Subgroups — C₁₃×#61651 #15747990

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3326	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3309	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3274	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3199	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#560	—	2	2	no	—
20	C₁₃×#553	C₂²	1	4	yes	complemented
21	C₁₃×#550	—	2	2	no	—
22	C₁₃×#550	C₂²	1	4	yes	complemented
23	C₁₃×#548	—	2	2	no	—
24	C₁₃×#548	C₂²	1	4	yes	complemented
25	D₄²×C₁₃	—	2	2	no	—
26	D₄²×C₁₃	C₂²	1	4	yes	complemented
27	C₁₃×#540	C₂²	1	2	yes	—
28	C₁₃×#538	—	2	2	no	—
29	C₁₃×#535	—	2	2	no	—
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#534	—	2	2	no	—
34	C₁₃×#525	—	2	2	no	—
35	C₁₃×#525	C₂²	1	1	yes	characteristic
36	C₁₃×#525	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#121	C₂²	1	2	yes	—
38	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#496	C₂²	1	2	yes	complemented
40	C₁₃×#493	C₂²	1	2	yes	complemented
41	C₁₃×#490	C₂²	1	2	yes	complemented
42	C₁₃×#488	C₂²	1	2	yes	complemented
43	C₁₃×#483	C₂²	1	2	yes	complemented
44	C₁₃×#482	C₂²	1	4	yes	complemented
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#480	C₂²	1	2	yes	complemented
47	C₁₃×#479	C₂²	1	4	yes	complemented
48	C₁₃×#469	C₂²	1	4	yes	complemented
49	C₁₃×#469	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#466	C₂²	1	4	yes	complemented
52	C₁₃×#463	C₂²	1	4	yes	complemented
53	C₁₃×#460	C₂²	1	4	yes	complemented
54	C₁₃×#459	C₂²	1	4	yes	complemented
55	C₁₃×#450	C₂²	1	2	yes	complemented
56	C₁₃×#449	C₂²	1	4	yes	complemented
57	C₁₃×#449	C₂²	1	4	yes	complemented
58	C₁₃×#449	C₂²	1	4	yes	complemented
59	C₁₃×#449	C₂²	1	4	yes	complemented
60	C₁₃×#448	C₂²	1	4	yes	complemented
61	C₁₃×#448	C₂²	1	4	yes	complemented
62	C₁₃×#447	C₂²	1	4	yes	complemented
63	C₁₃×#447	C₂²	1	4	yes	complemented
64	C₁₃×#447	C₂²	1	2	yes	complemented
65	C₁₃×#440	C₂²	1	4	yes	complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
67	C₁₃×#436	C₂²	1	4	yes	complemented
68	C₁₃×#435	C₂²	1	4	yes	complemented
69	C₁₃×#433	C₂²	1	2	yes	complemented
70	C₁₃×#419	C₂²	1	2	yes	complemented
71	C₁₃×#417	C₂²	1	4	yes	complemented
72	C₁₃×#416	C₂²	1	2	yes	complemented
73	C₁₃×#408	C₂²	1	2	yes	complemented
74	C₁₃×#407	C₂²	1	2	yes	complemented
75	C₁₃×2₋¹⁺⁴	—	4	4	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	4	4	no	—
80	C₂×C₁₃×#41	C₂³	1	2	yes	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	2	no	—
89	C₂²×D₄×C₁₃	—	2	4	no	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	—	2	1	no	—
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
96	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
97	C₂×C₁₃×SD₁₆	—	4	4	no	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×D₈	C₂³	1	4	yes	—
102	C₂×C₁₃×D₈	C₂³	1	4	yes	—
103	C₂×C₁₃×D₈	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
107	C₁₃×#127	—	2	4	no	—
108	C₁₃×#127	—	2	2	no	—
109	C₁₃×#127	—	2	1	no	—
110	C₁₃×#127	C₂³	1	2	yes	—
111	C₁₃×#127	C₂³	1	2	yes	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#125	C₂³	1	2	yes	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	1	no	—
116	C₁₃×#124	—	2	4	no	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	1	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	D₄	1	2	yes	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	—	2	4	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	4	no	—
131	C₁₃×#121	—	2	4	no	—
132	C₁₃×#121	—	2	4	no	—
133	C₁₃×#121	—	2	4	no	—
134	C₁₃×#121	D₄	1	2	yes	—
135	C₁₃×#121	C₂³	1	4	yes	—
136	C₁₃×#121	C₂³	1	4	yes	—
137	C₁₃×#121	C₂³	1	2	yes	—
138	C₁₃×#121	C₂³	1	4	yes	—
139	C₁₃×#121	C₂³	1	4	yes	—
140	C₁₃×#120	—	2	1	no	—
141	C₁₃×#120	—	2	2	no	—
142	C₁₃×#120	—	2	2	no	—
143	C₁₃×#120	—	2	2	no	—
144	C₁₃×#120	—	2	2	no	—
145	C₁₃×#120	—	2	4	no	—
146	C₁₃×#120	—	2	4	no	—
147	C₁₃×#120	D₄	1	2	yes	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	4	no	—
152	C₄×D₄×C₁₃	—	2	4	no	—
153	C₄×D₄×C₁₃	—	2	4	no	—
154	C₄×D₄×C₁₃	C₂³	1	4	yes	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₁₃×#117	C₂³	1	1	yes	characteristic
159	C₁₃×#117	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#106	C₂³	1	4	yes	—
164	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
165	C₁₃×#103	C₂³	1	4	yes	—
166	C₁₃×#103	C₂³	1	4	yes	—
167	C₁₃×#103	C₂³	1	4	yes	—
168	C₁₃×#102	C₂³	1	4	yes	—
169	C₁₃×#102	C₂³	1	4	yes	—
170	C₁₃×#102	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×#97	C₂³	1	2	yes	—
178	C₄×C₈×C₁₃	C₂³	1	2	yes	—
179	#61651	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	2	no	—
181	C₂⁴×C₁₃	—	2	1	no	—
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₁₃×#41	—	2	8	no	—
185	C₁₃×#41	—	2	4	no	—
186	C₁₃×#41	—	4	2	no	—
187	C₁₃×#41	—	4	4	no	—
188	C₁₃×#41	—	4	2	no	—
189	C₁₃×#41	—	4	2	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₁₃×#41	—	4	4	no	—
193	C₂×Q₈×C₁₃	—	2	4	no	—
194	C₂×Q₈×C₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₃	—	2	2	no	—
196	C₂×Q₈×C₁₃	—	2	4	no	—
197	C₂×Q₈×C₁₃	—	4	2	no	—
198	C₂×Q₈×C₁₃	—	4	4	no	—
199	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	2	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	—	8	8	no	—
221	C₂×D₄×C₁₃	—	8	4	no	—
222	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
223	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	4	no	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₁₃×SD₁₆	—	2	8	no	—
243	C₁₃×SD₁₆	—	2	8	no	—
244	C₁₃×SD₁₆	—	4	4	no	—
245	C₁₃×D₈	—	4	4	no	—
246	C₁₃×D₈	—	4	4	no	—
247	C₁₃×D₈	—	4	4	no	—
248	C₁₃×M₁₆	—	4	4	no	—
249	C₁₃×M₁₆	—	4	2	no	—
250	C₂×C₈×C₁₃	—	4	2	no	—
251	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
252	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	1	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	C₂⁴	1	2	yes	—
278	#3537	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3487	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#3326	C₂×C₁₃	1	4	yes	complemented
281	#3309	C₂×C₁₃	1	4	yes	complemented
282	#3274	C₂×C₁₃	1	4	yes	complemented
283	#3265	C₂×C₁₃	1	4	yes	complemented
284	#3220	C₂×C₁₃	1	2	yes	complemented
285	#3199	C₂×C₁₃	1	2	yes	complemented
286	#3194	C₂×C₁₃	1	2	yes	complemented
287	#3126	C₂×C₁₃	1	2	yes	complemented
288	#3010	C₂×C₁₃	1	2	yes	complemented
289	#3006	C₂×C₁₃	1	2	yes	complemented
290	#2978	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	—	4	2	no	—
296	C₂³×C₁₃	—	4	2	no	—
297	C₂³×C₁₃	—	4	4	no	—
298	C₂³×C₁₃	—	8	2	no	—
299	C₂³×C₁₃	—	8	2	no	—
300	C₂³×C₁₃	—	8	2	no	—
301	C₂³×C₁₃	—	8	2	no	—
302	C₂³×C₁₃	—	8	4	no	—
303	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
306	Q₈×C₁₃	—	2	4	no	—
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	4	1	no	—
310	Q₈×C₁₃	—	4	4	no	—
311	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
312	D₄×C₁₃	—	2	4	no	—
313	D₄×C₁₃	—	2	4	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	2	4	no	—
316	D₄×C₁₃	—	4	4	no	—
317	D₄×C₁₃	—	4	1	no	—
318	D₄×C₁₃	—	4	2	no	—
319	D₄×C₁₃	—	4	8	no	—
320	D₄×C₁₃	—	4	4	no	—
321	D₄×C₁₃	—	4	2	no	—
322	D₄×C₁₃	—	4	8	no	—
323	D₄×C₁₃	—	4	2	no	—
324	D₄×C₁₃	—	8	4	no	—
325	D₄×C₁₃	—	8	2	no	—
326	D₄×C₁₃	—	8	2	no	—
327	D₄×C₁₃	—	8	4	no	—
328	D₄×C₁₃	—	8	2	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	D₄×C₁₃	—	8	4	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	4	2	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	2	no	—
347	C₂×C₄×C₁₃	—	8	4	no	—
348	C₂×C₄×C₁₃	—	8	2	no	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
354	C₈×C₁₃	—	2	4	no	—
355	C₈×C₁₃	—	2	4	no	—
356	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
357	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
358	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
359	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
360	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
361	#560	—	2	2	no	—
362	#553	C₂²×C₁₃	1	4	yes	complemented
363	#550	—	2	2	no	—
364	#550	C₂²×C₁₃	1	4	yes	complemented
365	#548	—	2	2	no	—
366	#548	C₂²×C₁₃	1	4	yes	complemented
367	D₄²	—	2	2	no	—
368	D₄²	C₂²×C₁₃	1	4	yes	complemented
369	#540	C₂²×C₁₃	1	2	yes	—
370	#538	—	2	2	no	—
371	#535	—	2	2	no	—
372	#535	C₂²×C₁₃	1	2	yes	—
373	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
374	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
375	#534	—	2	2	no	—
376	#525	—	2	2	no	—
377	#525	C₂²×C₁₃	1	1	yes	characteristic
378	#525	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂×#121	C₂²×C₁₃	1	2	yes	—
380	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#496	C₂²×C₁₃	1	2	yes	complemented
382	#493	C₂²×C₁₃	1	2	yes	complemented
383	#490	C₂²×C₁₃	1	2	yes	complemented
384	#488	C₂²×C₁₃	1	2	yes	complemented
385	#483	C₂²×C₁₃	1	2	yes	complemented
386	#482	C₂²×C₁₃	1	4	yes	complemented
387	#482	C₂²×C₁₃	1	4	yes	complemented
388	#480	C₂²×C₁₃	1	2	yes	complemented
389	#479	C₂²×C₁₃	1	4	yes	complemented
390	#469	C₂²×C₁₃	1	4	yes	complemented
391	#469	C₂²×C₁₃	1	4	yes	complemented
392	#468	C₂²×C₁₃	1	4	yes	complemented
393	#466	C₂²×C₁₃	1	4	yes	complemented
394	#463	C₂²×C₁₃	1	4	yes	complemented
395	#460	C₂²×C₁₃	1	4	yes	complemented
396	#459	C₂²×C₁₃	1	4	yes	complemented
397	#450	C₂²×C₁₃	1	2	yes	complemented
398	#449	C₂²×C₁₃	1	4	yes	complemented
399	#449	C₂²×C₁₃	1	4	yes	complemented
400	#449	C₂²×C₁₃	1	4	yes	complemented
401	#449	C₂²×C₁₃	1	4	yes	complemented
402	#448	C₂²×C₁₃	1	4	yes	complemented
403	#448	C₂²×C₁₃	1	4	yes	complemented
404	#447	C₂²×C₁₃	1	2	yes	complemented
405	#447	C₂²×C₁₃	1	4	yes	complemented
406	#447	C₂²×C₁₃	1	4	yes	complemented
407	#440	C₂²×C₁₃	1	4	yes	complemented
408	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
409	#436	C₂²×C₁₃	1	4	yes	complemented
410	#435	C₂²×C₁₃	1	4	yes	complemented
411	#433	C₂²×C₁₃	1	2	yes	complemented
412	#419	C₂²×C₁₃	1	2	yes	complemented
413	#417	C₂²×C₁₃	1	4	yes	complemented
414	#416	C₂²×C₁₃	1	2	yes	complemented
415	#408	C₂²×C₁₃	1	2	yes	complemented
416	#407	C₂²×C₁₃	1	2	yes	complemented
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	4	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	1	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	4	4	no	—
425	C₂²×C₁₃	—	4	4	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	4	no	—
428	C₂²×C₁₃	—	4	1	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	4	no	—
431	C₂²×C₁₃	—	8	2	no	—
432	C₂²×C₁₃	—	8	4	no	—
433	C₂²×C₁₃	—	16	4	no	—
434	C₂²×C₁₃	—	16	4	no	—
435	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₁₃	—	2	4	no	—
437	C₄×C₁₃	—	2	4	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	1	no	—
444	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
445	2₋¹⁺⁴	—	4	4	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	4	4	no	—
450	C₂×#41	C₂³×C₁₃	1	4	yes	—
451	C₂×#41	C₂³×C₁₃	1	2	yes	—
452	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
465	AGL(1,ℤ/8)	—	4	8	no	—
466	AGL(1,ℤ/8)	—	4	4	no	—
467	C₂×SD₁₆	—	4	4	no	—
468	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
471	C₂×D₈	C₂³×C₁₃	1	4	yes	—
472	C₂×D₈	C₂³×C₁₃	1	4	yes	—
473	C₂×D₈	C₂³×C₁₃	1	4	yes	—
474	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
475	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
476	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
477	#127	—	2	4	no	—
478	#127	—	2	2	no	—
479	#127	—	2	1	no	—
480	#127	C₂³×C₁₃	1	2	yes	—
481	#127	C₂³×C₁₃	1	2	yes	—
482	#126	—	2	4	no	—
483	#125	C₂³×C₁₃	1	2	yes	—
484	#124	—	2	2	no	—
485	#124	—	2	1	no	—
486	#124	—	2	4	no	—
487	#124	C₂³×C₁₃	1	2	yes	—
488	#123	—	2	1	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	D₄×C₁₃	1	2	yes	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
494	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
495	#121	—	2	4	no	—
496	#121	—	2	4	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	4	no	—
501	#121	—	2	4	no	—
502	#121	—	2	4	no	—
503	#121	—	2	4	no	—
504	#121	D₄×C₁₃	1	2	yes	—
505	#121	C₂³×C₁₃	1	4	yes	—
506	#121	C₂³×C₁₃	1	4	yes	—
507	#121	C₂³×C₁₃	1	2	yes	—
508	#121	C₂³×C₁₃	1	4	yes	—
509	#121	C₂³×C₁₃	1	4	yes	—
510	#120	—	2	1	no	—
511	#120	—	2	2	no	—
512	#120	—	2	2	no	—
513	#120	—	2	2	no	—
514	#120	—	2	2	no	—
515	#120	—	2	4	no	—
516	#120	—	2	4	no	—
517	#120	D₄×C₁₃	1	2	yes	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	C₂³×C₁₃	1	4	yes	—
526	#117	—	2	2	no	—
527	#117	C₂³×C₁₃	1	1	yes	characteristic
528	#117	C₂³×C₁₃	1	2	yes	—
529	#117	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₂²⋊C₄	—	2	2	no	—
532	#107	C₂³×C₁₃	1	4	yes	—
533	#106	C₂³×C₁₃	1	4	yes	—
534	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
535	#103	C₂³×C₁₃	1	4	yes	—
536	#103	C₂³×C₁₃	1	4	yes	—
537	#103	C₂³×C₁₃	1	4	yes	—
538	#102	C₂³×C₁₃	1	4	yes	—
539	#102	C₂³×C₁₃	1	4	yes	—
540	#102	C₂³×C₁₃	1	4	yes	—
541	#102	C₂³×C₁₃	1	4	yes	—
542	#102	C₂³×C₁₃	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
545	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
546	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
547	#97	C₂³×C₁₃	1	2	yes	—
548	C₄×C₈	C₂³×C₁₃	1	2	yes	—
549	C₂×C₁₃	—	4	1	no	—
550	C₂×C₁₃	—	4	2	no	—
551	C₂×C₁₃	—	4	2	no	—
552	C₂×C₁₃	—	8	1	no	—
553	C₂×C₁₃	—	8	2	no	—
554	C₂×C₁₃	—	8	4	no	—
555	C₂×C₁₃	#3484	1	1	yes	characteristic
556	C₂×C₁₃	#3585	1	2	yes	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
561	#41	—	2	8	no	—
562	#41	—	2	4	no	—
563	#41	—	4	2	no	—
564	#41	—	4	4	no	—
565	#41	—	4	2	no	—
566	#41	—	4	2	no	—
567	#41	—	4	8	no	—
568	#41	—	4	8	no	—
569	#41	—	4	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	8	8	no	—
598	C₂×D₄	—	8	4	no	—
599	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
600	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	4	no	—
614	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
619	SD₁₆	—	2	8	no	—
620	SD₁₆	—	2	8	no	—
621	SD₁₆	—	4	4	no	—
622	D₈	—	4	4	no	—
623	D₈	—	4	4	no	—
624	D₈	—	4	4	no	—
625	M₁₆	—	4	4	no	—
626	M₁₆	—	4	2	no	—
627	C₂×C₈	—	4	2	no	—
628	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
629	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
649	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
650	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	C₂⁴×C₁₃	1	2	yes	—
655	C₁₃	#61651	1	1	yes	characteristic, direct product factor, Sylow
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	4	no	—
663	C₂³	—	8	2	no	—
664	C₂³	—	8	2	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	4	no	—
668	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
669	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	4	no	—
676	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
677	D₄	—	2	4	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	2	no	—
689	D₄	—	8	2	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	4	no	—
695	D₄	—	8	2	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
718	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
719	C₈	—	2	4	no	—
720	C₈	—	2	4	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	8	4	no	—
737	C₂²	—	16	4	no	—
738	C₂²	—	16	4	no	—
739	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
740	C₄	—	2	4	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
749	C₂	—	4	1	no	—
750	C₂	—	4	2	no	—
751	C₂	—	4	2	no	—
752	C₂	—	8	2	no	—
753	C₂	—	8	4	no	—
754	C₂	—	8	1	no	—
755	C₂	C₁₃×#3484	1	1	yes	characteristic
756	C₂	C₁₃×#3585	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. C₁₃×#3537	C₂	semidirect
2. C₁₃×#3487	C₂	semidirect
3. C₁₃×#3326	C₂	semidirect
4. C₁₃×#3309	C₂	semidirect
5. C₁₃×#3274	C₂	semidirect
6. C₁₃×#3265	C₂	semidirect
7. C₁₃×#3220	C₂	semidirect
8. C₁₃×#3199	C₂	semidirect
9. C₁₃×#3194	C₂	semidirect
10. C₁₃×#3126	C₂	semidirect
11. C₁₃×#3010	C₂	semidirect
12. C₁₃×#3006	C₂	semidirect
13. C₁₃×#2978	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₁₃×#553	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
24. C₁₃×#548	C₂²	semidirect
26. D₄²×C₁₃	C₂²	semidirect
31. C₁₃×#535	C₂²	semidirect
32. C₁₃×#535	C₂²	semidirect
36. C₁₃×#525	C₂²	semidirect
38. C₁₃×#519	C₂²	semidirect
39. C₁₃×#496	C₂²	semidirect
40. C₁₃×#493	C₂²	semidirect
41. C₁₃×#490	C₂²	semidirect
42. C₁₃×#488	C₂²	semidirect
43. C₁₃×#483	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#480	C₂²	semidirect
47. C₁₃×#479	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#469	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#466	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#460	C₂²	semidirect
54. C₁₃×#459	C₂²	semidirect
55. C₁₃×#450	C₂²	semidirect
56. C₁₃×#449	C₂²	semidirect
57. C₁₃×#449	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
59. C₁₃×#449	C₂²	semidirect
60. C₁₃×#448	C₂²	semidirect
61. C₁₃×#448	C₂²	semidirect
62. C₁₃×#447	C₂²	semidirect
63. C₁₃×#447	C₂²	semidirect
64. C₁₃×#447	C₂²	semidirect
65. C₁₃×#440	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₁₃×#436	C₂²	semidirect
68. C₁₃×#435	C₂²	semidirect
69. C₁₃×#433	C₂²	semidirect
70. C₁₃×#419	C₂²	semidirect
71. C₁₃×#417	C₂²	semidirect
72. C₁₃×#416	C₂²	semidirect
73. C₁₃×#408	C₂²	semidirect
74. C₁₃×#407	C₂²	semidirect
179. #61651	C₁₃	direct (N × H)
278. #3537	C₂×C₁₃	semidirect
279. #3487	C₂×C₁₃	semidirect
280. #3326	C₂×C₁₃	semidirect
281. #3309	C₂×C₁₃	semidirect
282. #3274	C₂×C₁₃	semidirect
283. #3265	C₂×C₁₃	semidirect
284. #3220	C₂×C₁₃	semidirect
285. #3199	C₂×C₁₃	semidirect
286. #3194	C₂×C₁₃	semidirect
287. #3126	C₂×C₁₃	semidirect
288. #3010	C₂×C₁₃	semidirect
289. #3006	C₂×C₁₃	semidirect
290. #2978	C₂×C₁₃	semidirect
356. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
357. C₂²×#41	C₂²×C₁₃	semidirect
358. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
359. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
360. C₂²×SD₁₆	C₂²×C₁₃	semidirect
362. #553	C₂²×C₁₃	semidirect
364. #550	C₂²×C₁₃	semidirect
366. #548	C₂²×C₁₃	semidirect
368. D₄²	C₂²×C₁₃	semidirect
373. #535	C₂²×C₁₃	semidirect
374. #535	C₂²×C₁₃	semidirect
378. #525	C₂²×C₁₃	semidirect
380. #519	C₂²×C₁₃	semidirect
381. #496	C₂²×C₁₃	semidirect
382. #493	C₂²×C₁₃	semidirect
383. #490	C₂²×C₁₃	semidirect
384. #488	C₂²×C₁₃	semidirect
385. #483	C₂²×C₁₃	semidirect
386. #482	C₂²×C₁₃	semidirect
387. #482	C₂²×C₁₃	semidirect
388. #480	C₂²×C₁₃	semidirect
389. #479	C₂²×C₁₃	semidirect
390. #469	C₂²×C₁₃	semidirect
391. #469	C₂²×C₁₃	semidirect
392. #468	C₂²×C₁₃	semidirect
393. #466	C₂²×C₁₃	semidirect
394. #463	C₂²×C₁₃	semidirect
395. #460	C₂²×C₁₃	semidirect
396. #459	C₂²×C₁₃	semidirect
397. #450	C₂²×C₁₃	semidirect
398. #449	C₂²×C₁₃	semidirect
399. #449	C₂²×C₁₃	semidirect
400. #449	C₂²×C₁₃	semidirect
401. #449	C₂²×C₁₃	semidirect
402. #448	C₂²×C₁₃	semidirect
403. #448	C₂²×C₁₃	semidirect
404. #447	C₂²×C₁₃	semidirect
405. #447	C₂²×C₁₃	semidirect
406. #447	C₂²×C₁₃	semidirect
407. #440	C₂²×C₁₃	semidirect
408. C₄×SD₁₆	C₂²×C₁₃	semidirect
409. #436	C₂²×C₁₃	semidirect
410. #435	C₂²×C₁₃	semidirect
411. #433	C₂²×C₁₃	semidirect
412. #419	C₂²×C₁₃	semidirect
413. #417	C₂²×C₁₃	semidirect
414. #416	C₂²×C₁₃	semidirect
415. #408	C₂²×C₁₃	semidirect
416. #407	C₂²×C₁₃	semidirect
655. C₁₃	#61651	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×#3537	2
C₁₃×#3487	2
C₁₃×#3326	2
C₁₃×#3309	2
C₁₃×#3274	2
C₁₃×#3265	2
C₁₃×#3220	2
C₁₃×#3199	2
C₁₃×#3194	2
C₁₃×#3126	2
C₁₃×#3010	2
C₁₃×#3006	2
C₁₃×#2978	2
#61651	13

Subgroups — C13×#61651 #15747990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61651 #15747990