Subgroups — C₁₃×#22434 #15708773

Order 3328.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#550	C₄	1	1	yes	characteristic, complemented
21	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
22	C₁₃×#548	C₄	1	1	yes	characteristic, complemented
23	C₁₃×#548	C₄	1	1	yes	characteristic, complemented
24	C₁₃×#547	—	2	1	no	—
25	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
26	C₁₃×#546	—	2	1	no	—
27	C₁₃×#546	—	2	1	no	—
28	C₁₃×#546	C₄	1	1	yes	characteristic, complemented
29	C₁₃×#546	C₄	1	1	yes	characteristic, complemented
30	D₄²×C₁₃	—	2	1	no	—
31	D₄²×C₁₃	C₄	1	1	yes	characteristic, complemented
32	C₁₃×#532	—	2	1	no	—
33	C₁₃×#532	C₂²	1	1	yes	characteristic
34	C₁₃×#525	—	2	1	no	—
35	C₁₃×#525	—	2	1	no	—
36	C₁₃×#525	C₂²	1	1	yes	characteristic
37	C₁₃×#525	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	—	2	1	no	—
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#436	—	2	1	no	—
44	C₁₃×#435	—	2	1	no	—
45	C₁₃×#435	—	2	1	no	—
46	C₈×D₄×C₁₃	—	2	1	no	—
47	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#421	—	2	4	no	—
49	C₂×C₁₃×#104	—	2	4	no	—
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#388	—	2	1	no	—
66	C₁₃×#387	—	2	1	no	—
67	C₁₃×#386	—	2	1	no	—
68	C₁₃×#385	—	2	1	no	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	1	no	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	2	no	—
83	C₂×C₁₃×#41	—	2	2	no	—
84	C₂×C₁₃×#41	—	2	2	no	—
85	C₂×C₁₃×#41	—	4	1	no	—
86	C₂×C₁₃×#41	—	4	1	no	—
87	C₂×C₁₃×#41	—	4	1	no	—
88	C₂×C₁₃×#41	—	4	1	no	—
89	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
91	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
103	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	—	2	1	no	—
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×M₁₆	—	2	1	no	—
110	C₂×C₁₃×M₁₆	—	2	1	no	—
111	C₂×C₁₃×M₁₆	—	2	2	no	—
112	C₂×C₁₃×M₁₆	—	2	2	no	—
113	C₂×C₁₃×M₁₆	—	4	1	no	—
114	C₂×C₁₃×M₁₆	—	4	1	no	—
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	—	2	1	no	—
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₁₃×C₄⋊Q₈	—	2	1	no	—
122	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
123	C₁₃×#127	—	2	1	no	—
124	C₁₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
128	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
129	C₁₃×#123	—	2	1	no	—
130	C₁₃×#123	—	2	1	no	—
131	C₁₃×#123	—	2	1	no	—
132	C₁₃×#123	—	2	1	no	—
133	C₁₃×#123	—	2	1	no	—
134	C₁₃×#123	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
140	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
141	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
142	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
143	C₁₃×#121	—	2	1	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
154	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
155	C₁₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
156	C₁₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
157	C₁₃×#120	—	2	1	no	—
158	C₁₃×#120	—	2	1	no	—
159	C₁₃×#120	—	2	1	no	—
160	C₁₃×#120	—	2	1	no	—
161	C₁₃×#120	—	2	1	no	—
162	C₁₃×#120	—	2	1	no	—
163	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
164	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
182	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
183	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	4	1	no	—
190	C₁₃×#117	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	—	2	1	no	—
203	C₂×C₄²×C₁₃	—	2	2	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	4	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×C₄⋊C₈	—	2	1	no	—
212	C₁₃×C₄⋊C₈	—	2	1	no	—
213	C₁₃×#104	—	2	2	no	—
214	C₁₃×#104	—	2	2	no	—
215	C₁₃×#104	—	2	2	no	—
216	C₁₃×#104	—	2	2	no	—
217	C₁₃×#104	—	2	2	no	—
218	C₁₃×#104	—	2	2	no	—
219	C₁₃×#104	—	2	2	no	—
220	C₁₃×#104	—	4	1	no	—
221	C₁₃×#104	—	4	1	no	—
222	C₁₃×#104	—	4	1	no	—
223	C₁₃×#104	—	4	1	no	—
224	C₁₃×#104	D₄	1	4	yes	complemented
225	C₁₃×C₂²⋊C₈	—	2	1	no	—
226	C₁₃×C₂²⋊C₈	—	2	1	no	—
227	C₁₃×C₂²⋊C₈	—	2	1	no	—
228	C₁₃×C₂²⋊C₈	—	2	1	no	—
229	C₁₃×#97	—	2	1	no	—
230	C₄×C₈×C₁₃	—	2	1	no	—
231	C₁₃×#95	—	2	1	no	—
232	C₁₃×#95	—	2	1	no	—
233	C₁₃×#95	—	2	1	no	—
234	C₁₃×#95	—	2	1	no	—
235	C₁₃×#95	—	2	1	no	—
236	#22434	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂⁴×C₁₃	—	2	1	no	—
238	C₂⁴×C₁₃	—	2	1	no	—
239	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₁₃×#41	—	2	1	no	—
242	C₁₃×#41	—	2	1	no	—
243	C₁₃×#41	—	2	2	no	—
244	C₁₃×#41	—	2	2	no	—
245	C₁₃×#41	—	2	2	no	—
246	C₁₃×#41	—	2	2	no	—
247	C₁₃×#41	—	2	1	no	—
248	C₁₃×#41	—	2	1	no	—
249	C₁₃×#41	—	2	1	no	—
250	C₁₃×#41	—	2	1	no	—
251	C₁₃×#41	—	2	1	no	—
252	C₁₃×#41	—	2	1	no	—
253	C₁₃×#41	—	2	1	no	—
254	C₁₃×#41	—	2	1	no	—
255	C₁₃×#41	—	4	2	no	—
256	C₁₃×#41	—	4	2	no	—
257	C₁₃×#41	—	4	2	no	—
258	C₁₃×#41	—	4	2	no	—
259	C₁₃×#41	—	4	1	no	—
260	C₁₃×#41	—	4	1	no	—
261	C₁₃×#41	—	4	1	no	—
262	C₁₃×#41	—	4	1	no	—
263	C₁₃×#41	—	4	2	no	—
264	C₁₃×#41	—	4	2	no	—
265	C₁₃×#41	—	4	2	no	—
266	C₁₃×#41	—	4	2	no	—
267	C₁₃×#41	C₂×D₄	1	2	yes	—
268	C₁₃×#41	#41	1	2	yes	—
269	C₂×Q₈×C₁₃	—	2	1	no	—
270	C₂×Q₈×C₁₃	—	2	1	no	—
271	C₂×Q₈×C₁₃	—	2	2	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	—	4	1	no	—
274	C₂×Q₈×C₁₃	—	4	1	no	—
275	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
276	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
277	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
278	C₂×D₄×C₁₃	—	2	1	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	1	no	—
282	C₂×D₄×C₁₃	—	2	1	no	—
283	C₂×D₄×C₁₃	—	2	1	no	—
284	C₂×D₄×C₁₃	—	2	1	no	—
285	C₂×D₄×C₁₃	—	2	1	no	—
286	C₂×D₄×C₁₃	—	2	1	no	—
287	C₂×D₄×C₁₃	—	2	1	no	—
288	C₂×D₄×C₁₃	—	2	1	no	—
289	C₂×D₄×C₁₃	—	2	1	no	—
290	C₂×D₄×C₁₃	—	2	1	no	—
291	C₂×D₄×C₁₃	—	2	1	no	—
292	C₂×D₄×C₁₃	—	2	1	no	—
293	C₂×D₄×C₁₃	—	2	1	no	—
294	C₂×D₄×C₁₃	—	2	1	no	—
295	C₂×D₄×C₁₃	—	4	1	no	—
296	C₂×D₄×C₁₃	—	4	1	no	—
297	C₂×D₄×C₁₃	—	4	2	no	—
298	C₂×D₄×C₁₃	—	4	2	no	—
299	C₂×D₄×C₁₃	—	4	2	no	—
300	C₂×D₄×C₁₃	—	4	2	no	—
301	C₂×D₄×C₁₃	—	4	2	no	—
302	C₂×D₄×C₁₃	—	4	4	no	—
303	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
304	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
305	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
306	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
307	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
308	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
309	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	—	2	1	no	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	1	no	—
313	C₂²×C₄×C₁₃	—	2	1	no	—
314	C₂²×C₄×C₁₃	—	2	1	no	—
315	C₂²×C₄×C₁₃	—	2	1	no	—
316	C₂²×C₄×C₁₃	—	2	1	no	—
317	C₂²×C₄×C₁₃	—	2	1	no	—
318	C₂²×C₄×C₁₃	—	2	1	no	—
319	C₂²×C₄×C₁₃	—	2	1	no	—
320	C₂²×C₄×C₁₃	—	2	1	no	—
321	C₂²×C₄×C₁₃	—	2	1	no	—
322	C₂²×C₄×C₁₃	—	2	1	no	—
323	C₂²×C₄×C₁₃	—	2	1	no	—
324	C₂²×C₄×C₁₃	—	2	1	no	—
325	C₂²×C₄×C₁₃	—	2	1	no	—
326	C₂²×C₄×C₁₃	—	2	1	no	—
327	C₂²×C₄×C₁₃	—	2	1	no	—
328	C₂²×C₄×C₁₃	—	2	1	no	—
329	C₂²×C₄×C₁₃	—	2	1	no	—
330	C₂²×C₄×C₁₃	—	2	1	no	—
331	C₂²×C₄×C₁₃	—	2	1	no	—
332	C₂²×C₄×C₁₃	—	2	1	no	—
333	C₂²×C₄×C₁₃	—	4	2	no	—
334	C₂²×C₄×C₁₃	—	4	2	no	—
335	C₂²×C₄×C₁₃	—	4	2	no	—
336	C₂²×C₄×C₁₃	—	4	2	no	—
337	C₂²×C₄×C₁₃	—	4	2	no	—
338	C₂²×C₄×C₁₃	—	4	2	no	—
339	C₂²×C₄×C₁₃	—	4	2	no	—
340	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₁₃×M₁₆	—	2	1	no	—
354	C₁₃×M₁₆	—	2	1	no	—
355	C₁₃×M₁₆	—	2	1	no	—
356	C₁₃×M₁₆	—	2	1	no	—
357	C₁₃×M₁₆	—	2	1	no	—
358	C₁₃×M₁₆	—	2	1	no	—
359	C₁₃×M₁₆	—	2	1	no	—
360	C₁₃×M₁₆	—	4	2	no	—
361	C₁₃×M₁₆	—	4	2	no	—
362	C₁₃×M₁₆	C₂×D₄	1	2	yes	complemented
363	C₂×C₈×C₁₃	—	2	1	no	—
364	C₂×C₈×C₁₃	—	2	1	no	—
365	C₂×C₈×C₁₃	—	2	1	no	—
366	C₂×C₈×C₁₃	—	2	1	no	—
367	C₂×C₈×C₁₃	—	4	2	no	—
368	C₂×C₈×C₁₃	—	4	2	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	4	2	no	—
378	C₁₃×C₄⋊C₄	—	4	2	no	—
379	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
381	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
382	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
383	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	C₁₃×C₂²⋊C₄	—	2	1	no	—
386	C₁₃×C₂²⋊C₄	—	2	1	no	—
387	C₁₃×C₂²⋊C₄	—	2	1	no	—
388	C₁₃×C₂²⋊C₄	—	2	1	no	—
389	C₁₃×C₂²⋊C₄	—	2	1	no	—
390	C₁₃×C₂²⋊C₄	—	2	1	no	—
391	C₁₃×C₂²⋊C₄	—	2	1	no	—
392	C₁₃×C₂²⋊C₄	—	2	1	no	—
393	C₁₃×C₂²⋊C₄	—	2	1	no	—
394	C₁₃×C₂²⋊C₄	—	2	1	no	—
395	C₁₃×C₂²⋊C₄	—	2	1	no	—
396	C₁₃×C₂²⋊C₄	—	2	1	no	—
397	C₁₃×C₂²⋊C₄	—	2	1	no	—
398	C₁₃×C₂²⋊C₄	—	2	1	no	—
399	C₁₃×C₂²⋊C₄	—	2	1	no	—
400	C₁₃×C₂²⋊C₄	—	4	2	no	—
401	C₁₃×C₂²⋊C₄	—	4	2	no	—
402	C₁₃×C₂²⋊C₄	—	4	2	no	—
403	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
404	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
405	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
406	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
407	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
408	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
409	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
410	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
411	C₄²×C₁₃	—	2	1	no	—
412	C₄²×C₁₃	—	2	1	no	—
413	C₄²×C₁₃	—	2	1	no	—
414	C₄²×C₁₃	—	2	1	no	—
415	C₄²×C₁₃	—	2	1	no	—
416	C₄²×C₁₃	—	2	1	no	—
417	C₄²×C₁₃	—	2	1	no	—
418	C₄²×C₁₃	—	2	1	no	—
419	C₄²×C₁₃	—	2	1	no	—
420	C₄²×C₁₃	—	2	1	no	—
421	C₄²×C₁₃	—	4	2	no	—
422	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
424	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
426	C₄²×C₁₃	C₂×D₄	1	2	yes	complemented
427	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
428	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
429	C₂×#421	C₂×C₁₃	1	1	yes	characteristic, complemented
430	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
431	#2290	C₂×C₁₃	1	1	yes	characteristic, complemented
432	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
433	#1963	C₂×C₁₃	1	1	yes	characteristic, complemented
434	#1897	C₂×C₁₃	1	1	yes	characteristic, complemented
435	#1896	C₂×C₁₃	1	1	yes	characteristic, complemented
436	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
437	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
438	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#1789	C₂×C₁₃	1	1	yes	characteristic, complemented
440	#1789	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
442	C₂³×C₁₃	—	2	1	no	—
443	C₂³×C₁₃	—	2	1	no	—
444	C₂³×C₁₃	—	2	1	no	—
445	C₂³×C₁₃	—	2	2	no	—
446	C₂³×C₁₃	—	2	1	no	—
447	C₂³×C₁₃	—	2	1	no	—
448	C₂³×C₁₃	—	2	1	no	—
449	C₂³×C₁₃	—	2	1	no	—
450	C₂³×C₁₃	—	4	1	no	—
451	C₂³×C₁₃	—	4	1	no	—
452	C₂³×C₁₃	—	4	1	no	—
453	C₂³×C₁₃	—	4	2	no	—
454	C₂³×C₁₃	—	4	2	no	—
455	C₂³×C₁₃	—	4	2	no	—
456	C₂³×C₁₃	—	4	2	no	—
457	C₂³×C₁₃	—	8	1	no	—
458	C₂³×C₁₃	—	8	1	no	—
459	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₁₃	—	2	1	no	—
465	Q₈×C₁₃	—	2	1	no	—
466	Q₈×C₁₃	—	2	1	no	—
467	Q₈×C₁₃	—	2	1	no	—
468	Q₈×C₁₃	—	2	1	no	—
469	Q₈×C₁₃	—	4	2	no	—
470	Q₈×C₁₃	—	4	2	no	—
471	Q₈×C₁₃	C₄×D₄	1	2	yes	—
472	D₄×C₁₃	—	2	2	no	—
473	D₄×C₁₃	—	2	2	no	—
474	D₄×C₁₃	—	2	2	no	—
475	D₄×C₁₃	—	2	2	no	—
476	D₄×C₁₃	—	2	1	no	—
477	D₄×C₁₃	—	2	1	no	—
478	D₄×C₁₃	—	2	1	no	—
479	D₄×C₁₃	—	2	1	no	—
480	D₄×C₁₃	—	2	1	no	—
481	D₄×C₁₃	—	4	1	no	—
482	D₄×C₁₃	—	4	1	no	—
483	D₄×C₁₃	—	4	2	no	—
484	D₄×C₁₃	—	4	2	no	—
485	D₄×C₁₃	—	4	2	no	—
486	D₄×C₁₃	—	4	2	no	—
487	D₄×C₁₃	—	4	2	no	—
488	D₄×C₁₃	—	4	2	no	—
489	D₄×C₁₃	—	4	2	no	—
490	D₄×C₁₃	—	4	2	no	—
491	D₄×C₁₃	—	4	1	no	—
492	D₄×C₁₃	—	4	1	no	—
493	D₄×C₁₃	—	4	1	no	—
494	D₄×C₁₃	—	4	1	no	—
495	D₄×C₁₃	—	4	2	no	—
496	D₄×C₁₃	—	8	1	no	—
497	D₄×C₁₃	—	8	1	no	—
498	D₄×C₁₃	—	8	1	no	—
499	D₄×C₁₃	C₄×D₄	1	2	yes	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	1	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	2	1	no	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	1	no	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	2	no	—
529	C₂×C₄×C₁₃	—	4	1	no	—
530	C₂×C₄×C₁₃	—	4	1	no	—
531	C₂×C₄×C₁₃	—	4	2	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	4	1	no	—
539	C₂×C₄×C₁₃	—	4	1	no	—
540	C₂×C₄×C₁₃	—	4	1	no	—
541	C₂×C₄×C₁₃	—	4	8	no	—
542	C₂×C₄×C₁₃	—	4	1	no	—
543	C₂×C₄×C₁₃	—	4	1	no	—
544	C₂×C₄×C₁₃	—	4	1	no	—
545	C₂×C₄×C₁₃	—	4	1	no	—
546	C₂×C₄×C₁₃	—	4	1	no	—
547	C₂×C₄×C₁₃	—	4	1	no	—
548	C₂×C₄×C₁₃	—	4	1	no	—
549	C₂×C₄×C₁₃	—	4	1	no	—
550	C₂×C₄×C₁₃	—	4	1	no	—
551	C₂×C₄×C₁₃	—	4	1	no	—
552	C₂×C₄×C₁₃	—	4	1	no	—
553	C₂×C₄×C₁₃	—	8	1	no	—
554	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
555	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
556	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
557	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
558	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
559	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
560	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
563	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
566	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
568	C₈×C₁₃	—	2	2	no	—
569	C₈×C₁₃	—	4	1	no	—
570	C₈×C₁₃	—	4	1	no	—
571	C₈×C₁₃	—	4	1	no	—
572	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
573	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
574	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
575	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#550	C₄×C₁₃	1	1	yes	characteristic, complemented
577	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
578	#548	C₄×C₁₃	1	1	yes	characteristic, complemented
579	#548	C₄×C₁₃	1	1	yes	characteristic, complemented
580	#547	—	2	1	no	—
581	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
582	#546	—	2	1	no	—
583	#546	—	2	1	no	—
584	#546	C₄×C₁₃	1	1	yes	characteristic, complemented
585	#546	C₄×C₁₃	1	1	yes	characteristic, complemented
586	D₄²	—	2	1	no	—
587	D₄²	C₄×C₁₃	1	1	yes	characteristic, complemented
588	#532	—	2	1	no	—
589	#532	C₂²×C₁₃	1	1	yes	characteristic
590	#525	—	2	1	no	—
591	#525	—	2	1	no	—
592	#525	C₂²×C₁₃	1	1	yes	characteristic
593	#525	C₂²×C₁₃	1	1	yes	characteristic
594	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
595	C₂×C₄×D₄	—	2	1	no	—
596	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
597	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
599	#436	—	2	1	no	—
600	#435	—	2	1	no	—
601	#435	—	2	1	no	—
602	C₈×D₄	—	2	1	no	—
603	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#421	—	2	4	no	—
605	C₂×#104	—	2	4	no	—
606	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
607	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
608	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
609	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
610	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
618	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#388	—	2	1	no	—
622	#387	—	2	1	no	—
623	#386	—	2	1	no	—
624	#385	—	2	1	no	—
625	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	C₂²×C₁₃	—	2	1	no	—
634	C₂²×C₁₃	—	2	1	no	—
635	C₂²×C₁₃	—	2	1	no	—
636	C₂²×C₁₃	—	2	1	no	—
637	C₂²×C₁₃	—	2	1	no	—
638	C₂²×C₁₃	—	2	1	no	—
639	C₂²×C₁₃	—	2	1	no	—
640	C₂²×C₁₃	—	2	2	no	—
641	C₂²×C₁₃	—	2	1	no	—
642	C₂²×C₁₃	—	2	1	no	—
643	C₂²×C₁₃	—	2	1	no	—
644	C₂²×C₁₃	—	2	1	no	—
645	C₂²×C₁₃	—	2	1	no	—
646	C₂²×C₁₃	—	2	1	no	—
647	C₂²×C₁₃	—	4	2	no	—
648	C₂²×C₁₃	—	4	2	no	—
649	C₂²×C₁₃	—	4	1	no	—
650	C₂²×C₁₃	—	4	1	no	—
651	C₂²×C₁₃	—	4	1	no	—
652	C₂²×C₁₃	—	4	1	no	—
653	C₂²×C₁₃	—	4	1	no	—
654	C₂²×C₁₃	—	4	1	no	—
655	C₂²×C₁₃	—	4	1	no	—
656	C₂²×C₁₃	—	4	1	no	—
657	C₂²×C₁₃	—	8	1	no	—
658	C₂²×C₁₃	—	8	1	no	—
659	C₂²×C₁₃	—	8	4	no	—
660	C₂²×C₁₃	—	8	4	no	—
661	C₂²×C₁₃	#421	1	2	yes	complemented
662	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
663	C₂²×C₁₃	D₄²	1	1	yes	characteristic
664	C₂²×C₁₃	#546	1	1	yes	characteristic
665	C₄×C₁₃	—	2	1	no	—
666	C₄×C₁₃	—	2	1	no	—
667	C₄×C₁₃	—	2	1	no	—
668	C₄×C₁₃	—	2	1	no	—
669	C₄×C₁₃	—	2	2	no	—
670	C₄×C₁₃	—	2	1	no	—
671	C₄×C₁₃	—	2	1	no	—
672	C₄×C₁₃	—	2	1	no	—
673	C₄×C₁₃	—	2	1	no	—
674	C₄×C₁₃	—	4	2	no	—
675	C₄×C₁₃	—	4	2	no	—
676	C₄×C₁₃	—	4	1	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	1	no	—
679	C₄×C₁₃	—	4	1	no	—
680	C₄×C₁₃	—	8	1	no	—
681	C₄×C₁₃	—	8	1	no	—
682	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
683	C₄×C₁₃	#518	1	1	yes	characteristic
684	C₄×C₁₃	D₄²	1	1	yes	characteristic
685	C₄×C₁₃	#546	1	1	yes	characteristic
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	1	no	—
688	C₂×#41	—	2	1	no	—
689	C₂×#41	—	2	1	no	—
690	C₂×#41	—	2	2	no	—
691	C₂×#41	—	2	2	no	—
692	C₂×#41	—	2	2	no	—
693	C₂×#41	—	2	2	no	—
694	C₂×#41	—	4	1	no	—
695	C₂×#41	—	4	1	no	—
696	C₂×#41	—	4	1	no	—
697	C₂×#41	—	4	1	no	—
698	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
699	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
700	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
701	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
702	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
704	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
705	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
706	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
711	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
712	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	C₂³×C₄	—	2	1	no	—
715	C₂³×C₄	—	2	1	no	—
716	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×M₁₆	—	2	1	no	—
719	C₂×M₁₆	—	2	1	no	—
720	C₂×M₁₆	—	2	2	no	—
721	C₂×M₁₆	—	2	2	no	—
722	C₂×M₁₆	—	4	1	no	—
723	C₂×M₁₆	—	4	1	no	—
724	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂²×C₈	—	2	1	no	—
729	C₂²×C₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
732	#127	—	2	1	no	—
733	#127	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
737	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
738	#123	—	2	1	no	—
739	#123	—	2	1	no	—
740	#123	—	2	1	no	—
741	#123	—	2	1	no	—
742	#123	—	2	1	no	—
743	#123	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
751	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	1	no	—
758	#121	—	2	1	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
763	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
764	#121	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
765	#121	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
766	#120	—	2	1	no	—
767	#120	—	2	1	no	—
768	#120	—	2	1	no	—
769	#120	—	2	1	no	—
770	#120	—	2	1	no	—
771	#120	—	2	1	no	—
772	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
773	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
787	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
788	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
789	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
790	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
791	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
792	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
793	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
794	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
795	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
796	#117	—	2	1	no	—
797	#117	—	2	2	no	—
798	#117	—	4	1	no	—
799	#117	C₂³×C₁₃	1	1	yes	characteristic
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	—	2	1	no	—
805	C₂×C₂²⋊C₄	—	2	1	no	—
806	C₂×C₂²⋊C₄	—	2	1	no	—
807	C₂×C₂²⋊C₄	—	2	1	no	—
808	C₂×C₂²⋊C₄	—	2	1	no	—
809	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
810	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
811	C₂×C₄²	—	2	1	no	—
812	C₂×C₄²	—	2	2	no	—
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	—	4	1	no	—
815	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
820	C₄⋊C₈	—	2	1	no	—
821	C₄⋊C₈	—	2	1	no	—
822	#104	—	2	2	no	—
823	#104	—	2	2	no	—
824	#104	—	2	2	no	—
825	#104	—	2	2	no	—
826	#104	—	2	2	no	—
827	#104	—	2	2	no	—
828	#104	—	2	2	no	—
829	#104	—	4	1	no	—
830	#104	—	4	1	no	—
831	#104	—	4	1	no	—
832	#104	—	4	1	no	—
833	#104	D₄×C₁₃	1	4	yes	complemented
834	C₂²⋊C₈	—	2	1	no	—
835	C₂²⋊C₈	—	2	1	no	—
836	C₂²⋊C₈	—	2	1	no	—
837	C₂²⋊C₈	—	2	1	no	—
838	#97	—	2	1	no	—
839	C₄×C₈	—	2	1	no	—
840	#95	—	2	1	no	—
841	#95	—	2	1	no	—
842	#95	—	2	1	no	—
843	#95	—	2	1	no	—
844	#95	—	2	1	no	—
845	C₂×C₁₃	—	2	1	no	—
846	C₂×C₁₃	—	2	1	no	—
847	C₂×C₁₃	—	2	2	no	—
848	C₂×C₁₃	—	4	1	no	—
849	C₂×C₁₃	—	4	1	no	—
850	C₂×C₁₃	—	4	1	no	—
851	C₂×C₁₃	—	4	2	no	—
852	C₂×C₁₃	—	8	1	no	—
853	C₂×C₁₃	—	8	1	no	—
854	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
855	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
856	C₂×C₁₃	#2901	1	1	yes	characteristic
857	C₂⁴	—	2	1	no	—
858	C₂⁴	—	2	1	no	—
859	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
861	#41	—	2	1	no	—
862	#41	—	2	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	2	1	no	—
868	#41	—	2	1	no	—
869	#41	—	2	1	no	—
870	#41	—	2	1	no	—
871	#41	—	2	1	no	—
872	#41	—	2	1	no	—
873	#41	—	2	1	no	—
874	#41	—	2	1	no	—
875	#41	—	4	2	no	—
876	#41	—	4	2	no	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	1	no	—
880	#41	—	4	1	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	4	2	no	—
887	#41	C₂×D₄×C₁₃	1	2	yes	—
888	#41	C₁₃×#41	1	2	yes	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	—	4	1	no	—
895	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
896	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
897	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	4	1	no	—
916	C₂×D₄	—	4	1	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	4	no	—
923	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
924	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
925	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
926	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
927	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
928	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
929	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	4	2	no	—
954	C₂²×C₄	—	4	2	no	—
955	C₂²×C₄	—	4	2	no	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	—	4	2	no	—
958	C₂²×C₄	—	4	2	no	—
959	C₂²×C₄	—	4	2	no	—
960	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
961	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
962	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
963	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
964	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
966	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
968	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
969	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
970	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
971	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
972	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
973	M₁₆	—	2	1	no	—
974	M₁₆	—	2	1	no	—
975	M₁₆	—	2	1	no	—
976	M₁₆	—	2	1	no	—
977	M₁₆	—	2	1	no	—
978	M₁₆	—	2	1	no	—
979	M₁₆	—	2	1	no	—
980	M₁₆	—	4	2	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
983	C₂×C₈	—	2	1	no	—
984	C₂×C₈	—	2	1	no	—
985	C₂×C₈	—	2	1	no	—
986	C₂×C₈	—	2	1	no	—
987	C₂×C₈	—	4	2	no	—
988	C₂×C₈	—	4	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	4	2	no	—
999	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1000	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1001	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1002	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1003	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	2	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1024	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1025	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1026	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1027	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1028	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1029	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1030	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
1043	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
1044	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1045	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1046	C₄²	C₂×D₄×C₁₃	1	2	yes	complemented
1047	C₁₃	#22434	1	1	yes	characteristic, direct product factor, Sylow
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	4	2	no	—
1061	C₂³	—	4	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	1	no	—
1065	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1066	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1067	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1068	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1069	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	4	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	C₄×D₄×C₁₃	1	2	yes	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	1	no	—
1099	D₄	—	4	1	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	1	no	—
1105	D₄	C₄×D₄×C₁₃	1	2	yes	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	8	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1161	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1162	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1164	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1165	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1166	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1167	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1168	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1171	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
1172	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1174	C₈	—	2	2	no	—
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₈	—	4	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	4	no	—
1205	C₂²	—	8	4	no	—
1206	C₂²	C₁₃×#421	1	2	yes	complemented
1207	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1208	C₂²	D₄²×C₁₃	1	1	yes	characteristic
1209	C₂²	C₁₃×#546	1	1	yes	characteristic
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
1228	C₄	C₁₃×#518	1	1	yes	characteristic
1229	C₄	D₄²×C₁₃	1	1	yes	characteristic
1230	C₄	C₁₃×#546	1	1	yes	characteristic
1231	C₂	—	2	1	no	—
1232	C₂	—	2	1	no	—
1233	C₂	—	2	2	no	—
1234	C₂	—	4	1	no	—
1235	C₂	—	4	1	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	2	no	—
1238	C₂	—	8	1	no	—
1239	C₂	—	8	1	no	—
1240	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
1241	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
1242	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	D₄×C₁₃×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₁₃×M₁₆	C₂	semidirect
3. C₂×C₁₃×#421	C₂	semidirect
4. C₂²×C₁₃×#104	C₂	semidirect
5. C₁₃×#2290	C₂	semidirect
6. C₁₃×#1980	C₂	semidirect
7. C₁₃×#1963	C₂	semidirect
8. C₁₃×#1897	C₂	semidirect
9. C₁₃×#1896	C₂	semidirect
10. C₁₃×#1871	C₂	semidirect
11. C₁₃×#1871	C₂	semidirect
12. C₁₃×#1806	C₂	semidirect
13. C₁₃×#1789	C₂	semidirect
14. C₁₃×#1789	C₂	semidirect
15. C₁₃×#1759	C₂	semidirect
18. C₂²×C₁₃×M₁₆	C₂²	semidirect
19. C₂²×C₁₃×M₁₆	C₂²	semidirect
20. C₁₃×#550	C₄	semidirect
21. D₄×Q₈×C₁₃	C₄	semidirect
22. C₁₃×#548	C₄	semidirect
23. C₁₃×#548	C₄	semidirect
25. C₁₃×#547	C₄	semidirect
28. C₁₃×#546	C₄	semidirect
29. C₁₃×#546	C₄	semidirect
31. D₄²×C₁₃	C₄	semidirect
41. C₂×C₁₃×#117	C₂²	semidirect
42. C₂²×C₄²×C₁₃	C₂²	semidirect
47. C₁₃×#423	C₂²	semidirect
54. C₂×C₁₃×#104	C₂²	semidirect
55. C₂×C₁₃×#104	C₂²	semidirect
56. C₂×C₁₃×#104	C₂²	semidirect
57. C₂×C₁₃×#104	C₂²	semidirect
58. C₂×C₁₃×#104	C₂²	semidirect
59. C₂×C₁₃×#104	C₂²	semidirect
60. C₂×C₁₃×#104	C₂²	semidirect
61. C₂×C₁₃×#104	C₂²	semidirect
62. C₁₃×#407	C₂²	semidirect
63. C₁₃×#407	C₂²	semidirect
64. C₄×C₁₃×M₁₆	C₂²	semidirect
69. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
70. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
71. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
72. C₁₃×#376	C₂²	semidirect
73. C₁₃×#339	C₂²	semidirect
74. C₁₃×#339	C₂²	semidirect
75. C₁₃×#339	C₂²	semidirect
76. C₁₃×#339	C₂²	semidirect
91. C₂×C₁₃×#41	C₂×C₄	semidirect
92. C₂×C₁₃×#41	C₂×C₄	semidirect
97. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
102. C₂²×D₄×C₁₃	C₂×C₄	semidirect
122. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
124. C₁₃×#127	C₂×C₄	semidirect
127. C₁₃×#124	C₂×C₄	semidirect
128. C₁₃×#124	C₂×C₄	semidirect
141. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
155. C₁₃×#121	C₂×C₄	semidirect
156. C₁₃×#121	C₂×C₄	semidirect
163. C₄×Q₈×C₁₃	C₂×C₄	semidirect
164. C₄×Q₈×C₁₃	C₂×C₄	semidirect
181. C₄×D₄×C₁₃	C₂×C₄	semidirect
182. C₄×D₄×C₁₃	C₂×C₄	semidirect
224. C₁₃×#104	D₄	semidirect
236. #22434	C₁₃	direct (N × H)
362. C₁₃×M₁₆	C₂×D₄	semidirect
426. C₄²×C₁₃	C₂×D₄	semidirect
428. D₄×M₁₆	C₂×C₁₃	semidirect
429. C₂×#421	C₂×C₁₃	semidirect
430. C₂²×#104	C₂×C₁₃	semidirect
431. #2290	C₂×C₁₃	semidirect
432. #1980	C₂×C₁₃	semidirect
433. #1963	C₂×C₁₃	semidirect
434. #1897	C₂×C₁₃	semidirect
435. #1896	C₂×C₁₃	semidirect
436. #1871	C₂×C₁₃	semidirect
437. #1871	C₂×C₁₃	semidirect
438. #1806	C₂×C₁₃	semidirect
439. #1789	C₂×C₁₃	semidirect
440. #1789	C₂×C₁₃	semidirect
441. #1759	C₂×C₁₃	semidirect
574. C₂²×M₁₆	C₂²×C₁₃	semidirect
575. C₂²×M₁₆	C₂²×C₁₃	semidirect
576. #550	C₄×C₁₃	semidirect
577. D₄×Q₈	C₄×C₁₃	semidirect
578. #548	C₄×C₁₃	semidirect
579. #548	C₄×C₁₃	semidirect
581. #547	C₄×C₁₃	semidirect
584. #546	C₄×C₁₃	semidirect
585. #546	C₄×C₁₃	semidirect
587. D₄²	C₄×C₁₃	semidirect
597. C₂×#117	C₂²×C₁₃	semidirect
598. C₂²×C₄²	C₂²×C₁₃	semidirect
603. #423	C₂²×C₁₃	semidirect
610. C₂×#104	C₂²×C₁₃	semidirect
611. C₂×#104	C₂²×C₁₃	semidirect
612. C₂×#104	C₂²×C₁₃	semidirect
613. C₂×#104	C₂²×C₁₃	semidirect
614. C₂×#104	C₂²×C₁₃	semidirect
615. C₂×#104	C₂²×C₁₃	semidirect
616. C₂×#104	C₂²×C₁₃	semidirect
617. C₂×#104	C₂²×C₁₃	semidirect
618. #407	C₂²×C₁₃	semidirect
619. #407	C₂²×C₁₃	semidirect
620. C₄×M₁₆	C₂²×C₁₃	semidirect
625. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
626. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
627. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
628. #376	C₂²×C₁₃	semidirect
629. #339	C₂²×C₁₃	semidirect
630. #339	C₂²×C₁₃	semidirect
631. #339	C₂²×C₁₃	semidirect
632. #339	C₂²×C₁₃	semidirect
661. C₂²×C₁₃	#421	semidirect
700. C₂×#41	C₂×C₄×C₁₃	semidirect
701. C₂×#41	C₂×C₄×C₁₃	semidirect
706. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
711. C₂²×D₄	C₂×C₄×C₁₃	semidirect
731. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
733. #127	C₂×C₄×C₁₃	semidirect
736. #124	C₂×C₄×C₁₃	semidirect
737. #124	C₂×C₄×C₁₃	semidirect
750. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
751. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
764. #121	C₂×C₄×C₁₃	semidirect
765. #121	C₂×C₄×C₁₃	semidirect
772. C₄×Q₈	C₂×C₄×C₁₃	semidirect
773. C₄×Q₈	C₂×C₄×C₁₃	semidirect
790. C₄×D₄	C₂×C₄×C₁₃	semidirect
791. C₄×D₄	C₂×C₄×C₁₃	semidirect
833. #104	D₄×C₁₃	semidirect
982. M₁₆	C₂×D₄×C₁₃	semidirect
1046. C₄²	C₂×D₄×C₁₃	semidirect
1047. C₁₃	#22434	direct (N × H)
1206. C₂²	C₁₃×#421	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×#41	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#421	2
C₂²×C₁₃×#104	2
C₁₃×#2290	2
C₁₃×#1980	2
C₁₃×#1963	2
C₁₃×#1897	2
C₁₃×#1896	2
C₁₃×#1871	2
C₁₃×#1806	2
C₁₃×#1789	2
C₁₃×#1759	2
#22434	13

Subgroups — C13×#22434 #15708773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22434 #15708773