Subgroups — C₂×#11703805 #72253511

Order 1536.

92740 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11703805	C₂	1	64	yes	maximal, direct product factor
2	C₂×#85697	C₂	1	6	yes	maximal, complemented
3	C₂×#85913	C₂	1	12	yes	maximal, complemented
4	C₂×#87239	C₂	1	6	yes	maximal, complemented
5	C₂×#85919	C₂	1	12	yes	maximal, complemented
6	C₂×#85921	C₂	1	24	yes	maximal, complemented
7	C₂³×#953	C₂	1	2	yes	maximal, complemented
8	C₂³×C₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#62817	—	3	1	no	maximal, Sylow
10	C₂⁷×C₃	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₃×D₄	C₂²	1	3	yes	complemented
12	C₂⁴×#67	C₂²	1	6	yes	complemented
13	C₂²×#1004	C₂²	1	6	yes	complemented
14	C₂²×C₃×#120	C₂²	1	12	yes	complemented
15	C₂²×C₃×#120	C₂²	1	12	yes	complemented
16	C₂²×C₃×#120	C₂²	1	32	yes	complemented
17	C₂³×C₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
18	C₂²×#953	C₂²	1	12	yes	complemented
19	C₂²×#953	C₂²	1	12	yes	complemented
20	C₂²×#953	C₂²	1	24	yes	complemented
21	C₂²×#953	C₂²	1	4	yes	complemented
22	C₂²×#953	C₂²	1	64	yes	complemented
23	C₂³×#217	C₂²	1	6	yes	complemented
24	#87239	C₂²	1	192	yes	complemented
25	C₂×D₄×#67	C₂²	1	48	yes	complemented
26	C₂×#5805	C₂²	1	12	yes	complemented
27	C₂×#5804	C₂²	1	12	yes	complemented
28	C₂×#5804	C₂²	1	12	yes	complemented
29	C₂×#5806	C₂²	1	48	yes	complemented
30	C₂×#5798	C₂²	1	6	yes	complemented
31	C₂×#5791	C₂²	1	12	yes	complemented
32	#85921	C₂²	1	768	yes	complemented
33	C₂×#5595	C₂²	1	24	yes	complemented
34	#85919	C₂²	1	384	yes	complemented
35	C₂×#5591	C₂²	1	48	yes	complemented
36	C₂×#5590	C₂²	1	24	yes	complemented
37	C₂×#5589	C₂²	1	24	yes	complemented
38	C₂×D₃×#120	C₂²	1	8	yes	complemented
39	C₂×#5594	C₂²	1	8	yes	complemented
40	#85913	C₂²	1	384	yes	complemented
41	C₂×#5587	C₂²	1	24	yes	complemented
42	C₂×#5593	C₂²	1	48	yes	complemented
43	C₂×#5592	C₂²	1	24	yes	complemented
44	C₂×#5586	C₂²	1	24	yes	complemented
45	#85697	C₂²	1	192	yes	complemented
46	C₂×#5490	C₂²	1	48	yes	complemented
47	C₂×#5494	C₂²	1	24	yes	complemented
48	C₂×#5493	C₂²	1	6	yes	complemented
49	C₂×#5486	C₂²	1	12	yes	complemented
50	C₂×#5495	C₂²	1	48	yes	complemented
51	C₂×#5483	C₂²	1	6	yes	complemented
52	#62817	—	3	64	no	—
53	C₂×#3490	—	3	12	no	—
54	C₂×#3490	—	3	6	no	—
55	C₂×#3484	—	3	12	no	—
56	C₂×#3484	—	3	6	no	—
57	C₂×#3532	—	3	24	no	—
58	C₂³×#120	—	3	2	no	—
59	C₂³×#120	D₃	1	1	yes	characteristic, complemented
60	C₂⁶×C₃	—	4	24	no	—
61	C₂⁶×C₃	C₂³	1	6	yes	—
62	C₂⁶×C₃	C₂³	1	3	yes	—
63	C₂⁶×C₃	C₂³	1	6	yes	—
64	C₂⁶×C₃	C₂³	1	16	yes	complemented
65	C₂⁶×C₃	C₂³	1	1	yes	characteristic, complemented
66	C₂⁵×D₃	C₂³	1	2	yes	complemented
67	C₂³×C₃×D₄	—	4	24	no	—
68	C₂³×C₃×D₄	C₂³	1	6	yes	—
69	C₂³×C₃×D₄	C₂³	1	24	yes	complemented
70	C₂³×C₃×D₄	C₂³	1	6	yes	complemented
71	C₂³×C₃×D₄	C₂³	1	48	yes	complemented
72	C₂⁴×C₃×C₄	C₂³	1	3	yes	complemented
73	C₂³×#67	—	4	48	no	—
74	C₂³×#67	C₂³	1	12	yes	—
75	C₂³×#67	C₂³	1	12	yes	complemented
76	C₂³×#67	C₂³	1	24	yes	complemented
77	C₂³×#67	C₂³	1	24	yes	complemented
78	C₂³×#67	C₂³	1	96	yes	complemented
79	C₂³×#67	C₂³	1	12	yes	complemented
80	C₂⁴×Dic₃	C₂³	1	6	yes	complemented
81	C₂×#1004	—	4	48	no	—
82	C₂×#1004	C₂³	1	96	yes	complemented
83	C₂²×#237	C₂³	1	24	yes	complemented
84	C₂²×D₃×D₄	C₂³	1	24	yes	complemented
85	C₂²×#235	C₂³	1	12	yes	complemented
86	C₂×C₃×#120	C₂³	1	24	yes	—
87	C₂×C₃×#120	C₂³	1	8	yes	complemented
88	C₂×C₃×#120	C₂³	1	24	yes	complemented
89	C₂×C₃×#120	C₂³	1	8	yes	complemented
90	C₂×C₃×#120	C₂³	1	192	yes	complemented
91	C₂×C₃×#120	C₂³	1	192	yes	complemented
92	C₂²×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
93	C₂²×C₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
94	C₂²×C₃×C₂²⋊C₄	C₂³	1	6	yes	complemented
95	C₂²×C₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
96	C₂×#953	C₂³	1	48	yes	—
97	C₂×#953	C₂³	1	8	yes	complemented
98	C₂×#953	C₂³	1	8	yes	complemented
99	C₂×#953	C₂³	1	24	yes	complemented
100	C₂×#953	C₂³	1	16	yes	complemented
101	C₂×#953	C₂³	1	24	yes	complemented
102	C₂×#953	C₂³	1	192	yes	complemented
103	C₂×#953	C₂³	1	192	yes	complemented
104	C₂×#953	C₂³	1	24	yes	complemented
105	C₂×#953	C₂³	1	384	yes	complemented
106	C₂×#953	C₂³	1	64	yes	complemented
107	C₂²×#217	C₂³	1	12	yes	—
108	C₂²×#217	C₂³	1	12	yes	complemented
109	C₂²×#217	C₂³	1	24	yes	complemented
110	C₂²×#217	C₂³	1	24	yes	complemented
111	C₂²×#217	C₂³	1	96	yes	complemented
112	C₂²×#217	C₂³	1	12	yes	complemented
113	#5806	C₂³	1	768	yes	complemented
114	#5805	C₂³	1	192	yes	complemented
115	#5804	C₂³	1	192	yes	complemented
116	#5804	C₂³	1	192	yes	complemented
117	C₂×#940	C₂³	1	24	yes	complemented
118	C₂×#939	C₂³	1	48	yes	complemented
119	C₂×#939	C₂³	1	48	yes	complemented
120	D₄×#67	C₂³	1	768	yes	complemented
121	C₂×#938	C₂³	1	48	yes	complemented
122	C₂×#937	C₂³	1	24	yes	complemented
123	C₂×#937	C₂³	1	24	yes	complemented
124	#5798	C₂³	1	96	yes	complemented
125	C₂×#936	C₂³	1	24	yes	complemented
126	C₂×#935	C₂³	1	24	yes	complemented
127	C₂×#935	C₂³	1	24	yes	complemented
128	C₂×D₄×Dic₃	C₂³	1	48	yes	complemented
129	#5791	C₂³	1	192	yes	complemented
130	C₂×#930	C₂³	1	24	yes	complemented
131	C₂×#929	C₂³	1	24	yes	complemented
132	C₂×C₄×#67	C₂³	1	48	yes	complemented
133	C₂×#926	C₂³	1	12	yes	complemented
134	C₂×#924	C₂³	1	24	yes	complemented
135	#5595	C₂³	1	384	yes	complemented
136	#5594	C₂³	1	128	yes	complemented
137	#5593	C₂³	1	768	yes	complemented
138	#5592	C₂³	1	384	yes	complemented
139	#5591	C₂³	1	768	yes	complemented
140	#5590	C₂³	1	384	yes	complemented
141	#5589	C₂³	1	384	yes	complemented
142	D₃×#120	C₂³	1	128	yes	complemented
143	#5587	C₂³	1	384	yes	complemented
144	#5586	C₂³	1	384	yes	complemented
145	#5495	C₂³	1	768	yes	complemented
146	#5494	C₂³	1	384	yes	complemented
147	#5493	C₂³	1	96	yes	complemented
148	C₂×#886	C₂³	1	24	yes	complemented
149	C₂×#885	C₂³	1	48	yes	complemented
150	#5490	C₂³	1	768	yes	complemented
151	C₂×#884	C₂³	1	48	yes	complemented
152	C₂×#883	C₂³	1	48	yes	complemented
153	C₂×#882	C₂³	1	24	yes	complemented
154	#5486	C₂³	1	192	yes	complemented
155	C₂×#67⋊C₄	C₂³	1	48	yes	complemented
156	C₂×D₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
157	#5483	C₂³	1	96	yes	complemented
158	C₂×#879	C₂³	1	48	yes	complemented
159	C₂×#878	C₂³	1	48	yes	complemented
160	C₂×#877	C₂³	1	24	yes	complemented
161	C₂⁷	C₂×D₃	1	1	yes	characteristic, complemented
162	C₂²×H(5,𝔽₂)	—	3	6	no	—
163	C₂⁴×D₄	—	3	6	no	—
164	C₂⁴×D₄	C₂×D₃	1	3	yes	complemented
165	#3532	—	3	768	no	—
166	C₂×H(3,𝔽₄)	—	3	8	no	—
167	C₂×#560	—	3	24	no	—
168	#3490	—	3	384	no	—
169	#3490	—	3	192	no	—
170	#3484	—	3	192	no	—
171	#3484	—	3	384	no	—
172	C₂×#551	—	3	24	no	—
173	C₂×#551	—	3	48	no	—
174	C₂×#546	—	3	48	no	—
175	C₂×#546	—	3	48	no	—
176	C₂×#546	—	3	48	no	—
177	C₂×D₄²	—	3	48	no	—
178	C₂×D₄²	—	3	24	no	—
179	C₂×#543	—	3	6	no	—
180	C₂×#538	—	3	48	no	—
181	C₂×#538	—	3	24	no	—
182	C₂×#535	—	3	12	no	—
183	C₂×#535	—	3	24	no	—
184	C₂×#534	—	3	12	no	—
185	C₂×#534	—	3	12	no	—
186	C₂×#534	—	3	24	no	—
187	C₂×#534	—	3	6	no	—
188	C₂×#525	—	3	12	no	—
189	C₂×#525	—	3	24	no	—
190	C₂²×#120	—	3	12	no	—
191	C₂²×#120	—	3	12	no	—
192	C₂²×#120	—	3	24	no	—
193	C₂²×#120	—	3	4	no	—
194	C₂²×#120	—	3	64	no	—
195	C₂²×#120	—	3	8	no	—
196	C₂²×#120	C₂×D₃	1	12	yes	complemented
197	C₂²×#120	C₂×D₃	1	12	yes	complemented
198	C₂²×#120	C₂×D₃	1	32	yes	complemented
199	C₂×#518	—	3	6	no	—
200	C₂×#518	—	3	12	no	—
201	C₂³×C₂²⋊C₄	—	3	6	no	—
202	C₂³×C₂²⋊C₄	C₂×D₃	1	3	yes	complemented
203	C₂⁵×C₃	—	2	48	no	—
204	C₂⁵×C₃	—	2	24	no	—
205	C₂⁵×C₃	—	4	24	no	—
206	C₂⁵×C₃	—	4	48	no	—
207	C₂⁵×C₃	—	4	48	no	—
208	C₂⁵×C₃	—	4	24	no	—
209	C₂⁵×C₃	—	4	192	no	—
210	C₂⁵×C₃	—	4	12	no	—
211	C₂⁵×C₃	—	4	256	no	—
212	C₂⁵×C₃	C₂⁴	1	2	yes	—
213	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
214	C₂⁵×C₃	C₂⁴	1	6	yes	—
215	C₂⁵×C₃	C₂⁴	1	12	yes	—
216	C₂⁵×C₃	C₂⁴	1	6	yes	—
217	C₂⁵×C₃	C₂⁴	1	6	yes	—
218	C₂⁵×C₃	C₂⁴	1	48	yes	—
219	C₂⁵×C₃	C₂⁴	1	3	yes	—
220	C₂⁵×C₃	C₂⁴	1	24	yes	—
221	C₂⁵×C₃	C₂⁴	1	2	yes	—
222	C₂⁵×C₃	C₂⁴	1	48	yes	—
223	C₂⁵×C₃	C₂⁴	1	3	yes	—
224	C₂⁵×C₃	C₂⁴	1	8	yes	complemented
225	C₂⁴×D₃	—	4	24	no	—
226	C₂⁴×D₃	C₂⁴	1	12	yes	—
227	C₂⁴×D₃	C₂⁴	1	16	yes	complemented
228	C₂⁴×D₃	C₂⁴	1	4	yes	complemented
229	C₂²×C₃×D₄	—	2	48	no	—
230	C₂²×C₃×D₄	—	4	24	no	—
231	C₂²×C₃×D₄	—	4	96	no	—
232	C₂²×C₃×D₄	—	4	192	no	—
233	C₂²×C₃×D₄	C₂⁴	1	24	yes	—
234	C₂²×C₃×D₄	C₂⁴	1	48	yes	—
235	C₂²×C₃×D₄	C₂⁴	1	24	yes	—
236	C₂²×C₃×D₄	C₂⁴	1	192	yes	complemented
237	C₂²×C₃×D₄	C₂⁴	1	48	yes	complemented
238	C₂³×C₃×C₄	—	4	12	no	—
239	C₂³×C₃×C₄	C₂⁴	1	6	yes	—
240	C₂³×C₃×C₄	C₂⁴	1	12	yes	—
241	C₂³×C₃×C₄	C₂⁴	1	24	yes	complemented
242	C₂²×#67	—	2	96	no	—
243	C₂²×#67	—	4	48	no	—
244	C₂²×#67	—	4	48	no	—
245	C₂²×#67	—	4	96	no	—
246	C₂²×#67	—	4	96	no	—
247	C₂²×#67	—	4	384	no	—
248	C₂²×#67	C₂⁴	1	24	yes	—
249	C₂²×#67	C₂⁴	1	24	yes	—
250	C₂²×#67	C₂⁴	1	96	yes	—
251	C₂²×#67	C₂⁴	1	48	yes	—
252	C₂²×#67	C₂⁴	1	192	yes	complemented
253	C₂²×#67	C₂⁴	1	96	yes	complemented
254	C₂²×#67	C₂⁴	1	192	yes	complemented
255	C₂²×#67	C₂⁴	1	24	yes	complemented
256	C₂²×#67	C₂⁴	1	96	yes	complemented
257	C₂³×Dic₃	—	4	24	no	—
258	C₂³×Dic₃	C₂⁴	1	12	yes	—
259	C₂³×Dic₃	C₂⁴	1	24	yes	—
260	C₂³×Dic₃	C₂⁴	1	48	yes	complemented
261	C₂³×Dic₃	C₂⁴	1	12	yes	complemented
262	#1004	—	4	384	no	—
263	C₂×#237	—	4	96	no	—
264	C₂×#237	C₂⁴	1	192	yes	complemented
265	C₂×D₃×D₄	—	4	96	no	—
266	C₂×D₃×D₄	C₂⁴	1	192	yes	complemented
267	C₂×#235	—	4	48	no	—
268	C₂×#235	C₂⁴	1	96	yes	complemented
269	C₂²×D₁₂	C₂⁴	1	12	yes	complemented
270	C₂²×C₄×D₃	C₂⁴	1	24	yes	complemented
271	C₂²×Dic₆	C₂⁴	1	12	yes	complemented
272	C₃×#120	C₂⁴	1	192	yes	—
273	C₃×#120	C₂⁴	1	64	yes	complemented
274	C₃×#120	C₂⁴	1	192	yes	complemented
275	C₃×#120	C₂⁴	1	64	yes	complemented
276	C₂×C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂⁴	1	192	yes	complemented
280	C₂×C₃×C₂²⋊C₄	C₂⁴	1	48	yes	complemented
281	#953	C₂⁴	1	384	yes	—
282	#953	C₂⁴	1	192	yes	complemented
283	#953	C₂⁴	1	64	yes	complemented
284	#953	C₂⁴	1	64	yes	complemented
285	#953	C₂⁴	1	192	yes	complemented
286	#953	C₂⁴	1	128	yes	complemented
287	#953	C₂⁴	1	192	yes	complemented
288	C₂×#217	C₂⁴	1	24	yes	—
289	C₂×#217	C₂⁴	1	48	yes	—
290	C₂×#217	C₂⁴	1	96	yes	—
291	C₂×#217	C₂⁴	1	24	yes	—
292	C₂×#217	C₂⁴	1	192	yes	complemented
293	C₂×#217	C₂⁴	1	192	yes	complemented
294	C₂×#217	C₂⁴	1	96	yes	complemented
295	C₂×#217	C₂⁴	1	96	yes	complemented
296	C₂×#217	C₂⁴	1	24	yes	complemented
297	#940	C₂⁴	1	192	yes	complemented
298	#939	C₂⁴	1	384	yes	complemented
299	#939	C₂⁴	1	384	yes	complemented
300	#938	C₂⁴	1	384	yes	complemented
301	#937	C₂⁴	1	192	yes	complemented
302	#937	C₂⁴	1	192	yes	complemented
303	#936	C₂⁴	1	192	yes	complemented
304	#935	C₂⁴	1	192	yes	complemented
305	#935	C₂⁴	1	192	yes	complemented
306	D₄×Dic₃	C₂⁴	1	384	yes	complemented
307	#930	C₂⁴	1	192	yes	complemented
308	#929	C₂⁴	1	192	yes	complemented
309	C₄×#67	C₂⁴	1	384	yes	complemented
310	C₂×(C₂×D₃)⋊C₄	C₂⁴	1	48	yes	complemented
311	#926	C₂⁴	1	96	yes	complemented
312	C₂×C₄⋊Dic₃	C₂⁴	1	24	yes	complemented
313	#924	C₂⁴	1	192	yes	complemented
314	C₂×Dic₃⋊C₄	C₂⁴	1	48	yes	complemented
315	C₂×C₄×Dic₃	C₂⁴	1	24	yes	complemented
316	#886	C₂⁴	1	192	yes	complemented
317	#885	C₂⁴	1	384	yes	complemented
318	#884	C₂⁴	1	384	yes	complemented
319	#883	C₂⁴	1	384	yes	complemented
320	#882	C₂⁴	1	192	yes	complemented
321	#67⋊C₄	C₂⁴	1	384	yes	complemented
322	D₃×C₂²⋊C₄	C₂⁴	1	192	yes	complemented
323	#879	C₂⁴	1	384	yes	complemented
324	#878	C₂⁴	1	384	yes	complemented
325	#877	C₂⁴	1	192	yes	complemented
326	C₂⁶	—	3	2	no	—
327	C₂⁶	—	4	24	no	—
328	C₂⁶	C₂²×D₃	1	6	yes	—
329	C₂⁶	C₂²×D₃	1	3	yes	—
330	C₂⁶	C₂²×D₃	1	6	yes	—
331	C₂⁶	C₂²×D₃	1	16	yes	complemented
332	C₂⁶	C₂²×D₃	1	1	yes	characteristic, complemented
333	C₂×H(5,𝔽₂)	—	3	96	no	—
334	C₂×H(5,𝔽₂)	—	12	48	no	—
335	C₂²×#41	—	3	24	no	—
336	C₂²×#41	—	3	12	no	—
337	C₂³×D₄	—	3	12	no	—
338	C₂³×D₄	—	3	12	no	—
339	C₂³×D₄	—	3	24	no	—
340	C₂³×D₄	—	3	24	no	—
341	C₂³×D₄	—	3	96	no	—
342	C₂³×D₄	—	3	12	no	—
343	C₂³×D₄	—	3	24	no	—
344	C₂³×D₄	—	4	24	no	—
345	C₂³×D₄	—	12	48	no	—
346	C₂³×D₄	C₂²×D₃	1	6	yes	—
347	C₂³×D₄	C₂²×D₃	1	6	yes	complemented
348	C₂³×D₄	C₂²×D₃	1	24	yes	complemented
349	C₂³×D₄	C₂²×D₃	1	48	yes	complemented
350	C₂⁴×C₄	—	3	6	no	—
351	C₂⁴×C₄	C₂²×D₃	1	3	yes	complemented
352	H(3,𝔽₄)	—	3	128	no	—
353	#560	—	3	384	no	—
354	#551	—	3	384	no	—
355	#551	—	3	768	no	—
356	#546	—	3	768	no	—
357	#546	—	3	768	no	—
358	#546	—	3	768	no	—
359	D₄²	—	3	768	no	—
360	D₄²	—	3	384	no	—
361	#543	—	3	96	no	—
362	#538	—	3	768	no	—
363	#538	—	3	384	no	—
364	#535	—	3	192	no	—
365	#535	—	3	384	no	—
366	#534	—	3	192	no	—
367	#534	—	3	192	no	—
368	#534	—	3	384	no	—
369	#534	—	3	96	no	—
370	C₂×#127	—	3	24	no	—
371	C₂×#126	—	3	48	no	—
372	C₂×#124	—	3	24	no	—
373	C₂×#124	—	3	48	no	—
374	#525	—	3	192	no	—
375	#525	—	3	384	no	—
376	C₂×#123	—	3	24	no	—
377	C₂×#123	—	3	24	no	—
378	C₂×#123	—	3	24	no	—
379	C₂×#123	—	3	24	no	—
380	C₂×#123	—	3	48	no	—
381	C₂×C₂²⋊Q₈	—	3	24	no	—
382	C₂×C₂²⋊Q₈	—	3	48	no	—
383	C₂×#121	—	3	48	no	—
384	C₂×#121	—	3	48	no	—
385	C₂×#121	—	3	48	no	—
386	C₂×#121	—	3	24	no	—
387	C₂×#121	—	3	48	no	—
388	C₂×#120	—	3	8	no	—
389	C₂×#120	—	3	8	no	—
390	C₂×#120	—	3	24	no	—
391	C₂×#120	—	3	24	no	—
392	C₂×#120	—	3	48	no	—
393	C₂×#120	—	3	192	no	—
394	C₂×#120	—	3	192	no	—
395	C₂×#120	—	3	16	no	—
396	C₂×#120	—	3	384	no	—
397	C₂×#120	—	3	24	no	—
398	C₂×#120	—	3	64	no	—
399	C₂×#120	—	3	24	no	—
400	C₂×#120	—	3	24	no	—
401	C₂×#120	—	3	128	no	—
402	C₂×#120	—	3	24	no	—
403	C₂×#120	C₂²×D₃	1	24	yes	—
404	C₂×#120	C₂²×D₃	1	8	yes	complemented
405	C₂×#120	C₂²×D₃	1	24	yes	complemented
406	C₂×#120	C₂²×D₃	1	8	yes	complemented
407	C₂×#120	C₂²×D₃	1	192	yes	complemented
408	C₂×#120	C₂²×D₃	1	192	yes	complemented
409	#518	—	3	96	no	—
410	#518	—	3	192	no	—
411	C₂×C₄×D₄	—	3	48	no	—
412	C₂×C₄×D₄	—	3	48	no	—
413	C₂×C₄×D₄	—	3	48	no	—
414	C₂×#117	—	3	12	no	—
415	C₂×#117	—	3	24	no	—
416	C₂²×C₂²⋊C₄	—	3	12	no	—
417	C₂²×C₂²⋊C₄	—	3	12	no	—
418	C₂²×C₂²⋊C₄	—	3	24	no	—
419	C₂²×C₂²⋊C₄	—	3	24	no	—
420	C₂²×C₂²⋊C₄	—	3	96	no	—
421	C₂²×C₂²⋊C₄	—	3	12	no	—
422	C₂²×C₂²⋊C₄	—	3	24	no	—
423	C₂²×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
424	C₂²×C₂²⋊C₄	C₂²×D₃	1	6	yes	complemented
425	C₂²×C₂²⋊C₄	C₂²×D₃	1	24	yes	complemented
426	C₂²×C₂²⋊C₄	C₂²×D₃	1	48	yes	complemented
427	C₂⁴×C₃	—	2	12	no	—
428	C₂⁴×C₃	—	2	24	no	—
429	C₂⁴×C₃	—	2	48	no	—
430	C₂⁴×C₃	—	2	48	no	—
431	C₂⁴×C₃	—	2	24	no	—
432	C₂⁴×C₃	—	2	48	no	—
433	C₂⁴×C₃	—	2	12	no	—
434	C₂⁴×C₃	—	2	192	no	—
435	C₂⁴×C₃	—	2	96	no	—
436	C₂⁴×C₃	—	2	24	no	—
437	C₂⁴×C₃	—	4	12	no	—
438	C₂⁴×C₃	—	4	12	no	—
439	C₂⁴×C₃	—	4	24	no	—
440	C₂⁴×C₃	—	4	24	no	—
441	C₂⁴×C₃	—	4	192	no	—
442	C₂⁴×C₃	—	4	12	no	—
443	C₂⁴×C₃	—	4	96	no	—
444	C₂⁴×C₃	—	4	12	no	—
445	C₂⁴×C₃	—	4	192	no	—
446	C₂⁴×C₃	—	4	96	no	—
447	C₂⁴×C₃	—	4	24	no	—
448	C₂⁴×C₃	—	4	48	no	—
449	C₂⁴×C₃	—	4	384	no	—
450	C₂⁴×C₃	—	4	192	no	—
451	C₂⁴×C₃	—	4	384	no	—
452	C₂⁴×C₃	—	4	1024	no	—
453	C₂⁴×C₃	—	8	32	no	—
454	C₂⁴×C₃	H(5,𝔽₂)	1	24	yes	complemented
455	C₂⁴×C₃	C₂⁵	1	4	yes	—
456	C₂⁴×C₃	C₂⁵	1	6	yes	—
457	C₂⁴×C₃	C₂⁵	1	8	yes	—
458	C₂⁴×C₃	C₂⁵	1	4	yes	—
459	C₂⁴×C₃	C₂⁵	1	24	yes	—
460	C₂⁴×C₃	C₂⁵	1	48	yes	—
461	C₂⁴×C₃	C₂⁵	1	3	yes	—
462	C₂⁴×C₃	C₂⁵	1	6	yes	—
463	C₂⁴×C₃	C₂⁵	1	24	yes	—
464	C₂⁴×C₃	C₂⁵	1	12	yes	—
465	C₂⁴×C₃	C₂⁵	1	24	yes	—
466	C₂⁴×C₃	C₂⁵	1	8	yes	—
467	C₂⁴×C₃	C₂⁵	1	12	yes	—
468	C₂³×D₃	—	2	48	no	—
469	C₂³×D₃	—	4	48	no	—
470	C₂³×D₃	—	4	96	no	—
471	C₂³×D₃	—	4	24	no	—
472	C₂³×D₃	—	8	64	no	—
473	C₂³×D₃	C₂⁵	1	8	yes	—
474	C₂³×D₃	C₂⁵	1	48	yes	—
475	C₂³×D₃	C₂⁵	1	16	yes	complemented
476	C₂×C₃×D₄	—	2	96	no	—
477	C₂×C₃×D₄	—	2	192	no	—
478	C₂×C₃×D₄	—	4	48	no	—
479	C₂×C₃×D₄	—	4	96	no	—
480	C₂×C₃×D₄	—	4	384	no	—
481	C₂×C₃×D₄	C₂⁵	1	96	yes	—
482	C₂×C₃×D₄	C₂⁵	1	96	yes	—
483	C₂²×C₃×C₄	—	2	24	no	—
484	C₂²×C₃×C₄	—	4	24	no	—
485	C₂²×C₃×C₄	—	4	48	no	—
486	C₂²×C₃×C₄	C₂⁵	1	12	yes	—
487	C₂²×C₃×C₄	C₂⁵	1	24	yes	—
488	C₂²×C₃×C₄	C₂⁵	1	48	yes	—
489	C₂×#67	—	2	96	no	—
490	C₂×#67	—	2	96	no	—
491	C₂×#67	—	2	384	no	—
492	C₂×#67	—	4	48	no	—
493	C₂×#67	—	4	96	no	—
494	C₂×#67	—	4	192	no	—
495	C₂×#67	—	4	192	no	—
496	C₂×#67	—	4	384	no	—
497	C₂×#67	—	4	384	no	—
498	C₂×#67	C₂⁵	1	96	yes	—
499	C₂×#67	C₂⁵	1	96	yes	—
500	C₂×#67	C₂⁵	1	192	yes	—
501	C₂×#67	C₂⁵	1	96	yes	complemented
502	C₂²×Dic₃	—	2	48	no	—
503	C₂²×Dic₃	—	4	24	no	—
504	C₂²×Dic₃	—	4	48	no	—
505	C₂²×Dic₃	—	4	96	no	—
506	C₂²×Dic₃	C₂⁵	1	48	yes	—
507	C₂²×Dic₃	C₂⁵	1	24	yes	—
508	C₂²×Dic₃	C₂⁵	1	96	yes	—
509	C₂²×Dic₃	C₂⁵	1	48	yes	complemented
510	#237	—	4	384	no	—
511	D₃×D₄	—	4	384	no	—
512	#235	—	4	192	no	—
513	C₂×D₁₂	—	4	24	no	—
514	C₂×D₁₂	C₂⁵	1	48	yes	complemented
515	C₂×C₄×D₃	—	4	48	no	—
516	C₂×C₄×D₃	C₂⁵	1	96	yes	complemented
517	C₂×Dic₆	—	4	24	no	—
518	C₂×Dic₆	C₂⁵	1	48	yes	complemented
519	C₃×C₂²⋊C₄	C₂⁵	1	96	yes	—
520	C₃×C₂²⋊C₄	C₂⁵	1	96	yes	—
521	#217	C₂⁵	1	96	yes	—
522	#217	C₂⁵	1	192	yes	—
523	#217	C₂⁵	1	96	yes	—
524	#217	C₂⁵	1	96	yes	complemented
525	(C₂×D₃)⋊C₄	C₂⁵	1	192	yes	complemented
526	C₄⋊Dic₃	C₂⁵	1	96	yes	complemented
527	Dic₃⋊C₄	C₂⁵	1	192	yes	complemented
528	C₄×Dic₃	C₂⁵	1	96	yes	complemented
529	C₂⁵	—	2	24	no	—
530	C₂⁵	—	2	48	no	—
531	C₂⁵	—	3	12	no	—
532	C₂⁵	—	3	16	no	—
533	C₂⁵	—	3	4	no	—
534	C₂⁵	—	4	24	no	—
535	C₂⁵	—	4	48	no	—
536	C₂⁵	—	4	48	no	—
537	C₂⁵	—	4	24	no	—
538	C₂⁵	—	4	192	no	—
539	C₂⁵	—	4	12	no	—
540	C₂⁵	—	4	256	no	—
541	C₂⁵	—	12	24	no	—
542	C₂⁵	C₂³×D₃	1	1	yes	characteristic
543	C₂⁵	C₂³×D₃	1	2	yes	—
544	C₂⁵	C₂³×D₃	1	6	yes	—
545	C₂⁵	C₂³×D₃	1	12	yes	—
546	C₂⁵	C₂³×D₃	1	6	yes	—
547	C₂⁵	C₂³×D₃	1	48	yes	—
548	C₂⁵	C₂³×D₃	1	6	yes	—
549	C₂⁵	C₂³×D₃	1	3	yes	—
550	C₂⁵	C₂³×D₃	1	24	yes	—
551	C₂⁵	C₂³×D₃	1	2	yes	—
552	C₂⁵	C₂³×D₃	1	48	yes	—
553	C₂⁵	C₂³×D₃	1	3	yes	—
554	C₂⁵	C₂³×D₃	1	8	yes	complemented
555	H(5,𝔽₂)	—	12	384	no	—
556	C₂×#41	—	3	192	no	—
557	C₂×#41	—	3	96	no	—
558	C₂×#41	—	12	48	no	—
559	C₂×#41	—	12	96	no	—
560	C₂²×Q₈	—	3	12	no	—
561	C₂²×D₄	—	2	48	no	—
562	C₂²×D₄	—	3	24	no	—
563	C₂²×D₄	—	3	24	no	—
564	C₂²×D₄	—	3	96	no	—
565	C₂²×D₄	—	3	48	no	—
566	C₂²×D₄	—	3	24	no	—
567	C₂²×D₄	—	3	96	no	—
568	C₂²×D₄	—	3	192	no	—
569	C₂²×D₄	—	3	192	no	—
570	C₂²×D₄	—	3	96	no	—
571	C₂²×D₄	—	3	192	no	—
572	C₂²×D₄	—	3	12	no	—
573	C₂²×D₄	—	4	24	no	—
574	C₂²×D₄	—	4	96	no	—
575	C₂²×D₄	—	4	192	no	—
576	C₂²×D₄	—	6	96	no	—
577	C₂²×D₄	—	12	48	no	—
578	C₂²×D₄	—	12	96	no	—
579	C₂²×D₄	—	12	96	no	—
580	C₂²×D₄	—	12	96	no	—
581	C₂²×D₄	—	12	384	no	—
582	C₂²×D₄	—	12	48	no	—
583	C₂²×D₄	C₂³×D₃	1	24	yes	—
584	C₂²×D₄	C₂³×D₃	1	48	yes	—
585	C₂²×D₄	C₂³×D₃	1	24	yes	—
586	C₂²×D₄	C₂³×D₃	1	48	yes	complemented
587	C₂²×D₄	C₂³×D₃	1	192	yes	complemented
588	C₂³×C₄	—	3	12	no	—
589	C₂³×C₄	—	3	24	no	—
590	C₂³×C₄	—	3	48	no	—
591	C₂³×C₄	—	3	12	no	—
592	C₂³×C₄	—	3	24	no	—
593	C₂³×C₄	—	4	12	no	—
594	C₂³×C₄	—	12	24	no	—
595	C₂³×C₄	C₂³×D₃	1	6	yes	—
596	C₂³×C₄	C₂³×D₃	1	12	yes	—
597	C₂³×C₄	C₂³×D₃	1	24	yes	complemented
598	#127	—	3	192	no	—
599	#126	—	3	384	no	—
600	#124	—	3	192	no	—
601	#124	—	3	384	no	—
602	#123	—	3	192	no	—
603	#123	—	3	192	no	—
604	#123	—	3	192	no	—
605	#123	—	3	192	no	—
606	#123	—	3	384	no	—
607	C₂²⋊Q₈	—	3	192	no	—
608	C₂²⋊Q₈	—	3	384	no	—
609	#121	—	3	384	no	—
610	#121	—	3	384	no	—
611	#121	—	3	384	no	—
612	#121	—	3	192	no	—
613	#121	—	3	384	no	—
614	#120	—	3	64	no	—
615	#120	—	3	64	no	—
616	#120	—	3	192	no	—
617	#120	—	3	192	no	—
618	#120	—	3	384	no	—
619	#120	—	3	128	no	—
620	#120	—	3	192	no	—
621	#120	—	3	192	no	—
622	#120	—	3	192	no	—
623	#120	—	3	192	no	—
624	#120	C₂³×D₃	1	192	yes	—
625	#120	C₂³×D₃	1	64	yes	complemented
626	#120	C₂³×D₃	1	192	yes	complemented
627	#120	C₂³×D₃	1	64	yes	complemented
628	C₄×D₄	—	3	384	no	—
629	C₄×D₄	—	3	384	no	—
630	C₄×D₄	—	3	384	no	—
631	#117	—	3	96	no	—
632	#117	—	3	192	no	—
633	C₂×C₄⋊C₄	—	3	48	no	—
634	C₂×C₄⋊C₄	—	3	24	no	—
635	C₂×C₂²⋊C₄	—	3	24	no	—
636	C₂×C₂²⋊C₄	—	3	24	no	—
637	C₂×C₂²⋊C₄	—	3	96	no	—
638	C₂×C₂²⋊C₄	—	3	48	no	—
639	C₂×C₂²⋊C₄	—	3	96	no	—
640	C₂×C₂²⋊C₄	—	3	192	no	—
641	C₂×C₂²⋊C₄	—	3	192	no	—
642	C₂×C₂²⋊C₄	—	3	24	no	—
643	C₂×C₂²⋊C₄	—	3	96	no	—
644	C₂×C₂²⋊C₄	—	3	48	no	—
645	C₂×C₂²⋊C₄	—	3	192	no	—
646	C₂×C₂²⋊C₄	C₂³×D₃	1	24	yes	—
647	C₂×C₂²⋊C₄	C₂³×D₃	1	48	yes	—
648	C₂×C₂²⋊C₄	C₂³×D₃	1	24	yes	—
649	C₂×C₂²⋊C₄	C₂³×D₃	1	48	yes	complemented
650	C₂×C₂²⋊C₄	C₂³×D₃	1	192	yes	complemented
651	C₂×C₄²	—	3	24	no	—
652	C₂³×C₃	—	2	64	no	—
653	C₂³×C₃	—	2	32	no	—
654	C₂³×C₃	—	2	48	no	—
655	C₂³×C₃	—	2	24	no	—
656	C₂³×C₃	—	2	24	no	—
657	C₂³×C₃	—	2	12	no	—
658	C₂³×C₃	—	2	24	no	—
659	C₂³×C₃	—	2	96	no	—
660	C₂³×C₃	—	2	96	no	—
661	C₂³×C₃	—	2	48	no	—
662	C₂³×C₃	—	2	24	no	—
663	C₂³×C₃	—	2	96	no	—
664	C₂³×C₃	—	2	24	no	—
665	C₂³×C₃	—	2	12	no	—
666	C₂³×C₃	—	2	48	no	—
667	C₂³×C₃	—	4	48	no	—
668	C₂³×C₃	—	4	24	no	—
669	C₂³×C₃	—	4	24	no	—
670	C₂³×C₃	—	4	48	no	—
671	C₂³×C₃	—	4	48	no	—
672	C₂³×C₃	—	4	24	no	—
673	C₂³×C₃	—	4	24	no	—
674	C₂³×C₃	—	4	48	no	—
675	C₂³×C₃	—	4	96	no	—
676	C₂³×C₃	—	4	192	no	—
677	C₂³×C₃	—	4	768	no	—
678	C₂³×C₃	—	4	384	no	—
679	C₂³×C₃	—	4	96	no	—
680	C₂³×C₃	—	4	48	no	—
681	C₂³×C₃	—	4	768	no	—
682	C₂³×C₃	—	4	32	no	—
683	C₂³×C₃	—	8	48	no	—
684	C₂³×C₃	—	8	64	no	—
685	C₂³×C₃	C₂×H(5,𝔽₂)	1	24	yes	—
686	C₂³×C₃	C₂×H(5,𝔽₂)	1	12	yes	—
687	C₂³×C₃	C₂×H(5,𝔽₂)	1	48	yes	complemented
688	C₂³×C₃	C₂⁶	1	12	yes	—
689	C₂³×C₃	C₂⁶	1	8	yes	—
690	C₂³×C₃	C₂⁶	1	6	yes	—
691	C₂³×C₃	C₂⁶	1	12	yes	—
692	C₂³×C₃	C₂⁶	1	1	yes	characteristic
693	C₂²×D₃	—	2	48	no	—
694	C₂²×D₃	—	2	96	no	—
695	C₂²×D₃	—	4	96	no	—
696	C₂²×D₃	—	4	48	no	—
697	C₂²×D₃	—	8	96	no	—
698	C₂²×D₃	—	8	128	no	—
699	C₂²×D₃	—	16	16	no	—
700	C₂²×D₃	C₂⁶	1	16	yes	—
701	C₃×D₄	—	2	192	no	—
702	C₃×D₄	—	4	96	no	—
703	C₂×C₃×C₄	—	2	24	no	—
704	C₂×C₃×C₄	—	2	48	no	—
705	C₂×C₃×C₄	—	4	48	no	—
706	C₂×C₃×C₄	C₂⁶	1	24	yes	—
707	#67	—	2	192	no	—
708	#67	—	2	192	no	—
709	#67	—	4	96	no	—
710	#67	—	4	192	no	—
711	C₂×Dic₃	—	2	48	no	—
712	C₂×Dic₃	—	2	96	no	—
713	C₂×Dic₃	—	4	48	no	—
714	C₂×Dic₃	—	4	96	no	—
715	C₂×Dic₃	C₂⁶	1	48	yes	—
716	D₁₂	—	4	48	no	—
717	C₄×D₃	—	4	96	no	—
718	Dic₆	—	4	48	no	—
719	C₂⁴	—	2	12	no	—
720	C₂⁴	—	2	24	no	—
721	C₂⁴	—	2	48	no	—
722	C₂⁴	—	2	12	no	—
723	C₂⁴	—	2	48	no	—
724	C₂⁴	—	2	48	no	—
725	C₂⁴	—	2	24	no	—
726	C₂⁴	—	2	96	no	—
727	C₂⁴	—	2	192	no	—
728	C₂⁴	—	2	24	no	—
729	C₂⁴	—	3	8	no	—
730	C₂⁴	—	3	48	no	—
731	C₂⁴	—	3	16	no	—
732	C₂⁴	—	4	12	no	—
733	C₂⁴	—	4	24	no	—
734	C₂⁴	—	4	12	no	—
735	C₂⁴	—	4	96	no	—
736	C₂⁴	—	4	12	no	—
737	C₂⁴	—	4	24	no	—
738	C₂⁴	—	4	192	no	—
739	C₂⁴	—	4	12	no	—
740	C₂⁴	—	4	192	no	—
741	C₂⁴	—	4	96	no	—
742	C₂⁴	—	4	24	no	—
743	C₂⁴	—	4	48	no	—
744	C₂⁴	—	4	192	no	—
745	C₂⁴	—	4	384	no	—
746	C₂⁴	—	4	384	no	—
747	C₂⁴	—	4	1024	no	—
748	C₂⁴	—	6	48	no	—
749	C₂⁴	—	8	32	no	—
750	C₂⁴	—	12	48	no	—
751	C₂⁴	—	12	96	no	—
752	C₂⁴	—	12	24	no	—
753	C₂⁴	—	24	64	no	—
754	C₂⁴	#1004	1	24	yes	complemented
755	C₂⁴	C₂⁴×D₃	1	4	yes	—
756	C₂⁴	C₂⁴×D₃	1	8	yes	—
757	C₂⁴	C₂⁴×D₃	1	6	yes	—
758	C₂⁴	C₂⁴×D₃	1	4	yes	—
759	C₂⁴	C₂⁴×D₃	1	24	yes	—
760	C₂⁴	C₂⁴×D₃	1	48	yes	—
761	C₂⁴	C₂⁴×D₃	1	3	yes	—
762	C₂⁴	C₂⁴×D₃	1	6	yes	—
763	C₂⁴	C₂⁴×D₃	1	24	yes	—
764	C₂⁴	C₂⁴×D₃	1	24	yes	—
765	C₂⁴	C₂⁴×D₃	1	12	yes	—
766	C₂⁴	C₂⁴×D₃	1	8	yes	—
767	C₂⁴	C₂⁴×D₃	1	12	yes	—
768	#41	—	12	192	no	—
769	#41	—	12	384	no	—
770	C₂×Q₈	—	3	48	no	—
771	C₂×Q₈	—	12	24	no	—
772	C₂×D₄	—	2	96	no	—
773	C₂×D₄	—	2	192	no	—
774	C₂×D₄	—	3	96	no	—
775	C₂×D₄	—	3	96	no	—
776	C₂×D₄	—	3	192	no	—
777	C₂×D₄	—	3	96	no	—
778	C₂×D₄	—	3	48	no	—
779	C₂×D₄	—	4	48	no	—
780	C₂×D₄	—	4	96	no	—
781	C₂×D₄	—	4	384	no	—
782	C₂×D₄	—	6	96	no	—
783	C₂×D₄	—	6	96	no	—
784	C₂×D₄	—	6	384	no	—
785	C₂×D₄	—	12	24	no	—
786	C₂×D₄	—	12	96	no	—
787	C₂×D₄	—	12	192	no	—
788	C₂×D₄	—	12	48	no	—
789	C₂×D₄	—	12	384	no	—
790	C₂×D₄	—	12	384	no	—
791	C₂×D₄	—	12	384	no	—
792	C₂×D₄	—	12	192	no	—
793	C₂×D₄	C₂⁴×D₃	1	96	yes	—
794	C₂×D₄	C₂⁴×D₃	1	96	yes	—
795	C₂²×C₄	—	2	24	no	—
796	C₂²×C₄	—	3	48	no	—
797	C₂²×C₄	—	3	24	no	—
798	C₂²×C₄	—	3	96	no	—
799	C₂²×C₄	—	3	48	no	—
800	C₂²×C₄	—	3	96	no	—
801	C₂²×C₄	—	4	24	no	—
802	C₂²×C₄	—	4	48	no	—
803	C₂²×C₄	—	6	48	no	—
804	C₂²×C₄	—	12	48	no	—
805	C₂²×C₄	—	12	48	no	—
806	C₂²×C₄	—	12	96	no	—
807	C₂²×C₄	—	12	24	no	—
808	C₂²×C₄	C₂⁴×D₃	1	24	yes	—
809	C₂²×C₄	C₂⁴×D₃	1	12	yes	—
810	C₂²×C₄	C₂⁴×D₃	1	48	yes	—
811	C₄⋊C₄	—	3	192	no	—
812	C₄⋊C₄	—	3	96	no	—
813	C₂²⋊C₄	—	3	96	no	—
814	C₂²⋊C₄	—	3	96	no	—
815	C₂²⋊C₄	—	3	192	no	—
816	C₂²⋊C₄	—	3	96	no	—
817	C₂²⋊C₄	—	3	192	no	—
818	C₂²⋊C₄	C₂⁴×D₃	1	96	yes	—
819	C₂²⋊C₄	C₂⁴×D₃	1	96	yes	—
820	C₄²	—	3	96	no	—
821	C₂²×C₃	—	2	64	no	—
822	C₂²×C₃	—	2	32	no	—
823	C₂²×C₃	—	2	48	no	—
824	C₂²×C₃	—	2	24	no	—
825	C₂²×C₃	—	2	24	no	—
826	C₂²×C₃	—	2	12	no	—
827	C₂²×C₃	—	2	24	no	—
828	C₂²×C₃	—	2	24	no	—
829	C₂²×C₃	—	2	12	no	—
830	C₂²×C₃	—	4	48	no	—
831	C₂²×C₃	—	4	96	no	—
832	C₂²×C₃	—	4	192	no	—
833	C₂²×C₃	—	4	96	no	—
834	C₂²×C₃	—	4	48	no	—
835	C₂²×C₃	—	4	32	no	—
836	C₂²×C₃	—	4	16	no	—
837	C₂²×C₃	—	4	24	no	—
838	C₂²×C₃	—	8	48	no	—
839	C₂²×C₃	C₂²×H(5,𝔽₂)	1	24	yes	—
840	C₂²×C₃	C₂²×H(5,𝔽₂)	1	12	yes	—
841	C₂²×C₃	C₂²×H(5,𝔽₂)	1	6	yes	—
842	C₂²×C₃	C₂⁷	1	1	yes	characteristic
843	C₂×D₃	—	2	48	no	—
844	C₂×D₃	—	4	32	no	—
845	C₂×D₃	—	8	96	no	—
846	C₂×D₃	—	16	16	no	—
847	C₃×C₄	—	2	24	no	—
848	Dic₃	—	2	48	no	—
849	C₂³	—	2	32	no	—
850	C₂³	—	2	64	no	—
851	C₂³	—	2	24	no	—
852	C₂³	—	2	12	no	—
853	C₂³	—	2	48	no	—
854	C₂³	—	2	24	no	—
855	C₂³	—	2	24	no	—
856	C₂³	—	2	96	no	—
857	C₂³	—	2	24	no	—
858	C₂³	—	2	12	no	—
859	C₂³	—	2	96	no	—
860	C₂³	—	2	96	no	—
861	C₂³	—	2	48	no	—
862	C₂³	—	2	24	no	—
863	C₂³	—	2	48	no	—
864	C₂³	—	3	16	no	—
865	C₂³	—	4	48	no	—
866	C₂³	—	4	24	no	—
867	C₂³	—	4	48	no	—
868	C₂³	—	4	24	no	—
869	C₂³	—	4	24	no	—
870	C₂³	—	4	48	no	—
871	C₂³	—	4	24	no	—
872	C₂³	—	4	48	no	—
873	C₂³	—	4	192	no	—
874	C₂³	—	4	96	no	—
875	C₂³	—	4	384	no	—
876	C₂³	—	4	768	no	—
877	C₂³	—	4	48	no	—
878	C₂³	—	4	96	no	—
879	C₂³	—	4	768	no	—
880	C₂³	—	4	32	no	—
881	C₂³	—	6	48	no	—
882	C₂³	—	6	96	no	—
883	C₂³	—	8	48	no	—
884	C₂³	—	8	64	no	—
885	C₂³	—	12	96	no	—
886	C₂³	—	12	48	no	—
887	C₂³	—	24	96	no	—
888	C₂³	—	24	128	no	—
889	C₂³	—	48	16	no	—
890	C₂³	C₂×#1004	1	12	yes	—
891	C₂³	C₂×#1004	1	24	yes	—
892	C₂³	C₂×#1004	1	48	yes	complemented
893	C₂³	C₂⁵×D₃	1	12	yes	—
894	C₂³	C₂⁵×D₃	1	8	yes	—
895	C₂³	C₂⁵×D₃	1	6	yes	—
896	C₂³	C₂⁵×D₃	1	12	yes	—
897	C₂³	C₂⁵×D₃	1	1	yes	characteristic
898	Q₈	—	12	48	no	—
899	D₄	—	2	192	no	—
900	D₄	—	4	96	no	—
901	D₄	—	6	192	no	—
902	D₄	—	6	192	no	—
903	D₄	—	12	48	no	—
904	D₄	—	12	192	no	—
905	D₄	—	12	96	no	—
906	C₂×C₄	—	2	24	no	—
907	C₂×C₄	—	2	48	no	—
908	C₂×C₄	—	3	48	no	—
909	C₂×C₄	—	4	48	no	—
910	C₂×C₄	—	6	48	no	—
911	C₂×C₄	—	6	96	no	—
912	C₂×C₄	—	12	96	no	—
913	C₂×C₄	—	12	96	no	—
914	C₂×C₄	—	12	48	no	—
915	C₂×C₄	C₂⁵×D₃	1	24	yes	—
916	C₂×C₃	—	2	24	no	—
917	C₂×C₃	—	2	12	no	—
918	C₂×C₃	—	4	8	no	—
919	C₂×C₃	—	4	12	no	—
920	C₂×C₃	#62817	1	4	yes	complemented
921	C₂×C₃	C₂³×H(5,𝔽₂)	1	3	yes	—
922	D₃	—	4	16	no	—
923	C₂²	—	2	32	no	—
924	C₂²	—	2	64	no	—
925	C₂²	—	2	12	no	—
926	C₂²	—	2	24	no	—
927	C₂²	—	2	24	no	—
928	C₂²	—	2	48	no	—
929	C₂²	—	2	24	no	—
930	C₂²	—	2	12	no	—
931	C₂²	—	2	24	no	—
932	C₂²	—	4	48	no	—
933	C₂²	—	4	192	no	—
934	C₂²	—	4	96	no	—
935	C₂²	—	4	48	no	—
936	C₂²	—	4	96	no	—
937	C₂²	—	4	32	no	—
938	C₂²	—	4	24	no	—
939	C₂²	—	4	16	no	—
940	C₂²	—	6	48	no	—
941	C₂²	—	8	48	no	—
942	C₂²	—	12	32	no	—
943	C₂²	—	24	96	no	—
944	C₂²	—	48	16	no	—
945	C₂²	C₂²×#1004	1	12	yes	—
946	C₂²	C₂²×#1004	1	24	yes	—
947	C₂²	C₂²×#1004	1	6	yes	—
948	C₂²	C₂⁶×D₃	1	1	yes	characteristic
949	C₄	—	2	24	no	—
950	C₄	—	6	48	no	—
951	C₃	C₂×#62817	1	1	yes	characteristic, complemented, Sylow
952	C₂	—	2	12	no	—
953	C₂	—	2	24	no	—
954	C₂	—	4	12	no	—
955	C₂	—	4	8	no	—
956	C₂	—	12	16	no	—
957	C₂	#11703805	1	4	yes	direct product factor
958	C₂	C₂³×#1004	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁵×D₃
commutator, cosocle	C₂²×C₃	C₂⁷
Frattini	C₂²	C₂⁶×D₃
Fitting	C₂³×C₃×#120	C₂
socle	C₂³×C₃	C₂⁶
hypercenter	C₂³×#120	D₃
hypocenter	C₃	C₂×#62817
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂³×#120

Complements

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

N	H ≅ G/N	type
1. #11703805	C₂	direct (N × H)
2. C₂×#85697	C₂	semidirect
3. C₂×#85913	C₂	semidirect
4. C₂×#87239	C₂	semidirect
5. C₂×#85919	C₂	semidirect
6. C₂×#85921	C₂	semidirect
7. C₂³×#953	C₂	semidirect
8. C₂³×C₃×#120	C₂	semidirect
10. C₂⁷×C₃	C₂²	semidirect
11. C₂⁴×C₃×D₄	C₂²	semidirect
12. C₂⁴×#67	C₂²	semidirect
13. C₂²×#1004	C₂²	semidirect
14. C₂²×C₃×#120	C₂²	semidirect
15. C₂²×C₃×#120	C₂²	semidirect
16. C₂²×C₃×#120	C₂²	semidirect
17. C₂³×C₃×C₂²⋊C₄	C₂²	semidirect
18. C₂²×#953	C₂²	semidirect
19. C₂²×#953	C₂²	semidirect
20. C₂²×#953	C₂²	semidirect
21. C₂²×#953	C₂²	semidirect
22. C₂²×#953	C₂²	semidirect
23. C₂³×#217	C₂²	semidirect
24. #87239	C₂²	semidirect
25. C₂×D₄×#67	C₂²	semidirect
26. C₂×#5805	C₂²	semidirect
27. C₂×#5804	C₂²	semidirect
28. C₂×#5804	C₂²	semidirect
29. C₂×#5806	C₂²	semidirect
30. C₂×#5798	C₂²	semidirect
31. C₂×#5791	C₂²	semidirect
32. #85921	C₂²	semidirect
33. C₂×#5595	C₂²	semidirect
34. #85919	C₂²	semidirect
35. C₂×#5591	C₂²	semidirect
36. C₂×#5590	C₂²	semidirect
37. C₂×#5589	C₂²	semidirect
38. C₂×D₃×#120	C₂²	semidirect
39. C₂×#5594	C₂²	semidirect
40. #85913	C₂²	semidirect
41. C₂×#5587	C₂²	semidirect
42. C₂×#5593	C₂²	semidirect
43. C₂×#5592	C₂²	semidirect
44. C₂×#5586	C₂²	semidirect
45. #85697	C₂²	semidirect
46. C₂×#5490	C₂²	semidirect
47. C₂×#5494	C₂²	semidirect
48. C₂×#5493	C₂²	semidirect
49. C₂×#5486	C₂²	semidirect
50. C₂×#5495	C₂²	semidirect
51. C₂×#5483	C₂²	semidirect
59. C₂³×#120	D₃	semidirect
64. C₂⁶×C₃	C₂³	semidirect
65. C₂⁶×C₃	C₂³	semidirect
66. C₂⁵×D₃	C₂³	semidirect
69. C₂³×C₃×D₄	C₂³	semidirect
70. C₂³×C₃×D₄	C₂³	semidirect
71. C₂³×C₃×D₄	C₂³	semidirect
72. C₂⁴×C₃×C₄	C₂³	semidirect
75. C₂³×#67	C₂³	semidirect
76. C₂³×#67	C₂³	semidirect
77. C₂³×#67	C₂³	semidirect
78. C₂³×#67	C₂³	semidirect
79. C₂³×#67	C₂³	semidirect
80. C₂⁴×Dic₃	C₂³	semidirect
82. C₂×#1004	C₂³	semidirect
83. C₂²×#237	C₂³	semidirect
84. C₂²×D₃×D₄	C₂³	semidirect
85. C₂²×#235	C₂³	semidirect
87. C₂×C₃×#120	C₂³	semidirect
88. C₂×C₃×#120	C₂³	semidirect
89. C₂×C₃×#120	C₂³	semidirect
90. C₂×C₃×#120	C₂³	semidirect
91. C₂×C₃×#120	C₂³	semidirect
93. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
94. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
95. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
97. C₂×#953	C₂³	semidirect
98. C₂×#953	C₂³	semidirect
99. C₂×#953	C₂³	semidirect
100. C₂×#953	C₂³	semidirect
101. C₂×#953	C₂³	semidirect
102. C₂×#953	C₂³	semidirect
103. C₂×#953	C₂³	semidirect
104. C₂×#953	C₂³	semidirect
105. C₂×#953	C₂³	semidirect
106. C₂×#953	C₂³	semidirect
108. C₂²×#217	C₂³	semidirect
109. C₂²×#217	C₂³	semidirect
110. C₂²×#217	C₂³	semidirect
111. C₂²×#217	C₂³	semidirect
112. C₂²×#217	C₂³	semidirect
113. #5806	C₂³	semidirect
114. #5805	C₂³	semidirect
115. #5804	C₂³	semidirect
116. #5804	C₂³	semidirect
117. C₂×#940	C₂³	semidirect
118. C₂×#939	C₂³	semidirect
119. C₂×#939	C₂³	semidirect
120. D₄×#67	C₂³	semidirect
121. C₂×#938	C₂³	semidirect
122. C₂×#937	C₂³	semidirect
123. C₂×#937	C₂³	semidirect
124. #5798	C₂³	semidirect
125. C₂×#936	C₂³	semidirect
126. C₂×#935	C₂³	semidirect
127. C₂×#935	C₂³	semidirect
128. C₂×D₄×Dic₃	C₂³	semidirect
129. #5791	C₂³	semidirect
130. C₂×#930	C₂³	semidirect
131. C₂×#929	C₂³	semidirect
132. C₂×C₄×#67	C₂³	semidirect
133. C₂×#926	C₂³	semidirect
134. C₂×#924	C₂³	semidirect
135. #5595	C₂³	semidirect
136. #5594	C₂³	semidirect
137. #5593	C₂³	semidirect
138. #5592	C₂³	semidirect
139. #5591	C₂³	semidirect
140. #5590	C₂³	semidirect
141. #5589	C₂³	semidirect
142. D₃×#120	C₂³	semidirect
143. #5587	C₂³	semidirect
144. #5586	C₂³	semidirect
145. #5495	C₂³	semidirect
146. #5494	C₂³	semidirect
147. #5493	C₂³	semidirect
148. C₂×#886	C₂³	semidirect
149. C₂×#885	C₂³	semidirect
150. #5490	C₂³	semidirect
151. C₂×#884	C₂³	semidirect
152. C₂×#883	C₂³	semidirect
153. C₂×#882	C₂³	semidirect
154. #5486	C₂³	semidirect
155. C₂×#67⋊C₄	C₂³	semidirect
156. C₂×D₃×C₂²⋊C₄	C₂³	semidirect
157. #5483	C₂³	semidirect
158. C₂×#879	C₂³	semidirect
159. C₂×#878	C₂³	semidirect
160. C₂×#877	C₂³	semidirect
161. C₂⁷	C₂×D₃	semidirect
164. C₂⁴×D₄	C₂×D₃	semidirect
196. C₂²×#120	C₂×D₃	semidirect
197. C₂²×#120	C₂×D₃	semidirect
198. C₂²×#120	C₂×D₃	semidirect
202. C₂³×C₂²⋊C₄	C₂×D₃	semidirect
224. C₂⁵×C₃	C₂⁴	semidirect
227. C₂⁴×D₃	C₂⁴	semidirect
228. C₂⁴×D₃	C₂⁴	semidirect
236. C₂²×C₃×D₄	C₂⁴	semidirect
237. C₂²×C₃×D₄	C₂⁴	semidirect
241. C₂³×C₃×C₄	C₂⁴	semidirect
252. C₂²×#67	C₂⁴	semidirect
253. C₂²×#67	C₂⁴	semidirect
254. C₂²×#67	C₂⁴	semidirect
255. C₂²×#67	C₂⁴	semidirect
256. C₂²×#67	C₂⁴	semidirect
260. C₂³×Dic₃	C₂⁴	semidirect
261. C₂³×Dic₃	C₂⁴	semidirect
264. C₂×#237	C₂⁴	semidirect
266. C₂×D₃×D₄	C₂⁴	semidirect
268. C₂×#235	C₂⁴	semidirect
269. C₂²×D₁₂	C₂⁴	semidirect
270. C₂²×C₄×D₃	C₂⁴	semidirect
271. C₂²×Dic₆	C₂⁴	semidirect
273. C₃×#120	C₂⁴	semidirect
274. C₃×#120	C₂⁴	semidirect
275. C₃×#120	C₂⁴	semidirect
279. C₂×C₃×C₂²⋊C₄	C₂⁴	semidirect
280. C₂×C₃×C₂²⋊C₄	C₂⁴	semidirect
282. #953	C₂⁴	semidirect
283. #953	C₂⁴	semidirect
284. #953	C₂⁴	semidirect
285. #953	C₂⁴	semidirect
286. #953	C₂⁴	semidirect
287. #953	C₂⁴	semidirect
292. C₂×#217	C₂⁴	semidirect
293. C₂×#217	C₂⁴	semidirect
294. C₂×#217	C₂⁴	semidirect
295. C₂×#217	C₂⁴	semidirect
296. C₂×#217	C₂⁴	semidirect
297. #940	C₂⁴	semidirect
298. #939	C₂⁴	semidirect
299. #939	C₂⁴	semidirect
300. #938	C₂⁴	semidirect
301. #937	C₂⁴	semidirect
302. #937	C₂⁴	semidirect
303. #936	C₂⁴	semidirect
304. #935	C₂⁴	semidirect
305. #935	C₂⁴	semidirect
306. D₄×Dic₃	C₂⁴	semidirect
307. #930	C₂⁴	semidirect
308. #929	C₂⁴	semidirect
309. C₄×#67	C₂⁴	semidirect
310. C₂×(C₂×D₃)⋊C₄	C₂⁴	semidirect
311. #926	C₂⁴	semidirect
312. C₂×C₄⋊Dic₃	C₂⁴	semidirect
313. #924	C₂⁴	semidirect
314. C₂×Dic₃⋊C₄	C₂⁴	semidirect
315. C₂×C₄×Dic₃	C₂⁴	semidirect
316. #886	C₂⁴	semidirect
317. #885	C₂⁴	semidirect
318. #884	C₂⁴	semidirect
319. #883	C₂⁴	semidirect
320. #882	C₂⁴	semidirect
321. #67⋊C₄	C₂⁴	semidirect
322. D₃×C₂²⋊C₄	C₂⁴	semidirect
323. #879	C₂⁴	semidirect
324. #878	C₂⁴	semidirect
325. #877	C₂⁴	semidirect
331. C₂⁶	C₂²×D₃	semidirect
332. C₂⁶	C₂²×D₃	semidirect
347. C₂³×D₄	C₂²×D₃	semidirect
348. C₂³×D₄	C₂²×D₃	semidirect
349. C₂³×D₄	C₂²×D₃	semidirect
351. C₂⁴×C₄	C₂²×D₃	semidirect
404. C₂×#120	C₂²×D₃	semidirect
405. C₂×#120	C₂²×D₃	semidirect
406. C₂×#120	C₂²×D₃	semidirect
407. C₂×#120	C₂²×D₃	semidirect
408. C₂×#120	C₂²×D₃	semidirect
424. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
425. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
426. C₂²×C₂²⋊C₄	C₂²×D₃	semidirect
454. C₂⁴×C₃	H(5,𝔽₂)	semidirect
475. C₂³×D₃	C₂⁵	semidirect
501. C₂×#67	C₂⁵	semidirect
509. C₂²×Dic₃	C₂⁵	semidirect
514. C₂×D₁₂	C₂⁵	semidirect
516. C₂×C₄×D₃	C₂⁵	semidirect
518. C₂×Dic₆	C₂⁵	semidirect
524. #217	C₂⁵	semidirect
525. (C₂×D₃)⋊C₄	C₂⁵	semidirect
526. C₄⋊Dic₃	C₂⁵	semidirect
527. Dic₃⋊C₄	C₂⁵	semidirect
528. C₄×Dic₃	C₂⁵	semidirect
554. C₂⁵	C₂³×D₃	semidirect
586. C₂²×D₄	C₂³×D₃	semidirect
587. C₂²×D₄	C₂³×D₃	semidirect
597. C₂³×C₄	C₂³×D₃	semidirect
625. #120	C₂³×D₃	semidirect
626. #120	C₂³×D₃	semidirect
627. #120	C₂³×D₃	semidirect
649. C₂×C₂²⋊C₄	C₂³×D₃	semidirect
650. C₂×C₂²⋊C₄	C₂³×D₃	semidirect
687. C₂³×C₃	C₂×H(5,𝔽₂)	semidirect
754. C₂⁴	#1004	semidirect
892. C₂³	C₂×#1004	semidirect
920. C₂×C₃	#62817	semidirect
951. C₃	C₂×#62817	semidirect
957. C₂	#11703805	direct (N × H)

Maximal subgroups

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

subgroup	index
#11703805	2
C₂×#85697	2
C₂×#85913	2
C₂×#87239	2
C₂×#85919	2
C₂×#85921	2
C₂³×#953	2
C₂³×C₃×#120	2
C₂×#62817	3

Subgroups — C2×#11703805 #72253511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11703805 #72253511