Subgroups — C₁₃×#61049 #15747388

Order 3328.

3074 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3280	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×D₈	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3264	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
17	C₁₃×#576	—	2	8	no	—
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×D₈	—	2	8	no	—
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
27	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
28	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#546	—	2	4	no	—
33	C₁₃×#546	C₂²	1	8	yes	complemented
34	D₄²×C₁₃	—	2	4	no	—
35	D₄²×C₁₃	C₂²	1	8	yes	complemented
36	C₁₃×#535	C₂²	1	2	yes	complemented
37	C₁₃×#535	C₂²	1	2	yes	complemented
38	C₁₃×#534	—	2	4	no	—
39	C₁₃×#525	C₂²	1	1	yes	characteristic
40	C₁₃×#525	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#120	—	2	4	no	—
42	C₁₃×#518	C₂²	1	2	yes	complemented
43	C₁₃×#496	C₂²	1	4	yes	complemented
44	C₁₃×#495	C₂²	1	2	yes	complemented
45	C₁₃×#493	C₂²	1	2	yes	complemented
46	C₁₃×#469	C₂²	1	4	yes	complemented
47	C₁₃×#467	C₂²	1	2	yes	complemented
48	C₁₃×#466	C₂²	1	2	yes	complemented
49	C₁₃×#466	C₂²	1	4	yes	complemented
50	C₁₃×#465	C₂²	1	4	yes	complemented
51	C₁₃×#463	C₂²	1	8	yes	complemented
52	C₁₃×#459	C₂²	1	8	yes	complemented
53	C₁₃×#450	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#447	C₂²	1	8	yes	complemented
56	C₁₃×#447	C₂²	1	8	yes	complemented
57	C₁₃×#442	C₂²	1	4	yes	complemented
58	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
59	C₁₃×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
61	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#418	C₂²	1	2	yes	complemented
64	C₁₃×#418	C₂²	1	2	yes	complemented
65	C₁₃×#416	C₂²	1	2	yes	complemented
66	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₁₃	—	2	2	no	—
70	C₁₃×H(5,𝔽₂)	—	2	8	no	—
71	C₁₃×H(5,𝔽₂)	—	4	4	no	—
72	C₂×C₁₃×#41	—	2	2	no	—
73	C₂×C₁₃×#41	C₂³	1	2	yes	—
74	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
76	C₂²×D₄×C₁₃	—	2	8	no	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	—	2	2	no	—
79	C₂²×D₄×C₁₃	—	2	8	no	—
80	C₂²×D₄×C₁₃	—	2	2	no	—
81	C₂²×D₄×C₁₃	—	2	4	no	—
82	C₂²×D₄×C₁₃	—	4	4	no	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
89	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
90	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
91	C₁₃×#135	—	2	8	no	—
92	C₁₃×#135	—	2	4	no	—
93	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
95	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
96	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
97	C₂×C₁₃×D₈	—	2	8	no	—
98	C₂×C₁₃×D₈	—	2	16	no	—
99	C₂×C₁₃×D₈	—	2	16	no	—
100	C₂×C₁₃×D₈	—	2	8	no	—
101	C₂×C₁₃×D₈	—	2	4	no	—
102	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
103	C₂×C₁₃×D₈	C₂³	1	8	yes	—
104	C₂×C₁₃×D₈	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
107	C₂×C₁₃×D₈	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
109	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
111	C₁₃×#131	—	2	4	no	—
112	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
115	C₂²×C₈×C₁₃	—	2	4	no	—
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
118	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	complemented
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	C₂³	1	4	yes	complemented
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	C₂³	1	4	yes	complemented
125	C₁₃×#123	—	2	2	no	—
126	C₁₃×#123	—	2	8	no	—
127	C₁₃×#123	D₄	1	2	yes	—
128	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×#121	—	2	8	no	—
131	C₁₃×#121	—	2	4	no	—
132	C₁₃×#121	—	2	8	no	—
133	C₁₃×#121	D₄	1	2	yes	—
134	C₁₃×#121	C₂³	1	4	yes	—
135	C₁₃×#121	C₂³	1	8	yes	complemented
136	C₁₃×#120	—	2	2	no	—
137	C₁₃×#120	—	2	4	no	—
138	C₁₃×#120	—	2	8	no	—
139	C₁₃×#120	—	2	4	no	—
140	C₁₃×#120	—	2	8	no	—
141	C₁₃×#120	—	2	8	no	—
142	C₁₃×#120	D₄	1	2	yes	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	C₂³	1	4	yes	—
146	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
147	C₁₃×#117	C₂³	1	2	yes	—
148	C₁₃×#117	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
151	C₁₃×#107	C₂³	1	2	yes	complemented
152	C₁₃×#106	C₂³	1	2	yes	complemented
153	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
154	C₁₃×#103	C₂³	1	4	yes	complemented
155	C₁₃×#102	C₂³	1	4	yes	complemented
156	C₁₃×#102	C₂³	1	8	yes	complemented
157	C₁₃×#102	C₂³	1	8	yes	complemented
158	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
160	C₁₃×#97	C₂³	1	2	yes	complemented
161	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
162	#61049	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	2	no	—
164	C₂⁴×C₁₃	—	2	8	no	—
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	2	4	no	—
167	C₂⁴×C₁₃	—	4	8	no	—
168	C₂⁴×C₁₃	—	8	8	no	—
169	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₁₃×#41	—	2	2	no	—
171	C₁₃×#41	—	2	2	no	—
172	C₁₃×#41	—	2	8	no	—
173	C₁₃×#41	—	2	4	no	—
174	C₁₃×#41	—	2	4	no	—
175	C₁₃×#41	—	4	4	no	—
176	C₁₃×#41	—	4	8	no	—
177	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	16	no	—
180	C₂×D₄×C₁₃	—	2	8	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	2	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	8	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	2	2	no	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	4	8	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	4	16	no	—
196	C₂×D₄×C₁₃	—	4	8	no	—
197	C₂×D₄×C₁₃	—	4	8	no	—
198	C₂×D₄×C₁₃	—	4	16	no	—
199	C₂×D₄×C₁₃	—	8	16	no	—
200	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
201	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	complemented
204	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
206	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	8	no	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×Q₁₆	—	2	2	no	—
218	C₁₃×SD₁₆	—	2	8	no	—
219	C₁₃×SD₁₆	—	2	4	no	—
220	C₁₃×SD₁₆	—	4	4	no	—
221	C₁₃×D₈	—	2	16	no	—
222	C₁₃×D₈	—	2	8	no	—
223	C₁₃×D₈	—	2	4	no	—
224	C₁₃×D₈	—	2	4	no	—
225	C₁₃×D₈	—	2	2	no	—
226	C₁₃×D₈	—	4	4	no	—
227	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
228	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
229	C₁₃×M₁₆	—	2	2	no	—
230	C₁₃×M₁₆	—	2	2	no	—
231	C₁₃×M₁₆	—	2	4	no	—
232	C₂×C₈×C₁₃	—	2	2	no	—
233	C₂×C₈×C₁₃	—	2	4	no	—
234	C₂×C₈×C₁₃	—	2	4	no	—
235	C₂×C₈×C₁₃	—	2	4	no	—
236	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
244	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	8	no	—
249	C₁₃×C₂²⋊C₄	—	2	8	no	—
250	C₁₃×C₂²⋊C₄	—	2	8	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
254	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	C₂⁴	1	2	yes	—
257	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂³×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#3484	C₂×C₁₃	1	2	yes	complemented
260	#3280	C₂×C₁₃	1	4	yes	complemented
261	D₄×D₈	C₂×C₁₃	1	4	yes	complemented
262	#3264	C₂×C₁₃	1	8	yes	complemented
263	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#3041	C₂×C₁₃	1	2	yes	complemented
267	#3008	C₂×C₁₃	1	2	yes	complemented
268	#3003	C₂×C₁₃	1	2	yes	complemented
269	#2948	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	2	4	no	—
273	C₂³×C₁₃	—	2	4	no	—
274	C₂³×C₁₃	—	2	8	no	—
275	C₂³×C₁₃	—	2	4	no	—
276	C₂³×C₁₃	—	2	2	no	—
277	C₂³×C₁₃	—	4	16	no	—
278	C₂³×C₁₃	—	4	8	no	—
279	C₂³×C₁₃	—	4	4	no	—
280	C₂³×C₁₃	—	4	16	no	—
281	C₂³×C₁₃	—	8	4	no	—
282	C₂³×C₁₃	—	8	8	no	—
283	C₂³×C₁₃	—	8	4	no	—
284	C₂³×C₁₃	—	8	8	no	—
285	C₂³×C₁₃	—	8	32	no	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
289	Q₈×C₁₃	—	2	2	no	—
290	Q₈×C₁₃	—	2	2	no	—
291	Q₈×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	2	4	no	—
293	D₄×C₁₃	—	2	8	no	—
294	D₄×C₁₃	—	2	8	no	—
295	D₄×C₁₃	—	2	2	no	—
296	D₄×C₁₃	—	2	4	no	—
297	D₄×C₁₃	—	2	2	no	—
298	D₄×C₁₃	—	2	4	no	—
299	D₄×C₁₃	—	2	2	no	—
300	D₄×C₁₃	—	2	4	no	—
301	D₄×C₁₃	—	4	16	no	—
302	D₄×C₁₃	—	4	8	no	—
303	D₄×C₁₃	—	4	8	no	—
304	D₄×C₁₃	—	4	4	no	—
305	D₄×C₁₃	—	4	8	no	—
306	D₄×C₁₃	—	4	4	no	—
307	D₄×C₁₃	—	8	8	no	—
308	D₄×C₁₃	—	8	8	no	—
309	D₄×C₁₃	C₂²×D₄	1	8	yes	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	4	8	no	—
319	C₂×C₄×C₁₃	—	4	4	no	—
320	C₂×C₄×C₁₃	—	8	8	no	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
327	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
328	C₈×C₁₃	—	2	2	no	—
329	C₈×C₁₃	—	2	2	no	—
330	C₈×C₁₃	—	2	2	no	—
331	C₈×C₁₃	C₂²×D₄	1	2	yes	—
332	C₈×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
334	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
335	#576	—	2	8	no	—
336	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
337	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
338	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
339	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
341	C₂²×D₈	—	2	8	no	—
342	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
343	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
344	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
345	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
346	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
347	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
348	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
350	#546	—	2	4	no	—
351	#546	C₂²×C₁₃	1	8	yes	complemented
352	D₄²	—	2	4	no	—
353	D₄²	C₂²×C₁₃	1	8	yes	complemented
354	#535	C₂²×C₁₃	1	2	yes	complemented
355	#535	C₂²×C₁₃	1	2	yes	complemented
356	#534	—	2	4	no	—
357	#525	C₂²×C₁₃	1	1	yes	characteristic
358	#525	C₂²×C₁₃	1	2	yes	complemented
359	C₂×#120	—	2	4	no	—
360	#518	C₂²×C₁₃	1	2	yes	complemented
361	#496	C₂²×C₁₃	1	4	yes	complemented
362	#495	C₂²×C₁₃	1	2	yes	complemented
363	#493	C₂²×C₁₃	1	2	yes	complemented
364	#469	C₂²×C₁₃	1	4	yes	complemented
365	#467	C₂²×C₁₃	1	2	yes	complemented
366	#466	C₂²×C₁₃	1	2	yes	complemented
367	#466	C₂²×C₁₃	1	4	yes	complemented
368	#465	C₂²×C₁₃	1	4	yes	complemented
369	#463	C₂²×C₁₃	1	8	yes	complemented
370	#459	C₂²×C₁₃	1	8	yes	complemented
371	#450	C₂²×C₁₃	1	8	yes	complemented
372	#449	C₂²×C₁₃	1	8	yes	complemented
373	#447	C₂²×C₁₃	1	8	yes	complemented
374	#447	C₂²×C₁₃	1	8	yes	complemented
375	#442	C₂²×C₁₃	1	4	yes	complemented
376	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
377	#435	C₂²×C₁₃	1	4	yes	complemented
378	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
379	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#418	C₂²×C₁₃	1	2	yes	complemented
382	#418	C₂²×C₁₃	1	2	yes	complemented
383	#416	C₂²×C₁₃	1	2	yes	complemented
384	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂²×C₁₃	—	2	8	no	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	2	8	no	—
393	C₂²×C₁₃	—	2	4	no	—
394	C₂²×C₁₃	—	4	8	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	4	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	8	no	—
399	C₂²×C₁₃	—	8	8	no	—
400	C₂²×C₁₃	—	8	32	no	—
401	C₂²×C₁₃	—	8	8	no	—
402	C₂²×C₁₃	—	16	8	no	—
403	C₂²×C₁₃	D₄²	1	2	yes	—
404	C₂²×C₁₃	#576	1	4	yes	complemented
405	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
406	C₄×C₁₃	—	2	2	no	—
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	4	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	4	no	—
411	C₄×C₁₃	D₄²	1	2	yes	—
412	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂⁵	—	2	2	no	—
415	H(5,𝔽₂)	—	2	8	no	—
416	H(5,𝔽₂)	—	4	4	no	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	C₂³×C₁₃	1	2	yes	—
419	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
421	C₂²×D₄	—	2	8	no	—
422	C₂²×D₄	—	2	4	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	8	no	—
425	C₂²×D₄	—	2	2	no	—
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	—	4	4	no	—
428	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
430	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
431	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
432	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
433	AGL(1,ℤ/8)	—	2	8	no	—
434	AGL(1,ℤ/8)	—	2	16	no	—
435	AGL(1,ℤ/8)	—	4	4	no	—
436	#135	—	2	8	no	—
437	#135	—	2	4	no	—
438	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
439	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
440	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
441	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
442	C₂×D₈	—	2	8	no	—
443	C₂×D₈	—	2	16	no	—
444	C₂×D₈	—	2	16	no	—
445	C₂×D₈	—	2	8	no	—
446	C₂×D₈	—	2	4	no	—
447	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
448	C₂×D₈	C₂³×C₁₃	1	8	yes	—
449	C₂×D₈	C₂³×C₁₃	1	2	yes	—
450	C₂×D₈	C₂³×C₁₃	1	2	yes	—
451	C₂×D₈	C₂³×C₁₃	1	2	yes	—
452	C₂×D₈	C₂³×C₁₃	1	2	yes	—
453	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
454	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
455	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
456	#131	—	2	4	no	—
457	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
460	C₂²×C₈	—	2	4	no	—
461	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
463	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
464	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₁₃	1	2	yes	complemented
466	#127	—	2	2	no	—
467	#127	C₂³×C₁₃	1	4	yes	complemented
468	#124	—	2	2	no	—
469	#124	C₂³×C₁₃	1	4	yes	complemented
470	#123	—	2	2	no	—
471	#123	—	2	8	no	—
472	#123	D₄×C₁₃	1	2	yes	—
473	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
474	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
475	#121	—	2	8	no	—
476	#121	—	2	4	no	—
477	#121	—	2	8	no	—
478	#121	D₄×C₁₃	1	2	yes	—
479	#121	C₂³×C₁₃	1	4	yes	—
480	#121	C₂³×C₁₃	1	8	yes	complemented
481	#120	—	2	2	no	—
482	#120	—	2	4	no	—
483	#120	—	2	8	no	—
484	#120	—	2	4	no	—
485	#120	—	2	8	no	—
486	#120	—	2	8	no	—
487	#120	D₄×C₁₃	1	2	yes	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	C₂³×C₁₃	1	4	yes	—
491	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
492	#117	C₂³×C₁₃	1	2	yes	—
493	#117	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	—	2	4	no	—
495	C₂×C₂²⋊C₄	—	2	8	no	—
496	#107	C₂³×C₁₃	1	2	yes	complemented
497	#106	C₂³×C₁₃	1	2	yes	complemented
498	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
499	#103	C₂³×C₁₃	1	4	yes	complemented
500	#102	C₂³×C₁₃	1	4	yes	complemented
501	#102	C₂³×C₁₃	1	8	yes	complemented
502	#102	C₂³×C₁₃	1	8	yes	complemented
503	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
504	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
505	#97	C₂³×C₁₃	1	2	yes	complemented
506	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
507	C₂×C₁₃	—	2	2	no	—
508	C₂×C₁₃	—	2	4	no	—
509	C₂×C₁₃	—	4	2	no	—
510	C₂×C₁₃	—	4	8	no	—
511	C₂×C₁₃	—	8	4	no	—
512	C₂×C₁₃	—	8	2	no	—
513	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
514	C₂×C₁₃	C₂×#576	1	2	yes	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	8	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	4	no	—
519	C₂⁴	—	4	8	no	—
520	C₂⁴	—	8	8	no	—
521	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	8	no	—
525	#41	—	2	4	no	—
526	#41	—	2	4	no	—
527	#41	—	4	4	no	—
528	#41	—	4	8	no	—
529	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
531	C₂×D₄	—	2	16	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	4	8	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	16	no	—
548	C₂×D₄	—	4	8	no	—
549	C₂×D₄	—	4	8	no	—
550	C₂×D₄	—	4	16	no	—
551	C₂×D₄	—	8	16	no	—
552	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
553	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
554	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	complemented
556	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
557	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
558	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
569	Q₁₆	—	2	2	no	—
570	SD₁₆	—	2	8	no	—
571	SD₁₆	—	2	4	no	—
572	SD₁₆	—	4	4	no	—
573	D₈	—	2	16	no	—
574	D₈	—	2	8	no	—
575	D₈	—	2	4	no	—
576	D₈	—	2	4	no	—
577	D₈	—	2	2	no	—
578	D₈	—	4	4	no	—
579	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
580	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
581	M₁₆	—	2	2	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	4	no	—
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	4	no	—
586	C₂×C₈	—	2	4	no	—
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
589	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
590	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
593	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
597	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	8	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
605	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
606	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
607	C₄²	—	2	2	no	—
608	C₄²	C₂⁴×C₁₃	1	2	yes	—
609	C₁₃	#61049	1	1	yes	characteristic, direct product factor, Sylow
610	C₂³	—	2	2	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	4	16	no	—
617	C₂³	—	4	8	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	4	16	no	—
620	C₂³	—	8	4	no	—
621	C₂³	—	8	8	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	—	8	32	no	—
625	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	8	no	—
633	D₄	—	2	8	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	4	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	4	16	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	4	no	—
646	D₄	—	8	8	no	—
647	D₄	—	8	8	no	—
648	D₄	C₂²×D₄×C₁₃	1	8	yes	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	8	8	no	—
660	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
661	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
665	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	C₂²×D₄×C₁₃	1	2	yes	—
671	C₈	C₂²×D₄×C₁₃	1	2	yes	—
672	C₂²	—	2	8	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	8	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	8	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	8	8	no	—
685	C₂²	—	8	32	no	—
686	C₂²	—	8	8	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₁₃	1	2	yes	—
689	C₂²	C₁₃×#576	1	4	yes	complemented
690	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	2	no	—
696	C₄	D₄²×C₁₃	1	2	yes	—
697	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
698	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂	—	2	2	no	—
700	C₂	—	2	4	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	8	no	—
703	C₂	—	8	4	no	—
704	C₂	—	8	2	no	—
705	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
706	C₂	C₂×C₁₃×#576	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₂³×C₁₃×D₈	C₂	semidirect
3. C₁₃×#3484	C₂	semidirect
4. C₁₃×#3280	C₂	semidirect
5. D₄×C₁₃×D₈	C₂	semidirect
6. C₁₃×#3264	C₂	semidirect
7. C₁₃×#3155	C₂	semidirect
8. C₁₃×#3058	C₂	semidirect
9. C₁₃×#3050	C₂	semidirect
10. C₁₃×#3041	C₂	semidirect
11. C₁₃×#3008	C₂	semidirect
12. C₁₃×#3003	C₂	semidirect
13. C₁₃×#2948	C₂	semidirect
14. C₁₃×#2929	C₂	semidirect
15. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
25. C₂²×C₁₃×D₈	C₂²	semidirect
26. C₂²×C₁₃×D₈	C₂²	semidirect
27. C₂²×C₁₃×D₈	C₂²	semidirect
28. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₂×C₁₃×#131	C₂²	semidirect
31. C₂³×C₈×C₁₃	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
35. D₄²×C₁₃	C₂²	semidirect
36. C₁₃×#535	C₂²	semidirect
37. C₁₃×#535	C₂²	semidirect
40. C₁₃×#525	C₂²	semidirect
42. C₁₃×#518	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#493	C₂²	semidirect
46. C₁₃×#469	C₂²	semidirect
47. C₁₃×#467	C₂²	semidirect
48. C₁₃×#466	C₂²	semidirect
49. C₁₃×#466	C₂²	semidirect
50. C₁₃×#465	C₂²	semidirect
51. C₁₃×#463	C₂²	semidirect
52. C₁₃×#459	C₂²	semidirect
53. C₁₃×#450	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#447	C₂²	semidirect
56. C₁₃×#447	C₂²	semidirect
57. C₁₃×#442	C₂²	semidirect
58. C₄×C₁₃×D₈	C₂²	semidirect
59. C₁₃×#435	C₂²	semidirect
60. C₈×D₄×C₁₃	C₂²	semidirect
61. C₁₃×#427	C₂²	semidirect
62. C₁₃×#424	C₂²	semidirect
63. C₁₃×#418	C₂²	semidirect
64. C₁₃×#418	C₂²	semidirect
65. C₁₃×#416	C₂²	semidirect
66. C₁₃×#408	C₂²	semidirect
67. C₁₃×#407	C₂²	semidirect
68. C₁₃×#405	C₂²	semidirect
75. C₂×C₁₃×#41	C₂³	semidirect
86. C₂²×D₄×C₁₃	C₂³	semidirect
93. C₂×C₁₃×Q₁₆	C₂³	semidirect
94. C₂×C₁₃×SD₁₆	C₂³	semidirect
95. C₂×C₁₃×SD₁₆	C₂³	semidirect
96. C₂×C₁₃×SD₁₆	C₂³	semidirect
102. C₂×C₁₃×D₈	D₄	semidirect
108. C₂×C₁₃×D₈	C₂³	semidirect
109. C₂×C₁₃×D₈	C₂³	semidirect
110. C₂×C₁₃×D₈	C₂³	semidirect
114. C₂×C₁₃×M₁₆	C₂³	semidirect
120. C₂²×C₈×C₁₃	C₂³	semidirect
122. C₁₃×#127	C₂³	semidirect
124. C₁₃×#124	C₂³	semidirect
135. C₁₃×#121	C₂³	semidirect
146. C₄×D₄×C₁₃	C₂³	semidirect
151. C₁₃×#107	C₂³	semidirect
152. C₁₃×#106	C₂³	semidirect
153. C₁₃×C₄⋊C₈	C₂³	semidirect
154. C₁₃×#103	C₂³	semidirect
155. C₁₃×#102	C₂³	semidirect
156. C₁₃×#102	C₂³	semidirect
157. C₁₃×#102	C₂³	semidirect
159. C₁₃×C₂²⋊C₈	C₂³	semidirect
160. C₁₃×#97	C₂³	semidirect
161. C₄×C₈×C₁₃	C₂³	semidirect
162. #61049	C₁₃	direct (N × H)
203. C₂×D₄×C₁₃	C₂×D₄	semidirect
227. C₁₃×D₈	C₂×D₄	semidirect
228. C₁₃×D₈	C₂×D₄	semidirect
236. C₂×C₈×C₁₃	C₂×D₄	semidirect
257. C₂×#576	C₂×C₁₃	semidirect
258. C₂³×D₈	C₂×C₁₃	semidirect
259. #3484	C₂×C₁₃	semidirect
260. #3280	C₂×C₁₃	semidirect
261. D₄×D₈	C₂×C₁₃	semidirect
262. #3264	C₂×C₁₃	semidirect
263. #3155	C₂×C₁₃	semidirect
264. #3058	C₂×C₁₃	semidirect
265. #3050	C₂×C₁₃	semidirect
266. #3041	C₂×C₁₃	semidirect
267. #3008	C₂×C₁₃	semidirect
268. #3003	C₂×C₁₃	semidirect
269. #2948	C₂×C₁₃	semidirect
270. #2929	C₂×C₁₃	semidirect
333. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
334. C₂³×D₄	C₂²×C₁₃	semidirect
336. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
337. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
338. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
339. C₂×#135	C₂²×C₁₃	semidirect
340. C₂×#135	C₂²×C₁₃	semidirect
343. C₂²×D₈	C₂²×C₁₃	semidirect
344. C₂²×D₈	C₂²×C₁₃	semidirect
345. C₂²×D₈	C₂²×C₁₃	semidirect
346. C₂²×D₈	C₂²×C₁₃	semidirect
347. C₂²×D₈	C₂²×C₁₃	semidirect
348. C₂×#131	C₂²×C₁₃	semidirect
349. C₂³×C₈	C₂²×C₁₃	semidirect
351. #546	C₂²×C₁₃	semidirect
353. D₄²	C₂²×C₁₃	semidirect
354. #535	C₂²×C₁₃	semidirect
355. #535	C₂²×C₁₃	semidirect
358. #525	C₂²×C₁₃	semidirect
360. #518	C₂²×C₁₃	semidirect
361. #496	C₂²×C₁₃	semidirect
362. #495	C₂²×C₁₃	semidirect
363. #493	C₂²×C₁₃	semidirect
364. #469	C₂²×C₁₃	semidirect
365. #467	C₂²×C₁₃	semidirect
366. #466	C₂²×C₁₃	semidirect
367. #466	C₂²×C₁₃	semidirect
368. #465	C₂²×C₁₃	semidirect
369. #463	C₂²×C₁₃	semidirect
370. #459	C₂²×C₁₃	semidirect
371. #450	C₂²×C₁₃	semidirect
372. #449	C₂²×C₁₃	semidirect
373. #447	C₂²×C₁₃	semidirect
374. #447	C₂²×C₁₃	semidirect
375. #442	C₂²×C₁₃	semidirect
376. C₄×D₈	C₂²×C₁₃	semidirect
377. #435	C₂²×C₁₃	semidirect
378. C₈×D₄	C₂²×C₁₃	semidirect
379. #427	C₂²×C₁₃	semidirect
380. #424	C₂²×C₁₃	semidirect
381. #418	C₂²×C₁₃	semidirect
382. #418	C₂²×C₁₃	semidirect
383. #416	C₂²×C₁₃	semidirect
384. #408	C₂²×C₁₃	semidirect
385. #407	C₂²×C₁₃	semidirect
386. #405	C₂²×C₁₃	semidirect
404. C₂²×C₁₃	#576	semidirect
420. C₂×#41	C₂³×C₁₃	semidirect
431. C₂²×D₄	C₂³×C₁₃	semidirect
438. C₂×Q₁₆	C₂³×C₁₃	semidirect
439. C₂×SD₁₆	C₂³×C₁₃	semidirect
440. C₂×SD₁₆	C₂³×C₁₃	semidirect
441. C₂×SD₁₆	C₂³×C₁₃	semidirect
447. C₂×D₈	D₄×C₁₃	semidirect
453. C₂×D₈	C₂³×C₁₃	semidirect
454. C₂×D₈	C₂³×C₁₃	semidirect
455. C₂×D₈	C₂³×C₁₃	semidirect
459. C₂×M₁₆	C₂³×C₁₃	semidirect
465. C₂²×C₈	C₂³×C₁₃	semidirect
467. #127	C₂³×C₁₃	semidirect
469. #124	C₂³×C₁₃	semidirect
480. #121	C₂³×C₁₃	semidirect
491. C₄×D₄	C₂³×C₁₃	semidirect
496. #107	C₂³×C₁₃	semidirect
497. #106	C₂³×C₁₃	semidirect
498. C₄⋊C₈	C₂³×C₁₃	semidirect
499. #103	C₂³×C₁₃	semidirect
500. #102	C₂³×C₁₃	semidirect
501. #102	C₂³×C₁₃	semidirect
502. #102	C₂³×C₁₃	semidirect
504. C₂²⋊C₈	C₂³×C₁₃	semidirect
505. #97	C₂³×C₁₃	semidirect
506. C₄×C₈	C₂³×C₁₃	semidirect
555. C₂×D₄	C₂×D₄×C₁₃	semidirect
579. D₈	C₂×D₄×C₁₃	semidirect
580. D₈	C₂×D₄×C₁₃	semidirect
588. C₂×C₈	C₂×D₄×C₁₃	semidirect
609. C₁₃	#61049	direct (N × H)
689. C₂²	C₁₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#576	2
C₂³×C₁₃×D₈	2
C₁₃×#3484	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3264	2
C₁₃×#3155	2
C₁₃×#3058	2
C₁₃×#3050	2
C₁₃×#3041	2
C₁₃×#3008	2
C₁₃×#3003	2
C₁₃×#2948	2
C₁₃×#2929	2
#61049	13

Subgroups — C13×#61049 #15747388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61049 #15747388