Subgroups — C₁₃×#60864 #15747203

Order 3328.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3235	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3234	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3228	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3227	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3226	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3165	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3138	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3094	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3077	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₁₃×#533	—	2	1	no	—
15	C₁₃×#533	—	2	1	no	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	—	2	1	no	—
18	C₁₃×#533	C₂²	1	2	yes	—
19	C₁₃×#533	C₂²	1	2	yes	—
20	C₁₃×#533	C₂²	1	2	yes	complemented
21	C₁₃×#533	C₂²	1	2	yes	complemented
22	C₁₃×#532	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	—	2	1	no	—
25	C₁₃×#532	—	2	1	no	—
26	C₁₃×#532	C₂²	1	2	yes	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₁₃×#121	—	2	1	no	—
39	C₂×C₁₃×#121	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
41	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
44	C₂×C₁₃×#117	C₂²	1	2	yes	—
45	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#501	C₂²	1	8	yes	complemented
47	C₁₃×#500	C₂²	1	4	yes	complemented
48	C₁₃×#498	C₂²	1	4	yes	complemented
49	C₁₃×#490	C₂²	1	8	yes	complemented
50	C₁₃×#486	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	4	yes	complemented
52	C₁₃×#482	C₂²	1	16	yes	complemented
53	C₁₃×#481	C₂²	1	8	yes	complemented
54	C₁₃×#480	C₂²	1	8	yes	complemented
55	C₁₃×#478	C₂²	1	16	yes	complemented
56	C₁₃×#476	C₂²	1	8	yes	complemented
57	C₁₃×#474	C₂²	1	8	yes	complemented
58	C₁₃×#432	C₂²	1	2	yes	complemented
59	C₁₃×#432	C₂²	1	2	yes	complemented
60	C₁₃×#431	C₂²	1	2	yes	complemented
61	C₁₃×#431	C₂²	1	2	yes	complemented
62	C₁₃×#428	C₂²	1	8	yes	—
63	C₁₃×#423	C₂²	1	2	yes	—
64	C₁₃×#418	C₂²	1	8	yes	—
65	C₁₃×#407	C₂²	1	2	yes	—
66	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	4	8	no	—
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂²×Q₈×C₁₃	—	2	1	no	—
74	C₂²×Q₈×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	—	2	2	no	—
80	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	—	2	1	no	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	1	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₃×#127	—	2	1	no	—
97	C₁₃×#127	—	2	1	no	—
98	C₁₃×#127	C₂³	1	2	yes	—
99	C₁₃×#127	C₂³	1	2	yes	—
100	C₁₃×#125	—	2	2	no	—
101	C₁₃×#125	—	2	2	no	—
102	C₁₃×#125	C₂³	1	4	yes	—
103	C₁₃×#125	C₂³	1	4	yes	—
104	C₁₃×#124	—	2	2	no	—
105	C₁₃×#124	—	2	2	no	—
106	C₁₃×#124	—	2	2	no	—
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	—	2	2	no	—
109	C₁₃×C₂²⋊Q₈	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×#121	—	2	2	no	—
117	C₁₃×#121	—	2	2	no	—
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#121	—	2	2	no	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	C₂³	1	4	yes	—
123	C₁₃×#121	C₂³	1	4	yes	—
124	C₄×Q₈×C₁₃	—	2	2	no	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	—	2	2	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₁₃×#117	—	2	2	no	—
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	C₂³	1	4	yes	—
143	C₁₃×#117	C₂³	1	4	yes	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₂×C₄²×C₁₃	—	2	2	no	—
156	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	16	yes	—
169	C₁₃×#106	C₂³	1	16	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	16	yes	—
173	C₁₃×#102	C₂³	1	16	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	4	yes	—
177	C₄×C₈×C₁₃	C₂³	1	4	yes	—
178	#60864	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂⁴×C₁₃	—	2	2	no	—
180	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₁₃×#41	—	4	8	no	—
182	C₁₃×#41	—	4	8	no	—
183	C₁₃×#41	—	4	8	no	—
184	C₁₃×#41	—	4	8	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	4	4	no	—
192	C₂×Q₈×C₁₃	—	4	4	no	—
193	C₂×Q₈×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	8	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	4	no	—
204	C₂×D₄×C₁₃	—	4	8	no	—
205	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	4	2	no	—
214	C₂²×C₄×C₁₃	—	4	8	no	—
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₁₃×M₁₆	—	2	8	no	—
234	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
249	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
250	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₄²×C₁₃	—	2	4	no	—
258	C₄²×C₁₃	—	2	4	no	—
259	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
277	#3235	C₂×C₁₃	1	4	yes	complemented
278	#3234	C₂×C₁₃	1	4	yes	complemented
279	#3228	C₂×C₁₃	1	4	yes	complemented
280	#3227	C₂×C₁₃	1	2	yes	complemented
281	#3226	C₂×C₁₃	1	2	yes	complemented
282	#3165	C₂×C₁₃	1	2	yes	complemented
283	#3138	C₂×C₁₃	1	2	yes	complemented
284	#3094	C₂×C₁₃	1	4	yes	complemented
285	#3077	C₂×C₁₃	1	4	yes	complemented
286	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	4	no	—
292	C₂³×C₁₃	—	4	4	no	—
293	C₂³×C₁₃	—	4	4	no	—
294	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₁₃	—	4	4	no	—
298	Q₈×C₁₃	—	4	4	no	—
299	Q₈×C₁₃	—	4	4	no	—
300	Q₈×C₁₃	—	4	4	no	—
301	Q₈×C₁₃	—	4	4	no	—
302	Q₈×C₁₃	—	4	4	no	—
303	D₄×C₁₃	—	2	8	no	—
304	D₄×C₁₃	—	4	4	no	—
305	D₄×C₁₃	—	4	4	no	—
306	D₄×C₁₃	—	4	8	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	4	4	no	—
310	D₄×C₁₃	—	4	4	no	—
311	C₂×C₄×C₁₃	—	2	2	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	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	8	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	4	no	—
333	C₂×C₄×C₁₃	—	4	4	no	—
334	C₂×C₄×C₁₃	—	4	8	no	—
335	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
348	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
349	C₈×C₁₃	—	2	8	no	—
350	C₂²×#41	—	2	1	no	—
351	#533	—	2	1	no	—
352	#533	—	2	1	no	—
353	#533	—	2	1	no	—
354	#533	—	2	1	no	—
355	#533	C₂²×C₁₃	1	2	yes	—
356	#533	C₂²×C₁₃	1	2	yes	—
357	#533	C₂²×C₁₃	1	2	yes	complemented
358	#533	C₂²×C₁₃	1	2	yes	complemented
359	#532	—	2	1	no	—
360	#532	—	2	1	no	—
361	#532	—	2	1	no	—
362	#532	—	2	1	no	—
363	#532	C₂²×C₁₃	1	2	yes	—
364	#532	C₂²×C₁₃	1	2	yes	—
365	#532	C₂²×C₁₃	1	2	yes	—
366	#532	C₂²×C₁₃	1	2	yes	—
367	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
369	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
370	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
372	C₂×#124	—	2	1	no	—
373	C₂×C₂²⋊Q₈	—	2	1	no	—
374	C₂×C₂²⋊Q₈	—	2	1	no	—
375	C₂×#121	—	2	1	no	—
376	C₂×#121	C₂²×C₁₃	1	2	yes	—
377	C₂×C₄×Q₈	—	2	1	no	—
378	C₂×C₄×Q₈	—	2	1	no	—
379	C₂×C₄×D₄	—	2	1	no	—
380	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
381	C₂×#117	C₂²×C₁₃	1	2	yes	—
382	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
383	#501	C₂²×C₁₃	1	8	yes	complemented
384	#500	C₂²×C₁₃	1	4	yes	complemented
385	#498	C₂²×C₁₃	1	4	yes	complemented
386	#490	C₂²×C₁₃	1	8	yes	complemented
387	#486	C₂²×C₁₃	1	4	yes	complemented
388	#486	C₂²×C₁₃	1	4	yes	complemented
389	#482	C₂²×C₁₃	1	16	yes	complemented
390	#481	C₂²×C₁₃	1	8	yes	complemented
391	#480	C₂²×C₁₃	1	8	yes	complemented
392	#478	C₂²×C₁₃	1	16	yes	complemented
393	#476	C₂²×C₁₃	1	8	yes	complemented
394	#474	C₂²×C₁₃	1	8	yes	complemented
395	#432	C₂²×C₁₃	1	2	yes	complemented
396	#432	C₂²×C₁₃	1	2	yes	complemented
397	#431	C₂²×C₁₃	1	2	yes	complemented
398	#431	C₂²×C₁₃	1	2	yes	complemented
399	#428	C₂²×C₁₃	1	8	yes	—
400	#423	C₂²×C₁₃	1	2	yes	—
401	#418	C₂²×C₁₃	1	8	yes	—
402	#407	C₂²×C₁₃	1	2	yes	—
403	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
404	C₂²×C₁₃	—	2	1	no	—
405	C₂²×C₁₃	—	2	1	no	—
406	C₂²×C₁₃	—	2	1	no	—
407	C₂²×C₁₃	—	2	1	no	—
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	4	4	no	—
412	C₂²×C₁₃	—	4	4	no	—
413	C₂²×C₁₃	—	4	4	no	—
414	C₂²×C₁₃	—	4	4	no	—
415	C₂²×C₁₃	—	8	8	no	—
416	C₂²×C₁₃	#536	1	2	yes	—
417	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
418	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₁₃	—	2	1	no	—
420	C₄×C₁₃	—	2	1	no	—
421	C₄×C₁₃	—	2	1	no	—
422	C₄×C₁₃	—	2	1	no	—
423	C₄×C₁₃	—	2	1	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	4	4	no	—
427	C₄×C₁₃	—	4	4	no	—
428	C₄×C₁₃	—	4	4	no	—
429	C₄×C₁₃	#536	1	2	yes	—
430	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
431	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
432	C₄×C₁₃	#575	1	2	yes	—
433	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	4	8	no	—
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
446	C₂³×C₄	—	2	2	no	—
447	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	1	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	—	2	1	no	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
458	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
459	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
461	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
462	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
463	#127	—	2	1	no	—
464	#127	—	2	1	no	—
465	#127	C₂³×C₁₃	1	2	yes	—
466	#127	C₂³×C₁₃	1	2	yes	—
467	#125	—	2	2	no	—
468	#125	—	2	2	no	—
469	#125	C₂³×C₁₃	1	4	yes	—
470	#125	C₂³×C₁₃	1	4	yes	—
471	#124	—	2	2	no	—
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	C₂³×C₁₃	1	4	yes	—
490	#121	C₂³×C₁₃	1	4	yes	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	C₂³×C₁₃	1	4	yes	—
506	C₄×D₄	C₂³×C₁₃	1	4	yes	—
507	#117	—	2	2	no	—
508	#117	—	2	2	no	—
509	#117	C₂³×C₁₃	1	4	yes	—
510	#117	C₂³×C₁₃	1	4	yes	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₂²⋊C₄	—	2	2	no	—
520	C₂×C₂²⋊C₄	—	2	2	no	—
521	C₂×C₂²⋊C₄	—	2	2	no	—
522	C₂×C₄²	—	2	2	no	—
523	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
525	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
535	#107	C₂³×C₁₃	1	16	yes	—
536	#106	C₂³×C₁₃	1	16	yes	—
537	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
538	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
539	#102	C₂³×C₁₃	1	16	yes	—
540	#102	C₂³×C₁₃	1	16	yes	—
541	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
542	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
543	#97	C₂³×C₁₃	1	4	yes	—
544	C₄×C₈	C₂³×C₁₃	1	4	yes	—
545	C₂×C₁₃	—	2	2	no	—
546	C₂×C₁₃	—	2	2	no	—
547	C₂×C₁₃	—	4	1	no	—
548	C₂×C₁₃	—	8	4	no	—
549	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
550	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
551	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
552	C₂⁴	—	2	2	no	—
553	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
554	#41	—	4	8	no	—
555	#41	—	4	8	no	—
556	#41	—	4	8	no	—
557	#41	—	4	8	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	4	4	no	—
565	C₂×Q₈	—	4	4	no	—
566	C₂×Q₈	—	4	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	8	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	8	no	—
578	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	8	no	—
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	M₁₆	—	2	8	no	—
607	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
623	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
634	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
635	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
645	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
646	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₁₃	#60864	1	1	yes	characteristic, direct product factor, Sylow
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
657	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
658	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	Q₈	—	4	4	no	—
660	Q₈	—	4	4	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	4	no	—
665	D₄	—	2	8	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	8	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
709	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
710	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
711	C₈	—	2	8	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	8	8	no	—
724	C₂²	C₁₃×#536	1	2	yes	—
725	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
726	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	4	no	—
737	C₄	C₁₃×#536	1	2	yes	—
738	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
739	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
740	C₄	C₁₃×#575	1	2	yes	—
741	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	8	4	no	—
746	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
747	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
748	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3235	C₂	semidirect
4. C₁₃×#3234	C₂	semidirect
5. C₁₃×#3228	C₂	semidirect
6. C₁₃×#3227	C₂	semidirect
7. C₁₃×#3226	C₂	semidirect
8. C₁₃×#3165	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3094	C₂	semidirect
11. C₁₃×#3077	C₂	semidirect
12. C₁₃×#2920	C₂	semidirect
20. C₁₃×#533	C₂²	semidirect
21. C₁₃×#533	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₁₃×#125	C₂²	semidirect
46. C₁₃×#501	C₂²	semidirect
47. C₁₃×#500	C₂²	semidirect
48. C₁₃×#498	C₂²	semidirect
49. C₁₃×#490	C₂²	semidirect
50. C₁₃×#486	C₂²	semidirect
51. C₁₃×#486	C₂²	semidirect
52. C₁₃×#482	C₂²	semidirect
53. C₁₃×#481	C₂²	semidirect
54. C₁₃×#480	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#476	C₂²	semidirect
57. C₁₃×#474	C₂²	semidirect
58. C₁₃×#432	C₂²	semidirect
59. C₁₃×#432	C₂²	semidirect
60. C₁₃×#431	C₂²	semidirect
61. C₁₃×#431	C₂²	semidirect
178. #60864	C₁₃	direct (N × H)
275. C₂×#533	C₂×C₁₃	semidirect
277. #3235	C₂×C₁₃	semidirect
278. #3234	C₂×C₁₃	semidirect
279. #3228	C₂×C₁₃	semidirect
280. #3227	C₂×C₁₃	semidirect
281. #3226	C₂×C₁₃	semidirect
282. #3165	C₂×C₁₃	semidirect
283. #3138	C₂×C₁₃	semidirect
284. #3094	C₂×C₁₃	semidirect
285. #3077	C₂×C₁₃	semidirect
286. #2920	C₂×C₁₃	semidirect
357. #533	C₂²×C₁₃	semidirect
358. #533	C₂²×C₁₃	semidirect
368. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
369. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
371. C₂×#125	C₂²×C₁₃	semidirect
383. #501	C₂²×C₁₃	semidirect
384. #500	C₂²×C₁₃	semidirect
385. #498	C₂²×C₁₃	semidirect
386. #490	C₂²×C₁₃	semidirect
387. #486	C₂²×C₁₃	semidirect
388. #486	C₂²×C₁₃	semidirect
389. #482	C₂²×C₁₃	semidirect
390. #481	C₂²×C₁₃	semidirect
391. #480	C₂²×C₁₃	semidirect
392. #478	C₂²×C₁₃	semidirect
393. #476	C₂²×C₁₃	semidirect
394. #474	C₂²×C₁₃	semidirect
395. #432	C₂²×C₁₃	semidirect
396. #432	C₂²×C₁₃	semidirect
397. #431	C₂²×C₁₃	semidirect
398. #431	C₂²×C₁₃	semidirect
648. C₁₃	#60864	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×#533	2
C₂×C₁₃×#532	2
C₁₃×#3235	2
C₁₃×#3234	2
C₁₃×#3228	2
C₁₃×#3227	2
C₁₃×#3226	2
C₁₃×#3165	2
C₁₃×#3138	2
C₁₃×#3094	2
C₁₃×#3077	2
C₁₃×#2920	2
#60864	13

Subgroups — C13×#60864 #15747203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60864 #15747203