Subgroups — C₁₃×#25188 #15711527

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#537	C₂²	1	1	yes	characteristic
24	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₁₃×#520	C₂²	1	1	yes	characteristic
27	C₁₃×#469	—	2	1	no	—
28	C₁₃×#468	—	2	1	no	—
29	C₁₃×#466	—	2	1	no	—
30	C₁₃×#465	—	2	1	no	—
31	C₁₃×#464	—	2	1	no	—
32	C₁₃×#463	—	2	1	no	—
33	C₁₃×#460	—	2	1	no	—
34	C₁₃×#459	—	2	1	no	—
35	C₁₃×#453	—	2	4	no	—
36	C₁₃×#452	—	2	1	no	—
37	C₁₃×#450	—	2	1	no	—
38	C₁₃×#449	—	2	1	no	—
39	C₁₃×#447	—	2	1	no	—
40	C₁₃×#443	—	2	4	no	—
41	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#418	—	2	1	no	—
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#417	—	2	1	no	—
50	C₁₃×#417	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#416	—	2	1	no	—
54	C₁₃×#416	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#102	—	2	1	no	—
56	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#408	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×H(5,𝔽₂)	—	2	2	no	—
70	C₁₃×H(5,𝔽₂)	—	2	2	no	—
71	C₁₃×H(5,𝔽₂)	—	2	2	no	—
72	C₁₃×H(5,𝔽₂)	—	4	1	no	—
73	C₂×C₁₃×#41	—	2	1	no	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	—	4	1	no	—
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
85	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₁₃×#135	—	2	2	no	—
91	C₁₃×#135	—	2	2	no	—
92	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
93	C₂×C₁₃×SD₁₆	—	2	1	no	—
94	C₂×C₁₃×SD₁₆	—	2	1	no	—
95	C₂×C₁₃×SD₁₆	—	2	1	no	—
96	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic, complemented
97	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic, complemented
98	C₂×C₁₃×D₈	—	2	1	no	—
99	C₂×C₁₃×D₈	—	2	1	no	—
100	C₂×C₁₃×D₈	—	2	1	no	—
101	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic, complemented
102	C₁₃×#131	—	2	2	no	—
103	C₁₃×#131	—	2	2	no	—
104	C₁₃×#131	—	4	1	no	—
105	C₁₃×#131	—	4	1	no	—
106	C₂×C₁₃×M₁₆	—	2	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₃	—	2	1	no	—
113	C₂²×C₈×C₁₃	—	2	1	no	—
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#127	—	2	1	no	—
117	C₁₃×#127	—	2	2	no	—
118	C₁₃×#127	—	2	2	no	—
119	C₁₃×#124	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×#121	—	2	1	no	—
123	C₁₃×#121	—	2	1	no	—
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	—	2	1	no	—
126	C₁₃×#121	—	4	1	no	—
127	C₁₃×#120	—	4	1	no	—
128	C₄×Q₈×C₁₃	—	2	1	no	—
129	C₄×D₄×C₁₃	—	2	1	no	—
130	C₄×D₄×C₁₃	—	4	1	no	—
131	C₁₃×#117	—	2	1	no	—
132	C₁₃×#117	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₁₃×#108	—	2	2	no	—
139	C₁₃×#107	—	2	1	no	—
140	C₁₃×#106	—	2	1	no	—
141	C₁₃×C₄⋊C₈	—	2	1	no	—
142	C₁₃×C₄⋊C₈	—	2	1	no	—
143	C₁₃×#104	—	2	2	no	—
144	C₁₃×#104	—	2	2	no	—
145	C₁₃×#104	D₄	1	4	yes	complemented
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#103	—	2	1	no	—
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	D₄	1	1	yes	characteristic, complemented
150	C₁₃×#103	D₄	1	1	yes	characteristic, complemented
151	C₁₃×#102	—	2	1	no	—
152	C₁₃×#102	—	2	1	no	—
153	C₁₃×#102	—	2	1	no	—
154	C₁₃×#102	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#102	—	2	1	no	—
159	C₁₃×#102	—	2	1	no	—
160	C₁₃×#102	—	2	1	no	—
161	C₁₃×#102	—	2	1	no	—
162	C₁₃×#102	—	2	1	no	—
163	C₁₃×#102	—	2	1	no	—
164	C₁₃×#102	D₄	1	1	yes	characteristic, complemented
165	C₁₃×#102	D₄	1	1	yes	characteristic, complemented
166	C₁₃×#100	—	2	2	no	—
167	C₁₃×#100	—	4	1	no	—
168	C₁₃×C₂²⋊C₈	—	2	1	no	—
169	C₁₃×C₂²⋊C₈	—	2	1	no	—
170	C₄×C₈×C₁₃	—	2	2	no	—
171	#25188	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂⁴×C₁₃	—	2	1	no	—
173	C₂⁴×C₁₃	—	2	1	no	—
174	C₂⁴×C₁₃	—	4	1	no	—
175	C₁₃×#41	—	2	1	no	—
176	C₁₃×#41	—	2	1	no	—
177	C₁₃×#41	—	2	4	no	—
178	C₁₃×#41	—	2	1	no	—
179	C₁₃×#41	—	2	1	no	—
180	C₁₃×#41	—	2	1	no	—
181	C₁₃×#41	—	2	1	no	—
182	C₁₃×#41	—	2	1	no	—
183	C₁₃×#41	—	2	1	no	—
184	C₁₃×#41	—	2	1	no	—
185	C₁₃×#41	—	2	1	no	—
186	C₁₃×#41	—	4	2	no	—
187	C₁₃×#41	—	4	2	no	—
188	C₁₃×#41	—	4	2	no	—
189	C₁₃×#41	C₂×D₄	1	2	yes	—
190	C₁₃×#41	#41	1	2	yes	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	4	2	no	—
210	C₂×D₄×C₁₃	—	4	1	no	—
211	C₂×D₄×C₁₃	—	4	1	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	1	no	—
214	C₂×D₄×C₁₃	—	4	1	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	2	no	—
219	C₂×D₄×C₁₃	—	4	1	no	—
220	C₂×D₄×C₁₃	—	8	2	no	—
221	C₂×D₄×C₁₃	—	8	2	no	—
222	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₁₃	#41	1	2	yes	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	4	1	no	—
233	C₂²×C₄×C₁₃	—	4	1	no	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×Q₁₆	—	2	2	no	—
236	C₁₃×SD₁₆	—	2	2	no	—
237	C₁₃×SD₁₆	—	2	2	no	—
238	C₁₃×SD₁₆	—	4	2	no	—
239	C₁₃×SD₁₆	—	4	2	no	—
240	C₁₃×SD₁₆	—	4	2	no	—
241	C₁₃×D₈	—	2	2	no	—
242	C₁₃×D₈	—	4	2	no	—
243	C₁₃×D₈	—	4	2	no	—
244	C₁₃×D₈	—	4	2	no	—
245	C₁₃×M₁₆	—	2	1	no	—
246	C₁₃×M₁₆	—	2	1	no	—
247	C₁₃×M₁₆	—	2	1	no	—
248	C₁₃×M₁₆	—	2	1	no	—
249	C₁₃×M₁₆	—	2	1	no	—
250	C₁₃×M₁₆	—	2	1	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	—	4	2	no	—
253	C₁₃×M₁₆	—	4	2	no	—
254	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	—	2	1	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	4	2	no	—
264	C₂×C₈×C₁₃	—	4	2	no	—
265	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	8	2	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
277	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₁₃×C₂²⋊C₄	—	2	1	no	—
279	C₁₃×C₂²⋊C₄	—	4	1	no	—
280	C₁₃×C₂²⋊C₄	—	4	1	no	—
281	C₁₃×C₂²⋊C₄	—	4	1	no	—
282	C₁₃×C₂²⋊C₄	—	4	1	no	—
283	C₁₃×C₂²⋊C₄	—	4	1	no	—
284	C₄²×C₁₃	—	2	1	no	—
285	C₄²×C₁₃	—	2	1	no	—
286	C₄²×C₁₃	—	4	1	no	—
287	C₄²×C₁₃	C₂×D₄	1	2	yes	—
288	#3062	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3045	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#453	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3012	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#443	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2897	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2002	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#1937	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂³×C₁₃	—	2	1	no	—
304	C₂³×C₁₃	—	2	1	no	—
305	C₂³×C₁₃	—	2	1	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	4	4	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	8	1	no	—
314	C₂³×C₁₃	—	8	1	no	—
315	C₂³×C₁₃	—	8	1	no	—
316	C₂³×C₁₃	—	8	1	no	—
317	C₂³×C₁₃	—	16	1	no	—
318	C₂³×C₁₃	—	16	1	no	—
319	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
320	Q₈×C₁₃	—	2	1	no	—
321	Q₈×C₁₃	—	2	1	no	—
322	Q₈×C₁₃	—	2	1	no	—
323	Q₈×C₁₃	—	2	1	no	—
324	Q₈×C₁₃	—	2	1	no	—
325	Q₈×C₁₃	#121	1	2	yes	—
326	D₄×C₁₃	—	2	2	no	—
327	D₄×C₁₃	—	2	2	no	—
328	D₄×C₁₃	—	2	1	no	—
329	D₄×C₁₃	—	2	1	no	—
330	D₄×C₁₃	—	2	2	no	—
331	D₄×C₁₃	—	2	1	no	—
332	D₄×C₁₃	—	2	1	no	—
333	D₄×C₁₃	—	2	1	no	—
334	D₄×C₁₃	—	2	2	no	—
335	D₄×C₁₃	—	4	4	no	—
336	D₄×C₁₃	—	4	4	no	—
337	D₄×C₁₃	—	4	1	no	—
338	D₄×C₁₃	—	4	1	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	4	1	no	—
342	D₄×C₁₃	—	4	1	no	—
343	D₄×C₁₃	—	4	1	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	8	8	no	—
348	D₄×C₁₃	—	16	1	no	—
349	D₄×C₁₃	—	16	1	no	—
350	D₄×C₁₃	—	16	1	no	—
351	D₄×C₁₃	#121	1	2	yes	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	4	4	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	8	1	no	—
370	C₂×C₄×C₁₃	—	8	1	no	—
371	C₂×C₄×C₁₃	—	16	1	no	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
378	C₈×C₁₃	—	2	1	no	—
379	C₈×C₁₃	—	2	1	no	—
380	C₈×C₁₃	—	2	1	no	—
381	C₈×C₁₃	—	2	1	no	—
382	C₈×C₁₃	—	2	2	no	—
383	C₈×C₁₃	—	4	1	no	—
384	C₈×C₁₃	—	4	1	no	—
385	C₈×C₁₃	—	4	1	no	—
386	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	#537	C₂²×C₁₃	1	1	yes	characteristic
394	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
396	#520	C₂²×C₁₃	1	1	yes	characteristic
397	#469	—	2	1	no	—
398	#468	—	2	1	no	—
399	#466	—	2	1	no	—
400	#465	—	2	1	no	—
401	#464	—	2	1	no	—
402	#463	—	2	1	no	—
403	#460	—	2	1	no	—
404	#459	—	2	1	no	—
405	#453	—	2	4	no	—
406	#452	—	2	1	no	—
407	#450	—	2	1	no	—
408	#449	—	2	1	no	—
409	#447	—	2	1	no	—
410	#443	—	2	4	no	—
411	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#418	—	2	1	no	—
418	#418	C₂²×C₁₃	1	1	yes	characteristic
419	#417	—	2	1	no	—
420	#417	C₂²×C₁₃	1	1	yes	characteristic
421	#417	C₂²×C₁₃	1	1	yes	characteristic
422	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#416	—	2	1	no	—
424	#416	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#102	—	2	1	no	—
426	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#408	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂²×C₁₃	—	2	1	no	—
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	4	1	no	—
443	C₂²×C₁₃	—	4	1	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	1	no	—
447	C₂²×C₁₃	—	4	1	no	—
448	C₂²×C₁₃	—	4	1	no	—
449	C₂²×C₁₃	—	4	1	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	8	2	no	—
452	C₂²×C₁₃	—	8	2	no	—
453	C₂²×C₁₃	—	8	1	no	—
454	C₂²×C₁₃	—	8	1	no	—
455	C₂²×C₁₃	—	8	1	no	—
456	C₂²×C₁₃	—	8	1	no	—
457	C₂²×C₁₃	—	8	1	no	—
458	C₂²×C₁₃	—	16	1	no	—
459	C₂²×C₁₃	—	16	1	no	—
460	C₂²×C₁₃	—	16	4	no	—
461	C₂²×C₁₃	#538	1	1	yes	characteristic
462	C₂²×C₁₃	D₄²	1	1	yes	characteristic
463	C₂²×C₁₃	#546	1	1	yes	characteristic
464	C₄×C₁₃	—	2	4	no	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	4	1	no	—
470	C₄×C₁₃	—	8	1	no	—
471	C₄×C₁₃	—	8	1	no	—
472	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
473	C₄×C₁₃	#525	1	1	yes	characteristic
474	C₄×C₁₃	D₄²	1	1	yes	characteristic
475	C₄×C₁₃	#546	1	1	yes	characteristic
476	H(5,𝔽₂)	—	2	2	no	—
477	H(5,𝔽₂)	—	2	2	no	—
478	H(5,𝔽₂)	—	2	2	no	—
479	H(5,𝔽₂)	—	4	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	4	1	no	—
488	C₂²×D₄	—	4	1	no	—
489	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
491	AGL(1,ℤ/8)	—	2	2	no	—
492	AGL(1,ℤ/8)	—	2	2	no	—
493	AGL(1,ℤ/8)	—	2	2	no	—
494	AGL(1,ℤ/8)	—	2	2	no	—
495	AGL(1,ℤ/8)	—	4	1	no	—
496	AGL(1,ℤ/8)	—	4	1	no	—
497	#135	—	2	2	no	—
498	#135	—	2	2	no	—
499	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic, complemented
500	C₂×SD₁₆	—	2	1	no	—
501	C₂×SD₁₆	—	2	1	no	—
502	C₂×SD₁₆	—	2	1	no	—
503	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic, complemented
504	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic, complemented
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	2	1	no	—
507	C₂×D₈	—	2	1	no	—
508	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic, complemented
509	#131	—	2	2	no	—
510	#131	—	2	2	no	—
511	#131	—	4	1	no	—
512	#131	—	4	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×C₈	—	2	1	no	—
520	C₂²×C₈	—	2	1	no	—
521	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
523	#127	—	2	1	no	—
524	#127	—	2	2	no	—
525	#127	—	2	2	no	—
526	#124	—	2	1	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	4	1	no	—
534	#120	—	4	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	4	1	no	—
538	#117	—	2	1	no	—
539	#117	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	4	1	no	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
545	#108	—	2	2	no	—
546	#107	—	2	1	no	—
547	#106	—	2	1	no	—
548	C₄⋊C₈	—	2	1	no	—
549	C₄⋊C₈	—	2	1	no	—
550	#104	—	2	2	no	—
551	#104	—	2	2	no	—
552	#104	D₄×C₁₃	1	4	yes	complemented
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	D₄×C₁₃	1	1	yes	characteristic, complemented
557	#103	D₄×C₁₃	1	1	yes	characteristic, complemented
558	#102	—	2	1	no	—
559	#102	—	2	1	no	—
560	#102	—	2	1	no	—
561	#102	—	2	1	no	—
562	#102	—	2	1	no	—
563	#102	—	2	1	no	—
564	#102	—	2	1	no	—
565	#102	—	2	1	no	—
566	#102	—	2	1	no	—
567	#102	—	2	1	no	—
568	#102	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	D₄×C₁₃	1	1	yes	characteristic, complemented
572	#102	D₄×C₁₃	1	1	yes	characteristic, complemented
573	#100	—	2	2	no	—
574	#100	—	4	1	no	—
575	C₂²⋊C₈	—	2	1	no	—
576	C₂²⋊C₈	—	2	1	no	—
577	C₄×C₈	—	2	2	no	—
578	C₂×C₁₃	—	2	1	no	—
579	C₂×C₁₃	—	2	1	no	—
580	C₂×C₁₃	—	4	2	no	—
581	C₂×C₁₃	—	8	1	no	—
582	C₂×C₁₃	—	8	1	no	—
583	C₂×C₁₃	—	8	2	no	—
584	C₂×C₁₃	—	16	1	no	—
585	C₂×C₁₃	#2424	1	1	yes	characteristic
586	C₂×C₁₃	#3291	1	1	yes	characteristic
587	C₂×C₁₃	#3292	1	1	yes	characteristic
588	C₂⁴	—	2	1	no	—
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	4	1	no	—
591	#41	—	2	1	no	—
592	#41	—	2	1	no	—
593	#41	—	2	4	no	—
594	#41	—	2	1	no	—
595	#41	—	2	1	no	—
596	#41	—	2	1	no	—
597	#41	—	2	1	no	—
598	#41	—	2	1	no	—
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	4	2	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	C₂×D₄×C₁₃	1	2	yes	—
606	#41	C₁₃×#41	1	2	yes	—
607	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	8	2	no	—
637	C₂×D₄	—	8	2	no	—
638	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂×D₄	C₁₃×#41	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
651	Q₁₆	—	2	2	no	—
652	SD₁₆	—	2	2	no	—
653	SD₁₆	—	2	2	no	—
654	SD₁₆	—	4	2	no	—
655	SD₁₆	—	4	2	no	—
656	SD₁₆	—	4	2	no	—
657	D₈	—	2	2	no	—
658	D₈	—	4	2	no	—
659	D₈	—	4	2	no	—
660	D₈	—	4	2	no	—
661	M₁₆	—	2	1	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	4	2	no	—
669	M₁₆	—	4	2	no	—
670	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	4	2	no	—
680	C₂×C₈	—	4	2	no	—
681	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
684	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	8	2	no	—
692	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	4	1	no	—
698	C₂²⋊C₄	—	4	1	no	—
699	C₂²⋊C₄	—	4	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	4	1	no	—
703	C₄²	C₂×D₄×C₁₃	1	2	yes	—
704	C₁₃	#25188	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	4	4	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	—	8	1	no	—
718	C₂³	—	8	1	no	—
719	C₂³	—	16	1	no	—
720	C₂³	—	16	1	no	—
721	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
722	Q₈	—	2	1	no	—
723	Q₈	—	2	1	no	—
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	C₁₃×#121	1	2	yes	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	1	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	8	8	no	—
750	D₄	—	16	1	no	—
751	D₄	—	16	1	no	—
752	D₄	—	16	1	no	—
753	D₄	C₁₃×#121	1	2	yes	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	16	1	no	—
774	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
777	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
778	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
779	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₈	—	2	1	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	—	2	1	no	—
784	C₈	—	2	2	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₈	—	4	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	8	2	no	—
801	C₂²	—	8	2	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	16	1	no	—
808	C₂²	—	16	1	no	—
809	C₂²	—	16	4	no	—
810	C₂²	C₁₃×#538	1	1	yes	characteristic
811	C₂²	D₄²×C₁₃	1	1	yes	characteristic
812	C₂²	C₁₃×#546	1	1	yes	characteristic
813	C₄	—	2	4	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	8	1	no	—
820	C₄	—	8	1	no	—
821	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
822	C₄	C₁₃×#525	1	1	yes	characteristic
823	C₄	D₄²×C₁₃	1	1	yes	characteristic
824	C₄	C₁₃×#546	1	1	yes	characteristic
825	C₂	—	2	1	no	—
826	C₂	—	2	1	no	—
827	C₂	—	4	2	no	—
828	C₂	—	8	1	no	—
829	C₂	—	8	1	no	—
830	C₂	—	8	2	no	—
831	C₂	—	16	1	no	—
832	C₂	C₁₃×#2424	1	1	yes	characteristic
833	C₂	C₁₃×#3291	1	1	yes	characteristic
834	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3062	C₂	semidirect
2. C₁₃×#3045	C₂	semidirect
3. C₂×C₁₃×#453	C₂	semidirect
4. C₁₃×#3012	C₂	semidirect
5. C₂×C₁₃×#443	C₂	semidirect
6. C₁₃×#2897	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#2039	C₂	semidirect
10. C₁₃×#2002	C₂	semidirect
11. C₁₃×#1957	C₂	semidirect
12. C₁₃×#1937	C₂	semidirect
13. C₁₃×#1907	C₂	semidirect
14. C₁₃×#1907	C₂	semidirect
15. C₁₃×#1859	C₂	semidirect
22. C₂×C₁₃×#131	C₂²	semidirect
24. C₁₃×#535	C₂²	semidirect
41. C₂×C₁₃×#108	C₂²	semidirect
42. C₁₃×#428	C₂²	semidirect
43. C₁₃×#424	C₂²	semidirect
46. C₂×C₁₃×#104	C₂²	semidirect
52. C₁₃×#417	C₂²	semidirect
58. C₂×C₁₃×#102	C₂²	semidirect
59. C₂×C₁₃×#102	C₂²	semidirect
61. C₂×C₁₃×#100	C₂²	semidirect
63. C₂×C₄×C₈×C₁₃	C₂²	semidirect
64. C₁₃×#384	C₂²	semidirect
65. C₁₃×#343	C₂²	semidirect
66. C₁₃×#343	C₂²	semidirect
67. C₁₃×#341	C₂²	semidirect
68. C₁₃×#339	C₂²	semidirect
92. C₂×C₁₃×Q₁₆	D₄	semidirect
96. C₂×C₁₃×SD₁₆	D₄	semidirect
97. C₂×C₁₃×SD₁₆	D₄	semidirect
101. C₂×C₁₃×D₈	D₄	semidirect
145. C₁₃×#104	D₄	semidirect
149. C₁₃×#103	D₄	semidirect
150. C₁₃×#103	D₄	semidirect
164. C₁₃×#102	D₄	semidirect
165. C₁₃×#102	D₄	semidirect
171. #25188	C₁₃	direct (N × H)
288. #3062	C₂×C₁₃	semidirect
289. #3045	C₂×C₁₃	semidirect
290. C₂×#453	C₂×C₁₃	semidirect
291. #3012	C₂×C₁₃	semidirect
292. C₂×#443	C₂×C₁₃	semidirect
293. #2897	C₂×C₁₃	semidirect
294. #2063	C₂×C₁₃	semidirect
295. #2051	C₂×C₁₃	semidirect
296. #2039	C₂×C₁₃	semidirect
297. #2002	C₂×C₁₃	semidirect
298. #1957	C₂×C₁₃	semidirect
299. #1937	C₂×C₁₃	semidirect
300. #1907	C₂×C₁₃	semidirect
301. #1907	C₂×C₁₃	semidirect
302. #1859	C₂×C₁₃	semidirect
392. C₂×#131	C₂²×C₁₃	semidirect
394. #535	C₂²×C₁₃	semidirect
411. C₂×#108	C₂²×C₁₃	semidirect
412. #428	C₂²×C₁₃	semidirect
413. #424	C₂²×C₁₃	semidirect
416. C₂×#104	C₂²×C₁₃	semidirect
422. #417	C₂²×C₁₃	semidirect
428. C₂×#102	C₂²×C₁₃	semidirect
429. C₂×#102	C₂²×C₁₃	semidirect
431. C₂×#100	C₂²×C₁₃	semidirect
433. C₂×C₄×C₈	C₂²×C₁₃	semidirect
434. #384	C₂²×C₁₃	semidirect
435. #343	C₂²×C₁₃	semidirect
436. #343	C₂²×C₁₃	semidirect
437. #341	C₂²×C₁₃	semidirect
438. #339	C₂²×C₁₃	semidirect
499. C₂×Q₁₆	D₄×C₁₃	semidirect
503. C₂×SD₁₆	D₄×C₁₃	semidirect
504. C₂×SD₁₆	D₄×C₁₃	semidirect
508. C₂×D₈	D₄×C₁₃	semidirect
552. #104	D₄×C₁₃	semidirect
556. #103	D₄×C₁₃	semidirect
557. #103	D₄×C₁₃	semidirect
571. #102	D₄×C₁₃	semidirect
572. #102	D₄×C₁₃	semidirect
704. C₁₃	#25188	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3062	2
C₁₃×#3045	2
C₂×C₁₃×#453	2
C₁₃×#3012	2
C₂×C₁₃×#443	2
C₁₃×#2897	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#2039	2
C₁₃×#2002	2
C₁₃×#1957	2
C₁₃×#1937	2
C₁₃×#1907	2
C₁₃×#1859	2
#25188	13

Subgroups — C13×#25188 #15711527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25188 #15711527