Subgroups — C₁₃×#61090 #15747429

Order 3328.

2714 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×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3500	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3280	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3275	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₁₃×#578	—	2	8	no	—
18	C₁₃×#576	—	2	8	no	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
23	C₂×C₁₃×#135	C₂²	1	2	yes	—
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
30	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#548	C₂²	1	8	yes	complemented
34	C₁₃×#546	—	2	8	no	—
35	C₁₃×#546	C₂²	1	8	yes	complemented
36	C₁₃×#536	—	2	2	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#535	—	2	2	no	—
39	C₁₃×#535	C₂²	1	2	yes	complemented
40	C₁₃×#532	—	2	2	no	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#124	—	2	2	no	—
43	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
44	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
45	C₁₃×#495	C₂²	1	4	yes	complemented
46	C₁₃×#495	C₂²	1	4	yes	complemented
47	C₁₃×#470	C₂²	1	4	yes	complemented
48	C₁₃×#469	C₂²	1	4	yes	complemented
49	C₁₃×#467	C₂²	1	4	yes	complemented
50	C₁₃×#466	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#463	C₂²	1	8	yes	complemented
53	C₁₃×#452	C₂²	1	8	yes	complemented
54	C₁₃×#450	C₂²	1	8	yes	complemented
55	C₁₃×#449	C₂²	1	8	yes	complemented
56	C₁₃×#448	C₂²	1	8	yes	complemented
57	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
58	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
59	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
60	C₁₃×#436	C₂²	1	4	yes	complemented
61	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
62	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#419	C₂²	1	2	yes	complemented
65	C₁₃×#418	C₂²	1	2	yes	complemented
66	C₁₃×#416	C₂²	1	2	yes	complemented
67	C₁₃×#408	C₂²	1	1	yes	characteristic
68	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×2₋¹⁺⁴	—	2	8	no	—
71	C₁₃×2₋¹⁺⁴	—	4	4	no	—
72	C₁₃×H(5,𝔽₂)	—	2	8	no	—
73	C₁₃×H(5,𝔽₂)	—	4	4	no	—
74	C₂×C₁₃×#41	—	2	2	no	—
75	C₂×C₁₃×#41	—	2	2	no	—
76	C₂×C₁₃×#41	—	2	4	no	—
77	C₂×C₁₃×#41	C₂³	1	4	yes	—
78	C₂×C₁₃×#41	C₂³	1	4	yes	—
79	C₂×C₁₃×#41	C₂³	1	2	yes	—
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₃	—	2	2	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₁₃	—	2	2	no	—
86	C₂²×D₄×C₁₃	—	2	4	no	—
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
89	C₁₃×#137	—	2	8	no	—
90	C₁₃×#137	—	2	16	no	—
91	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
92	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
93	C₁₃×#135	—	2	8	no	—
94	C₁₃×#135	—	2	8	no	—
95	C₁₃×#135	D₄	1	8	yes	complemented
96	C₂×C₁₃×Q₁₆	—	2	8	no	—
97	C₂×C₁₃×Q₁₆	—	2	4	no	—
98	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×SD₁₆	—	4	4	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×D₈	—	2	8	no	—
108	C₂×C₁₃×D₈	—	2	4	no	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	2	yes	—
111	C₂×C₁₃×D₈	C₂³	1	2	yes	—
112	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
113	C₁₃×#131	—	2	4	no	—
114	C₁₃×#131	—	2	4	no	—
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	—	2	2	no	—
124	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
125	C₁₃×#127	—	2	2	no	—
126	C₁₃×#127	D₄	1	1	yes	characteristic
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	8	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	D₄	1	1	yes	characteristic
133	C₁₃×#124	D₄	1	1	yes	characteristic
134	C₁₃×#124	C₂³	1	8	yes	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	8	no	—
137	C₁₃×C₂²⋊Q₈	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
139	C₁₃×#121	—	2	8	no	—
140	C₁₃×#121	—	2	8	no	—
141	C₁₃×#121	D₄	1	4	yes	—
142	C₁₃×#121	C₂³	1	8	yes	—
143	C₁₃×#120	—	2	8	no	—
144	C₁₃×#120	—	2	4	no	—
145	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	2	8	no	—
148	C₄×D₄×C₁₃	C₂³	1	4	yes	—
149	C₄×D₄×C₁₃	C₂³	1	4	yes	—
150	C₁₃×#117	—	2	2	no	—
151	C₁₃×#117	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₂×C₄²×C₁₃	—	2	2	no	—
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#107	C₂³	1	2	yes	—
157	C₁₃×#106	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
159	C₁₃×#103	C₂³	1	4	yes	—
160	C₁₃×#103	C₂³	1	8	yes	—
161	C₁₃×#102	C₂³	1	4	yes	—
162	C₁₃×#102	C₂³	1	8	yes	—
163	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₄×C₈×C₁₃	C₂³	1	2	yes	—
166	C₄×C₈×C₁₃	C₂³	1	2	yes	—
167	#61090	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	4	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₁₃×#41	—	2	2	no	—
171	C₁₃×#41	—	2	2	no	—
172	C₁₃×#41	—	2	2	no	—
173	C₁₃×#41	—	2	4	no	—
174	C₁₃×#41	—	2	2	no	—
175	C₁₃×#41	—	2	8	no	—
176	C₁₃×#41	—	2	8	no	—
177	C₁₃×#41	—	4	4	no	—
178	C₁₃×#41	—	4	4	no	—
179	C₁₃×#41	—	4	8	no	—
180	C₁₃×#41	—	4	8	no	—
181	C₁₃×#41	—	4	16	no	—
182	C₁₃×#41	C₂×D₄	1	8	yes	—
183	C₂×Q₈×C₁₃	—	2	4	no	—
184	C₂×Q₈×C₁₃	—	2	2	no	—
185	C₂×Q₈×C₁₃	—	2	8	no	—
186	C₂×Q₈×C₁₃	—	2	4	no	—
187	C₂×Q₈×C₁₃	—	2	4	no	—
188	C₂×Q₈×C₁₃	—	4	4	no	—
189	C₂×Q₈×C₁₃	—	4	8	no	—
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
193	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	8	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	8	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	4	4	no	—
204	C₂×D₄×C₁₃	—	4	8	no	—
205	C₂×D₄×C₁₃	—	4	16	no	—
206	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
211	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
212	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×Q₁₆	—	2	8	no	—
224	C₁₃×Q₁₆	—	2	4	no	—
225	C₁₃×Q₁₆	—	2	4	no	—
226	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
227	C₁₃×SD₁₆	—	2	8	no	—
228	C₁₃×SD₁₆	—	2	8	no	—
229	C₁₃×SD₁₆	—	4	8	no	—
230	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
231	C₁₃×D₈	—	2	8	no	—
232	C₁₃×D₈	—	2	4	no	—
233	C₁₃×D₈	—	2	4	no	—
234	C₁₃×D₈	C₂×D₄	1	4	yes	—
235	C₁₃×M₁₆	—	2	2	no	—
236	C₁₃×M₁₆	—	2	2	no	—
237	C₁₃×M₁₆	—	2	4	no	—
238	C₁₃×M₁₆	—	2	4	no	—
239	C₂×C₈×C₁₃	—	2	2	no	—
240	C₂×C₈×C₁₃	—	2	4	no	—
241	C₂×C₈×C₁₃	—	2	4	no	—
242	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	8	no	—
250	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
251	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
252	C₁₃×C₂²⋊C₄	—	2	8	no	—
253	C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×C₂²⋊C₄	—	2	8	no	—
255	C₁₃×C₂²⋊C₄	—	2	8	no	—
256	C₁₃×C₂²⋊C₄	—	2	8	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
260	C₄²×C₁₃	—	2	2	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₃	C₂⁴	1	2	yes	—
265	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#3500	C₂×C₁₃	1	2	yes	complemented
268	#3285	C₂×C₁₃	1	4	yes	complemented
269	#3280	C₂×C₁₃	1	4	yes	complemented
270	#3275	C₂×C₁₃	1	8	yes	complemented
271	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#3040	C₂×C₁₃	1	2	yes	complemented
275	#3010	C₂×C₁₃	1	2	yes	complemented
276	#3009	C₂×C₁₃	1	2	yes	complemented
277	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	4	no	—
281	C₂³×C₁₃	—	4	8	no	—
282	C₂³×C₁₃	—	4	4	no	—
283	C₂³×C₁₃	—	8	4	no	—
284	C₂³×C₁₃	—	8	8	no	—
285	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₁₃	—	2	2	no	—
289	Q₈×C₁₃	—	2	2	no	—
290	Q₈×C₁₃	—	2	2	no	—
291	Q₈×C₁₃	—	2	4	no	—
292	Q₈×C₁₃	—	2	4	no	—
293	Q₈×C₁₃	—	4	8	no	—
294	Q₈×C₁₃	—	4	4	no	—
295	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
296	D₄×C₁₃	—	2	8	no	—
297	D₄×C₁₃	—	2	4	no	—
298	D₄×C₁₃	—	2	4	no	—
299	D₄×C₁₃	—	2	2	no	—
300	D₄×C₁₃	—	2	2	no	—
301	D₄×C₁₃	—	2	4	no	—
302	D₄×C₁₃	—	2	2	no	—
303	D₄×C₁₃	—	2	4	no	—
304	D₄×C₁₃	—	4	4	no	—
305	D₄×C₁₃	—	4	8	no	—
306	D₄×C₁₃	—	4	8	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	8	8	no	—
310	D₄×C₁₃	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	8	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	2	no	—
317	C₂×C₄×C₁₃	—	2	4	no	—
318	C₂×C₄×C₁₃	—	2	4	no	—
319	C₂×C₄×C₁₃	—	4	2	no	—
320	C₂×C₄×C₁₃	—	4	8	no	—
321	C₂×C₄×C₁₃	—	4	8	no	—
322	C₂×C₄×C₁₃	—	4	8	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	8	4	no	—
325	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₁₃	—	2	2	no	—
334	C₈×C₁₃	—	2	2	no	—
335	C₈×C₁₃	—	2	2	no	—
336	C₈×C₁₃	C₂²×D₄	1	2	yes	—
337	C₈×C₁₃	C₂²×D₄	1	2	yes	—
338	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
339	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
340	#578	—	2	8	no	—
341	#576	—	2	8	no	—
342	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
343	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
344	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
345	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
346	C₂×#135	C₂²×C₁₃	1	2	yes	—
347	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
349	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
350	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
351	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
352	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
354	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
356	#548	C₂²×C₁₃	1	8	yes	complemented
357	#546	—	2	8	no	—
358	#546	C₂²×C₁₃	1	8	yes	complemented
359	#536	—	2	2	no	—
360	#536	C₂²×C₁₃	1	2	yes	—
361	#535	—	2	2	no	—
362	#535	C₂²×C₁₃	1	2	yes	complemented
363	#532	—	2	2	no	—
364	#532	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#124	—	2	2	no	—
366	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
367	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
368	#495	C₂²×C₁₃	1	4	yes	complemented
369	#495	C₂²×C₁₃	1	4	yes	complemented
370	#470	C₂²×C₁₃	1	4	yes	complemented
371	#469	C₂²×C₁₃	1	4	yes	complemented
372	#467	C₂²×C₁₃	1	4	yes	complemented
373	#466	C₂²×C₁₃	1	4	yes	complemented
374	#464	C₂²×C₁₃	1	8	yes	complemented
375	#463	C₂²×C₁₃	1	8	yes	complemented
376	#452	C₂²×C₁₃	1	8	yes	complemented
377	#450	C₂²×C₁₃	1	8	yes	complemented
378	#449	C₂²×C₁₃	1	8	yes	complemented
379	#448	C₂²×C₁₃	1	8	yes	complemented
380	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
381	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
382	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
383	#436	C₂²×C₁₃	1	4	yes	complemented
384	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
385	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	#419	C₂²×C₁₃	1	2	yes	complemented
388	#418	C₂²×C₁₃	1	2	yes	complemented
389	#416	C₂²×C₁₃	1	2	yes	complemented
390	#408	C₂²×C₁₃	1	1	yes	characteristic
391	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂²×C₁₃	—	2	2	no	—
394	C₂²×C₁₃	—	2	4	no	—
395	C₂²×C₁₃	—	2	4	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	4	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	4	4	no	—
400	C₂²×C₁₃	—	4	8	no	—
401	C₂²×C₁₃	—	4	4	no	—
402	C₂²×C₁₃	—	16	4	no	—
403	C₂²×C₁₃	—	16	8	no	—
404	C₂²×C₁₃	D₄²	1	2	yes	—
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	—	2	2	no	—
410	C₄×C₁₃	—	2	2	no	—
411	C₄×C₁₃	—	4	4	no	—
412	C₄×C₁₃	—	4	4	no	—
413	C₄×C₁₃	D₄²	1	2	yes	—
414	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	2₋¹⁺⁴	—	2	8	no	—
417	2₋¹⁺⁴	—	4	4	no	—
418	H(5,𝔽₂)	—	2	8	no	—
419	H(5,𝔽₂)	—	4	4	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	C₂³×C₁₃	1	4	yes	—
424	C₂×#41	C₂³×C₁₃	1	4	yes	—
425	C₂×#41	C₂³×C₁₃	1	2	yes	—
426	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×Q₈	—	2	2	no	—
429	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
430	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
431	C₂²×D₄	—	2	2	no	—
432	C₂²×D₄	—	2	4	no	—
433	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
434	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
435	#137	—	2	8	no	—
436	#137	—	2	16	no	—
437	AGL(1,ℤ/8)	—	2	8	no	—
438	AGL(1,ℤ/8)	—	2	16	no	—
439	#135	—	2	8	no	—
440	#135	—	2	8	no	—
441	#135	D₄×C₁₃	1	8	yes	complemented
442	C₂×Q₁₆	—	2	8	no	—
443	C₂×Q₁₆	—	2	4	no	—
444	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
445	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
446	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
447	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×SD₁₆	—	4	4	no	—
449	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
450	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
451	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
452	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
453	C₂×D₈	—	2	8	no	—
454	C₂×D₈	—	2	4	no	—
455	C₂×D₈	C₂³×C₁₃	1	2	yes	—
456	C₂×D₈	C₂³×C₁₃	1	4	yes	—
457	C₂×D₈	C₂³×C₁₃	1	2	yes	—
458	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
459	#131	—	2	4	no	—
460	#131	—	2	4	no	—
461	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
463	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
466	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
467	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
471	#127	—	2	2	no	—
472	#127	D₄×C₁₃	1	1	yes	characteristic
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	#124	—	2	8	no	—
476	#124	—	2	2	no	—
477	#124	—	2	2	no	—
478	#124	D₄×C₁₃	1	1	yes	characteristic
479	#124	D₄×C₁₃	1	1	yes	characteristic
480	#124	C₂³×C₁₃	1	8	yes	—
481	#123	—	2	4	no	—
482	#123	—	2	8	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
485	#121	—	2	8	no	—
486	#121	—	2	8	no	—
487	#121	D₄×C₁₃	1	4	yes	—
488	#121	C₂³×C₁₃	1	8	yes	—
489	#120	—	2	8	no	—
490	#120	—	2	4	no	—
491	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	C₂³×C₁₃	1	4	yes	—
495	C₄×D₄	C₂³×C₁₃	1	4	yes	—
496	#117	—	2	2	no	—
497	#117	C₂³×C₁₃	1	2	yes	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	8	no	—
500	C₂×C₄²	—	2	2	no	—
501	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
502	#107	C₂³×C₁₃	1	2	yes	—
503	#106	C₂³×C₁₃	1	2	yes	—
504	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
505	#103	C₂³×C₁₃	1	4	yes	—
506	#103	C₂³×C₁₃	1	8	yes	—
507	#102	C₂³×C₁₃	1	4	yes	—
508	#102	C₂³×C₁₃	1	8	yes	—
509	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
510	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
511	C₄×C₈	C₂³×C₁₃	1	2	yes	—
512	C₄×C₈	C₂³×C₁₃	1	2	yes	—
513	C₂×C₁₃	—	2	2	no	—
514	C₂×C₁₃	—	4	2	no	—
515	C₂×C₁₃	—	4	2	no	—
516	C₂×C₁₃	—	4	4	no	—
517	C₂×C₁₃	—	8	4	no	—
518	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
519	C₂×C₁₃	#3584	1	2	yes	—
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	4	no	—
526	#41	—	2	2	no	—
527	#41	—	2	8	no	—
528	#41	—	2	8	no	—
529	#41	—	4	4	no	—
530	#41	—	4	4	no	—
531	#41	—	4	8	no	—
532	#41	—	4	8	no	—
533	#41	—	4	16	no	—
534	#41	C₂×D₄×C₁₃	1	8	yes	—
535	C₂×Q₈	—	2	4	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	8	no	—
538	C₂×Q₈	—	2	4	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	—	4	8	no	—
542	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
545	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	—	4	16	no	—
558	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
559	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
560	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
563	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
564	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
575	Q₁₆	—	2	8	no	—
576	Q₁₆	—	2	4	no	—
577	Q₁₆	—	2	4	no	—
578	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
579	SD₁₆	—	2	8	no	—
580	SD₁₆	—	2	8	no	—
581	SD₁₆	—	4	8	no	—
582	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
583	D₈	—	2	8	no	—
584	D₈	—	2	4	no	—
585	D₈	—	2	4	no	—
586	D₈	C₂×D₄×C₁₃	1	4	yes	—
587	M₁₆	—	2	2	no	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	2	4	no	—
590	M₁₆	—	2	4	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
595	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
596	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
597	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
598	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
603	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
611	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	4	no	—
614	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₄²	C₂⁴×C₁₃	1	2	yes	—
617	C₁₃	#61090	1	1	yes	characteristic, direct product factor, Sylow
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	8	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
625	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	4	no	—
631	Q₈	—	2	4	no	—
632	Q₈	—	4	8	no	—
633	Q₈	—	4	4	no	—
634	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
635	D₄	—	2	8	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	8	no	—
649	D₄	C₂²×D₄×C₁₃	1	4	yes	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
666	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
670	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
671	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	C₂²×D₄×C₁₃	1	2	yes	—
676	C₈	C₂²×D₄×C₁₃	1	2	yes	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	8	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	16	4	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₁₃	1	2	yes	—
689	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	D₄²×C₁₃	1	2	yes	—
698	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
699	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	4	no	—
704	C₂	—	8	4	no	—
705	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
706	C₂	C₁₃×#3584	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×#578	C₂	semidirect
2. C₂×C₁₃×#576	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3285	C₂	semidirect
5. C₁₃×#3280	C₂	semidirect
6. C₁₃×#3275	C₂	semidirect
7. C₂×C₁₃×#495	C₂	semidirect
8. C₁₃×#3059	C₂	semidirect
9. C₁₃×#3058	C₂	semidirect
10. C₁₃×#3040	C₂	semidirect
11. C₁₃×#3010	C₂	semidirect
12. C₁₃×#3009	C₂	semidirect
13. C₄×C₁₃×#135	C₂	semidirect
14. C₁₃×#2931	C₂	semidirect
15. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂²×C₁₃×Q₁₆	C₂²	semidirect
27. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
32. C₂×C₁₃×#131	C₂²	semidirect
33. C₁₃×#548	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
44. C₄×C₁₃×#41	C₂²	semidirect
45. C₁₃×#495	C₂²	semidirect
46. C₁₃×#495	C₂²	semidirect
47. C₁₃×#470	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#467	C₂²	semidirect
50. C₁₃×#466	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#452	C₂²	semidirect
54. C₁₃×#450	C₂²	semidirect
55. C₁₃×#449	C₂²	semidirect
56. C₁₃×#448	C₂²	semidirect
57. C₄×C₁₃×Q₁₆	C₂²	semidirect
58. C₄×C₁₃×SD₁₆	C₂²	semidirect
59. C₄×C₁₃×D₈	C₂²	semidirect
60. C₁₃×#436	C₂²	semidirect
61. C₈×D₄×C₁₃	C₂²	semidirect
62. C₁₃×#427	C₂²	semidirect
63. C₁₃×#423	C₂²	semidirect
64. C₁₃×#419	C₂²	semidirect
65. C₁₃×#418	C₂²	semidirect
66. C₁₃×#416	C₂²	semidirect
68. C₁₃×#408	C₂²	semidirect
69. C₂×C₄×C₈×C₁₃	C₂²	semidirect
95. C₁₃×#135	D₄	semidirect
167. #61090	C₁₃	direct (N × H)
265. C₂×#578	C₂×C₁₃	semidirect
266. C₂×#576	C₂×C₁₃	semidirect
267. #3500	C₂×C₁₃	semidirect
268. #3285	C₂×C₁₃	semidirect
269. #3280	C₂×C₁₃	semidirect
270. #3275	C₂×C₁₃	semidirect
271. C₂×#495	C₂×C₁₃	semidirect
272. #3059	C₂×C₁₃	semidirect
273. #3058	C₂×C₁₃	semidirect
274. #3040	C₂×C₁₃	semidirect
275. #3010	C₂×C₁₃	semidirect
276. #3009	C₂×C₁₃	semidirect
277. C₄×#135	C₂×C₁₃	semidirect
278. #2931	C₂×C₁₃	semidirect
338. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
342. C₂×#137	C₂²×C₁₃	semidirect
343. C₂×#137	C₂²×C₁₃	semidirect
348. C₂×#135	C₂²×C₁₃	semidirect
349. C₂²×Q₁₆	C₂²×C₁₃	semidirect
350. C₂²×Q₁₆	C₂²×C₁₃	semidirect
351. C₂²×SD₁₆	C₂²×C₁₃	semidirect
355. C₂×#131	C₂²×C₁₃	semidirect
356. #548	C₂²×C₁₃	semidirect
358. #546	C₂²×C₁₃	semidirect
362. #535	C₂²×C₁₃	semidirect
366. C₂×#124	C₂²×C₁₃	semidirect
367. C₄×#41	C₂²×C₁₃	semidirect
368. #495	C₂²×C₁₃	semidirect
369. #495	C₂²×C₁₃	semidirect
370. #470	C₂²×C₁₃	semidirect
371. #469	C₂²×C₁₃	semidirect
372. #467	C₂²×C₁₃	semidirect
373. #466	C₂²×C₁₃	semidirect
374. #464	C₂²×C₁₃	semidirect
375. #463	C₂²×C₁₃	semidirect
376. #452	C₂²×C₁₃	semidirect
377. #450	C₂²×C₁₃	semidirect
378. #449	C₂²×C₁₃	semidirect
379. #448	C₂²×C₁₃	semidirect
380. C₄×Q₁₆	C₂²×C₁₃	semidirect
381. C₄×SD₁₆	C₂²×C₁₃	semidirect
382. C₄×D₈	C₂²×C₁₃	semidirect
383. #436	C₂²×C₁₃	semidirect
384. C₈×D₄	C₂²×C₁₃	semidirect
385. #427	C₂²×C₁₃	semidirect
386. #423	C₂²×C₁₃	semidirect
387. #419	C₂²×C₁₃	semidirect
388. #418	C₂²×C₁₃	semidirect
389. #416	C₂²×C₁₃	semidirect
391. #408	C₂²×C₁₃	semidirect
392. C₂×C₄×C₈	C₂²×C₁₃	semidirect
441. #135	D₄×C₁₃	semidirect
617. C₁₃	#61090	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#578	2
C₂×C₁₃×#576	2
C₁₃×#3500	2
C₁₃×#3285	2
C₁₃×#3280	2
C₁₃×#3275	2
C₂×C₁₃×#495	2
C₁₃×#3059	2
C₁₃×#3058	2
C₁₃×#3040	2
C₁₃×#3010	2
C₁₃×#3009	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
#61090	13

Subgroups — C13×#61090 #15747429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61090 #15747429