Subgroups — C₁₃×#61087 #15747426

Order 3328.

2786 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3278	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
18	C₁₃×#577	—	2	16	no	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
25	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
29	C₁₃×#550	C₂²	1	4	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
31	C₁₃×#547	—	2	4	no	—
32	C₁₃×#547	C₂²	1	4	yes	complemented
33	D₄²×C₁₃	—	2	4	no	—
34	D₄²×C₁₃	C₂²	1	4	yes	—
35	C₁₃×#536	—	2	2	no	—
36	C₁₃×#536	C₂²	1	2	yes	complemented
37	C₁₃×#535	—	2	2	no	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#127	—	2	1	no	—
45	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#492	C₂²	1	4	yes	complemented
49	C₁₃×#492	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	8	yes	complemented
51	C₁₃×#465	C₂²	1	8	yes	complemented
52	C₁₃×#462	C₂²	1	4	yes	complemented
53	C₁₃×#461	C₂²	1	4	yes	complemented
54	C₁₃×#460	C₂²	1	4	yes	complemented
55	C₁₃×#459	C₂²	1	4	yes	complemented
56	C₁₃×#452	C₂²	1	8	yes	complemented
57	C₁₃×#450	C₂²	1	8	yes	complemented
58	C₁₃×#449	C₂²	1	8	yes	complemented
59	C₁₃×#448	C₂²	1	8	yes	complemented
60	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
61	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
62	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
63	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
64	C₁₃×#436	C₂²	1	4	yes	complemented
65	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
66	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#419	C₂²	1	2	yes	complemented
69	C₁₃×#418	C₂²	1	2	yes	complemented
70	C₁₃×#416	C₂²	1	1	yes	characteristic
71	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#408	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×2₋¹⁺⁴	—	2	8	no	—
75	C₁₃×2₋¹⁺⁴	—	4	4	no	—
76	C₁₃×H(5,𝔽₂)	—	2	8	no	—
77	C₁₃×H(5,𝔽₂)	—	4	4	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	4	no	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂×C₁₃×#41	C₂³	1	4	yes	—
83	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	—	2	2	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₁₃	—	2	2	no	—
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	2	4	no	—
92	C₂²×D₄×C₁₃	—	2	2	no	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
95	C₁₃×#137	—	2	8	no	—
96	C₁₃×#137	—	2	16	no	—
97	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
98	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
99	C₁₃×#135	—	2	16	no	—
100	C₁₃×#135	D₄	1	8	yes	complemented
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×SD₁₆	—	2	16	no	—
104	C₂×C₁₃×SD₁₆	—	2	8	no	—
105	C₂×C₁₃×SD₁₆	—	4	4	no	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×D₈	C₂³	1	4	yes	—
114	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
115	C₁₃×#131	—	2	8	no	—
116	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
118	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
120	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	—	2	2	no	—
122	C₁₃×C₄⋊Q₈	—	2	4	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	—	2	1	no	—
125	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
127	C₁₃×#127	—	2	2	no	—
128	C₁₃×#127	—	2	4	no	—
129	C₁₃×#127	—	2	1	no	—
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	D₄	1	1	yes	characteristic
132	C₁₃×#127	C₂³	1	4	yes	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	D₄	1	2	yes	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	—	2	8	no	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	—	2	8	no	—
143	C₁₃×#121	D₄	1	4	yes	—
144	C₁₃×#121	C₂³	1	8	yes	—
145	C₁₃×#120	—	2	4	no	—
146	C₁₃×#120	—	2	8	no	—
147	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×D₄×C₁₃	—	2	4	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	4	no	—
153	C₄×D₄×C₁₃	C₂³	1	2	yes	—
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₁₃×#117	—	2	1	no	—
157	C₁₃×#117	—	2	1	no	—
158	C₁₃×#117	C₂³	1	1	yes	characteristic
159	C₁₃×#117	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₂×C₄²×C₁₃	—	2	1	no	—
163	C₂×C₄²×C₁₃	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₁₃×#107	C₂³	1	2	yes	—
166	C₁₃×#106	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	2	yes	—
169	C₁₃×#103	C₂³	1	2	yes	—
170	C₁₃×#103	C₂³	1	8	yes	—
171	C₁₃×#102	C₂³	1	2	yes	—
172	C₁₃×#102	C₂³	1	2	yes	—
173	C₁₃×#102	C₂³	1	8	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
175	C₄×C₈×C₁₃	C₂³	1	2	yes	—
176	C₄×C₈×C₁₃	C₂³	1	2	yes	—
177	#61087	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂⁴×C₁₃	—	2	4	no	—
179	C₂⁴×C₁₃	—	2	2	no	—
180	C₁₃×#41	—	2	4	no	—
181	C₁₃×#41	—	2	2	no	—
182	C₁₃×#41	—	2	4	no	—
183	C₁₃×#41	—	2	2	no	—
184	C₁₃×#41	—	2	8	no	—
185	C₁₃×#41	—	2	8	no	—
186	C₁₃×#41	—	4	4	no	—
187	C₁₃×#41	—	4	4	no	—
188	C₁₃×#41	—	4	8	no	—
189	C₁₃×#41	—	4	8	no	—
190	C₁₃×#41	—	4	16	no	—
191	C₁₃×#41	C₂×D₄	1	4	yes	—
192	C₁₃×#41	C₂×D₄	1	4	yes	complemented
193	C₂×Q₈×C₁₃	—	2	4	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	2	8	no	—
196	C₂×Q₈×C₁₃	—	2	4	no	—
197	C₂×Q₈×C₁₃	—	2	4	no	—
198	C₂×Q₈×C₁₃	—	4	4	no	—
199	C₂×Q₈×C₁₃	—	4	8	no	—
200	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
202	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	8	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	8	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	8	no	—
218	C₂×D₄×C₁₃	—	4	16	no	—
219	C₂×D₄×C₁₃	—	8	4	no	—
220	C₂×D₄×C₁₃	—	8	8	no	—
221	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
223	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
225	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₁₃×Q₁₆	—	2	8	no	—
239	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
240	C₁₃×SD₁₆	—	2	8	no	—
241	C₁₃×SD₁₆	—	2	8	no	—
242	C₁₃×SD₁₆	—	2	8	no	—
243	C₁₃×SD₁₆	—	2	8	no	—
244	C₁₃×SD₁₆	—	4	8	no	—
245	C₁₃×SD₁₆	C₂×D₄	1	4	yes	complemented
246	C₁₃×SD₁₆	C₂×D₄	1	4	yes	complemented
247	C₁₃×D₈	—	2	8	no	—
248	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
249	C₁₃×M₁₆	—	2	4	no	—
250	C₁₃×M₁₆	—	2	8	no	—
251	C₂×C₈×C₁₃	—	2	2	no	—
252	C₂×C₈×C₁₃	—	2	8	no	—
253	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
254	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
256	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	8	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₂²⋊C₄	—	2	1	no	—
267	C₁₃×C₂²⋊C₄	—	2	1	no	—
268	C₁₃×C₂²⋊C₄	—	2	8	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	8	no	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
273	C₄²×C₁₃	—	2	1	no	—
274	C₄²×C₁₃	—	2	1	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂⁴	1	2	yes	—
280	C₂×#577	C₂×C₁₃	1	2	yes	complemented
281	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#3284	C₂×C₁₃	1	4	yes	complemented
284	D₄×SD₁₆	C₂×C₁₃	1	4	yes	complemented
285	#3278	C₂×C₁₃	1	4	yes	complemented
286	#3272	C₂×C₁₃	1	4	yes	complemented
287	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#3057	C₂×C₁₃	1	2	yes	complemented
289	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3010	C₂×C₁₃	1	2	yes	complemented
292	#3009	C₂×C₁₃	1	2	yes	complemented
293	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	4	no	—
298	C₂³×C₁₃	—	4	8	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	—	8	4	no	—
301	C₂³×C₁₃	—	8	8	no	—
302	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₁₃	—	2	4	no	—
305	Q₈×C₁₃	—	2	1	no	—
306	Q₈×C₁₃	—	2	1	no	—
307	Q₈×C₁₃	—	2	4	no	—
308	Q₈×C₁₃	—	2	4	no	—
309	Q₈×C₁₃	—	4	8	no	—
310	Q₈×C₁₃	—	4	4	no	—
311	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
312	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
313	D₄×C₁₃	—	2	4	no	—
314	D₄×C₁₃	—	2	4	no	—
315	D₄×C₁₃	—	2	8	no	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	8	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	1	no	—
320	D₄×C₁₃	—	2	1	no	—
321	D₄×C₁₃	—	2	4	no	—
322	D₄×C₁₃	—	4	8	no	—
323	D₄×C₁₃	—	4	8	no	—
324	D₄×C₁₃	—	4	8	no	—
325	D₄×C₁₃	—	4	4	no	—
326	D₄×C₁₃	—	4	8	no	—
327	D₄×C₁₃	—	8	4	no	—
328	D₄×C₁₃	—	8	8	no	—
329	D₄×C₁₃	C₂²×D₄	1	2	yes	—
330	D₄×C₁₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	4	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	4	8	no	—
342	C₂×C₄×C₁₃	—	4	8	no	—
343	C₂×C₄×C₁₃	—	4	8	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
353	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
354	C₈×C₁₃	—	2	4	no	—
355	C₈×C₁₃	—	2	2	no	—
356	C₈×C₁₃	C₂²×D₄	1	2	yes	—
357	C₈×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
359	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
360	#577	—	2	16	no	—
361	C₂×#137	C₂²×C₁₃	1	2	yes	—
362	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
363	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
364	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
365	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
367	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
368	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
369	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
370	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
371	#550	C₂²×C₁₃	1	4	yes	—
372	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
373	#547	—	2	4	no	—
374	#547	C₂²×C₁₃	1	4	yes	complemented
375	D₄²	—	2	4	no	—
376	D₄²	C₂²×C₁₃	1	4	yes	—
377	#536	—	2	2	no	—
378	#536	C₂²×C₁₃	1	2	yes	complemented
379	#535	—	2	2	no	—
380	#535	C₂²×C₁₃	1	2	yes	—
381	#532	—	2	1	no	—
382	#532	—	2	1	no	—
383	#532	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊Q₈	—	2	1	no	—
385	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#127	—	2	1	no	—
387	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
388	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
389	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	#492	C₂²×C₁₃	1	4	yes	complemented
391	#492	C₂²×C₁₃	1	4	yes	complemented
392	#468	C₂²×C₁₃	1	8	yes	complemented
393	#465	C₂²×C₁₃	1	8	yes	complemented
394	#462	C₂²×C₁₃	1	4	yes	complemented
395	#461	C₂²×C₁₃	1	4	yes	complemented
396	#460	C₂²×C₁₃	1	4	yes	complemented
397	#459	C₂²×C₁₃	1	4	yes	complemented
398	#452	C₂²×C₁₃	1	8	yes	complemented
399	#450	C₂²×C₁₃	1	8	yes	complemented
400	#449	C₂²×C₁₃	1	8	yes	complemented
401	#448	C₂²×C₁₃	1	8	yes	complemented
402	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
403	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
404	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
405	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
406	#436	C₂²×C₁₃	1	4	yes	complemented
407	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
408	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	#419	C₂²×C₁₃	1	2	yes	complemented
411	#418	C₂²×C₁₃	1	2	yes	complemented
412	#416	C₂²×C₁₃	1	1	yes	characteristic
413	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#408	C₂²×C₁₃	1	2	yes	complemented
415	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	4	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	8	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	4	no	—
424	C₂²×C₁₃	—	4	8	no	—
425	C₂²×C₁₃	—	16	4	no	—
426	C₂²×C₁₃	—	16	8	no	—
427	C₂²×C₁₃	D₄²	1	2	yes	—
428	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
429	C₄×C₁₃	—	2	2	no	—
430	C₄×C₁₃	—	2	2	no	—
431	C₄×C₁₃	—	2	4	no	—
432	C₄×C₁₃	—	2	2	no	—
433	C₄×C₁₃	—	4	4	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	D₄²	1	2	yes	—
437	C₄×C₁₃	#577	1	4	yes	complemented
438	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	2₋¹⁺⁴	—	2	8	no	—
441	2₋¹⁺⁴	—	4	4	no	—
442	H(5,𝔽₂)	—	2	8	no	—
443	H(5,𝔽₂)	—	4	4	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	4	no	—
447	C₂×#41	C₂³×C₁₃	1	4	yes	—
448	C₂×#41	C₂³×C₁₃	1	4	yes	—
449	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×#41	C₂³×C₁₃	1	2	yes	—
452	C₂²×Q₈	—	2	2	no	—
453	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
454	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
455	C₂²×D₄	—	2	2	no	—
456	C₂²×D₄	—	2	4	no	—
457	C₂²×D₄	—	2	4	no	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
460	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
461	#137	—	2	8	no	—
462	#137	—	2	16	no	—
463	AGL(1,ℤ/8)	—	2	8	no	—
464	AGL(1,ℤ/8)	—	2	16	no	—
465	#135	—	2	16	no	—
466	#135	D₄×C₁₃	1	8	yes	complemented
467	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
468	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×SD₁₆	—	2	16	no	—
470	C₂×SD₁₆	—	2	8	no	—
471	C₂×SD₁₆	—	4	4	no	—
472	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
473	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
476	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
477	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×D₈	C₂³×C₁₃	1	4	yes	—
480	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
481	#131	—	2	8	no	—
482	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
483	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
484	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	1	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
493	#127	—	2	2	no	—
494	#127	—	2	4	no	—
495	#127	—	2	1	no	—
496	#127	—	2	1	no	—
497	#127	D₄×C₁₃	1	1	yes	characteristic
498	#127	C₂³×C₁₃	1	4	yes	—
499	#124	—	2	2	no	—
500	#124	—	2	2	no	—
501	#124	D₄×C₁₃	1	2	yes	—
502	#123	—	2	4	no	—
503	#123	—	2	8	no	—
504	C₂²⋊Q₈	—	2	8	no	—
505	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	—	2	8	no	—
509	#121	D₄×C₁₃	1	4	yes	—
510	#121	C₂³×C₁₃	1	8	yes	—
511	#120	—	2	4	no	—
512	#120	—	2	8	no	—
513	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	C₂³×C₁₃	1	2	yes	—
520	C₄×D₄	C₂³×C₁₃	1	2	yes	—
521	C₄×D₄	C₂³×C₁₃	1	4	yes	—
522	#117	—	2	1	no	—
523	#117	—	2	1	no	—
524	#117	C₂³×C₁₃	1	1	yes	characteristic
525	#117	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	#107	C₂³×C₁₃	1	2	yes	—
532	#106	C₂³×C₁₃	1	2	yes	—
533	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
534	#103	C₂³×C₁₃	1	2	yes	—
535	#103	C₂³×C₁₃	1	2	yes	—
536	#103	C₂³×C₁₃	1	8	yes	—
537	#102	C₂³×C₁₃	1	2	yes	—
538	#102	C₂³×C₁₃	1	2	yes	—
539	#102	C₂³×C₁₃	1	8	yes	—
540	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
541	C₄×C₈	C₂³×C₁₃	1	2	yes	—
542	C₄×C₈	C₂³×C₁₃	1	2	yes	—
543	C₂×C₁₃	—	2	2	no	—
544	C₂×C₁₃	—	4	4	no	—
545	C₂×C₁₃	—	4	2	no	—
546	C₂×C₁₃	—	4	2	no	—
547	C₂×C₁₃	—	8	4	no	—
548	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
549	C₂×C₁₃	C₂×#577	1	2	yes	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	2	no	—
552	#41	—	2	4	no	—
553	#41	—	2	2	no	—
554	#41	—	2	4	no	—
555	#41	—	2	2	no	—
556	#41	—	2	8	no	—
557	#41	—	2	8	no	—
558	#41	—	4	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	8	no	—
561	#41	—	4	8	no	—
562	#41	—	4	16	no	—
563	#41	C₂×D₄×C₁₃	1	4	yes	—
564	#41	C₂×D₄×C₁₃	1	4	yes	complemented
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	8	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	8	no	—
572	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
573	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
574	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	8	no	—
590	C₂×D₄	—	4	16	no	—
591	C₂×D₄	—	8	4	no	—
592	C₂×D₄	—	8	8	no	—
593	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
594	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
595	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
596	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
597	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
598	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	Q₁₆	—	2	8	no	—
611	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
612	SD₁₆	—	2	8	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	8	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	4	8	no	—
617	SD₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
618	SD₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
619	D₈	—	2	8	no	—
620	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
621	M₁₆	—	2	4	no	—
622	M₁₆	—	2	8	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	8	no	—
625	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
626	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
627	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
628	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	8	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₄²	C₂⁴×C₁₃	1	2	yes	—
652	C₁₃	#61087	1	1	yes	characteristic, direct product factor, Sylow
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	8	no	—
660	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
661	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	Q₈	—	2	4	no	—
663	Q₈	—	2	1	no	—
664	Q₈	—	2	1	no	—
665	Q₈	—	2	4	no	—
666	Q₈	—	2	4	no	—
667	Q₈	—	4	8	no	—
668	Q₈	—	4	4	no	—
669	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
670	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	8	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	8	no	—
687	D₄	C₂²×D₄×C₁₃	1	2	yes	—
688	D₄	C₂²×D₄×C₁₃	1	2	yes	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
710	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
711	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
712	C₈	—	2	4	no	—
713	C₈	—	2	2	no	—
714	C₈	C₂²×D₄×C₁₃	1	2	yes	—
715	C₈	C₂²×D₄×C₁₃	1	2	yes	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	8	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	16	4	no	—
726	C₂²	—	16	8	no	—
727	C₂²	D₄²×C₁₃	1	2	yes	—
728	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	D₄²×C₁₃	1	2	yes	—
737	C₄	C₁₃×#577	1	4	yes	complemented
738	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
739	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂	—	2	2	no	—
741	C₂	—	4	4	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	4	no	—
745	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
746	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3498	C₂	semidirect
4. C₁₃×#3284	C₂	semidirect
5. D₄×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3278	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₂×C₁₃×#492	C₂	semidirect
9. C₁₃×#3057	C₂	semidirect
10. C₁₃×#3039	C₂	semidirect
11. C₁₃×#3038	C₂	semidirect
12. C₁₃×#3010	C₂	semidirect
13. C₁₃×#3009	C₂	semidirect
14. C₄×C₁₃×#135	C₂	semidirect
15. C₁₃×#2931	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
25. C₂²×C₁₃×SD₁₆	C₂²	semidirect
26. C₂²×C₁₃×SD₁₆	C₂²	semidirect
27. C₂²×C₁₃×SD₁₆	C₂²	semidirect
28. C₂×C₁₃×#131	C₂²	semidirect
30. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
36. C₁₃×#536	C₂²	semidirect
43. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
47. C₄×C₁₃×#41	C₂²	semidirect
48. C₁₃×#492	C₂²	semidirect
49. C₁₃×#492	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#465	C₂²	semidirect
52. C₁₃×#462	C₂²	semidirect
53. C₁₃×#461	C₂²	semidirect
54. C₁₃×#460	C₂²	semidirect
55. C₁₃×#459	C₂²	semidirect
56. C₁₃×#452	C₂²	semidirect
57. C₁₃×#450	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
59. C₁₃×#448	C₂²	semidirect
60. C₄×C₁₃×Q₁₆	C₂²	semidirect
61. C₄×C₁₃×SD₁₆	C₂²	semidirect
62. C₄×C₁₃×SD₁₆	C₂²	semidirect
63. C₄×C₁₃×D₈	C₂²	semidirect
64. C₁₃×#436	C₂²	semidirect
65. C₈×D₄×C₁₃	C₂²	semidirect
66. C₁₃×#427	C₂²	semidirect
67. C₁₃×#423	C₂²	semidirect
68. C₁₃×#419	C₂²	semidirect
69. C₁₃×#418	C₂²	semidirect
71. C₁₃×#416	C₂²	semidirect
72. C₁₃×#408	C₂²	semidirect
73. C₂×C₄×C₈×C₁₃	C₂²	semidirect
100. C₁₃×#135	D₄	semidirect
177. #61087	C₁₃	direct (N × H)
192. C₁₃×#41	C₂×D₄	semidirect
239. C₁₃×Q₁₆	C₂×D₄	semidirect
245. C₁₃×SD₁₆	C₂×D₄	semidirect
246. C₁₃×SD₁₆	C₂×D₄	semidirect
248. C₁₃×D₈	C₂×D₄	semidirect
253. C₂×C₈×C₁₃	C₂×D₄	semidirect
280. C₂×#577	C₂×C₁₃	semidirect
281. #3499	C₂×C₁₃	semidirect
282. #3498	C₂×C₁₃	semidirect
283. #3284	C₂×C₁₃	semidirect
284. D₄×SD₁₆	C₂×C₁₃	semidirect
285. #3278	C₂×C₁₃	semidirect
286. #3272	C₂×C₁₃	semidirect
287. C₂×#492	C₂×C₁₃	semidirect
288. #3057	C₂×C₁₃	semidirect
289. #3039	C₂×C₁₃	semidirect
290. #3038	C₂×C₁₃	semidirect
291. #3010	C₂×C₁₃	semidirect
292. #3009	C₂×C₁₃	semidirect
293. C₄×#135	C₂×C₁₃	semidirect
294. #2931	C₂×C₁₃	semidirect
358. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
362. C₂×#137	C₂²×C₁₃	semidirect
363. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
364. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
366. C₂×#135	C₂²×C₁₃	semidirect
367. C₂²×SD₁₆	C₂²×C₁₃	semidirect
368. C₂²×SD₁₆	C₂²×C₁₃	semidirect
369. C₂²×SD₁₆	C₂²×C₁₃	semidirect
370. C₂×#131	C₂²×C₁₃	semidirect
372. D₄×Q₈	C₂²×C₁₃	semidirect
374. #547	C₂²×C₁₃	semidirect
378. #536	C₂²×C₁₃	semidirect
385. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
389. C₄×#41	C₂²×C₁₃	semidirect
390. #492	C₂²×C₁₃	semidirect
391. #492	C₂²×C₁₃	semidirect
392. #468	C₂²×C₁₃	semidirect
393. #465	C₂²×C₁₃	semidirect
394. #462	C₂²×C₁₃	semidirect
395. #461	C₂²×C₁₃	semidirect
396. #460	C₂²×C₁₃	semidirect
397. #459	C₂²×C₁₃	semidirect
398. #452	C₂²×C₁₃	semidirect
399. #450	C₂²×C₁₃	semidirect
400. #449	C₂²×C₁₃	semidirect
401. #448	C₂²×C₁₃	semidirect
402. C₄×Q₁₆	C₂²×C₁₃	semidirect
403. C₄×SD₁₆	C₂²×C₁₃	semidirect
404. C₄×SD₁₆	C₂²×C₁₃	semidirect
405. C₄×D₈	C₂²×C₁₃	semidirect
406. #436	C₂²×C₁₃	semidirect
407. C₈×D₄	C₂²×C₁₃	semidirect
408. #427	C₂²×C₁₃	semidirect
409. #423	C₂²×C₁₃	semidirect
410. #419	C₂²×C₁₃	semidirect
411. #418	C₂²×C₁₃	semidirect
413. #416	C₂²×C₁₃	semidirect
414. #408	C₂²×C₁₃	semidirect
415. C₂×C₄×C₈	C₂²×C₁₃	semidirect
437. C₄×C₁₃	#577	semidirect
466. #135	D₄×C₁₃	semidirect
564. #41	C₂×D₄×C₁₃	semidirect
611. Q₁₆	C₂×D₄×C₁₃	semidirect
617. SD₁₆	C₂×D₄×C₁₃	semidirect
618. SD₁₆	C₂×D₄×C₁₃	semidirect
620. D₈	C₂×D₄×C₁₃	semidirect
625. C₂×C₈	C₂×D₄×C₁₃	semidirect
652. C₁₃	#61087	direct (N × H)
737. C₄	C₁₃×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#577	2
C₁₃×#3499	2
C₁₃×#3498	2
C₁₃×#3284	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3278	2
C₁₃×#3272	2
C₂×C₁₃×#492	2
C₁₃×#3057	2
C₁₃×#3039	2
C₁₃×#3038	2
C₁₃×#3010	2
C₁₃×#3009	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
#61087	13

Subgroups — C13×#61087 #15747426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61087 #15747426