Subgroups — C₁₃×#24403 #15710742

Order 3328.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1785	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	C₁₃×#575	—	2	4	no	—
19	C₁₃×#575	—	2	4	no	—
20	C₂×C₁₃×#137	—	2	1	no	—
21	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	—	2	1	no	—
29	C₂×C₁₃×#135	—	2	1	no	—
30	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₃×#473	—	2	4	no	—
37	C₁₃×#471	—	2	4	no	—
38	C₁₃×#452	—	2	1	no	—
39	C₁₃×#452	—	2	1	no	—
40	C₁₃×#452	—	2	1	no	—
41	C₁₃×#452	—	2	1	no	—
42	C₁₃×#452	—	2	1	no	—
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#451	—	2	1	no	—
45	C₁₃×#450	—	2	1	no	—
46	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#408	—	2	1	no	—
59	C₁₃×#408	—	2	1	no	—
60	C₁₃×#408	C₂²	1	1	yes	characteristic
61	C₁₃×#408	C₂²	1	1	yes	characteristic
62	C₁₃×#407	—	2	1	no	—
63	C₁₃×#407	C₂²	1	1	yes	characteristic
64	C₁₃×#407	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	2	2	no	—
74	C₂×C₁₃×#41	—	2	2	no	—
75	C₂×C₁₃×#41	—	2	2	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
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	—	4	1	no	—
82	C₂×C₁₃×#41	—	4	1	no	—
83	C₂×C₁₃×#41	—	4	1	no	—
84	C₂×C₁₃×#41	—	4	1	no	—
85	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
86	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#137	—	2	8	no	—
100	C₁₃×#137	—	2	2	no	—
101	C₁₃×#137	—	2	2	no	—
102	C₁₃×#137	—	2	2	no	—
103	C₁₃×#137	—	2	2	no	—
104	C₁₃×#137	—	2	2	no	—
105	C₁₃×#137	—	4	1	no	—
106	C₁₃×#137	—	4	1	no	—
107	C₁₃×#137	D₄	1	4	yes	—
108	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
109	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
112	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	—
113	C₁₃×#135	—	2	8	no	—
114	C₁₃×#135	—	2	8	no	—
115	C₂×C₁₃×Q₁₆	—	2	1	no	—
116	C₂×C₁₃×Q₁₆	—	2	1	no	—
117	C₂×C₁₃×Q₁₆	—	2	1	no	—
118	C₂×C₁₃×Q₁₆	—	2	1	no	—
119	C₂×C₁₃×Q₁₆	—	2	2	no	—
120	C₂×C₁₃×Q₁₆	—	2	1	no	—
121	C₂×C₁₃×Q₁₆	—	2	1	no	—
122	C₂×C₁₃×Q₁₆	—	4	1	no	—
123	C₂×C₁₃×SD₁₆	—	2	1	no	—
124	C₂×C₁₃×SD₁₆	—	2	1	no	—
125	C₂×C₁₃×SD₁₆	—	2	1	no	—
126	C₂×C₁₃×SD₁₆	—	2	1	no	—
127	C₂×C₁₃×SD₁₆	—	2	1	no	—
128	C₂×C₁₃×SD₁₆	—	2	1	no	—
129	C₂×C₁₃×SD₁₆	—	2	2	no	—
130	C₂×C₁₃×SD₁₆	—	2	1	no	—
131	C₂×C₁₃×SD₁₆	—	2	1	no	—
132	C₂×C₁₃×SD₁₆	—	4	1	no	—
133	C₂×C₁₃×D₈	—	2	1	no	—
134	C₂×C₁₃×D₈	—	2	1	no	—
135	C₁₃×#131	—	2	2	no	—
136	C₁₃×#131	—	2	2	no	—
137	C₁₃×#131	—	4	1	no	—
138	C₁₃×#131	—	4	1	no	—
139	C₂×C₁₃×M₁₆	—	2	1	no	—
140	C₂×C₁₃×M₁₆	—	2	2	no	—
141	C₂×C₁₃×M₁₆	—	2	2	no	—
142	C₂×C₁₃×M₁₆	—	2	1	no	—
143	C₂×C₁₃×M₁₆	—	2	1	no	—
144	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₃	—	2	1	no	—
151	C₂²×C₈×C₁₃	—	2	1	no	—
152	C₂²×C₈×C₁₃	—	2	1	no	—
153	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₁₃×C₂²⋊Q₈	—	2	1	no	—
156	C₁₃×C₂²⋊Q₈	—	2	1	no	—
157	C₁₃×C₂²⋊Q₈	—	2	1	no	—
158	C₁₃×C₂²⋊Q₈	—	2	1	no	—
159	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₁₃×#108	—	2	2	no	—
163	C₁₃×#108	—	2	2	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#103	—	2	1	no	—
167	C₁₃×#103	—	2	1	no	—
168	C₁₃×#102	—	2	1	no	—
169	C₁₃×#102	—	2	1	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×#102	—	2	1	no	—
172	C₁₃×#101	—	2	2	no	—
173	C₁₃×#101	—	2	2	no	—
174	C₁₃×#101	—	2	2	no	—
175	C₁₃×#101	—	4	1	no	—
176	C₁₃×#100	—	2	2	no	—
177	C₁₃×#100	—	4	1	no	—
178	C₁₃×C₂²⋊C₈	—	2	1	no	—
179	C₁₃×C₂²⋊C₈	—	2	1	no	—
180	C₁₃×C₂²⋊C₈	—	2	1	no	—
181	C₁₃×C₂²⋊C₈	—	2	1	no	—
182	C₁₃×C₂²⋊C₈	—	2	1	no	—
183	C₁₃×C₂²⋊C₈	—	2	1	no	—
184	C₁₃×C₂²⋊C₈	—	2	1	no	—
185	C₁₃×C₂²⋊C₈	—	2	1	no	—
186	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
187	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
190	#24403	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂⁴×C₁₃	—	2	1	no	—
192	C₂⁴×C₁₃	—	2	1	no	—
193	C₂⁴×C₁₃	#41	1	1	yes	characteristic
194	C₁₃×#41	—	2	1	no	—
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	4	no	—
197	C₁₃×#41	—	2	4	no	—
198	C₁₃×#41	—	2	2	no	—
199	C₁₃×#41	—	2	2	no	—
200	C₁₃×#41	—	2	1	no	—
201	C₁₃×#41	—	2	1	no	—
202	C₁₃×#41	—	2	1	no	—
203	C₁₃×#41	—	2	1	no	—
204	C₁₃×#41	—	4	2	no	—
205	C₁₃×#41	—	4	2	no	—
206	C₁₃×#41	—	4	1	no	—
207	C₁₃×#41	—	4	1	no	—
208	C₁₃×#41	—	4	2	no	—
209	C₁₃×#41	—	4	2	no	—
210	C₁₃×#41	—	4	2	no	—
211	C₁₃×#41	—	4	2	no	—
212	C₁₃×#41	—	4	2	no	—
213	C₁₃×#41	—	4	2	no	—
214	C₁₃×#41	—	4	2	no	—
215	C₁₃×#41	—	4	2	no	—
216	C₁₃×#41	C₂×D₄	1	2	yes	—
217	C₁₃×#41	C₂×D₄	1	2	yes	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	1	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	4	1	no	—
232	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	4	1	no	—
247	C₂×D₄×C₁₃	—	4	2	no	—
248	C₂×D₄×C₁₃	—	4	2	no	—
249	C₂×D₄×C₁₃	—	4	2	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	1	no	—
252	C₂×D₄×C₁₃	—	4	1	no	—
253	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	—	4	2	no	—
270	C₂²×C₄×C₁₃	—	4	2	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	1	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×Q₁₆	—	2	4	no	—
281	C₁₃×Q₁₆	—	2	4	no	—
282	C₁₃×Q₁₆	—	4	2	no	—
283	C₁₃×Q₁₆	—	4	2	no	—
284	C₁₃×Q₁₆	—	4	2	no	—
285	C₁₃×Q₁₆	—	4	2	no	—
286	C₁₃×SD₁₆	—	2	4	no	—
287	C₁₃×SD₁₆	—	2	4	no	—
288	C₁₃×SD₁₆	—	2	4	no	—
289	C₁₃×SD₁₆	—	2	4	no	—
290	C₁₃×SD₁₆	—	4	2	no	—
291	C₁₃×SD₁₆	—	4	2	no	—
292	C₁₃×SD₁₆	—	4	2	no	—
293	C₁₃×SD₁₆	—	4	2	no	—
294	C₁₃×D₈	—	2	4	no	—
295	C₁₃×D₈	—	2	4	no	—
296	C₁₃×M₁₆	—	2	4	no	—
297	C₁₃×M₁₆	—	2	1	no	—
298	C₁₃×M₁₆	—	2	1	no	—
299	C₁₃×M₁₆	—	2	1	no	—
300	C₁₃×M₁₆	—	2	1	no	—
301	C₁₃×M₁₆	—	2	1	no	—
302	C₁₃×M₁₆	—	2	1	no	—
303	C₁₃×M₁₆	—	2	1	no	—
304	C₁₃×M₁₆	—	2	1	no	—
305	C₁₃×M₁₆	—	2	1	no	—
306	C₁₃×M₁₆	—	2	1	no	—
307	C₁₃×M₁₆	—	4	2	no	—
308	C₁₃×M₁₆	—	4	2	no	—
309	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
310	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
311	C₂×C₈×C₁₃	—	2	4	no	—
312	C₂×C₈×C₁₃	—	2	1	no	—
313	C₂×C₈×C₁₃	—	2	1	no	—
314	C₂×C₈×C₁₃	—	2	1	no	—
315	C₂×C₈×C₁₃	—	2	1	no	—
316	C₂×C₈×C₁₃	—	2	1	no	—
317	C₂×C₈×C₁₃	—	2	1	no	—
318	C₂×C₈×C₁₃	—	2	1	no	—
319	C₂×C₈×C₁₃	—	2	1	no	—
320	C₂×C₈×C₁₃	—	2	1	no	—
321	C₂×C₈×C₁₃	—	2	1	no	—
322	C₂×C₈×C₁₃	—	4	2	no	—
323	C₂×C₈×C₁₃	—	4	2	no	—
324	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	1	no	—
330	C₁₃×C₄⋊C₄	—	4	1	no	—
331	C₁₃×C₄⋊C₄	—	4	1	no	—
332	C₁₃×C₂²⋊C₄	—	4	1	no	—
333	C₁₃×C₂²⋊C₄	—	4	1	no	—
334	C₂×#575	C₂×C₁₃	1	1	yes	characteristic
335	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2020	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#1785	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	4	1	no	—
355	C₂³×C₁₃	—	4	1	no	—
356	C₂³×C₁₃	—	4	2	no	—
357	C₂³×C₁₃	—	4	2	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	8	1	no	—
361	C₂³×C₁₃	—	8	1	no	—
362	C₂³×C₁₃	—	8	1	no	—
363	C₂³×C₁₃	#121	1	1	yes	characteristic
364	C₂³×C₁₃	#121	1	1	yes	characteristic
365	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	—	4	1	no	—
373	Q₈×C₁₃	—	4	1	no	—
374	Q₈×C₁₃	—	4	1	no	—
375	Q₈×C₁₃	—	4	1	no	—
376	Q₈×C₁₃	—	4	1	no	—
377	Q₈×C₁₃	—	4	1	no	—
378	Q₈×C₁₃	#120	1	2	yes	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	1	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	1	no	—
392	D₄×C₁₃	—	4	1	no	—
393	D₄×C₁₃	—	4	1	no	—
394	D₄×C₁₃	—	4	1	no	—
395	D₄×C₁₃	#120	1	2	yes	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	1	no	—
417	C₂×C₄×C₁₃	—	4	1	no	—
418	C₂×C₄×C₁₃	—	4	1	no	—
419	C₂×C₄×C₁₃	—	4	1	no	—
420	C₂×C₄×C₁₃	—	4	1	no	—
421	C₂×C₄×C₁₃	—	4	1	no	—
422	C₂×C₄×C₁₃	—	4	1	no	—
423	C₂×C₄×C₁₃	—	4	1	no	—
424	C₂×C₄×C₁₃	—	8	1	no	—
425	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
426	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
433	C₈×C₁₃	—	2	2	no	—
434	C₈×C₁₃	—	2	2	no	—
435	C₈×C₁₃	—	2	1	no	—
436	C₈×C₁₃	—	2	1	no	—
437	C₈×C₁₃	—	2	1	no	—
438	C₈×C₁₃	—	2	1	no	—
439	C₈×C₁₃	—	4	1	no	—
440	C₈×C₁₃	—	4	1	no	—
441	C₈×C₁₃	—	4	1	no	—
442	C₈×C₁₃	—	4	1	no	—
443	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
445	#575	—	2	4	no	—
446	#575	—	2	4	no	—
447	C₂×#137	—	2	1	no	—
448	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×AGL(1,ℤ/8)	—	2	1	no	—
453	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#135	—	2	1	no	—
456	C₂×#135	—	2	1	no	—
457	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
461	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	#473	—	2	4	no	—
464	#471	—	2	4	no	—
465	#452	—	2	1	no	—
466	#452	—	2	1	no	—
467	#452	—	2	1	no	—
468	#452	—	2	1	no	—
469	#452	—	2	1	no	—
470	#452	—	2	1	no	—
471	#451	—	2	1	no	—
472	#450	—	2	1	no	—
473	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#417	C₂²×C₁₃	1	1	yes	characteristic
476	#417	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	#408	—	2	1	no	—
486	#408	—	2	1	no	—
487	#408	C₂²×C₁₃	1	1	yes	characteristic
488	#408	C₂²×C₁₃	1	1	yes	characteristic
489	#407	—	2	1	no	—
490	#407	C₂²×C₁₃	1	1	yes	characteristic
491	#407	C₂²×C₁₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₈	—	2	1	no	—
493	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
494	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	8	1	no	—
514	C₂²×C₁₃	—	8	1	no	—
515	C₂²×C₁₃	—	8	2	no	—
516	C₂²×C₁₃	—	8	2	no	—
517	C₂²×C₁₃	—	8	4	no	—
518	C₂²×C₁₃	—	8	1	no	—
519	C₂²×C₁₃	—	8	1	no	—
520	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
521	C₂²×C₁₃	#546	1	1	yes	characteristic
522	C₂²×C₁₃	#546	1	1	yes	characteristic
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	8	1	no	—
529	C₄×C₁₃	—	8	1	no	—
530	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
531	C₄×C₁₃	#534	1	1	yes	characteristic
532	C₄×C₁₃	D₄²	1	1	yes	characteristic
533	C₄×C₁₃	D₄²	1	1	yes	characteristic
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	4	1	no	—
545	C₂×#41	—	4	1	no	—
546	C₂×#41	—	4	1	no	—
547	C₂×#41	—	4	1	no	—
548	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
549	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
550	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
553	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	#137	—	2	8	no	—
563	#137	—	2	2	no	—
564	#137	—	2	2	no	—
565	#137	—	2	2	no	—
566	#137	—	2	2	no	—
567	#137	—	2	2	no	—
568	#137	—	4	1	no	—
569	#137	—	4	1	no	—
570	#137	D₄×C₁₃	1	4	yes	—
571	AGL(1,ℤ/8)	—	2	8	no	—
572	AGL(1,ℤ/8)	—	2	2	no	—
573	AGL(1,ℤ/8)	—	2	2	no	—
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	—
576	#135	—	2	8	no	—
577	#135	—	2	8	no	—
578	C₂×Q₁₆	—	2	1	no	—
579	C₂×Q₁₆	—	2	1	no	—
580	C₂×Q₁₆	—	2	2	no	—
581	C₂×Q₁₆	—	2	1	no	—
582	C₂×Q₁₆	—	2	1	no	—
583	C₂×Q₁₆	—	2	1	no	—
584	C₂×Q₁₆	—	2	1	no	—
585	C₂×Q₁₆	—	4	1	no	—
586	C₂×SD₁₆	—	2	1	no	—
587	C₂×SD₁₆	—	2	1	no	—
588	C₂×SD₁₆	—	2	1	no	—
589	C₂×SD₁₆	—	2	1	no	—
590	C₂×SD₁₆	—	2	2	no	—
591	C₂×SD₁₆	—	2	1	no	—
592	C₂×SD₁₆	—	2	1	no	—
593	C₂×SD₁₆	—	2	1	no	—
594	C₂×SD₁₆	—	2	1	no	—
595	C₂×SD₁₆	—	4	1	no	—
596	C₂×D₈	—	2	1	no	—
597	C₂×D₈	—	2	1	no	—
598	#131	—	2	2	no	—
599	#131	—	2	2	no	—
600	#131	—	4	1	no	—
601	#131	—	4	1	no	—
602	C₂×M₁₆	—	2	1	no	—
603	C₂×M₁₆	—	2	2	no	—
604	C₂×M₁₆	—	2	2	no	—
605	C₂×M₁₆	—	2	1	no	—
606	C₂×M₁₆	—	2	1	no	—
607	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
613	C₂²×C₈	—	2	1	no	—
614	C₂²×C₈	—	2	1	no	—
615	C₂²×C₈	—	2	1	no	—
616	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	#108	—	2	2	no	—
626	#108	—	2	2	no	—
627	#103	—	2	1	no	—
628	#103	—	2	1	no	—
629	#103	—	2	1	no	—
630	#103	—	2	1	no	—
631	#102	—	2	1	no	—
632	#102	—	2	1	no	—
633	#102	—	2	1	no	—
634	#102	—	2	1	no	—
635	#101	—	2	2	no	—
636	#101	—	2	2	no	—
637	#101	—	2	2	no	—
638	#101	—	4	1	no	—
639	#100	—	2	2	no	—
640	#100	—	4	1	no	—
641	C₂²⋊C₈	—	2	1	no	—
642	C₂²⋊C₈	—	2	1	no	—
643	C₂²⋊C₈	—	2	1	no	—
644	C₂²⋊C₈	—	2	1	no	—
645	C₂²⋊C₈	—	2	1	no	—
646	C₂²⋊C₈	—	2	1	no	—
647	C₂²⋊C₈	—	2	1	no	—
648	C₂²⋊C₈	—	2	1	no	—
649	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
650	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
651	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
652	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
653	C₂×C₁₃	—	2	1	no	—
654	C₂×C₁₃	—	2	1	no	—
655	C₂×C₁₃	—	4	1	no	—
656	C₂×C₁₃	—	4	1	no	—
657	C₂×C₁₃	—	4	2	no	—
658	C₂×C₁₃	—	8	1	no	—
659	C₂×C₁₃	—	8	2	no	—
660	C₂×C₁₃	#2410	1	1	yes	characteristic
661	C₂×C₁₃	#3067	1	1	yes	characteristic
662	C₂×C₁₃	#3069	1	1	yes	characteristic
663	C₂⁴	—	2	1	no	—
664	C₂⁴	—	2	1	no	—
665	C₂⁴	C₁₃×#41	1	1	yes	characteristic
666	#41	—	2	1	no	—
667	#41	—	2	1	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	2	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	1	no	—
673	#41	—	2	1	no	—
674	#41	—	2	1	no	—
675	#41	—	2	1	no	—
676	#41	—	4	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	1	no	—
679	#41	—	4	1	no	—
680	#41	—	4	2	no	—
681	#41	—	4	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	2	no	—
688	#41	C₂×D₄×C₁₃	1	2	yes	—
689	#41	C₂×D₄×C₁₃	1	2	yes	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	1	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	4	1	no	—
704	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
705	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	Q₁₆	—	2	4	no	—
753	Q₁₆	—	2	4	no	—
754	Q₁₆	—	4	2	no	—
755	Q₁₆	—	4	2	no	—
756	Q₁₆	—	4	2	no	—
757	Q₁₆	—	4	2	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	4	2	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	D₈	—	2	4	no	—
767	D₈	—	2	4	no	—
768	M₁₆	—	2	4	no	—
769	M₁₆	—	2	1	no	—
770	M₁₆	—	2	1	no	—
771	M₁₆	—	2	1	no	—
772	M₁₆	—	2	1	no	—
773	M₁₆	—	2	1	no	—
774	M₁₆	—	2	1	no	—
775	M₁₆	—	2	1	no	—
776	M₁₆	—	2	1	no	—
777	M₁₆	—	2	1	no	—
778	M₁₆	—	2	1	no	—
779	M₁₆	—	4	2	no	—
780	M₁₆	—	4	2	no	—
781	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
782	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
783	C₂×C₈	—	2	4	no	—
784	C₂×C₈	—	2	1	no	—
785	C₂×C₈	—	2	1	no	—
786	C₂×C₈	—	2	1	no	—
787	C₂×C₈	—	2	1	no	—
788	C₂×C₈	—	2	1	no	—
789	C₂×C₈	—	2	1	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	4	2	no	—
795	C₂×C₈	—	4	2	no	—
796	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	1	no	—
806	C₁₃	#24403	1	1	yes	characteristic, direct product factor, Sylow
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	8	1	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	1	no	—
821	C₂³	C₁₃×#121	1	1	yes	characteristic
822	C₂³	C₁₃×#121	1	1	yes	characteristic
823	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	1	no	—
831	Q₈	—	4	1	no	—
832	Q₈	—	4	1	no	—
833	Q₈	—	4	1	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	4	1	no	—
836	Q₈	C₁₃×#120	1	2	yes	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	1	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	2	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	C₁₃×#120	1	2	yes	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	8	1	no	—
883	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
884	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
889	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	1	no	—
897	C₈	—	4	1	no	—
898	C₈	—	4	1	no	—
899	C₈	—	4	1	no	—
900	C₈	—	4	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	2	no	—
919	C₂²	—	8	2	no	—
920	C₂²	—	8	4	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
924	C₂²	C₁₃×#546	1	1	yes	characteristic
925	C₂²	C₁₃×#546	1	1	yes	characteristic
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	8	1	no	—
932	C₄	—	8	1	no	—
933	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
934	C₄	C₁₃×#534	1	1	yes	characteristic
935	C₄	D₄²×C₁₃	1	1	yes	characteristic
936	C₄	D₄²×C₁₃	1	1	yes	characteristic
937	C₂	—	2	1	no	—
938	C₂	—	2	1	no	—
939	C₂	—	4	1	no	—
940	C₂	—	4	1	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	1	no	—
943	C₂	—	8	2	no	—
944	C₂	C₁₃×#2410	1	1	yes	characteristic
945	C₂	C₁₃×#3067	1	1	yes	characteristic
946	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#473	C₂	semidirect
3. C₂×C₁₃×#471	C₂	semidirect
4. C₁₃×#3007	C₂	semidirect
5. C₂×C₁₃×#452	C₂	semidirect
6. C₁₃×#2880	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#2020	C₂	semidirect
10. C₁₃×#2019	C₂	semidirect
11. C₁₃×#1908	C₂	semidirect
12. C₁₃×#1907	C₂	semidirect
13. C₁₃×#1901	C₂	semidirect
14. C₁₃×#1855	C₂	semidirect
15. C₁₃×#1785	C₂	semidirect
30. C₂²×C₁₃×Q₁₆	C₂²	semidirect
31. C₂²×C₁₃×SD₁₆	C₂²	semidirect
46. C₂×C₁₃×#108	C₂²	semidirect
47. C₂×C₁₃×#108	C₂²	semidirect
50. C₂×C₁₃×#103	C₂²	semidirect
51. C₂×C₁₃×#102	C₂²	semidirect
52. C₂×C₁₃×#101	C₂²	semidirect
53. C₂×C₁₃×#101	C₂²	semidirect
54. C₂×C₁₃×#101	C₂²	semidirect
55. C₂×C₁₃×#101	C₂²	semidirect
56. C₂×C₁₃×#100	C₂²	semidirect
57. C₂×C₁₃×#100	C₂²	semidirect
67. C₁₃×#343	C₂²	semidirect
68. C₁₃×#343	C₂²	semidirect
69. C₁₃×#341	C₂²	semidirect
70. C₁₃×#341	C₂²	semidirect
190. #24403	C₁₃	direct (N × H)
335. C₂×#473	C₂×C₁₃	semidirect
336. C₂×#471	C₂×C₁₃	semidirect
337. #3007	C₂×C₁₃	semidirect
338. C₂×#452	C₂×C₁₃	semidirect
339. #2880	C₂×C₁₃	semidirect
340. #2052	C₂×C₁₃	semidirect
341. #2051	C₂×C₁₃	semidirect
342. #2020	C₂×C₁₃	semidirect
343. #2019	C₂×C₁₃	semidirect
344. #1908	C₂×C₁₃	semidirect
345. #1907	C₂×C₁₃	semidirect
346. #1901	C₂×C₁₃	semidirect
347. #1855	C₂×C₁₃	semidirect
348. #1785	C₂×C₁₃	semidirect
457. C₂²×Q₁₆	C₂²×C₁₃	semidirect
458. C₂²×SD₁₆	C₂²×C₁₃	semidirect
473. C₂×#108	C₂²×C₁₃	semidirect
474. C₂×#108	C₂²×C₁₃	semidirect
477. C₂×#103	C₂²×C₁₃	semidirect
478. C₂×#102	C₂²×C₁₃	semidirect
479. C₂×#101	C₂²×C₁₃	semidirect
480. C₂×#101	C₂²×C₁₃	semidirect
481. C₂×#101	C₂²×C₁₃	semidirect
482. C₂×#101	C₂²×C₁₃	semidirect
483. C₂×#100	C₂²×C₁₃	semidirect
484. C₂×#100	C₂²×C₁₃	semidirect
494. #343	C₂²×C₁₃	semidirect
495. #343	C₂²×C₁₃	semidirect
496. #341	C₂²×C₁₃	semidirect
497. #341	C₂²×C₁₃	semidirect
806. C₁₃	#24403	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#575	2
C₂×C₁₃×#473	2
C₂×C₁₃×#471	2
C₁₃×#3007	2
C₂×C₁₃×#452	2
C₁₃×#2880	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#2020	2
C₁₃×#2019	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1901	2
C₁₃×#1855	2
C₁₃×#1785	2
#24403	13

Subgroups — C13×#24403 #15710742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24403 #15710742