Subgroups — C₂×#13128883 #16770930

Order 3328.

7910 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128883	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719413	C₂	1	2	yes	maximal, complemented
6	C₂×#11719384	C₂	1	2	yes	maximal, complemented
7	C₂×#11719410	C₂	1	2	yes	maximal, complemented
8	C₂×#11719432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719382	C₂	1	2	yes	maximal, complemented
10	C₂×#11719336	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719316	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719317	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11719381	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11719266	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11719343	C₂	1	2	yes	maximal, complemented
16	C₂×#11719365	C₂	1	2	yes	maximal, complemented
17	C₂×#11719283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11719233	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#11719361	C₂	1	2	yes	maximal, complemented
20	C₂×D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
21	C₂×#11719279	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#11719228	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#6131	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
27	C₂²×#6129	C₂²	1	2	yes	complemented
28	C₂²×D₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²×#6127	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
31	C₁₃×#542	C₂²	1	16	yes	complemented
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×#88200	C₂²	1	1	yes	characteristic
44	C₂×#88200	C₂²	1	2	yes	—
45	C₂×#88200	C₂²	1	2	yes	complemented
46	C₂×#88200	C₂²	1	2	yes	complemented
47	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#88198	C₂²	1	1	yes	characteristic, complemented
49	C₂×#88192	C₂²	1	1	yes	characteristic
50	C₂×#88192	C₂²	1	2	yes	—
51	C₂×#88191	C₂²	1	2	yes	—
52	C₂×#88190	C₂²	1	1	yes	characteristic
53	C₂×#88189	C₂²	1	2	yes	complemented
54	C₂×D₄×Dic₁₃	C₂²	1	1	yes	characteristic
55	C₂×#88183	C₂²	1	2	yes	complemented
56	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
57	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#88178	C₂²	1	2	yes	complemented
61	#11719435	C₂²	1	16	yes	complemented
62	#11719432	C₂²	1	16	yes	complemented
63	#11719413	C₂²	1	32	yes	complemented
64	#11719410	C₂²	1	32	yes	complemented
65	#11719384	C₂²	1	32	yes	complemented
66	#11719382	C₂²	1	32	yes	complemented
67	#11719381	C₂²	1	16	yes	complemented
68	#11719376	C₂²	1	16	yes	complemented
69	#11719365	C₂²	1	32	yes	complemented
70	#11719361	C₂²	1	32	yes	complemented
71	#11719343	C₂²	1	32	yes	complemented
72	#11719340	C₂²	1	16	yes	complemented
73	#11719336	C₂²	1	16	yes	complemented
74	D₁₃×C₂²⋊Q₈	C₂²	1	32	yes	complemented
75	#11719317	C₂²	1	16	yes	complemented
76	#11719316	C₂²	1	16	yes	complemented
77	#11719283	C₂²	1	16	yes	complemented
78	#11719279	C₂²	1	16	yes	complemented
79	#11719266	C₂²	1	16	yes	complemented
80	C₄×D₄×D₁₃	C₂²	1	16	yes	complemented
81	#11719233	C₂²	1	16	yes	complemented
82	#11719228	C₂²	1	16	yes	complemented
83	C₂×#88152	C₂²	1	1	yes	characteristic, complemented
84	C₂×#88151	C₂²	1	1	yes	characteristic
85	C₂×#88151	C₂²	1	2	yes	—
86	C₂×#88151	C₂²	1	1	yes	characteristic, complemented
87	C₂×#88150	C₂²	1	1	yes	characteristic
88	C₂×#88150	C₂²	1	2	yes	—
89	C₂×#88150	C₂²	1	2	yes	complemented
90	C₂×#88150	C₂²	1	2	yes	complemented
91	C₂×#88148	C₂²	1	1	yes	characteristic
92	C₂×#88148	C₂²	1	2	yes	complemented
93	C₂×#88147	C₂²	1	1	yes	characteristic
94	C₂×#88147	C₂²	1	1	yes	characteristic
95	C₂×#88147	C₂²	1	2	yes	—
96	C₂×#88147	C₂²	1	2	yes	complemented
97	C₂×#88146	C₂²	1	2	yes	complemented
98	C₂×C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
99	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
100	C₂×C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
102	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
103	C₂×#88144	C₂²	1	2	yes	complemented
104	C₂×#88143	C₂²	1	1	yes	characteristic, complemented
105	C₂×#88143	C₂²	1	2	yes	complemented
106	C₂×#88143	C₂²	1	2	yes	complemented
107	C₂×#88142	C₂²	1	1	yes	characteristic, complemented
108	C₂×#88142	C₂²	1	1	yes	characteristic, complemented
109	C₂×#88139	C₂²	1	2	yes	complemented
110	C₂×#88139	C₂²	1	1	yes	characteristic, complemented
111	C₂×#88138	C₂²	1	2	yes	—
112	C₂×#88138	C₂²	1	1	yes	characteristic
113	C₂×#88138	C₂²	1	2	yes	complemented
114	C₂×#88137	C₂²	1	2	yes	—
115	C₂×#88137	C₂²	1	2	yes	—
116	C₂×#88137	C₂²	1	1	yes	characteristic
117	C₂×#88137	C₂²	1	2	yes	complemented
118	C₂×#88137	C₂²	1	2	yes	complemented
119	C₂×#88136	C₂²	1	2	yes	—
120	C₂×#88135	C₂²	1	2	yes	—
121	C₂×#88135	C₂²	1	2	yes	—
122	C₂×#88135	C₂²	1	2	yes	complemented
123	C₂×#88135	C₂²	1	2	yes	complemented
124	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
125	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
126	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
127	C₂×#88133	C₂²	1	2	yes	complemented
128	C₂×#88133	C₂²	1	2	yes	complemented
129	C₂×#88133	C₂²	1	2	yes	complemented
130	C₂×#88133	C₂²	1	1	yes	characteristic, complemented
131	C₂×#88132	C₂²	1	2	yes	complemented
132	C₂×#88132	C₂²	1	2	yes	complemented
133	C₂×#88132	C₂²	1	2	yes	complemented
134	C₂×#88131	C₂²	1	2	yes	complemented
135	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
136	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
137	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
138	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
139	C₂×#88126	C₂²	1	2	yes	—
140	C₂×#88126	C₂²	1	1	yes	characteristic, complemented
141	C₂×#88126	C₂²	1	2	yes	complemented
142	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
143	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
146	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₁₃	C₂³	1	2	yes	—
148	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
154	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
156	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
157	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
158	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
159	C₂³×Dic₁₃	C₂³	1	2	yes	—
160	C₂³×Dic₁₃	C₂³	1	2	yes	—
161	C₂×#6131	—	2	8	no	—
162	C₂×#6131	C₂³	1	8	yes	—
163	C₂×Q₈×D₁₃	—	4	8	no	—
164	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
165	C₂×#6129	—	4	8	no	—
166	C₂×#6129	C₂³	1	16	yes	complemented
167	C₂×D₄×D₁₃	—	2	8	no	—
168	C₂×D₄×D₁₃	C₂³	1	8	yes	—
169	C₂×#6127	—	2	8	no	—
170	C₂×#6127	C₂³	1	8	yes	—
171	C₂²×D₅₂	C₂³	1	1	yes	characteristic
172	C₂²×D₅₂	C₂³	1	2	yes	—
173	C₂²×D₅₂	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₁₃	—	4	8	no	—
175	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
179	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
180	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
181	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
182	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
184	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
187	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
188	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
190	C₂²×Dic₂₆	C₂³	1	2	yes	—
191	C₂²×Dic₂₆	C₂³	1	2	yes	—
192	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
193	C₁₃×#126	C₂³	1	16	yes	complemented
194	C₁₃×#124	C₂³	1	8	yes	—
195	C₁₃×#124	C₂³	1	16	yes	complemented
196	C₁₃×#123	C₂³	1	16	yes	complemented
197	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
201	C₄×D₄×C₁₃	C₂³	1	8	yes	—
202	C₁₃×#117	C₂³	1	8	yes	complemented
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
226	#88200	C₂³	1	16	yes	—
227	#88200	C₂³	1	8	yes	—
228	#88200	C₂³	1	16	yes	complemented
229	#88200	C₂³	1	16	yes	complemented
230	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
231	#88198	C₂³	1	8	yes	complemented
232	#88192	C₂³	1	8	yes	—
233	#88192	C₂³	1	16	yes	—
234	#88191	C₂³	1	16	yes	—
235	#88190	C₂³	1	8	yes	—
236	#88189	C₂³	1	16	yes	complemented
237	D₄×Dic₁₃	C₂³	1	8	yes	—
238	#88183	C₂³	1	16	yes	complemented
239	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	—
240	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
241	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
242	C₂×#6103	C₂³	1	2	yes	—
243	C₂×#6103	C₂³	1	2	yes	—
244	C₂×#6103	C₂³	1	2	yes	—
245	C₂×#6103	C₂³	1	1	yes	characteristic
246	C₂×#6103	C₂³	1	2	yes	—
247	C₂×#6103	C₂³	1	1	yes	characteristic
248	C₂×#6103	C₂³	1	1	yes	characteristic
249	C₂×#6103	C₂³	1	2	yes	—
250	C₂×#6103	C₂³	1	1	yes	characteristic
251	C₂×#6103	C₂³	1	1	yes	characteristic
252	C₂×#6103	C₂³	1	2	yes	—
253	C₂×#6103	C₂³	1	1	yes	characteristic
254	C₂×#6103	C₂³	1	2	yes	—
255	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
259	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
261	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
262	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
263	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	complemented
264	#88178	C₂³	1	16	yes	complemented
265	C₂×#6101	C₂³	1	1	yes	characteristic
266	C₂×#6101	C₂³	1	2	yes	—
267	C₂×#6101	C₂³	1	2	yes	—
268	C₂×#6101	C₂³	1	2	yes	—
269	C₂×#6101	C₂³	1	1	yes	characteristic
270	C₂×#6101	C₂³	1	2	yes	—
271	C₂×#6101	C₂³	1	2	yes	—
272	C₂×#6101	C₂³	1	2	yes	—
273	C₂×#6101	C₂³	1	1	yes	characteristic
274	C₂×#6101	C₂³	1	2	yes	—
275	C₂×#6101	C₂³	1	1	yes	characteristic
276	C₂×#6101	C₂³	1	1	yes	characteristic
277	C₂×#6101	C₂³	1	2	yes	—
278	C₂×#6101	C₂³	1	2	yes	—
279	C₂×#6101	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
282	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
285	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
287	#88152	C₂³	1	8	yes	complemented
288	#88151	C₂³	1	8	yes	—
289	#88151	C₂³	1	16	yes	—
290	#88151	C₂³	1	8	yes	complemented
291	#88150	C₂³	1	8	yes	—
292	#88150	C₂³	1	16	yes	—
293	#88150	C₂³	1	16	yes	complemented
294	#88150	C₂³	1	16	yes	complemented
295	#88148	C₂³	1	8	yes	—
296	#88148	C₂³	1	16	yes	complemented
297	#88147	C₂³	1	8	yes	—
298	#88147	C₂³	1	8	yes	—
299	#88147	C₂³	1	16	yes	—
300	#88147	C₂³	1	16	yes	complemented
301	#88146	C₂³	1	16	yes	complemented
302	C₄⋊C₄×D₁₃	C₂³	1	8	yes	—
303	C₄⋊C₄×D₁₃	C₂³	1	8	yes	complemented
304	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
305	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
306	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
307	#88144	C₂³	1	16	yes	complemented
308	#88143	C₂³	1	8	yes	complemented
309	#88143	C₂³	1	16	yes	complemented
310	#88143	C₂³	1	16	yes	complemented
311	#88142	C₂³	1	8	yes	complemented
312	#88142	C₂³	1	8	yes	complemented
313	#88139	C₂³	1	8	yes	complemented
314	#88139	C₂³	1	16	yes	complemented
315	#88138	C₂³	1	8	yes	—
316	#88138	C₂³	1	16	yes	—
317	#88138	C₂³	1	16	yes	complemented
318	#88137	C₂³	1	8	yes	—
319	#88137	C₂³	1	16	yes	—
320	#88137	C₂³	1	16	yes	—
321	#88137	C₂³	1	16	yes	complemented
322	#88137	C₂³	1	16	yes	complemented
323	#88136	C₂³	1	16	yes	—
324	#88135	C₂³	1	16	yes	—
325	#88135	C₂³	1	16	yes	—
326	#88135	C₂³	1	16	yes	complemented
327	#88135	C₂³	1	16	yes	complemented
328	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
329	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
330	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
331	#88133	C₂³	1	8	yes	complemented
332	#88133	C₂³	1	16	yes	complemented
333	#88133	C₂³	1	16	yes	complemented
334	#88133	C₂³	1	16	yes	complemented
335	#88132	C₂³	1	16	yes	complemented
336	#88132	C₂³	1	16	yes	complemented
337	#88132	C₂³	1	16	yes	complemented
338	#88131	C₂³	1	16	yes	complemented
339	C₄×D₅₂	C₂³	1	8	yes	—
340	C₄×D₅₂	C₂³	1	8	yes	—
341	C₄×D₅₂	C₂³	1	8	yes	—
342	C₄×D₅₂	C₂³	1	16	yes	complemented
343	#88126	C₂³	1	16	yes	—
344	#88126	C₂³	1	8	yes	complemented
345	#88126	C₂³	1	16	yes	complemented
346	C₄²×D₁₃	C₂³	1	8	yes	—
347	C₄×Dic₂₆	C₂³	1	8	yes	complemented
348	C₄×Dic₂₆	C₂³	1	8	yes	complemented
349	C₄×Dic₂₆	C₂³	1	8	yes	complemented
350	C₄×Dic₂₆	C₂³	1	16	yes	complemented
351	C₂×#3520	—	13	1	no	maximal, Sylow
352	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
353	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×D₁₃	—	2	8	no	—
355	C₂³×D₁₃	—	2	8	no	—
356	C₂³×D₁₃	—	4	4	no	—
357	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
358	C₂³×D₁₃	C₂⁴	1	8	yes	—
359	C₂³×D₁₃	C₂⁴	1	2	yes	—
360	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₁₃	—	2	4	no	—
362	C₂×Q₈×C₁₃	—	4	4	no	—
363	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
365	C₂×D₄×C₁₃	—	2	4	no	—
366	C₂×D₄×C₁₃	—	4	4	no	—
367	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
368	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₁₃	—	2	4	no	—
370	C₂²×C₄×C₁₃	—	4	4	no	—
371	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
381	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₂²⋊D₁₃	—	2	8	no	—
383	C₂×C₂²⋊D₁₃	—	2	8	no	—
384	C₂×C₂²⋊D₁₃	—	2	4	no	—
385	C₂×C₂²⋊D₁₃	—	2	4	no	—
386	C₂×C₂²⋊D₁₃	—	4	4	no	—
387	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
388	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
389	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
390	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
392	C₂²×Dic₁₃	—	2	8	no	—
393	C₂²×Dic₁₃	—	4	4	no	—
394	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
395	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
399	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
400	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
401	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
404	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
405	#6131	—	2	32	no	—
406	Q₈×D₁₃	—	4	32	no	—
407	#6129	—	4	32	no	—
408	D₄×D₁₃	—	2	32	no	—
409	#6127	—	2	32	no	—
410	C₂×D₅₂	—	2	8	no	—
411	C₂×D₅₂	—	2	4	no	—
412	C₂×D₅₂	#41	1	8	yes	complemented
413	C₂×D₅₂	C₂⁴	1	4	yes	—
414	C₂×D₅₂	C₂⁴	1	8	yes	—
415	C₂×D₅₂	C₂⁴	1	4	yes	—
416	C₂×C₄×D₁₃	—	2	8	no	—
417	C₂×C₄×D₁₃	—	2	8	no	—
418	C₂×C₄×D₁₃	—	2	4	no	—
419	C₂×C₄×D₁₃	—	2	4	no	—
420	C₂×C₄×D₁₃	—	2	4	no	—
421	C₂×C₄×D₁₃	—	2	4	no	—
422	C₂×C₄×D₁₃	—	2	8	no	—
423	C₂×C₄×D₁₃	—	4	32	no	—
424	C₂×C₄×D₁₃	—	4	4	no	—
425	C₂×C₄×D₁₃	—	4	4	no	—
426	C₂×C₄×D₁₃	—	4	4	no	—
427	C₂×C₄×D₁₃	—	4	4	no	—
428	C₂×C₄×D₁₃	—	4	4	no	—
429	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
430	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
431	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
432	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
433	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
434	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
435	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
436	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
437	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
438	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
439	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
440	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
441	C₂×Dic₂₆	—	2	4	no	—
442	C₂×Dic₂₆	—	2	8	no	—
443	C₂×Dic₂₆	—	2	4	no	—
444	C₂×Dic₂₆	—	4	4	no	—
445	C₂×Dic₂₆	C₂⁴	1	4	yes	—
446	C₂×Dic₂₆	C₂⁴	1	4	yes	—
447	C₂×Dic₂₆	C₂⁴	1	8	yes	—
448	C₂×Dic₂₆	C₂⁴	1	8	yes	—
449	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
451	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
452	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
453	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
454	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
455	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
456	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
457	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
458	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
459	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
460	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
461	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
462	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
463	C₄²×C₁₃	C₂⁴	1	4	yes	—
464	C₄²×C₁₃	C₂⁴	1	4	yes	—
465	C₄²×C₁₃	C₂⁴	1	8	yes	—
466	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
467	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
468	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
469	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
470	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
471	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
472	#6103	C₂⁴	1	8	yes	—
473	#6103	C₂⁴	1	8	yes	—
474	#6103	C₂⁴	1	8	yes	—
475	#6103	C₂⁴	1	4	yes	—
476	#6103	C₂⁴	1	8	yes	—
477	#6103	C₂⁴	1	4	yes	—
478	#6103	C₂⁴	1	4	yes	—
479	#6103	C₂⁴	1	8	yes	—
480	#6103	C₂⁴	1	4	yes	—
481	#6103	C₂⁴	1	4	yes	—
482	#6103	C₂⁴	1	8	yes	—
483	#6103	C₂⁴	1	4	yes	—
484	#6103	C₂⁴	1	8	yes	—
485	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
486	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
487	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
488	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
489	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
490	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
491	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
492	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
493	#6101	C₂⁴	1	4	yes	—
494	#6101	C₂⁴	1	8	yes	—
495	#6101	C₂⁴	1	8	yes	—
496	#6101	C₂⁴	1	8	yes	—
497	#6101	C₂⁴	1	4	yes	—
498	#6101	C₂⁴	1	8	yes	—
499	#6101	C₂⁴	1	8	yes	—
500	#6101	C₂⁴	1	8	yes	—
501	#6101	C₂⁴	1	4	yes	—
502	#6101	C₂⁴	1	8	yes	—
503	#6101	C₂⁴	1	4	yes	—
504	#6101	C₂⁴	1	4	yes	—
505	#6101	C₂⁴	1	8	yes	—
506	#6101	C₂⁴	1	8	yes	—
507	#6101	C₂⁴	1	4	yes	—
508	C₄×Dic₁₃	C₂⁴	1	4	yes	—
509	C₄×Dic₁₃	C₂⁴	1	8	yes	—
510	C₄×Dic₁₃	C₂⁴	1	4	yes	—
511	C₄×Dic₁₃	C₂⁴	1	4	yes	—
512	C₄×Dic₁₃	C₂⁴	1	8	yes	—
513	C₄×Dic₁₃	C₂⁴	1	4	yes	—
514	C₄×Dic₁₃	C₂⁴	1	8	yes	—
515	#3520	—	13	32	no	—
516	C₂×#556	—	13	1	no	—
517	C₂×#554	—	13	1	no	—
518	C₂×#554	—	13	1	no	—
519	C₂×#552	—	13	2	no	—
520	C₂×#551	—	13	2	no	—
521	C₂×#551	—	13	2	no	—
522	C₂×D₄×Q₈	—	13	1	no	—
523	C₂×#548	—	13	2	no	—
524	C₂×#547	—	13	1	no	—
525	C₂×#547	—	13	1	no	—
526	C₂×#546	—	13	1	no	—
527	C₂×#546	—	13	1	no	—
528	C₂×#542	—	13	1	no	—
529	C₂×#542	D₁₃	1	1	yes	characteristic, complemented
530	C₂×#539	—	13	2	no	—
531	C₂×#539	—	13	2	no	—
532	C₂×#533	—	13	1	no	—
533	C₂×#529	—	13	1	no	—
534	C₂×#525	—	13	2	no	—
535	C₂²×C₂²⋊Q₈	—	13	2	no	—
536	C₂×#520	—	13	1	no	—
537	C₂×#520	—	13	1	no	—
538	C₂²×C₄×D₄	—	13	1	no	—
539	C₂³×C₁₃	—	2	2	no	—
540	C₂³×C₁₃	—	2	4	no	—
541	C₂³×C₁₃	—	2	4	no	—
542	C₂³×C₁₃	—	2	2	no	—
543	C₂³×C₁₃	—	2	2	no	—
544	C₂³×C₁₃	—	2	4	no	—
545	C₂³×C₁₃	C₂⁵	1	4	yes	—
546	C₂³×C₁₃	C₂⁵	1	2	yes	—
547	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
548	C₂²×D₁₃	—	2	2	no	—
549	C₂²×D₁₃	—	2	4	no	—
550	C₂²×D₁₃	—	2	2	no	—
551	C₂²×D₁₃	—	2	4	no	—
552	C₂²×D₁₃	—	2	2	no	—
553	C₂²×D₁₃	—	2	2	no	—
554	C₂²×D₁₃	—	2	2	no	—
555	C₂²×D₁₃	—	2	16	no	—
556	C₂²×D₁₃	—	2	16	no	—
557	C₂²×D₁₃	—	4	8	no	—
558	C₂²×D₁₃	—	4	32	no	—
559	C₂²×D₁₃	C₂×#41	1	8	yes	—
560	C₂²×D₁₃	2₋¹⁺⁴	1	4	yes	—
561	C₂²×D₁₃	C₂⁵	1	2	yes	—
562	C₂²×D₁₃	C₂⁵	1	4	yes	—
563	C₂²×D₁₃	C₂⁵	1	2	yes	—
564	Q₈×C₁₃	—	2	8	no	—
565	Q₈×C₁₃	—	4	8	no	—
566	D₄×C₁₃	—	2	8	no	—
567	D₄×C₁₃	—	4	8	no	—
568	C₂×C₄×C₁₃	—	2	2	no	—
569	C₂×C₄×C₁₃	—	2	4	no	—
570	C₂×C₄×C₁₃	—	2	4	no	—
571	C₂×C₄×C₁₃	—	2	2	no	—
572	C₂×C₄×C₁₃	—	2	4	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	8	no	—
577	C₂×C₄×C₁₃	—	4	8	no	—
578	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
579	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
580	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
581	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
582	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
583	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
584	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
585	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
586	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
587	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
588	C₂²⋊D₁₃	—	2	16	no	—
589	C₂²⋊D₁₃	—	2	16	no	—
590	C₂²⋊D₁₃	—	2	8	no	—
591	C₂²⋊D₁₃	—	2	8	no	—
592	C₂²⋊D₁₃	—	4	8	no	—
593	C₂×Dic₁₃	—	2	4	no	—
594	C₂×Dic₁₃	—	2	2	no	—
595	C₂×Dic₁₃	—	2	2	no	—
596	C₂×Dic₁₃	—	2	2	no	—
597	C₂×Dic₁₃	—	2	4	no	—
598	C₂×Dic₁₃	—	2	4	no	—
599	C₂×Dic₁₃	—	2	2	no	—
600	C₂×Dic₁₃	—	2	2	no	—
601	C₂×Dic₁₃	—	2	16	no	—
602	C₂×Dic₁₃	—	4	8	no	—
603	C₂×Dic₁₃	H(5,𝔽₂)	1	4	yes	—
604	C₂×Dic₁₃	C₂⁵	1	2	yes	—
605	C₂×Dic₁₃	C₂⁵	1	2	yes	—
606	C₂×Dic₁₃	C₂⁵	1	2	yes	—
607	C₂×Dic₁₃	C₂⁵	1	4	yes	—
608	C₂×Dic₁₃	C₂⁵	1	4	yes	—
609	C₂×Dic₁₃	C₂⁵	1	4	yes	—
610	C₂×Dic₁₃	C₂⁵	1	2	yes	—
611	C₂×Dic₁₃	C₂⁵	1	2	yes	—
612	C₂×Dic₁₃	C₂⁵	1	2	yes	—
613	D₅₂	—	2	16	no	—
614	D₅₂	—	2	8	no	—
615	D₅₂	C₂×#41	1	16	yes	complemented
616	C₄×D₁₃	—	2	16	no	—
617	C₄×D₁₃	—	2	16	no	—
618	C₄×D₁₃	—	2	8	no	—
619	C₄×D₁₃	—	2	8	no	—
620	C₄×D₁₃	—	2	8	no	—
621	C₄×D₁₃	—	2	8	no	—
622	C₄×D₁₃	—	2	16	no	—
623	C₄×D₁₃	—	4	8	no	—
624	C₄×D₁₃	—	4	8	no	—
625	C₄×D₁₃	—	4	8	no	—
626	C₄×D₁₃	—	4	8	no	—
627	C₄×D₁₃	—	4	8	no	—
628	Dic₂₆	—	2	8	no	—
629	Dic₂₆	—	2	16	no	—
630	Dic₂₆	—	2	8	no	—
631	Dic₂₆	—	4	8	no	—
632	C₂²×#41	—	13	1	no	—
633	C₂²×#41	—	13	2	no	—
634	C₂²×#41	—	13	1	no	—
635	C₂³×Q₈	—	13	2	no	—
636	C₂³×D₄	—	13	1	no	—
637	C₂⁴×C₄	—	13	2	no	—
638	#556	—	13	16	no	—
639	#554	—	13	16	no	—
640	#554	—	13	16	no	—
641	#552	—	13	32	no	—
642	#551	—	13	32	no	—
643	#551	—	13	32	no	—
644	D₄×Q₈	—	13	16	no	—
645	#548	—	13	32	no	—
646	#547	—	13	16	no	—
647	#547	—	13	16	no	—
648	#546	—	13	16	no	—
649	#546	—	13	16	no	—
650	#542	—	13	16	no	—
651	#542	C₂×D₁₃	1	16	yes	complemented
652	#539	—	13	32	no	—
653	#539	—	13	32	no	—
654	#533	—	13	16	no	—
655	C₂×C₄⋊Q₈	—	13	1	no	—
656	C₂×C₄⋊Q₈	—	13	1	no	—
657	C₂×C₄⋊Q₈	—	13	1	no	—
658	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
659	#529	—	13	16	no	—
660	C₂×#126	—	13	1	no	—
661	C₂×#126	—	13	1	no	—
662	C₂×#126	—	13	2	no	—
663	C₂×#126	—	13	2	no	—
664	C₂×#126	—	13	2	no	—
665	C₂×#126	C₂×D₁₃	1	2	yes	complemented
666	C₂×#125	—	13	1	no	—
667	C₂×#125	—	13	2	no	—
668	C₂×#125	—	13	2	no	—
669	C₂×#125	—	13	2	no	—
670	C₂×#124	—	13	1	no	—
671	C₂×#124	—	13	1	no	—
672	C₂×#124	—	13	2	no	—
673	C₂×#124	C₂×D₁₃	1	1	yes	characteristic
674	C₂×#124	C₂×D₁₃	1	2	yes	complemented
675	#525	—	13	32	no	—
676	C₂×#123	—	13	2	no	—
677	C₂×#123	—	13	2	no	—
678	C₂×#123	—	13	1	no	—
679	C₂×#123	—	13	2	no	—
680	C₂×#123	—	13	1	no	—
681	C₂×#123	—	13	2	no	—
682	C₂×#123	—	13	2	no	—
683	C₂×#123	—	13	2	no	—
684	C₂×#123	—	13	2	no	—
685	C₂×#123	C₂×D₁₃	1	2	yes	complemented
686	C₂×C₂²⋊Q₈	—	13	2	no	—
687	C₂×C₂²⋊Q₈	—	13	1	no	—
688	C₂×C₂²⋊Q₈	—	13	2	no	—
689	C₂×C₂²⋊Q₈	—	13	2	no	—
690	C₂×C₂²⋊Q₈	—	13	2	no	—
691	C₂×C₂²⋊Q₈	—	13	32	no	—
692	C₂×C₂²⋊Q₈	—	13	1	no	—
693	C₂×C₂²⋊Q₈	—	13	2	no	—
694	C₂×C₂²⋊Q₈	—	13	2	no	—
695	C₂×C₂²⋊Q₈	—	13	2	no	—
696	C₂×C₂²⋊Q₈	—	13	2	no	—
697	C₂×C₂²⋊Q₈	—	13	1	no	—
698	C₂×C₂²⋊Q₈	—	13	1	no	—
699	C₂×C₂²⋊Q₈	—	13	2	no	—
700	C₂×C₂²⋊Q₈	—	13	2	no	—
701	C₂×C₂²⋊Q₈	—	13	2	no	—
702	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
703	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
704	C₂×#121	—	13	2	no	—
705	C₂×#121	—	13	1	no	—
706	C₂×#121	—	13	1	no	—
707	C₂×#121	—	13	2	no	—
708	C₂×#121	—	13	2	no	—
709	C₂×#121	C₂×D₁₃	1	1	yes	characteristic
710	C₂×#120	—	13	2	no	—
711	C₂×#120	—	13	2	no	—
712	#520	—	13	16	no	—
713	#520	—	13	16	no	—
714	C₂×C₄×Q₈	—	13	1	no	—
715	C₂×C₄×Q₈	—	13	1	no	—
716	C₂×C₄×Q₈	—	13	1	no	—
717	C₂×C₄×Q₈	—	13	1	no	—
718	C₂×C₄×Q₈	—	13	2	no	—
719	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
720	C₂×C₄×D₄	—	13	1	no	—
721	C₂×C₄×D₄	—	13	2	no	—
722	C₂×C₄×D₄	—	13	1	no	—
723	C₂×C₄×D₄	—	13	1	no	—
724	C₂×C₄×D₄	—	13	16	no	—
725	C₂×C₄×D₄	—	13	1	no	—
726	C₂×C₄×D₄	—	13	1	no	—
727	C₂×C₄×D₄	—	13	2	no	—
728	C₂×C₄×D₄	—	13	2	no	—
729	C₂×C₄×D₄	—	13	2	no	—
730	C₂×C₄×D₄	—	13	2	no	—
731	C₂×C₄×D₄	—	13	2	no	—
732	C₂×C₄×D₄	—	13	2	no	—
733	C₂×C₄×D₄	—	13	1	no	—
734	C₂×C₄×D₄	—	13	1	no	—
735	C₂×C₄×D₄	—	13	1	no	—
736	C₂×C₄×D₄	—	13	2	no	—
737	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
738	C₂×#117	—	13	2	no	—
739	C₂×#117	—	13	2	no	—
740	C₂×#117	—	13	2	no	—
741	C₂×#117	—	13	1	no	—
742	C₂×#117	—	13	2	no	—
743	C₂×#117	C₂×D₁₃	1	1	yes	characteristic, complemented
744	C₂²×C₄⋊C₄	—	13	1	no	—
745	C₂²×C₄⋊C₄	—	13	1	no	—
746	C₂²×C₄⋊C₄	—	13	2	no	—
747	C₂²×C₄⋊C₄	—	13	2	no	—
748	C₂²×C₄⋊C₄	—	13	1	no	—
749	C₂²×C₄⋊C₄	—	13	2	no	—
750	C₂²×C₂²⋊C₄	—	13	2	no	—
751	C₂²×C₂²⋊C₄	—	13	2	no	—
752	C₂²×C₂²⋊C₄	—	13	2	no	—
753	C₂²×C₄²	—	13	1	no	—
754	C₂²×C₁₃	—	2	2	no	—
755	C₂²×C₁₃	—	2	4	no	—
756	C₂²×C₁₃	—	2	4	no	—
757	C₂²×C₁₃	—	2	2	no	—
758	C₂²×C₁₃	—	2	2	no	—
759	C₂²×C₁₃	—	2	4	no	—
760	C₂²×C₁₃	—	4	8	no	—
761	C₂²×C₁₃	—	4	4	no	—
762	C₂²×C₁₃	C₂²×#41	1	2	yes	—
763	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
764	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
765	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
766	C₂×D₁₃	—	2	2	no	—
767	C₂×D₁₃	—	2	4	no	—
768	C₂×D₁₃	—	2	2	no	—
769	C₂×D₁₃	—	2	4	no	—
770	C₂×D₁₃	—	2	8	no	—
771	C₂×D₁₃	—	2	16	no	—
772	C₂×D₁₃	—	2	2	no	—
773	C₂×D₁₃	—	2	2	no	—
774	C₂×D₁₃	—	2	2	no	—
775	C₂×D₁₃	—	4	32	no	—
776	C₂×D₁₃	—	4	4	no	—
777	C₂×D₁₃	C₂²×#41	1	8	yes	—
778	C₂×D₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
779	C₄×C₁₃	—	2	2	no	—
780	C₄×C₁₃	—	2	4	no	—
781	C₄×C₁₃	—	2	4	no	—
782	C₄×C₁₃	—	2	2	no	—
783	C₄×C₁₃	—	2	4	no	—
784	C₄×C₁₃	—	2	2	no	—
785	C₄×C₁₃	—	2	2	no	—
786	C₄×C₁₃	—	2	2	no	—
787	C₄×C₁₃	C₂²×#41	1	4	yes	—
788	Dic₁₃	—	2	4	no	—
789	Dic₁₃	—	2	2	no	—
790	Dic₁₃	—	2	2	no	—
791	Dic₁₃	—	2	2	no	—
792	Dic₁₃	—	2	4	no	—
793	Dic₁₃	—	2	4	no	—
794	Dic₁₃	—	2	2	no	—
795	Dic₁₃	—	2	2	no	—
796	Dic₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
797	C₂⁵	—	13	2	no	—
798	C₂×#41	—	13	8	no	—
799	C₂×#41	—	13	16	no	—
800	C₂×#41	—	13	8	no	—
801	C₂×#41	—	26	8	no	—
802	C₂×#41	—	26	8	no	—
803	C₂×#41	—	52	8	no	—
804	C₂²×Q₈	—	13	16	no	—
805	C₂²×Q₈	—	13	1	no	—
806	C₂²×Q₈	—	13	1	no	—
807	C₂²×Q₈	—	13	2	no	—
808	C₂²×Q₈	—	13	2	no	—
809	C₂²×Q₈	—	52	8	no	—
810	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
811	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
812	C₂²×D₄	—	13	1	no	—
813	C₂²×D₄	—	13	2	no	—
814	C₂²×D₄	—	13	2	no	—
815	C₂²×D₄	—	13	1	no	—
816	C₂²×D₄	—	13	2	no	—
817	C₂²×D₄	—	13	8	no	—
818	C₂²×D₄	—	13	1	no	—
819	C₂²×D₄	—	13	1	no	—
820	C₂²×D₄	—	13	2	no	—
821	C₂²×D₄	—	26	8	no	—
822	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
823	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
824	C₂³×C₄	—	13	2	no	—
825	C₂³×C₄	—	13	2	no	—
826	C₂³×C₄	—	13	1	no	—
827	C₂³×C₄	—	13	2	no	—
828	C₂³×C₄	—	13	2	no	—
829	C₂³×C₄	—	13	1	no	—
830	C₂³×C₄	—	13	2	no	—
831	C₂³×C₄	—	13	1	no	—
832	C₂³×C₄	—	13	1	no	—
833	C₂³×C₄	—	13	2	no	—
834	C₂³×C₄	—	13	2	no	—
835	C₂³×C₄	—	13	2	no	—
836	C₂³×C₄	—	13	2	no	—
837	C₂³×C₄	—	13	2	no	—
838	C₂³×C₄	—	13	16	no	—
839	C₂³×C₄	—	52	8	no	—
840	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
841	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
842	C₄⋊Q₈	—	13	8	no	—
843	C₄⋊Q₈	—	13	8	no	—
844	C₄⋊Q₈	—	13	8	no	—
845	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
846	#126	—	13	8	no	—
847	#126	—	13	8	no	—
848	#126	—	13	16	no	—
849	#126	—	13	16	no	—
850	#126	—	13	16	no	—
851	#126	C₂²×D₁₃	1	16	yes	complemented
852	#125	—	13	8	no	—
853	#125	—	13	16	no	—
854	#125	—	13	16	no	—
855	#125	—	13	16	no	—
856	#124	—	13	8	no	—
857	#124	—	13	8	no	—
858	#124	—	13	16	no	—
859	#124	C₂²×D₁₃	1	8	yes	—
860	#124	C₂²×D₁₃	1	16	yes	complemented
861	#123	—	13	16	no	—
862	#123	—	13	16	no	—
863	#123	—	13	8	no	—
864	#123	—	13	16	no	—
865	#123	—	13	8	no	—
866	#123	—	13	16	no	—
867	#123	—	13	16	no	—
868	#123	—	13	16	no	—
869	#123	—	13	16	no	—
870	#123	C₂²×D₁₃	1	16	yes	complemented
871	C₂²⋊Q₈	—	13	16	no	—
872	C₂²⋊Q₈	—	13	8	no	—
873	C₂²⋊Q₈	—	13	16	no	—
874	C₂²⋊Q₈	—	13	16	no	—
875	C₂²⋊Q₈	—	13	16	no	—
876	C₂²⋊Q₈	—	13	8	no	—
877	C₂²⋊Q₈	—	13	16	no	—
878	C₂²⋊Q₈	—	13	16	no	—
879	C₂²⋊Q₈	—	13	16	no	—
880	C₂²⋊Q₈	—	13	8	no	—
881	C₂²⋊Q₈	—	13	16	no	—
882	C₂²⋊Q₈	—	13	8	no	—
883	C₂²⋊Q₈	—	13	16	no	—
884	C₂²⋊Q₈	—	13	16	no	—
885	C₂²⋊Q₈	—	13	16	no	—
886	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
887	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
888	#121	—	13	16	no	—
889	#121	—	13	8	no	—
890	#121	—	13	8	no	—
891	#121	—	13	16	no	—
892	#121	—	13	16	no	—
893	#121	C₂²×D₁₃	1	8	yes	—
894	#120	—	13	16	no	—
895	#120	—	13	16	no	—
896	C₄×Q₈	—	13	8	no	—
897	C₄×Q₈	—	13	8	no	—
898	C₄×Q₈	—	13	8	no	—
899	C₄×Q₈	—	13	8	no	—
900	C₄×Q₈	—	13	16	no	—
901	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
902	C₄×D₄	—	13	8	no	—
903	C₄×D₄	—	13	16	no	—
904	C₄×D₄	—	13	8	no	—
905	C₄×D₄	—	13	8	no	—
906	C₄×D₄	—	13	8	no	—
907	C₄×D₄	—	13	16	no	—
908	C₄×D₄	—	13	8	no	—
909	C₄×D₄	—	13	16	no	—
910	C₄×D₄	—	13	16	no	—
911	C₄×D₄	—	13	16	no	—
912	C₄×D₄	—	13	16	no	—
913	C₄×D₄	—	13	16	no	—
914	C₄×D₄	—	13	8	no	—
915	C₄×D₄	—	13	8	no	—
916	C₄×D₄	—	13	16	no	—
917	C₄×D₄	—	13	8	no	—
918	C₄×D₄	C₂²×D₁₃	1	8	yes	—
919	#117	—	13	16	no	—
920	#117	—	13	16	no	—
921	#117	—	13	8	no	—
922	#117	—	13	16	no	—
923	#117	—	13	16	no	—
924	#117	C₂²×D₁₃	1	8	yes	complemented
925	C₂×C₄⋊C₄	—	13	1	no	—
926	C₂×C₄⋊C₄	—	13	1	no	—
927	C₂×C₄⋊C₄	—	13	2	no	—
928	C₂×C₄⋊C₄	—	13	2	no	—
929	C₂×C₄⋊C₄	—	13	1	no	—
930	C₂×C₄⋊C₄	—	13	2	no	—
931	C₂×C₄⋊C₄	—	13	2	no	—
932	C₂×C₄⋊C₄	—	13	1	no	—
933	C₂×C₄⋊C₄	—	13	2	no	—
934	C₂×C₄⋊C₄	—	13	2	no	—
935	C₂×C₄⋊C₄	—	13	2	no	—
936	C₂×C₄⋊C₄	—	13	8	no	—
937	C₂×C₄⋊C₄	—	13	2	no	—
938	C₂×C₄⋊C₄	—	13	1	no	—
939	C₂×C₄⋊C₄	—	13	1	no	—
940	C₂×C₄⋊C₄	—	13	2	no	—
941	C₂×C₄⋊C₄	—	13	2	no	—
942	C₂×C₄⋊C₄	—	13	2	no	—
943	C₂×C₄⋊C₄	—	13	1	no	—
944	C₂×C₄⋊C₄	—	13	1	no	—
945	C₂×C₄⋊C₄	—	13	2	no	—
946	C₂×C₄⋊C₄	—	13	2	no	—
947	C₂×C₄⋊C₄	—	13	1	no	—
948	C₂×C₄⋊C₄	—	13	1	no	—
949	C₂×C₄⋊C₄	—	13	8	no	—
950	C₂×C₄⋊C₄	—	13	16	no	—
951	C₂×C₄⋊C₄	—	13	16	no	—
952	C₂×C₄⋊C₄	—	13	8	no	—
953	C₂×C₄⋊C₄	—	13	16	no	—
954	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
958	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
959	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
961	C₂×C₂²⋊C₄	—	13	2	no	—
962	C₂×C₂²⋊C₄	—	13	2	no	—
963	C₂×C₂²⋊C₄	—	13	2	no	—
964	C₂×C₂²⋊C₄	—	13	2	no	—
965	C₂×C₂²⋊C₄	—	13	1	no	—
966	C₂×C₂²⋊C₄	—	13	1	no	—
967	C₂×C₂²⋊C₄	—	13	1	no	—
968	C₂×C₂²⋊C₄	—	13	1	no	—
969	C₂×C₂²⋊C₄	—	13	2	no	—
970	C₂×C₂²⋊C₄	—	13	2	no	—
971	C₂×C₂²⋊C₄	—	13	2	no	—
972	C₂×C₂²⋊C₄	—	13	2	no	—
973	C₂×C₂²⋊C₄	—	13	2	no	—
974	C₂×C₂²⋊C₄	—	13	2	no	—
975	C₂×C₂²⋊C₄	—	13	1	no	—
976	C₂×C₂²⋊C₄	—	13	1	no	—
977	C₂×C₂²⋊C₄	—	13	1	no	—
978	C₂×C₂²⋊C₄	—	13	2	no	—
979	C₂×C₂²⋊C₄	—	13	1	no	—
980	C₂×C₂²⋊C₄	—	13	16	no	—
981	C₂×C₂²⋊C₄	—	13	16	no	—
982	C₂×C₂²⋊C₄	—	13	16	no	—
983	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
984	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
985	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
986	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
987	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
988	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
990	C₂×C₄²	—	13	2	no	—
991	C₂×C₄²	—	13	2	no	—
992	C₂×C₄²	—	13	2	no	—
993	C₂×C₄²	—	13	1	no	—
994	C₂×C₄²	—	13	1	no	—
995	C₂×C₄²	—	13	1	no	—
996	C₂×C₄²	—	13	1	no	—
997	C₂×C₄²	—	13	8	no	—
998	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
999	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
1000	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
1001	C₂×C₁₃	—	4	4	no	—
1002	C₂×C₁₃	—	4	2	no	—
1003	C₂×C₁₃	#3520	1	4	yes	complemented
1004	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
1005	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1006	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
1007	D₁₃	—	2	4	no	—
1008	D₁₃	—	2	8	no	—
1009	D₁₃	—	4	2	no	—
1010	C₂⁴	—	13	1	no	—
1011	C₂⁴	—	13	2	no	—
1012	C₂⁴	—	13	1	no	—
1013	C₂⁴	—	13	8	no	—
1014	C₂⁴	—	26	8	no	—
1015	C₂⁴	—	26	8	no	—
1016	C₂⁴	—	52	4	no	—
1017	C₂⁴	C₂³×D₁₃	1	2	yes	—
1018	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
1019	#41	—	26	32	no	—
1020	#41	—	26	32	no	—
1021	#41	—	52	32	no	—
1022	C₂×Q₈	—	2	4	no	—
1023	C₂×Q₈	—	4	4	no	—
1024	C₂×Q₈	—	13	4	no	—
1025	C₂×Q₈	—	13	4	no	—
1026	C₂×Q₈	—	13	8	no	—
1027	C₂×Q₈	—	13	8	no	—
1028	C₂×Q₈	—	26	4	no	—
1029	C₂×Q₈	—	26	8	no	—
1030	C₂×Q₈	—	26	4	no	—
1031	C₂×Q₈	—	52	4	no	—
1032	C₂×Q₈	—	52	32	no	—
1033	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
1034	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
1035	C₂×D₄	—	2	4	no	—
1036	C₂×D₄	—	4	4	no	—
1037	C₂×D₄	—	13	4	no	—
1038	C₂×D₄	—	13	8	no	—
1039	C₂×D₄	—	13	8	no	—
1040	C₂×D₄	—	13	4	no	—
1041	C₂×D₄	—	13	8	no	—
1042	C₂×D₄	—	13	8	no	—
1043	C₂×D₄	—	13	4	no	—
1044	C₂×D₄	—	13	4	no	—
1045	C₂×D₄	—	13	8	no	—
1046	C₂×D₄	—	26	8	no	—
1047	C₂×D₄	—	26	4	no	—
1048	C₂×D₄	—	26	4	no	—
1049	C₂×D₄	—	26	32	no	—
1050	C₂×D₄	—	26	8	no	—
1051	C₂×D₄	—	26	8	no	—
1052	C₂×D₄	—	26	4	no	—
1053	C₂×D₄	—	52	4	no	—
1054	C₂×D₄	C₂³×D₁₃	1	4	yes	—
1055	C₂×D₄	C₂³×D₁₃	1	8	yes	—
1056	C₂²×C₄	—	2	4	no	—
1057	C₂²×C₄	—	4	4	no	—
1058	C₂²×C₄	—	13	1	no	—
1059	C₂²×C₄	—	13	8	no	—
1060	C₂²×C₄	—	13	1	no	—
1061	C₂²×C₄	—	13	1	no	—
1062	C₂²×C₄	—	13	2	no	—
1063	C₂²×C₄	—	13	1	no	—
1064	C₂²×C₄	—	13	2	no	—
1065	C₂²×C₄	—	13	1	no	—
1066	C₂²×C₄	—	13	2	no	—
1067	C₂²×C₄	—	13	1	no	—
1068	C₂²×C₄	—	13	8	no	—
1069	C₂²×C₄	—	13	4	no	—
1070	C₂²×C₄	—	13	4	no	—
1071	C₂²×C₄	—	13	4	no	—
1072	C₂²×C₄	—	13	8	no	—
1073	C₂²×C₄	—	13	8	no	—
1074	C₂²×C₄	—	13	4	no	—
1075	C₂²×C₄	—	13	8	no	—
1076	C₂²×C₄	—	13	8	no	—
1077	C₂²×C₄	—	13	8	no	—
1078	C₂²×C₄	—	13	8	no	—
1079	C₂²×C₄	—	13	8	no	—
1080	C₂²×C₄	—	13	8	no	—
1081	C₂²×C₄	—	26	4	no	—
1082	C₂²×C₄	—	26	8	no	—
1083	C₂²×C₄	—	26	8	no	—
1084	C₂²×C₄	—	26	8	no	—
1085	C₂²×C₄	—	26	4	no	—
1086	C₂²×C₄	—	26	8	no	—
1087	C₂²×C₄	—	26	4	no	—
1088	C₂²×C₄	—	26	4	no	—
1089	C₂²×C₄	—	52	4	no	—
1090	C₂²×C₄	—	52	4	no	—
1091	C₂²×C₄	—	52	4	no	—
1092	C₂²×C₄	—	52	4	no	—
1093	C₂²×C₄	—	52	4	no	—
1094	C₂²×C₄	—	52	32	no	—
1095	C₂²×C₄	—	52	4	no	—
1096	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
1097	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1098	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1099	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1100	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1101	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1103	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1104	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1105	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
1106	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1107	C₄⋊C₄	—	13	4	no	—
1108	C₄⋊C₄	—	13	4	no	—
1109	C₄⋊C₄	—	13	8	no	—
1110	C₄⋊C₄	—	13	8	no	—
1111	C₄⋊C₄	—	13	4	no	—
1112	C₄⋊C₄	—	13	8	no	—
1113	C₄⋊C₄	—	13	8	no	—
1114	C₄⋊C₄	—	13	4	no	—
1115	C₄⋊C₄	—	13	8	no	—
1116	C₄⋊C₄	—	13	8	no	—
1117	C₄⋊C₄	—	13	8	no	—
1118	C₄⋊C₄	—	13	8	no	—
1119	C₄⋊C₄	—	13	4	no	—
1120	C₄⋊C₄	—	13	4	no	—
1121	C₄⋊C₄	—	13	8	no	—
1122	C₄⋊C₄	—	13	8	no	—
1123	C₄⋊C₄	—	13	8	no	—
1124	C₄⋊C₄	—	13	4	no	—
1125	C₄⋊C₄	—	13	4	no	—
1126	C₄⋊C₄	—	13	8	no	—
1127	C₄⋊C₄	—	13	8	no	—
1128	C₄⋊C₄	—	13	4	no	—
1129	C₄⋊C₄	—	13	4	no	—
1130	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1131	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1132	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1133	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1134	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1135	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1136	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1137	C₂²⋊C₄	—	13	8	no	—
1138	C₂²⋊C₄	—	13	8	no	—
1139	C₂²⋊C₄	—	13	8	no	—
1140	C₂²⋊C₄	—	13	8	no	—
1141	C₂²⋊C₄	—	13	4	no	—
1142	C₂²⋊C₄	—	13	4	no	—
1143	C₂²⋊C₄	—	13	4	no	—
1144	C₂²⋊C₄	—	13	4	no	—
1145	C₂²⋊C₄	—	13	8	no	—
1146	C₂²⋊C₄	—	13	8	no	—
1147	C₂²⋊C₄	—	13	8	no	—
1148	C₂²⋊C₄	—	13	8	no	—
1149	C₂²⋊C₄	—	13	8	no	—
1150	C₂²⋊C₄	—	13	8	no	—
1151	C₂²⋊C₄	—	13	4	no	—
1152	C₂²⋊C₄	—	13	4	no	—
1153	C₂²⋊C₄	—	13	4	no	—
1154	C₂²⋊C₄	—	13	8	no	—
1155	C₂²⋊C₄	—	13	4	no	—
1156	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1157	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1158	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1159	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1160	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
1161	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
1162	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1163	C₄²	—	13	4	no	—
1164	C₄²	—	13	4	no	—
1165	C₄²	—	13	4	no	—
1166	C₄²	—	13	8	no	—
1167	C₄²	—	13	8	no	—
1168	C₄²	—	13	8	no	—
1169	C₄²	—	13	4	no	—
1170	C₄²	C₂³×D₁₃	1	4	yes	—
1171	C₄²	C₂³×D₁₃	1	8	yes	—
1172	C₄²	C₂³×D₁₃	1	4	yes	—
1173	C₁₃	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
1174	C₂³	—	2	2	no	—
1175	C₂³	—	2	4	no	—
1176	C₂³	—	2	4	no	—
1177	C₂³	—	2	2	no	—
1178	C₂³	—	2	2	no	—
1179	C₂³	—	2	4	no	—
1180	C₂³	—	13	8	no	—
1181	C₂³	—	13	4	no	—
1182	C₂³	—	13	2	no	—
1183	C₂³	—	13	4	no	—
1184	C₂³	—	13	2	no	—
1185	C₂³	—	26	16	no	—
1186	C₂³	—	26	16	no	—
1187	C₂³	—	26	2	no	—
1188	C₂³	—	26	4	no	—
1189	C₂³	—	26	2	no	—
1190	C₂³	—	26	4	no	—
1191	C₂³	—	26	2	no	—
1192	C₂³	—	26	2	no	—
1193	C₂³	—	26	2	no	—
1194	C₂³	—	52	8	no	—
1195	C₂³	—	52	32	no	—
1196	C₂³	C₂⁴×D₁₃	1	4	yes	—
1197	C₂³	C₂⁴×D₁₃	1	2	yes	—
1198	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
1199	Q₈	—	2	8	no	—
1200	Q₈	—	4	8	no	—
1201	Q₈	—	26	8	no	—
1202	Q₈	—	26	16	no	—
1203	Q₈	—	26	8	no	—
1204	Q₈	—	52	8	no	—
1205	D₄	—	2	8	no	—
1206	D₄	—	4	8	no	—
1207	D₄	—	13	16	no	—
1208	D₄	—	26	8	no	—
1209	D₄	—	26	16	no	—
1210	D₄	—	26	8	no	—
1211	D₄	—	26	8	no	—
1212	D₄	—	26	16	no	—
1213	D₄	—	26	16	no	—
1214	D₄	—	52	8	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	4	no	—
1217	C₂×C₄	—	2	2	no	—
1218	C₂×C₄	—	2	4	no	—
1219	C₂×C₄	—	2	4	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	8	no	—
1224	C₂×C₄	—	4	8	no	—
1225	C₂×C₄	—	13	4	no	—
1226	C₂×C₄	—	13	2	no	—
1227	C₂×C₄	—	13	2	no	—
1228	C₂×C₄	—	13	2	no	—
1229	C₂×C₄	—	13	4	no	—
1230	C₂×C₄	—	13	2	no	—
1231	C₂×C₄	—	13	4	no	—
1232	C₂×C₄	—	13	2	no	—
1233	C₂×C₄	—	13	4	no	—
1234	C₂×C₄	—	13	2	no	—
1235	C₂×C₄	—	26	8	no	—
1236	C₂×C₄	—	26	16	no	—
1237	C₂×C₄	—	26	8	no	—
1238	C₂×C₄	—	26	16	no	—
1239	C₂×C₄	—	26	16	no	—
1240	C₂×C₄	—	26	16	no	—
1241	C₂×C₄	—	26	2	no	—
1242	C₂×C₄	—	26	2	no	—
1243	C₂×C₄	—	26	4	no	—
1244	C₂×C₄	—	26	4	no	—
1245	C₂×C₄	—	26	4	no	—
1246	C₂×C₄	—	26	2	no	—
1247	C₂×C₄	—	26	2	no	—
1248	C₂×C₄	—	26	2	no	—
1249	C₂×C₄	—	26	8	no	—
1250	C₂×C₄	—	26	8	no	—
1251	C₂×C₄	—	52	8	no	—
1252	C₂×C₄	—	52	8	no	—
1253	C₂×C₄	—	52	8	no	—
1254	C₂×C₄	—	52	8	no	—
1255	C₂×C₄	—	52	8	no	—
1256	C₂×C₄	—	52	8	no	—
1257	C₂×C₄	#41×D₁₃	1	4	yes	—
1258	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1259	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1260	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1261	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1262	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1263	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1264	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1265	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1266	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	2	4	no	—
1269	C₂²	—	2	4	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	4	no	—
1273	C₂²	—	4	4	no	—
1274	C₂²	—	4	8	no	—
1275	C₂²	—	13	8	no	—
1276	C₂²	—	13	4	no	—
1277	C₂²	—	26	2	no	—
1278	C₂²	—	26	4	no	—
1279	C₂²	—	26	2	no	—
1280	C₂²	—	26	4	no	—
1281	C₂²	—	26	16	no	—
1282	C₂²	—	26	8	no	—
1283	C₂²	—	26	2	no	—
1284	C₂²	—	26	2	no	—
1285	C₂²	—	26	2	no	—
1286	C₂²	—	52	32	no	—
1287	C₂²	—	52	4	no	—
1288	C₂²	C₂×#41×D₁₃	1	2	yes	—
1289	C₂²	D₁₃×H(5,𝔽₂)	1	2	yes	—
1290	C₂²	D₁₃×2₋¹⁺⁴	1	2	yes	—
1291	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
1292	C₄	—	2	2	no	—
1293	C₄	—	2	4	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	2	4	no	—
1297	C₄	—	2	2	no	—
1298	C₄	—	2	2	no	—
1299	C₄	—	2	2	no	—
1300	C₄	—	13	4	no	—
1301	C₄	—	26	2	no	—
1302	C₄	—	26	2	no	—
1303	C₄	—	26	4	no	—
1304	C₄	—	26	4	no	—
1305	C₄	—	26	4	no	—
1306	C₄	—	26	2	no	—
1307	C₄	—	26	2	no	—
1308	C₄	—	26	2	no	—
1309	C₄	C₂×#41×D₁₃	1	4	yes	—
1310	C₂	—	4	4	no	—
1311	C₂	—	4	2	no	—
1312	C₂	—	26	4	no	—
1313	C₂	—	26	8	no	—
1314	C₂	—	52	2	no	—
1315	C₂	#13128883	1	4	yes	direct product factor
1316	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
1317	C₂	C₂×D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1318	C₂	C₂×D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#542	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#542	D₁₃
hypocenter	C₁₃	C₂×#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #13128883	C₂	direct (N × H)
2. C₂×#11719376	C₂	semidirect
3. C₂×#11719435	C₂	semidirect
4. C₂×#11719340	C₂	semidirect
5. C₂×#11719413	C₂	semidirect
6. C₂×#11719384	C₂	semidirect
7. C₂×#11719410	C₂	semidirect
8. C₂×#11719432	C₂	semidirect
9. C₂×#11719382	C₂	semidirect
10. C₂×#11719336	C₂	semidirect
11. C₂×#11719316	C₂	semidirect
12. C₂×#11719317	C₂	semidirect
13. C₂×#11719381	C₂	semidirect
14. C₂×#11719266	C₂	semidirect
15. C₂×#11719343	C₂	semidirect
16. C₂×#11719365	C₂	semidirect
17. C₂×#11719283	C₂	semidirect
18. C₂×#11719233	C₂	semidirect
19. C₂×#11719361	C₂	semidirect
20. C₂×D₁₃×C₂²⋊Q₈	C₂	semidirect
21. C₂×#11719279	C₂	semidirect
22. C₂×#11719228	C₂	semidirect
23. C₂×C₄×D₄×D₁₃	C₂	semidirect
24. C₂×C₁₃×#542	C₂	semidirect
26. C₂²×Q₈×D₁₃	C₂²	semidirect
27. C₂²×#6129	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#126	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
36. C₂×C₁₃×#123	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
42. C₂×C₁₃×#117	C₂²	semidirect
45. C₂×#88200	C₂²	semidirect
46. C₂×#88200	C₂²	semidirect
47. C₂×Q₈×Dic₁₃	C₂²	semidirect
48. C₂×#88198	C₂²	semidirect
53. C₂×#88189	C₂²	semidirect
55. C₂×#88183	C₂²	semidirect
58. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
59. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
60. C₂×#88178	C₂²	semidirect
61. #11719435	C₂²	semidirect
62. #11719432	C₂²	semidirect
63. #11719413	C₂²	semidirect
64. #11719410	C₂²	semidirect
65. #11719384	C₂²	semidirect
66. #11719382	C₂²	semidirect
67. #11719381	C₂²	semidirect
68. #11719376	C₂²	semidirect
69. #11719365	C₂²	semidirect
70. #11719361	C₂²	semidirect
71. #11719343	C₂²	semidirect
72. #11719340	C₂²	semidirect
73. #11719336	C₂²	semidirect
74. D₁₃×C₂²⋊Q₈	C₂²	semidirect
75. #11719317	C₂²	semidirect
76. #11719316	C₂²	semidirect
77. #11719283	C₂²	semidirect
78. #11719279	C₂²	semidirect
79. #11719266	C₂²	semidirect
80. C₄×D₄×D₁₃	C₂²	semidirect
81. #11719233	C₂²	semidirect
82. #11719228	C₂²	semidirect
83. C₂×#88152	C₂²	semidirect
86. C₂×#88151	C₂²	semidirect
89. C₂×#88150	C₂²	semidirect
90. C₂×#88150	C₂²	semidirect
92. C₂×#88148	C₂²	semidirect
96. C₂×#88147	C₂²	semidirect
97. C₂×#88146	C₂²	semidirect
99. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
100. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
101. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
102. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
103. C₂×#88144	C₂²	semidirect
104. C₂×#88143	C₂²	semidirect
105. C₂×#88143	C₂²	semidirect
106. C₂×#88143	C₂²	semidirect
107. C₂×#88142	C₂²	semidirect
108. C₂×#88142	C₂²	semidirect
109. C₂×#88139	C₂²	semidirect
110. C₂×#88139	C₂²	semidirect
113. C₂×#88138	C₂²	semidirect
117. C₂×#88137	C₂²	semidirect
118. C₂×#88137	C₂²	semidirect
122. C₂×#88135	C₂²	semidirect
123. C₂×#88135	C₂²	semidirect
127. C₂×#88133	C₂²	semidirect
128. C₂×#88133	C₂²	semidirect
129. C₂×#88133	C₂²	semidirect
130. C₂×#88133	C₂²	semidirect
131. C₂×#88132	C₂²	semidirect
132. C₂×#88132	C₂²	semidirect
133. C₂×#88132	C₂²	semidirect
134. C₂×#88131	C₂²	semidirect
138. C₂×C₄×D₅₂	C₂²	semidirect
140. C₂×#88126	C₂²	semidirect
141. C₂×#88126	C₂²	semidirect
143. C₂×C₄×Dic₂₆	C₂²	semidirect
144. C₂×C₄×Dic₂₆	C₂²	semidirect
145. C₂×C₄×Dic₂₆	C₂²	semidirect
146. C₂×C₄×Dic₂₆	C₂²	semidirect
164. C₂×Q₈×D₁₃	C₂³	semidirect
166. C₂×#6129	C₂³	semidirect
192. C₁₃×C₄⋊Q₈	C₂³	semidirect
193. C₁₃×#126	C₂³	semidirect
195. C₁₃×#124	C₂³	semidirect
196. C₁₃×#123	C₂³	semidirect
197. C₁₃×C₂²⋊Q₈	C₂³	semidirect
198. C₁₃×C₂²⋊Q₈	C₂³	semidirect
200. C₄×Q₈×C₁₃	C₂³	semidirect
202. C₁₃×#117	C₂³	semidirect
228. #88200	C₂³	semidirect
229. #88200	C₂³	semidirect
230. Q₈×Dic₁₃	C₂³	semidirect
231. #88198	C₂³	semidirect
236. #88189	C₂³	semidirect
238. #88183	C₂³	semidirect
241. C₄×C₂²⋊D₁₃	C₂³	semidirect
263. C₂×C₄⋊Dic₁₃	C₂³	semidirect
264. #88178	C₂³	semidirect
287. #88152	C₂³	semidirect
290. #88151	C₂³	semidirect
293. #88150	C₂³	semidirect
294. #88150	C₂³	semidirect
296. #88148	C₂³	semidirect
300. #88147	C₂³	semidirect
301. #88146	C₂³	semidirect
303. C₄⋊C₄×D₁₃	C₂³	semidirect
304. C₄⋊C₄×D₁₃	C₂³	semidirect
305. C₄⋊C₄×D₁₃	C₂³	semidirect
306. C₄⋊C₄×D₁₃	C₂³	semidirect
307. #88144	C₂³	semidirect
308. #88143	C₂³	semidirect
309. #88143	C₂³	semidirect
310. #88143	C₂³	semidirect
311. #88142	C₂³	semidirect
312. #88142	C₂³	semidirect
313. #88139	C₂³	semidirect
314. #88139	C₂³	semidirect
317. #88138	C₂³	semidirect
321. #88137	C₂³	semidirect
322. #88137	C₂³	semidirect
326. #88135	C₂³	semidirect
327. #88135	C₂³	semidirect
331. #88133	C₂³	semidirect
332. #88133	C₂³	semidirect
333. #88133	C₂³	semidirect
334. #88133	C₂³	semidirect
335. #88132	C₂³	semidirect
336. #88132	C₂³	semidirect
337. #88132	C₂³	semidirect
338. #88131	C₂³	semidirect
342. C₄×D₅₂	C₂³	semidirect
344. #88126	C₂³	semidirect
345. #88126	C₂³	semidirect
347. C₄×Dic₂₆	C₂³	semidirect
348. C₄×Dic₂₆	C₂³	semidirect
349. C₄×Dic₂₆	C₂³	semidirect
350. C₄×Dic₂₆	C₂³	semidirect
412. C₂×D₅₂	#41	semidirect
529. C₂×#542	D₁₃	semidirect
615. D₅₂	C₂×#41	semidirect
651. #542	C₂×D₁₃	semidirect
658. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
665. C₂×#126	C₂×D₁₃	semidirect
674. C₂×#124	C₂×D₁₃	semidirect
685. C₂×#123	C₂×D₁₃	semidirect
702. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
703. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
719. C₂×C₄×Q₈	C₂×D₁₃	semidirect
743. C₂×#117	C₂×D₁₃	semidirect
845. C₄⋊Q₈	C₂²×D₁₃	semidirect
851. #126	C₂²×D₁₃	semidirect
860. #124	C₂²×D₁₃	semidirect
870. #123	C₂²×D₁₃	semidirect
886. C₂²⋊Q₈	C₂²×D₁₃	semidirect
887. C₂²⋊Q₈	C₂²×D₁₃	semidirect
901. C₄×Q₈	C₂²×D₁₃	semidirect
924. #117	C₂²×D₁₃	semidirect
1003. C₂×C₁₃	#3520	semidirect
1173. C₁₃	C₂×#3520	semidirect
1315. C₂	#13128883	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128883	2
C₂×#11719376	2
C₂×#11719435	2
C₂×#11719340	2
C₂×#11719413	2
C₂×#11719384	2
C₂×#11719410	2
C₂×#11719432	2
C₂×#11719382	2
C₂×#11719336	2
C₂×#11719316	2
C₂×#11719317	2
C₂×#11719381	2
C₂×#11719266	2
C₂×#11719343	2
C₂×#11719365	2
C₂×#11719283	2
C₂×#11719233	2
C₂×#11719361	2
C₂×D₁₃×C₂²⋊Q₈	2
C₂×#11719279	2
C₂×#11719228	2
C₂×C₄×D₄×D₁₃	2
C₂×C₁₃×#542	2
C₂×#3520	13

Subgroups — C2×#13128883 #16770930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128883 #16770930