117	C₂×D₃	1	1	yes	characteristic, complemented
528	#117	C₂×D₃	1	1	yes	characteristic, complemented
529	C₂×C₄⋊C₄	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
540	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
541	C₂³×C₃	—	2	2	no	—
542	C₂³×C₃	—	4	1	no	—
543	C₂³×C₃	—	4	1	no	—
544	C₂³×C₃	C₂⁴	1	1	yes	characteristic
545	C₂³×C₃	C₂⁴	1	1	yes	characteristic
546	C₂³×C₃	C₂⁴	1	1	yes	characteristic
547	C₂³×C₃	C₂⁴	1	1	yes	characteristic
548	C₂²×D₃	—	2	2	no	—
549	C₂²×D₃	—	2	2	no	—
550	C₂²×D₃	—	2	2	no	—
551	C₂²×D₃	—	2	2	no	—
552	C₂²×D₃	—	4	1	no	—
553	C₂²×D₃	—	4	1	no	—
554	C₂²×D₃	—	4	1	no	—
555	C₂²×D₃	—	4	1	no	—
556	C₂²×D₃	—	4	1	no	—
557	C₂²×D₃	—	4	1	no	—
558	C₂²×D₃	—	4	1	no	—
559	C₂²×D₃	—	4	1	no	—
560	C₂²×D₃	—	4	1	no	—
561	C₂²×D₃	—	4	1	no	—
562	C₂²×D₃	—	4	1	no	—
563	C₂²×D₃	C₂⁴	1	1	yes	characteristic
564	C₂²×D₃	C₂⁴	1	1	yes	characteristic
565	C₂²×D₃	C₂⁴	1	1	yes	characteristic
566	C₂²×D₃	C₂⁴	1	1	yes	characteristic
567	C₂²×D₃	C₂⁴	1	1	yes	characteristic
568	C₂²×D₃	C₂⁴	1	1	yes	characteristic
569	C₂²×D₃	C₂⁴	1	1	yes	characteristic
570	C₃×Q₈	—	4	1	no	—
571	C₃×D₄	—	2	2	no	—
572	C₃×D₄	—	4	1	no	—
573	C₃×D₄	—	4	1	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	4	1	no	—
576	C₂×C₃×C₄	—	4	1	no	—
577	C₂×C₃×C₄	—	4	1	no	—
578	C₂×C₃×C₄	—	4	1	no	—
579	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
584	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
590	#67	—	2	2	no	—
591	#67	—	2	2	no	—
592	#67	—	2	2	no	—
593	#67	—	2	2	no	—
594	#67	—	2	2	no	—
595	#67	—	4	1	no	—
596	#67	—	4	1	no	—
597	#67	—	4	1	no	—
598	#67	—	4	1	no	—
599	#67	—	4	1	no	—
600	#67	—	4	1	no	—
601	#67	—	4	1	no	—
602	#67	—	4	1	no	—
603	#67	—	4	1	no	—
604	#67	—	4	1	no	—
605	#67	—	4	1	no	—
606	#67	—	4	1	no	—
607	#67	—	4	1	no	—
608	C₂×Dic₃	—	2	2	no	—
609	C₂×Dic₃	—	4	1	no	—
610	C₂×Dic₃	—	4	1	no	—
611	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
612	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
613	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
614	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
615	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
616	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
617	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
618	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
619	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
620	D₁₂	—	2	2	no	—
621	D₁₂	—	2	2	no	—
622	D₁₂	—	2	2	no	—
623	D₁₂	—	2	2	no	—
624	D₁₂	—	4	1	no	—
625	D₁₂	—	4	1	no	—
626	D₁₂	—	4	1	no	—
627	D₁₂	—	4	1	no	—
628	D₁₂	—	4	1	no	—
629	D₁₂	—	4	1	no	—
630	D₁₂	—	4	1	no	—
631	D₁₂	—	4	1	no	—
632	D₁₂	—	4	1	no	—
633	D₁₂	—	4	1	no	—
634	D₁₂	—	4	1	no	—
635	D₁₂	—	4	1	no	—
636	C₄×D₃	—	2	2	no	—
637	C₄×D₃	—	4	1	no	—
638	C₄×D₃	—	4	1	no	—
639	C₄×D₃	—	4	1	no	—
640	C₄×D₃	—	4	1	no	—
641	C₄×D₃	—	4	1	no	—
642	C₄×D₃	—	4	1	no	—
643	C₄×D₃	—	4	1	no	—
644	C₄×D₃	—	4	1	no	—
645	C₄×D₃	—	4	1	no	—
646	C₄×D₃	—	4	1	no	—
647	C₄×D₃	—	4	1	no	—
648	C₄×D₃	—	4	1	no	—
649	C₄×D₃	—	4	1	no	—
650	C₄×D₃	—	4	1	no	—
651	Dic₆	—	4	1	no	—
652	Dic₆	—	4	1	no	—
653	C₂⁴	—	3	1	no	—
654	C₂⁴	—	3	1	no	—
655	C₂⁴	—	3	1	no	—
656	C₂⁴	—	3	1	no	—
657	C₂⁴	—	3	1	no	—
658	C₂⁴	C₂²×D₃	1	1	yes	characteristic
659	#41	—	12	2	no	—
660	#41	—	12	2	no	—
661	#41	—	12	2	no	—
662	C₂×Q₈	—	3	1	no	—
663	C₂×Q₈	—	3	1	no	—
664	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
665	C₂×D₄	—	3	1	no	—
666	C₂×D₄	—	3	1	no	—
667	C₂×D₄	—	3	1	no	—
668	C₂×D₄	—	3	1	no	—
669	C₂×D₄	—	3	1	no	—
670	C₂×D₄	—	3	1	no	—
671	C₂×D₄	—	3	1	no	—
672	C₂×D₄	—	3	1	no	—
673	C₂×D₄	—	3	1	no	—
674	C₂×D₄	—	3	1	no	—
675	C₂×D₄	—	3	1	no	—
676	C₂×D₄	—	3	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	3	1	no	—
681	C₂×D₄	—	3	1	no	—
682	C₂×D₄	—	3	1	no	—
683	C₂×D₄	—	3	1	no	—
684	C₂×D₄	—	3	1	no	—
685	C₂×D₄	—	3	1	no	—
686	C₂×D₄	—	3	1	no	—
687	C₂×D₄	—	3	1	no	—
688	C₂×D₄	—	3	1	no	—
689	C₂×D₄	—	3	1	no	—
690	C₂×D₄	—	3	1	no	—
691	C₂×D₄	—	3	1	no	—
692	C₂×D₄	—	3	1	no	—
693	C₂×D₄	—	3	1	no	—
694	C₂×D₄	—	3	1	no	—
695	C₂×D₄	—	3	1	no	—
696	C₂×D₄	—	3	1	no	—
697	C₂×D₄	—	3	1	no	—
698	C₂×D₄	—	3	1	no	—
699	C₂×D₄	—	12	2	no	—
700	C₂×D₄	—	12	2	no	—
701	C₂×D₄	—	12	2	no	—
702	C₂×D₄	—	12	2	no	—
703	C₂×D₄	—	12	2	no	—
704	C₂×D₄	—	12	2	no	—
705	C₂×D₄	—	12	2	no	—
706	C₂×D₄	—	12	2	no	—
707	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
709	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	—	12	2	no	—
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	C₄⋊C₄	—	3	1	no	—
735	C₄⋊C₄	—	3	1	no	—
736	C₄⋊C₄	—	3	1	no	—
737	C₄⋊C₄	—	3	1	no	—
738	C₄⋊C₄	—	3	1	no	—
739	C₄⋊C₄	—	3	1	no	—
740	C₄⋊C₄	—	3	1	no	—
741	C₄⋊C₄	—	3	1	no	—
742	C₄⋊C₄	—	3	1	no	—
743	C₄⋊C₄	—	3	1	no	—
744	C₄⋊C₄	—	3	1	no	—
745	C₄⋊C₄	—	3	1	no	—
746	C₄⋊C₄	—	3	1	no	—
747	C₄⋊C₄	—	3	1	no	—
748	C₄⋊C₄	—	3	1	no	—
749	C₄⋊C₄	—	3	1	no	—
750	C₄⋊C₄	—	3	1	no	—
751	C₄⋊C₄	—	3	1	no	—
752	C₄⋊C₄	—	3	1	no	—
753	C₄⋊C₄	—	3	1	no	—
754	C₄⋊C₄	—	3	1	no	—
755	C₄⋊C₄	—	3	1	no	—
756	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
764	C₂²⋊C₄	—	3	1	no	—
765	C₂²⋊C₄	—	3	1	no	—
766	C₂²⋊C₄	—	3	1	no	—
767	C₂²⋊C₄	—	3	1	no	—
768	C₂²⋊C₄	—	3	1	no	—
769	C₂²⋊C₄	—	3	1	no	—
770	C₂²⋊C₄	—	3	1	no	—
771	C₂²⋊C₄	—	3	1	no	—
772	C₂²⋊C₄	—	3	1	no	—
773	C₂²⋊C₄	—	3	1	no	—
774	C₂²⋊C₄	—	3	1	no	—
775	C₂²⋊C₄	—	3	1	no	—
776	C₂²⋊C₄	—	3	1	no	—
777	C₂²⋊C₄	—	3	1	no	—
778	C₂²⋊C₄	—	3	1	no	—
779	C₂²⋊C₄	—	3	1	no	—
780	C₂²⋊C₄	—	3	1	no	—
781	C₂²⋊C₄	—	3	1	no	—
782	C₂²⋊C₄	—	3	1	no	—
783	C₂²⋊C₄	—	3	1	no	—
784	C₂²⋊C₄	—	3	1	no	—
785	C₂²⋊C₄	—	3	1	no	—
786	C₂²⋊C₄	—	3	1	no	—
787	C₂²⋊C₄	—	3	1	no	—
788	C₂²⋊C₄	—	3	1	no	—
789	C₂²⋊C₄	—	3	1	no	—
790	C₂²⋊C₄	—	3	1	no	—
791	C₂²⋊C₄	—	3	1	no	—
792	C₂²⋊C₄	—	3	1	no	—
793	C₂²⋊C₄	—	3	1	no	—
794	C₂²⋊C₄	—	3	1	no	—
795	C₂²⋊C₄	—	3	1	no	—
796	C₂²⋊C₄	—	3	1	no	—
797	C₂²⋊C₄	—	3	1	no	—
798	C₂²⋊C₄	—	3	1	no	—
799	C₂²⋊C₄	—	3	1	no	—
800	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
814	C₄²	—	3	1	no	—
815	C₄²	—	3	1	no	—
816	C₄²	—	3	1	no	—
817	C₄²	C₂²×D₃	1	1	yes	characteristic
818	C₄²	C₂²×D₃	1	1	yes	characteristic
819	C₄²	C₂²×D₃	1	1	yes	characteristic
820	C₂²×C₃	—	2	1	no	—
821	C₂²×C₃	—	2	1	no	—
822	C₂²×C₃	—	2	1	no	—
823	C₂²×C₃	—	2	1	no	—
824	C₂²×C₃	—	2	1	no	—
825	C₂²×C₃	—	2	1	no	—
826	C₂²×C₃	—	2	1	no	—
827	C₂²×C₃	—	2	1	no	—
828	C₂²×C₃	—	2	1	no	—
829	C₂²×C₃	—	2	1	no	—
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	8	2	no	—
832	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
833	C₂²×C₃	C₂⁵	1	1	yes	characteristic
834	C₂×D₃	—	2	1	no	—
835	C₂×D₃	—	2	1	no	—
836	C₂×D₃	—	2	1	no	—
837	C₂×D₃	—	2	1	no	—
838	C₂×D₃	—	2	1	no	—
839	C₂×D₃	—	2	1	no	—
840	C₂×D₃	—	2	1	no	—
841	C₂×D₃	—	2	1	no	—
842	C₂×D₃	—	2	1	no	—
843	C₂×D₃	—	2	1	no	—
844	C₂×D₃	—	2	1	no	—
845	C₂×D₃	—	2	1	no	—
846	C₂×D₃	—	2	1	no	—
847	C₂×D₃	—	2	1	no	—
848	C₂×D₃	—	2	1	no	—
849	C₂×D₃	—	2	1	no	—
850	C₂×D₃	—	2	1	no	—
851	C₂×D₃	—	2	1	no	—
852	C₂×D₃	—	2	1	no	—
853	C₂×D₃	—	2	1	no	—
854	C₂×D₃	—	4	4	no	—
855	C₂×D₃	—	8	2	no	—
856	C₂×D₃	—	8	2	no	—
857	C₂×D₃	—	8	2	no	—
858	C₂×D₃	—	8	2	no	—
859	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
860	C₃×C₄	—	2	1	no	—
861	C₃×C₄	—	2	1	no	—
862	C₃×C₄	—	2	1	no	—
863	C₃×C₄	—	2	1	no	—
864	C₃×C₄	—	2	1	no	—
865	C₃×C₄	—	2	1	no	—
866	C₃×C₄	—	2	1	no	—
867	C₃×C₄	—	2	1	no	—
868	C₃×C₄	—	2	1	no	—
869	C₃×C₄	—	2	1	no	—
870	C₃×C₄	—	2	1	no	—
871	Dic₃	—	2	1	no	—
872	Dic₃	—	2	1	no	—
873	Dic₃	—	2	1	no	—
874	Dic₃	—	2	1	no	—
875	Dic₃	—	2	1	no	—
876	Dic₃	—	2	1	no	—
877	Dic₃	—	2	1	no	—
878	Dic₃	—	2	1	no	—
879	Dic₃	—	2	1	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	3	1	no	—
882	C₂³	—	3	1	no	—
883	C₂³	—	3	1	no	—
884	C₂³	—	3	1	no	—
885	C₂³	—	3	1	no	—
886	C₂³	—	3	1	no	—
887	C₂³	—	3	1	no	—
888	C₂³	—	4	1	no	—
889	C₂³	—	4	1	no	—
890	C₂³	—	6	2	no	—
891	C₂³	—	6	2	no	—
892	C₂³	—	6	2	no	—
893	C₂³	—	6	2	no	—
894	C₂³	—	12	1	no	—
895	C₂³	—	12	1	no	—
896	C₂³	—	12	1	no	—
897	C₂³	—	12	1	no	—
898	C₂³	—	12	1	no	—
899	C₂³	—	12	1	no	—
900	C₂³	—	12	1	no	—
901	C₂³	—	12	1	no	—
902	C₂³	—	12	1	no	—
903	C₂³	—	12	1	no	—
904	C₂³	—	12	1	no	—
905	C₂³	C₂³×D₃	1	1	yes	characteristic
906	C₂³	C₂³×D₃	1	1	yes	characteristic
907	C₂³	C₂³×D₃	1	1	yes	characteristic
908	C₂³	C₂³×D₃	1	1	yes	characteristic
909	Q₈	—	4	1	no	—
910	Q₈	—	12	1	no	—
911	Q₈	—	12	1	no	—
912	D₄	—	2	2	no	—
913	D₄	—	4	1	no	—
914	D₄	—	4	1	no	—
915	D₄	—	6	2	no	—
916	D₄	—	6	2	no	—
917	D₄	—	6	2	no	—
918	D₄	—	6	2	no	—
919	D₄	—	6	2	no	—
920	D₄	—	6	2	no	—
921	D₄	—	6	2	no	—
922	D₄	—	6	2	no	—
923	D₄	—	6	2	no	—
924	D₄	—	12	1	no	—
925	D₄	—	12	1	no	—
926	D₄	—	12	1	no	—
927	D₄	—	12	1	no	—
928	D₄	—	12	1	no	—
929	D₄	—	12	1	no	—
930	D₄	—	12	1	no	—
931	D₄	—	12	1	no	—
932	D₄	—	12	1	no	—
933	D₄	—	12	1	no	—
934	D₄	—	12	1	no	—
935	D₄	—	12	1	no	—
936	D₄	—	12	1	no	—
937	D₄	—	12	1	no	—
938	D₄	—	12	1	no	—
939	D₄	—	12	1	no	—
940	D₄	—	12	1	no	—
941	D₄	—	12	1	no	—
942	D₄	—	12	1	no	—
943	D₄	—	12	1	no	—
944	D₄	—	12	1	no	—
945	D₄	—	12	1	no	—
946	D₄	—	12	1	no	—
947	D₄	—	12	1	no	—
948	D₄	—	12	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	3	1	no	—
951	C₂×C₄	—	3	1	no	—
952	C₂×C₄	—	3	1	no	—
953	C₂×C₄	—	3	1	no	—
954	C₂×C₄	—	3	1	no	—
955	C₂×C₄	—	3	1	no	—
956	C₂×C₄	—	3	1	no	—
957	C₂×C₄	—	3	1	no	—
958	C₂×C₄	—	3	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	6	2	no	—
964	C₂×C₄	—	6	2	no	—
965	C₂×C₄	—	12	1	no	—
966	C₂×C₄	—	12	1	no	—
967	C₂×C₄	—	12	1	no	—
968	C₂×C₄	—	12	1	no	—
969	C₂×C₄	—	12	1	no	—
970	C₂×C₄	—	12	1	no	—
971	C₂×C₄	—	12	1	no	—
972	C₂×C₄	—	12	1	no	—
973	C₂×C₄	—	12	1	no	—
974	C₂×C₄	—	12	1	no	—
975	C₂×C₄	—	12	1	no	—
976	C₂×C₄	—	12	1	no	—
977	C₂×C₄	—	12	1	no	—
978	C₂×C₄	—	12	1	no	—
979	C₂×C₄	—	12	1	no	—
980	C₂×C₄	—	12	1	no	—
981	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
982	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
983	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
984	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
985	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
986	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
987	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
988	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
989	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
990	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
991	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
992	C₂×C₃	—	2	2	no	—
993	C₂×C₃	—	4	1	no	—
994	C₂×C₃	—	4	1	no	—
995	C₂×C₃	—	4	1	no	—
996	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
997	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
998	C₂×C₃	#585	1	1	yes	characteristic
999	D₃	—	2	2	no	—
1000	D₃	—	4	1	no	—
1001	D₃	—	4	1	no	—
1002	D₃	—	4	1	no	—
1003	D₃	—	4	1	no	—
1004	D₃	—	4	1	no	—
1005	D₃	—	4	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	3	2	no	—
1018	C₂²	—	6	1	no	—
1019	C₂²	—	6	1	no	—
1020	C₂²	—	6	1	no	—
1021	C₂²	—	6	1	no	—
1022	C₂²	—	6	1	no	—
1023	C₂²	—	6	1	no	—
1024	C₂²	—	6	1	no	—
1025	C₂²	—	6	1	no	—
1026	C₂²	—	6	1	no	—
1027	C₂²	—	6	1	no	—
1028	C₂²	—	6	1	no	—
1029	C₂²	—	6	1	no	—
1030	C₂²	—	6	1	no	—
1031	C₂²	—	6	1	no	—
1032	C₂²	—	6	1	no	—
1033	C₂²	—	6	1	no	—
1034	C₂²	—	6	1	no	—
1035	C₂²	—	6	1	no	—
1036	C₂²	—	6	1	no	—
1037	C₂²	—	6	1	no	—
1038	C₂²	—	8	2	no	—
1039	C₂²	—	12	4	no	—
1040	C₂²	—	24	2	no	—
1041	C₂²	—	24	2	no	—
1042	C₂²	—	24	2	no	—
1043	C₂²	—	24	2	no	—
1044	C₂²	#1009	1	2	yes	—
1045	C₂²	C₂⁴×D₃	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	6	1	no	—
1058	C₄	—	6	1	no	—
1059	C₄	—	6	1	no	—
1060	C₄	—	6	1	no	—
1061	C₄	—	6	1	no	—
1062	C₄	—	6	1	no	—
1063	C₄	—	6	1	no	—
1064	C₄	—	6	1	no	—
1065	C₄	—	6	1	no	—
1066	C₃	#3534	1	1	yes	characteristic, complemented, Sylow
1067	C₂	—	2	2	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	6	2	no	—
1072	C₂	—	12	1	no	—
1073	C₂	—	12	1	no	—
1074	C₂	—	12	1	no	—
1075	C₂	—	12	1	no	—
1076	C₂	—	12	1	no	—
1077	C₂	—	12	1	no	—
1078	C₂	C₂×#1009	1	1	yes	characteristic
1079	C₂	#5964	1	1	yes	characteristic
1080	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×#551	C₂
hypercenter	#551	D₃
hypocenter	C₃	#3534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₃×#551	C₂	semidirect
2. #5711	C₂	semidirect
3. #5709	C₂	semidirect
4. #5707	C₂	semidirect
5. #5704	C₂	semidirect
6. #5678	C₂	semidirect
7. #5676	C₂	semidirect
8. #5667	C₂	semidirect
9. #5666	C₂	semidirect
10. #5657	C₂	semidirect
11. #5654	C₂	semidirect
12. #5653	C₂	semidirect
13. D₃×#123	C₂	semidirect
14. #5647	C₂	semidirect
15. #5645	C₂	semidirect
16. #5630	C₂	semidirect
17. #5629	C₂	semidirect
18. #5590	C₂	semidirect
19. #5589	C₂	semidirect
20. #5564	C₂	semidirect
21. #5562	C₂	semidirect
22. #5550	C₂	semidirect
23. D₄×D₁₂	C₂	semidirect
24. #5535	C₂	semidirect
25. #5530	C₂	semidirect
26. #5527	C₂	semidirect
27. #5524	C₂	semidirect
28. #5493	C₂	semidirect
29. #5490	C₂	semidirect
30. #5490	C₂	semidirect
31. C₂×#884	C₂	semidirect
33. C₂²×#67	C₂²	semidirect
34. C₂²×#67	C₂²	semidirect
35. C₂²×#67	C₂²	semidirect
36. C₂×#239	C₂²	semidirect
38. C₂×D₃×D₄	C₂²	semidirect
39. C₂×D₃×D₄	C₂²	semidirect
40. C₂×#235	C₂²	semidirect
41. C₂×#235	C₂²	semidirect
42. C₂²×D₁₂	C₂²	semidirect
43. C₂²×D₁₂	C₂²	semidirect
44. C₂²×C₄×D₃	C₂²	semidirect
45. C₃×#126	C₂²	semidirect
46. C₃×#126	C₂²	semidirect
47. C₃×#124	C₂²	semidirect
48. C₃×#123	C₂²	semidirect
49. C₃×#123	C₂²	semidirect
50. C₃×#123	C₂²	semidirect
51. C₃×C₂²⋊Q₈	C₂²	semidirect
52. C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₃×C₄×D₄	C₂²	semidirect
55. C₃×C₄×D₄	C₂²	semidirect
56. C₃×#117	C₂²	semidirect
57. C₃×#117	C₂²	semidirect
58. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
59. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
60. #953	C₂²	semidirect
61. #947	C₂²	semidirect
62. #946	C₂²	semidirect
63. #946	C₂²	semidirect
64. #940	C₂²	semidirect
66. #939	C₂²	semidirect
67. #938	C₂²	semidirect
68. #938	C₂²	semidirect
69. #937	C₂²	semidirect
70. #937	C₂²	semidirect
71. #937	C₂²	semidirect
72. #935	C₂²	semidirect
74. #930	C₂²	semidirect
75. #930	C₂²	semidirect
76. #930	C₂²	semidirect
77. #930	C₂²	semidirect
78. #930	C₂²	semidirect
79. #930	C₂²	semidirect
80. #929	C₂²	semidirect
81. #929	C₂²	semidirect
82. #929	C₂²	semidirect
83. C₄×#67	C₂²	semidirect
84. C₄×#67	C₂²	semidirect
85. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
86. #924	C₂²	semidirect
87. C₂×Dic₃⋊C₄	C₂²	semidirect
88. #898	C₂²	semidirect
89. #898	C₂²	semidirect
90. #898	C₂²	semidirect
91. #897	C₂²	semidirect
92. #897	C₂²	semidirect
93. #896	C₂²	semidirect
94. #896	C₂²	semidirect
95. #896	C₂²	semidirect
96. #895	C₂²	semidirect
97. #895	C₂²	semidirect
98. #895	C₂²	semidirect
99. #895	C₂²	semidirect
100. #895	C₂²	semidirect
101. #895	C₂²	semidirect
102. #895	C₂²	semidirect
103. #895	C₂²	semidirect
104. #894	C₂²	semidirect
105. #894	C₂²	semidirect
106. #894	C₂²	semidirect
107. #894	C₂²	semidirect
108. #894	C₂²	semidirect
109. #894	C₂²	semidirect
110. #894	C₂²	semidirect
111. #894	C₂²	semidirect
112. #894	C₂²	semidirect
113. #893	C₂²	semidirect
114. #893	C₂²	semidirect
115. D₃×C₄⋊C₄	C₂²	semidirect
116. D₃×C₄⋊C₄	C₂²	semidirect
117. #890	C₂²	semidirect
118. #890	C₂²	semidirect
119. #889	C₂²	semidirect
120. #886	C₂²	semidirect
121. #886	C₂²	semidirect
122. #886	C₂²	semidirect
123. #886	C₂²	semidirect
124. #886	C₂²	semidirect
125. #885	C₂²	semidirect
126. #885	C₂²	semidirect
127. #885	C₂²	semidirect
129. #884	C₂²	semidirect
130. #884	C₂²	semidirect
131. #884	C₂²	semidirect
132. #884	C₂²	semidirect
133. #884	C₂²	semidirect
134. #884	C₂²	semidirect
135. #884	C₂²	semidirect
136. #884	C₂²	semidirect
137. #884	C₂²	semidirect
138. #884	C₂²	semidirect
139. #884	C₂²	semidirect
140. #884	C₂²	semidirect
141. #884	C₂²	semidirect
142. #884	C₂²	semidirect
143. #884	C₂²	semidirect
144. #884	C₂²	semidirect
145. #883	C₂²	semidirect
146. #883	C₂²	semidirect
147. #883	C₂²	semidirect
148. #883	C₂²	semidirect
149. #883	C₂²	semidirect
150. #883	C₂²	semidirect
151. #883	C₂²	semidirect
153. #882	C₂²	semidirect
154. #882	C₂²	semidirect
155. #882	C₂²	semidirect
156. #882	C₂²	semidirect
157. #882	C₂²	semidirect
158. #882	C₂²	semidirect
159. #882	C₂²	semidirect
160. #882	C₂²	semidirect
161. #882	C₂²	semidirect
162. #882	C₂²	semidirect
163. #67⋊C₄	C₂²	semidirect
164. #67⋊C₄	C₂²	semidirect
165. #67⋊C₄	C₂²	semidirect
166. #67⋊C₄	C₂²	semidirect
167. D₃×C₂²⋊C₄	C₂²	semidirect
168. D₃×C₂²⋊C₄	C₂²	semidirect
169. D₃×C₂²⋊C₄	C₂²	semidirect
170. D₃×C₂²⋊C₄	C₂²	semidirect
171. D₃×C₂²⋊C₄	C₂²	semidirect
172. D₃×C₂²⋊C₄	C₂²	semidirect
173. #879	C₂²	semidirect
174. #878	C₂²	semidirect
175. #878	C₂²	semidirect
176. #876	C₂²	semidirect
177. #876	C₂²	semidirect
178. #875	C₂²	semidirect
179. #874	C₂²	semidirect
180. C₄×D₁₂	C₂²	semidirect
181. C₄×D₁₂	C₂²	semidirect
182. C₄×D₁₂	C₂²	semidirect
183. C₄×D₁₂	C₂²	semidirect
184. C₄×D₁₂	C₂²	semidirect
185. C₄×D₁₂	C₂²	semidirect
186. #872	C₂²	semidirect
187. #870	C₂²	semidirect
195. #551	D₃	semidirect
406. #126	C₂×D₃	semidirect
407. #126	C₂×D₃	semidirect
417. #124	C₂×D₃	semidirect
443. #123	C₂×D₃	semidirect
444. #123	C₂×D₃	semidirect
445. #123	C₂×D₃	semidirect
456. C₂²⋊Q₈	C₂×D₃	semidirect
457. C₂²⋊Q₈	C₂×D₃	semidirect
524. C₄×D₄	C₂×D₃	semidirect
525. C₄×D₄	C₂×D₃	semidirect
527. #117	C₂×D₃	semidirect
528. #117	C₂×D₃	semidirect
539. C₂×C₂²⋊C₄	C₂×D₃	semidirect
540. C₂×C₂²⋊C₄	C₂×D₃	semidirect
1066. C₃	#3534	semidirect

Maximal subgroups

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

subgroup	index
C₃×#551	2
#5711	2
#5709	2
#5707	2
#5704	2
#5678	2
#5676	2
#5667	2
#5666	2
#5657	2
#5654	2
#5653	2
D₃×#123	2
#5647	2
#5645	2
#5630	2
#5629	2
#5590	2
#5589	2
#5564	2
#5562	2
#5550	2
D₄×D₁₂	2
#5535	2
#5530	2
#5527	2
#5524	2
#5493	2
#5490	2
C₂×#884	2
#3534	3