Subgroups — C₁₃×#61109 #15747448

Order 3328.

2626 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3586	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3585	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3290	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3289	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3288	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3069	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3068	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3018	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#455	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2956	C₂	1	2	yes	maximal, complemented
13	C₁₃×#585	C₂²	1	2	yes	complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
16	C₁₃×#578	—	2	4	no	—
17	C₁₃×#578	C₂²	1	8	yes	complemented
18	C₁₃×#577	—	2	4	no	—
19	C₁₃×#577	—	2	4	no	—
20	C₁₃×#577	C₂²	1	8	yes	complemented
21	C₁₃×#577	C₂²	1	8	yes	complemented
22	C₁₃×#576	—	2	4	no	—
23	C₁₃×#576	C₂²	1	8	yes	complemented
24	C₁₃×#575	—	2	4	no	—
25	C₁₃×#575	—	2	4	no	—
26	C₁₃×#575	C₂²	1	2	yes	—
27	C₁₃×#575	C₂²	1	2	yes	—
28	C₁₃×#575	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#137	—	2	4	no	—
30	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
32	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
33	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
34	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
35	C₁₃×#568	C₂²	1	2	yes	complemented
36	C₁₃×#568	C₂²	1	2	yes	complemented
37	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#497	C₂²	1	2	yes	complemented
40	C₁₃×#496	C₂²	1	2	yes	complemented
41	C₁₃×#495	C₂²	1	4	yes	complemented
42	C₁₃×#473	C₂²	1	8	yes	complemented
43	C₁₃×#472	C₂²	1	8	yes	complemented
44	C₁₃×#471	C₂²	1	8	yes	complemented
45	C₁₃×#471	C₂²	1	8	yes	complemented
46	C₁₃×#456	C₂²	1	4	yes	complemented
47	C₁₃×#455	C₂²	1	4	yes	complemented
48	C₁₃×#455	C₂²	1	4	yes	complemented
49	C₁₃×#455	C₂²	1	4	yes	complemented
50	C₁₃×#454	C₂²	1	4	yes	complemented
51	C₁₃×#454	C₂²	1	4	yes	complemented
52	C₁₃×#454	C₂²	1	4	yes	complemented
53	C₁₃×#453	C₂²	1	4	yes	complemented
54	C₁₃×#444	C₂²	1	8	yes	complemented
55	C₁₃×#443	C₂²	1	8	yes	complemented
56	C₁₃×#430	C₂²	1	2	yes	complemented
57	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
58	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
59	C₁₃×#413	C₂²	1	2	yes	complemented
60	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
62	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×2₋¹⁺⁴	—	2	4	no	—
64	C₁₃×2₋¹⁺⁴	—	2	2	no	—
65	C₁₃×2₋¹⁺⁴	—	2	2	no	—
66	C₁₃×2₋¹⁺⁴	—	4	1	no	—
67	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	—
68	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	complemented
69	C₁₃×H(5,𝔽₂)	—	2	4	no	—
70	C₁₃×H(5,𝔽₂)	—	2	2	no	—
71	C₁₃×H(5,𝔽₂)	—	2	2	no	—
72	C₁₃×H(5,𝔽₂)	—	4	2	no	—
73	C₁₃×H(5,𝔽₂)	—	4	1	no	—
74	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
75	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
76	C₂×C₁₃×#41	—	2	4	no	—
77	C₂×C₁₃×#41	—	2	4	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	4	1	no	—
81	C₂×C₁₃×#41	—	4	2	no	—
82	C₂×C₁₃×#41	C₂³	1	2	yes	—
83	C₂×C₁₃×#41	C₂³	1	2	yes	—
84	C₂×C₁₃×#41	C₂³	1	2	yes	—
85	C₂²×Q₈×C₁₃	—	2	2	no	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	—	4	1	no	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#137	—	2	4	no	—
91	C₁₃×#137	—	2	2	no	—
92	C₁₃×#137	—	2	2	no	—
93	C₁₃×#137	—	2	8	no	—
94	C₁₃×#137	—	2	8	no	—
95	C₁₃×#137	—	2	8	no	—
96	C₁₃×#137	—	2	8	no	—
97	C₁₃×#137	—	2	4	no	—
98	C₁₃×#137	—	2	4	no	—
99	C₁₃×#137	D₄	1	4	yes	complemented
100	C₁₃×#137	D₄	1	4	yes	complemented
101	C₁₃×#137	C₂³	1	8	yes	—
102	C₁₃×#137	C₂³	1	4	yes	—
103	C₁₃×#137	C₂³	1	4	yes	complemented
104	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
105	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
106	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
107	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
108	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
109	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
112	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
113	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
114	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
115	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
116	C₁₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
117	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	complemented
118	C₁₃×#135	—	2	4	no	—
119	C₁₃×#135	—	2	4	no	—
120	C₁₃×#135	—	2	8	no	—
121	C₁₃×#135	—	2	8	no	—
122	C₁₃×#135	—	2	8	no	—
123	C₁₃×#135	—	2	8	no	—
124	C₁₃×#135	C₂³	1	8	yes	—
125	C₂×C₁₃×Q₁₆	—	2	2	no	—
126	C₂×C₁₃×Q₁₆	—	2	8	no	—
127	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
128	C₂×C₁₃×SD₁₆	—	2	2	no	—
129	C₂×C₁₃×SD₁₆	—	2	2	no	—
130	C₂×C₁₃×SD₁₆	—	2	8	no	—
131	C₂×C₁₃×SD₁₆	—	2	8	no	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
134	C₂×C₁₃×D₈	—	2	2	no	—
135	C₂×C₁₃×D₈	—	2	8	no	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₁₃×#131	—	2	4	no	—
138	C₁₃×#131	—	2	4	no	—
139	C₁₃×#131	C₂³	1	8	yes	—
140	C₁₃×#131	C₂³	1	8	yes	complemented
141	C₂×C₁₃×M₁₆	—	2	4	no	—
142	C₂×C₁₃×M₁₆	—	2	4	no	—
143	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
146	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
147	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
148	C₁₃×#124	—	4	1	no	—
149	C₁₃×#124	C₂³	1	2	yes	—
150	C₁₃×#124	C₂³	1	2	yes	—
151	C₁₃×#124	C₂³	1	2	yes	complemented
152	C₁₃×#121	—	4	1	no	—
153	C₄×D₄×C₁₃	—	4	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#108	C₂³	1	8	yes	complemented
157	C₁₃×#104	C₂³	1	4	yes	—
158	C₁₃×#104	C₂³	1	4	yes	—
159	C₁₃×#104	C₂³	1	4	yes	complemented
160	C₁₃×#104	C₂³	1	4	yes	complemented
161	C₁₃×#101	C₂³	1	4	yes	complemented
162	C₁₃×#101	C₂³	1	4	yes	complemented
163	C₁₃×#100	C₂³	1	4	yes	—
164	C₁₃×#100	C₂³	1	4	yes	complemented
165	C₁₃×#97	C₂³	1	2	yes	complemented
166	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
167	#61109	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	1	no	—
169	C₂⁴×C₁₃	—	4	1	no	—
170	C₁₃×#41	—	2	2	no	—
171	C₁₃×#41	—	2	2	no	—
172	C₁₃×#41	—	2	2	no	—
173	C₁₃×#41	—	2	2	no	—
174	C₁₃×#41	—	2	4	no	—
175	C₁₃×#41	—	2	8	no	—
176	C₁₃×#41	—	2	4	no	—
177	C₁₃×#41	—	2	4	no	—
178	C₁₃×#41	—	2	8	no	—
179	C₁₃×#41	—	2	4	no	—
180	C₁₃×#41	—	2	2	no	—
181	C₁₃×#41	—	2	2	no	—
182	C₁₃×#41	—	2	2	no	—
183	C₁₃×#41	—	2	2	no	—
184	C₁₃×#41	—	4	4	no	—
185	C₁₃×#41	—	4	4	no	—
186	C₁₃×#41	—	4	4	no	—
187	C₁₃×#41	—	4	4	no	—
188	C₁₃×#41	—	4	4	no	—
189	C₁₃×#41	—	4	4	no	—
190	C₁₃×#41	—	4	4	no	—
191	C₁₃×#41	—	4	4	no	—
192	C₁₃×#41	—	4	2	no	—
193	C₁₃×#41	—	4	2	no	—
194	C₁₃×#41	C₂×D₄	1	4	yes	—
195	C₁₃×#41	C₂×D₄	1	4	yes	—
196	C₁₃×#41	C₂⁴	1	4	yes	—
197	C₁₃×#41	C₂⁴	1	4	yes	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	4	no	—
200	C₂×Q₈×C₁₃	—	2	8	no	—
201	C₂×Q₈×C₁₃	—	2	4	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	4	1	no	—
205	C₂×Q₈×C₁₃	—	4	4	no	—
206	C₂×Q₈×C₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	8	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	—	4	4	no	—
221	C₂×D₄×C₁₃	—	4	2	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	—	4	4	no	—
226	C₂×D₄×C₁₃	—	4	2	no	—
227	C₂×D₄×C₁₃	—	4	4	no	—
228	C₂×D₄×C₁₃	—	4	4	no	—
229	C₂×D₄×C₁₃	—	4	1	no	—
230	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	4	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₁₃×Q₁₆	—	2	8	no	—
244	C₁₃×Q₁₆	—	2	4	no	—
245	C₁₃×Q₁₆	—	2	4	no	—
246	C₁₃×Q₁₆	—	2	8	no	—
247	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
248	C₁₃×SD₁₆	—	2	8	no	—
249	C₁₃×SD₁₆	—	2	4	no	—
250	C₁₃×SD₁₆	—	2	4	no	—
251	C₁₃×SD₁₆	—	2	4	no	—
252	C₁₃×SD₁₆	—	2	8	no	—
253	C₁₃×SD₁₆	—	2	4	no	—
254	C₁₃×SD₁₆	—	2	8	no	—
255	C₁₃×SD₁₆	—	2	8	no	—
256	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
257	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
258	C₁₃×D₈	—	2	4	no	—
259	C₁₃×D₈	—	2	8	no	—
260	C₁₃×D₈	—	2	4	no	—
261	C₁₃×D₈	—	2	8	no	—
262	C₁₃×D₈	C₂×D₄	1	8	yes	—
263	C₁₃×M₁₆	—	2	2	no	—
264	C₁₃×M₁₆	—	2	2	no	—
265	C₁₃×M₁₆	—	2	8	no	—
266	C₁₃×M₁₆	—	2	8	no	—
267	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
268	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
269	C₁₃×M₁₆	C₂⁴	1	4	yes	—
270	C₁₃×M₁₆	C₂⁴	1	4	yes	—
271	C₂×C₈×C₁₃	—	2	2	no	—
272	C₂×C₈×C₁₃	—	2	2	no	—
273	C₂×C₈×C₁₃	—	2	8	no	—
274	C₂×C₈×C₁₃	—	2	8	no	—
275	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₄²×C₁₃	—	2	1	no	—
281	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
283	#3586	C₂×C₁₃	1	2	yes	complemented
284	#3585	C₂×C₁₃	1	2	yes	complemented
285	#3290	C₂×C₁₃	1	8	yes	complemented
286	#3289	C₂×C₁₃	1	4	yes	complemented
287	#3288	C₂×C₁₃	1	4	yes	complemented
288	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3069	C₂×C₁₃	1	2	yes	complemented
290	#3068	C₂×C₁₃	1	2	yes	complemented
291	#3018	C₂×C₁₃	1	2	yes	complemented
292	C₂×#454	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#455	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2956	C₂×C₁₃	1	2	yes	complemented
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	—	4	4	no	—
301	C₂³×C₁₃	—	4	1	no	—
302	C₂³×C₁₃	—	4	1	no	—
303	C₂³×C₁₃	—	8	2	no	—
304	C₂³×C₁₃	—	16	2	no	—
305	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
306	Q₈×C₁₃	—	2	2	no	—
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	4	no	—
310	Q₈×C₁₃	—	2	2	no	—
311	Q₈×C₁₃	—	4	4	no	—
312	Q₈×C₁₃	—	4	4	no	—
313	Q₈×C₁₃	—	4	2	no	—
314	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
315	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	4	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	4	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	4	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	8	no	—
326	D₄×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	4	2	no	—
331	D₄×C₁₃	—	4	2	no	—
332	D₄×C₁₃	—	4	2	no	—
333	D₄×C₁₃	—	8	2	no	—
334	D₄×C₁₃	C₂²×D₄	1	4	yes	—
335	D₄×C₁₃	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	4	4	no	—
349	C₂×C₄×C₁₃	—	4	4	no	—
350	C₂×C₄×C₁₃	—	4	8	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	2	no	—
354	C₂×C₄×C₁₃	—	4	2	no	—
355	C₂×C₄×C₁₃	—	8	1	no	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
360	C₈×C₁₃	—	2	4	no	—
361	C₈×C₁₃	—	2	4	no	—
362	C₈×C₁₃	C₂²×D₄	1	8	yes	—
363	#585	C₂²×C₁₃	1	2	yes	complemented
364	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
365	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
366	#578	—	2	4	no	—
367	#578	C₂²×C₁₃	1	8	yes	complemented
368	#577	—	2	4	no	—
369	#577	—	2	4	no	—
370	#577	C₂²×C₁₃	1	8	yes	complemented
371	#577	C₂²×C₁₃	1	8	yes	complemented
372	#576	—	2	4	no	—
373	#576	C₂²×C₁₃	1	8	yes	complemented
374	#575	—	2	4	no	—
375	#575	—	2	4	no	—
376	#575	C₂²×C₁₃	1	2	yes	—
377	#575	C₂²×C₁₃	1	2	yes	—
378	#575	C₂²×C₁₃	1	2	yes	complemented
379	C₂×#137	—	2	4	no	—
380	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
381	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
382	C₂×AGL(1,ℤ/8)	—	2	4	no	—
383	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
384	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
385	#568	C₂²×C₁₃	1	2	yes	complemented
386	#568	C₂²×C₁₃	1	2	yes	complemented
387	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#497	C₂²×C₁₃	1	2	yes	complemented
390	#496	C₂²×C₁₃	1	2	yes	complemented
391	#495	C₂²×C₁₃	1	4	yes	complemented
392	#473	C₂²×C₁₃	1	8	yes	complemented
393	#472	C₂²×C₁₃	1	8	yes	complemented
394	#471	C₂²×C₁₃	1	8	yes	complemented
395	#471	C₂²×C₁₃	1	8	yes	complemented
396	#456	C₂²×C₁₃	1	4	yes	complemented
397	#455	C₂²×C₁₃	1	4	yes	complemented
398	#455	C₂²×C₁₃	1	4	yes	complemented
399	#455	C₂²×C₁₃	1	4	yes	complemented
400	#454	C₂²×C₁₃	1	4	yes	complemented
401	#454	C₂²×C₁₃	1	4	yes	complemented
402	#454	C₂²×C₁₃	1	4	yes	complemented
403	#453	C₂²×C₁₃	1	4	yes	complemented
404	#444	C₂²×C₁₃	1	8	yes	complemented
405	#443	C₂²×C₁₃	1	8	yes	complemented
406	#430	C₂²×C₁₃	1	2	yes	complemented
407	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
408	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
409	#413	C₂²×C₁₃	1	2	yes	complemented
410	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂²×C₁₃	—	2	4	no	—
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	4	1	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	—	8	2	no	—
419	C₂²×C₁₃	—	8	2	no	—
420	C₂²×C₁₃	—	8	2	no	—
421	C₂²×C₁₃	—	8	2	no	—
422	C₂²×C₁₃	—	8	2	no	—
423	C₂²×C₁₃	—	16	1	no	—
424	C₂²×C₁₃	—	16	4	no	—
425	C₂²×C₁₃	—	16	4	no	—
426	C₂²×C₁₃	D₄²	1	1	yes	characteristic
427	C₂²×C₁₃	D₄²	1	1	yes	characteristic
428	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₄×C₁₃	—	2	4	no	—
430	C₄×C₁₃	—	2	4	no	—
431	C₄×C₁₃	—	4	1	no	—
432	C₄×C₁₃	—	4	1	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	D₄²	1	2	yes	—
436	C₄×C₁₃	C₂³×D₄	1	2	yes	—
437	2₋¹⁺⁴	—	2	4	no	—
438	2₋¹⁺⁴	—	2	2	no	—
439	2₋¹⁺⁴	—	2	2	no	—
440	2₋¹⁺⁴	—	4	1	no	—
441	2₋¹⁺⁴	C₂³×C₁₃	1	4	yes	—
442	2₋¹⁺⁴	C₂³×C₁₃	1	4	yes	complemented
443	H(5,𝔽₂)	—	2	4	no	—
444	H(5,𝔽₂)	—	2	2	no	—
445	H(5,𝔽₂)	—	2	2	no	—
446	H(5,𝔽₂)	—	4	2	no	—
447	H(5,𝔽₂)	—	4	1	no	—
448	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
449	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	—	2	4	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	4	1	no	—
455	C₂×#41	—	4	2	no	—
456	C₂×#41	C₂³×C₁₃	1	2	yes	—
457	C₂×#41	C₂³×C₁₃	1	2	yes	—
458	C₂×#41	C₂³×C₁₃	1	2	yes	—
459	C₂²×Q₈	—	2	2	no	—
460	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×D₄	—	2	2	no	—
462	C₂²×D₄	—	4	1	no	—
463	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
464	#137	—	2	4	no	—
465	#137	—	2	2	no	—
466	#137	—	2	2	no	—
467	#137	—	2	8	no	—
468	#137	—	2	8	no	—
469	#137	—	2	8	no	—
470	#137	—	2	8	no	—
471	#137	—	2	4	no	—
472	#137	—	2	4	no	—
473	#137	D₄×C₁₃	1	4	yes	complemented
474	#137	D₄×C₁₃	1	4	yes	complemented
475	#137	C₂³×C₁₃	1	8	yes	—
476	#137	C₂³×C₁₃	1	4	yes	—
477	#137	C₂³×C₁₃	1	4	yes	complemented
478	AGL(1,ℤ/8)	—	2	4	no	—
479	AGL(1,ℤ/8)	—	2	2	no	—
480	AGL(1,ℤ/8)	—	2	2	no	—
481	AGL(1,ℤ/8)	—	2	8	no	—
482	AGL(1,ℤ/8)	—	2	8	no	—
483	AGL(1,ℤ/8)	—	2	8	no	—
484	AGL(1,ℤ/8)	—	2	8	no	—
485	AGL(1,ℤ/8)	—	2	4	no	—
486	AGL(1,ℤ/8)	—	2	4	no	—
487	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	complemented
488	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	complemented
489	AGL(1,ℤ/8)	C₂³×C₁₃	1	8	yes	—
490	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	—
491	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	complemented
492	#135	—	2	4	no	—
493	#135	—	2	4	no	—
494	#135	—	2	8	no	—
495	#135	—	2	8	no	—
496	#135	—	2	8	no	—
497	#135	—	2	8	no	—
498	#135	C₂³×C₁₃	1	8	yes	—
499	C₂×Q₁₆	—	2	2	no	—
500	C₂×Q₁₆	—	2	8	no	—
501	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
502	C₂×SD₁₆	—	2	2	no	—
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	8	no	—
505	C₂×SD₁₆	—	2	8	no	—
506	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
508	C₂×D₈	—	2	2	no	—
509	C₂×D₈	—	2	8	no	—
510	C₂×D₈	C₂³×C₁₃	1	4	yes	—
511	#131	—	2	4	no	—
512	#131	—	2	4	no	—
513	#131	C₂³×C₁₃	1	8	yes	—
514	#131	C₂³×C₁₃	1	8	yes	complemented
515	C₂×M₁₆	—	2	4	no	—
516	C₂×M₁₆	—	2	4	no	—
517	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
518	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
519	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
521	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
522	#124	—	4	1	no	—
523	#124	C₂³×C₁₃	1	2	yes	—
524	#124	C₂³×C₁₃	1	2	yes	—
525	#124	C₂³×C₁₃	1	2	yes	complemented
526	#121	—	4	1	no	—
527	C₄×D₄	—	4	1	no	—
528	C₂×C₂²⋊C₄	—	4	1	no	—
529	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
530	#108	C₂³×C₁₃	1	8	yes	complemented
531	#104	C₂³×C₁₃	1	4	yes	—
532	#104	C₂³×C₁₃	1	4	yes	—
533	#104	C₂³×C₁₃	1	4	yes	complemented
534	#104	C₂³×C₁₃	1	4	yes	complemented
535	#101	C₂³×C₁₃	1	4	yes	complemented
536	#101	C₂³×C₁₃	1	4	yes	complemented
537	#100	C₂³×C₁₃	1	4	yes	—
538	#100	C₂³×C₁₃	1	4	yes	complemented
539	#97	C₂³×C₁₃	1	2	yes	complemented
540	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
541	C₂×C₁₃	—	2	1	no	—
542	C₂×C₁₃	—	2	1	no	—
543	C₂×C₁₃	—	2	1	no	—
544	C₂×C₁₃	—	4	4	no	—
545	C₂×C₁₃	—	4	4	no	—
546	C₂×C₁₃	—	8	2	no	—
547	C₂×C₁₃	—	8	2	no	—
548	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
549	C₂⁴	—	2	1	no	—
550	C₂⁴	—	4	1	no	—
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	2	2	no	—
555	#41	—	2	4	no	—
556	#41	—	2	8	no	—
557	#41	—	2	4	no	—
558	#41	—	2	4	no	—
559	#41	—	2	8	no	—
560	#41	—	2	4	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	4	4	no	—
566	#41	—	4	4	no	—
567	#41	—	4	4	no	—
568	#41	—	4	4	no	—
569	#41	—	4	4	no	—
570	#41	—	4	4	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	#41	—	4	2	no	—
574	#41	—	4	2	no	—
575	#41	C₂×D₄×C₁₃	1	4	yes	—
576	#41	C₂×D₄×C₁₃	1	4	yes	—
577	#41	C₂⁴×C₁₃	1	4	yes	—
578	#41	C₂⁴×C₁₃	1	4	yes	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	8	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	4	1	no	—
586	C₂×Q₈	—	4	4	no	—
587	C₂×Q₈	—	4	2	no	—
588	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
589	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
613	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	Q₁₆	—	2	8	no	—
625	Q₁₆	—	2	4	no	—
626	Q₁₆	—	2	4	no	—
627	Q₁₆	—	2	8	no	—
628	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
629	SD₁₆	—	2	8	no	—
630	SD₁₆	—	2	4	no	—
631	SD₁₆	—	2	4	no	—
632	SD₁₆	—	2	4	no	—
633	SD₁₆	—	2	8	no	—
634	SD₁₆	—	2	4	no	—
635	SD₁₆	—	2	8	no	—
636	SD₁₆	—	2	8	no	—
637	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
638	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
639	D₈	—	2	4	no	—
640	D₈	—	2	8	no	—
641	D₈	—	2	4	no	—
642	D₈	—	2	8	no	—
643	D₈	C₂×D₄×C₁₃	1	8	yes	—
644	M₁₆	—	2	2	no	—
645	M₁₆	—	2	2	no	—
646	M₁₆	—	2	8	no	—
647	M₁₆	—	2	8	no	—
648	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
649	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
650	M₁₆	C₂⁴×C₁₃	1	4	yes	—
651	M₁₆	C₂⁴×C₁₃	1	4	yes	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	2	8	no	—
655	C₂×C₈	—	2	8	no	—
656	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
657	C₄⋊C₄	—	4	1	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₄²	—	2	1	no	—
662	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
663	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₁₃	#61109	1	1	yes	characteristic, direct product factor, Sylow
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	16	2	no	—
675	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	4	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	2	no	—
684	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
685	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
686	D₄	—	2	4	no	—
687	D₄	—	2	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	8	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	8	2	no	—
704	D₄	C₂²×D₄×C₁₃	1	4	yes	—
705	D₄	C₂²×D₄×C₁₃	1	4	yes	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
730	C₈	—	2	4	no	—
731	C₈	—	2	4	no	—
732	C₈	C₂²×D₄×C₁₃	1	8	yes	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	8	2	no	—
739	C₂²	—	8	2	no	—
740	C₂²	—	8	2	no	—
741	C₂²	—	8	2	no	—
742	C₂²	—	8	2	no	—
743	C₂²	—	16	1	no	—
744	C₂²	—	16	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	D₄²×C₁₃	1	1	yes	characteristic
747	C₂²	D₄²×C₁₃	1	1	yes	characteristic
748	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	D₄²×C₁₃	1	2	yes	—
756	C₄	C₂³×D₄×C₁₃	1	2	yes	—
757	C₂	—	2	1	no	—
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	4	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3586	C₂	semidirect
2. C₁₃×#3585	C₂	semidirect
3. C₁₃×#3290	C₂	semidirect
4. C₁₃×#3289	C₂	semidirect
5. C₁₃×#3288	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₁₃×#3069	C₂	semidirect
8. C₁₃×#3068	C₂	semidirect
9. C₁₃×#3018	C₂	semidirect
10. C₂×C₁₃×#454	C₂	semidirect
11. C₂×C₁₃×#455	C₂	semidirect
12. C₁₃×#2956	C₂	semidirect
13. C₁₃×#585	C₂²	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
17. C₁₃×#578	C₂²	semidirect
20. C₁₃×#577	C₂²	semidirect
21. C₁₃×#577	C₂²	semidirect
23. C₁₃×#576	C₂²	semidirect
28. C₁₃×#575	C₂²	semidirect
30. C₂×C₁₃×#137	C₂²	semidirect
31. C₂×C₁₃×#137	C₂²	semidirect
33. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₁₃×#568	C₂²	semidirect
36. C₁₃×#568	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
38. C₂×C₁₃×#124	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#496	C₂²	semidirect
41. C₁₃×#495	C₂²	semidirect
42. C₁₃×#473	C₂²	semidirect
43. C₁₃×#472	C₂²	semidirect
44. C₁₃×#471	C₂²	semidirect
45. C₁₃×#471	C₂²	semidirect
46. C₁₃×#456	C₂²	semidirect
47. C₁₃×#455	C₂²	semidirect
48. C₁₃×#455	C₂²	semidirect
49. C₁₃×#455	C₂²	semidirect
50. C₁₃×#454	C₂²	semidirect
51. C₁₃×#454	C₂²	semidirect
52. C₁₃×#454	C₂²	semidirect
53. C₁₃×#453	C₂²	semidirect
54. C₁₃×#444	C₂²	semidirect
55. C₁₃×#443	C₂²	semidirect
56. C₁₃×#430	C₂²	semidirect
57. C₂×C₁₃×#104	C₂²	semidirect
58. C₂×C₁₃×#104	C₂²	semidirect
59. C₁₃×#413	C₂²	semidirect
60. C₂×C₁₃×#101	C₂²	semidirect
61. C₂×C₁₃×#100	C₂²	semidirect
62. C₄×C₁₃×M₁₆	C₂²	semidirect
68. C₁₃×2₋¹⁺⁴	C₂³	semidirect
99. C₁₃×#137	D₄	semidirect
100. C₁₃×#137	D₄	semidirect
103. C₁₃×#137	C₂³	semidirect
113. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
114. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
117. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
127. C₂×C₁₃×Q₁₆	C₂³	semidirect
133. C₂×C₁₃×SD₁₆	C₂³	semidirect
140. C₁₃×#131	C₂³	semidirect
146. C₁₃×C₄⋊Q₈	C₂³	semidirect
147. C₁₃×#127	C₂³	semidirect
151. C₁₃×#124	C₂³	semidirect
156. C₁₃×#108	C₂³	semidirect
159. C₁₃×#104	C₂³	semidirect
160. C₁₃×#104	C₂³	semidirect
161. C₁₃×#101	C₂³	semidirect
162. C₁₃×#101	C₂³	semidirect
164. C₁₃×#100	C₂³	semidirect
165. C₁₃×#97	C₂³	semidirect
166. C₄×C₈×C₁₃	C₂³	semidirect
167. #61109	C₁₃	direct (N × H)
283. #3586	C₂×C₁₃	semidirect
284. #3585	C₂×C₁₃	semidirect
285. #3290	C₂×C₁₃	semidirect
286. #3289	C₂×C₁₃	semidirect
287. #3288	C₂×C₁₃	semidirect
288. #3153	C₂×C₁₃	semidirect
289. #3069	C₂×C₁₃	semidirect
290. #3068	C₂×C₁₃	semidirect
291. #3018	C₂×C₁₃	semidirect
292. C₂×#454	C₂×C₁₃	semidirect
293. C₂×#455	C₂×C₁₃	semidirect
294. #2956	C₂×C₁₃	semidirect
363. #585	C₂²×C₁₃	semidirect
364. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
367. #578	C₂²×C₁₃	semidirect
370. #577	C₂²×C₁₃	semidirect
371. #577	C₂²×C₁₃	semidirect
373. #576	C₂²×C₁₃	semidirect
378. #575	C₂²×C₁₃	semidirect
380. C₂×#137	C₂²×C₁₃	semidirect
381. C₂×#137	C₂²×C₁₃	semidirect
383. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
384. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
385. #568	C₂²×C₁₃	semidirect
386. #568	C₂²×C₁₃	semidirect
387. #532	C₂²×C₁₃	semidirect
388. C₂×#124	C₂²×C₁₃	semidirect
389. #497	C₂²×C₁₃	semidirect
390. #496	C₂²×C₁₃	semidirect
391. #495	C₂²×C₁₃	semidirect
392. #473	C₂²×C₁₃	semidirect
393. #472	C₂²×C₁₃	semidirect
394. #471	C₂²×C₁₃	semidirect
395. #471	C₂²×C₁₃	semidirect
396. #456	C₂²×C₁₃	semidirect
397. #455	C₂²×C₁₃	semidirect
398. #455	C₂²×C₁₃	semidirect
399. #455	C₂²×C₁₃	semidirect
400. #454	C₂²×C₁₃	semidirect
401. #454	C₂²×C₁₃	semidirect
402. #454	C₂²×C₁₃	semidirect
403. #453	C₂²×C₁₃	semidirect
404. #444	C₂²×C₁₃	semidirect
405. #443	C₂²×C₁₃	semidirect
406. #430	C₂²×C₁₃	semidirect
407. C₂×#104	C₂²×C₁₃	semidirect
408. C₂×#104	C₂²×C₁₃	semidirect
409. #413	C₂²×C₁₃	semidirect
410. C₂×#101	C₂²×C₁₃	semidirect
411. C₂×#100	C₂²×C₁₃	semidirect
412. C₄×M₁₆	C₂²×C₁₃	semidirect
442. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
473. #137	D₄×C₁₃	semidirect
474. #137	D₄×C₁₃	semidirect
477. #137	C₂³×C₁₃	semidirect
487. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
488. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
491. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
501. C₂×Q₁₆	C₂³×C₁₃	semidirect
507. C₂×SD₁₆	C₂³×C₁₃	semidirect
514. #131	C₂³×C₁₃	semidirect
520. C₄⋊Q₈	C₂³×C₁₃	semidirect
521. #127	C₂³×C₁₃	semidirect
525. #124	C₂³×C₁₃	semidirect
530. #108	C₂³×C₁₃	semidirect
533. #104	C₂³×C₁₃	semidirect
534. #104	C₂³×C₁₃	semidirect
535. #101	C₂³×C₁₃	semidirect
536. #101	C₂³×C₁₃	semidirect
538. #100	C₂³×C₁₃	semidirect
539. #97	C₂³×C₁₃	semidirect
540. C₄×C₈	C₂³×C₁₃	semidirect
664. C₁₃	#61109	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×#3586	2
C₁₃×#3585	2
C₁₃×#3290	2
C₁₃×#3289	2
C₁₃×#3288	2
C₁₃×#3153	2
C₁₃×#3069	2
C₁₃×#3068	2
C₁₃×#3018	2
C₂×C₁₃×#454	2
C₂×C₁₃×#455	2
C₁₃×#2956	2
#61109	13

Subgroups — C13×#61109 #15747448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61109 #15747448