Subgroups — C₁₃×#62824 #15749163

Order 3328.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3558	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3545	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3514	C₂	1	16	yes	maximal, complemented
5	C₁₃×#3510	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3500	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3490	C₂	1	8	yes	maximal, complemented
8	C₁₃×#3486	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#563	C₂²	1	8	yes	complemented
17	C₁₃×#562	C₂²	1	16	yes	complemented
18	C₁₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₁₃×#559	C₂²	1	16	yes	complemented
20	C₁₃×#556	C₂²	1	16	yes	complemented
21	C₁₃×#555	C₂²	1	16	yes	complemented
22	C₁₃×#551	C₂²	1	32	yes	complemented
23	C₁₃×#551	C₂²	1	32	yes	complemented
24	C₁₃×#551	C₂²	1	16	yes	complemented
25	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
26	C₁₃×#548	C₂²	1	16	yes	complemented
27	C₁₃×#548	C₂²	1	16	yes	complemented
28	C₁₃×#546	C₂²	1	16	yes	complemented
29	C₁₃×#546	C₂²	1	32	yes	complemented
30	C₁₃×#546	C₂²	1	32	yes	complemented
31	C₁₃×#546	C₂²	1	16	yes	complemented
32	D₄²×C₁₃	C₂²	1	16	yes	complemented
33	C₁₃×#543	C₂²	1	8	yes	complemented
34	C₁₃×#542	C₂²	1	16	yes	complemented
35	C₁₃×#542	C₂²	1	32	yes	complemented
36	C₁₃×#538	C₂²	1	16	yes	complemented
37	C₁₃×#538	C₂²	1	16	yes	complemented
38	C₁₃×#538	C₂²	1	32	yes	complemented
39	C₁₃×#536	C₂²	1	8	yes	complemented
40	C₁₃×#536	C₂²	1	4	yes	complemented
41	C₁₃×#536	C₂²	1	8	yes	complemented
42	C₁₃×#535	C₂²	1	4	yes	—
43	C₁₃×#535	C₂²	1	8	yes	complemented
44	C₁₃×#534	C₂²	1	8	yes	complemented
45	C₁₃×#534	C₂²	1	8	yes	complemented
46	C₁₃×#533	C₂²	1	4	yes	complemented
47	C₁₃×#533	C₂²	1	2	yes	complemented
48	C₁₃×#532	C₂²	1	4	yes	complemented
49	C₁₃×#532	C₂²	1	2	yes	complemented
50	C₁₃×#532	C₂²	1	8	yes	complemented
51	C₁₃×#529	C₂²	1	8	yes	complemented
52	C₁₃×#529	C₂²	1	8	yes	complemented
53	C₁₃×#529	C₂²	1	8	yes	complemented
54	C₁₃×#529	C₂²	1	16	yes	complemented
55	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
57	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
59	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
60	C₁₃×#525	C₂²	1	4	yes	complemented
61	C₁₃×#525	C₂²	1	8	yes	complemented
62	C₁₃×#525	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
64	C₁₃×#519	C₂²	1	2	yes	complemented
65	C₁₃×#518	C₂²	1	2	yes	complemented
66	C₁₃×#518	C₂²	1	16	yes	complemented
67	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
68	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
69	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
70	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂⁵×C₁₃	C₂³	1	2	yes	—
72	C₁₃×2₋¹⁺⁴	—	4	8	no	—
73	C₁₃×H(5,𝔽₂)	—	4	8	no	—
74	C₂×C₁₃×#41	C₂³	1	4	yes	—
75	C₂×C₁₃×#41	C₂³	1	8	yes	—
76	C₂×C₁₃×#41	C₂³	1	8	yes	—
77	C₂×C₁₃×#41	C₂³	1	8	yes	—
78	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
79	C₂²×Q₈×C₁₃	—	4	4	no	—
80	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
83	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
84	C₂²×D₄×C₁₃	—	4	4	no	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
95	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
96	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
97	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
98	C₁₃×#127	C₂³	1	8	yes	—
99	C₁₃×#127	C₂³	1	2	yes	complemented
100	C₁₃×#126	C₂³	1	16	yes	complemented
101	C₁₃×#126	C₂³	1	32	yes	complemented
102	C₁₃×#126	C₂³	1	32	yes	complemented
103	C₁₃×#125	C₂³	1	4	yes	complemented
104	C₁₃×#125	C₂³	1	8	yes	complemented
105	C₁₃×#124	C₂³	1	8	yes	—
106	C₁₃×#124	C₂³	1	8	yes	—
107	C₁₃×#124	C₂³	1	16	yes	—
108	C₁₃×#124	C₂³	1	16	yes	—
109	C₁₃×#124	C₂³	1	8	yes	—
110	C₁₃×#124	C₂³	1	8	yes	—
111	C₁₃×#124	C₂³	1	8	yes	—
112	C₁₃×#124	C₂³	1	4	yes	complemented
113	C₁₃×#124	C₂³	1	8	yes	complemented
114	C₁₃×#124	C₂³	1	32	yes	complemented
115	C₁₃×#124	C₂³	1	8	yes	complemented
116	C₁₃×#124	C₂³	1	16	yes	complemented
117	C₁₃×#124	C₂³	1	32	yes	complemented
118	C₁₃×#123	C₂³	1	8	yes	—
119	C₁₃×#123	C₂³	1	16	yes	—
120	C₁₃×#123	C₂³	1	16	yes	—
121	C₁₃×#123	C₂³	1	16	yes	—
122	C₁₃×#123	C₂³	1	32	yes	complemented
123	C₁₃×#123	C₂³	1	32	yes	complemented
124	C₁₃×#123	C₂³	1	32	yes	complemented
125	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
126	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
130	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
131	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
132	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
133	C₁₃×#121	C₂³	1	8	yes	—
134	C₁₃×#121	C₂³	1	8	yes	—
135	C₁₃×#121	C₂³	1	8	yes	—
136	C₁₃×#121	C₂³	1	16	yes	—
137	C₁₃×#121	C₂³	1	16	yes	—
138	C₁₃×#121	C₂³	1	32	yes	—
139	C₁₃×#121	C₂³	1	32	yes	complemented
140	C₁₃×#121	C₂³	1	32	yes	complemented
141	C₁₃×#120	C₂³	1	8	yes	—
142	C₁₃×#120	C₂³	1	16	yes	—
143	C₁₃×#120	C₂³	1	32	yes	—
144	C₁₃×#120	C₂³	1	16	yes	—
145	C₁₃×#120	C₂³	1	32	yes	complemented
146	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
147	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
148	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
149	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
150	C₄×D₄×C₁₃	C₂³	1	16	yes	—
151	C₄×D₄×C₁₃	C₂³	1	16	yes	—
152	C₄×D₄×C₁₃	C₂³	1	16	yes	—
153	C₄×D₄×C₁₃	C₂³	1	32	yes	—
154	C₄×D₄×C₁₃	C₂³	1	16	yes	—
155	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
156	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
157	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
158	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
159	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
160	C₁₃×#117	C₂³	1	4	yes	—
161	C₁₃×#117	C₂³	1	8	yes	—
162	C₁₃×#117	C₂³	1	8	yes	—
163	C₁₃×#117	C₂³	1	8	yes	complemented
164	C₁₃×#117	C₂³	1	16	yes	complemented
165	C₁₃×#117	C₂³	1	32	yes	complemented
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
173	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
178	#62824	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂⁴×C₁₃	—	4	4	no	—
180	C₂⁴×C₁₃	—	4	8	no	—
181	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
183	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
184	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
185	C₁₃×#41	—	2	16	no	—
186	C₁₃×#41	—	4	16	no	—
187	C₁₃×#41	—	4	16	no	—
188	C₁₃×#41	—	4	16	no	—
189	C₁₃×#41	—	4	16	no	—
190	C₂×Q₈×C₁₃	—	2	8	no	—
191	C₂×Q₈×C₁₃	—	4	4	no	—
192	C₂×Q₈×C₁₃	—	4	16	no	—
193	C₂×Q₈×C₁₃	—	4	16	no	—
194	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
195	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
196	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
197	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
198	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
199	C₂×D₄×C₁₃	—	2	8	no	—
200	C₂×D₄×C₁₃	—	4	16	no	—
201	C₂×D₄×C₁₃	—	4	16	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	32	no	—
204	C₂×D₄×C₁₃	—	4	16	no	—
205	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
206	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
207	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
208	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
210	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
211	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
212	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
213	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	4	4	no	—
216	C₂²×C₄×C₁₃	—	4	4	no	—
217	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
235	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
236	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
237	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
238	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
239	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
240	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
241	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
242	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
243	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
244	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
245	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
246	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
247	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
248	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
249	C₄²×C₁₃	C₂⁴	1	2	yes	—
250	C₄²×C₁₃	C₂⁴	1	2	yes	—
251	C₄²×C₁₃	C₂⁴	1	2	yes	—
252	C₄²×C₁₃	C₂⁴	1	4	yes	—
253	C₄²×C₁₃	C₂⁴	1	4	yes	—
254	C₄²×C₁₃	C₂⁴	1	2	yes	—
255	C₄²×C₁₃	C₂⁴	1	16	yes	—
256	C₄²×C₁₃	C₂⁴	1	8	yes	—
257	C₄²×C₁₃	C₂⁴	1	16	yes	—
258	#3561	C₂×C₁₃	1	8	yes	complemented
259	#3558	C₂×C₁₃	1	8	yes	complemented
260	#3545	C₂×C₁₃	1	8	yes	complemented
261	#3514	C₂×C₁₃	1	16	yes	complemented
262	#3510	C₂×C₁₃	1	4	yes	complemented
263	#3500	C₂×C₁₃	1	4	yes	complemented
264	#3490	C₂×C₁₃	1	8	yes	complemented
265	#3486	C₂×C₁₃	1	2	yes	complemented
266	#3484	C₂×C₁₃	1	2	yes	complemented
267	#3444	C₂×C₁₃	1	2	yes	complemented
268	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂³×C₁₃	—	2	2	no	—
270	C₂³×C₁₃	—	2	4	no	—
271	C₂³×C₁₃	—	2	8	no	—
272	C₂³×C₁₃	—	2	16	no	—
273	C₂³×C₁₃	—	4	8	no	—
274	C₂³×C₁₃	—	4	8	no	—
275	C₂³×C₁₃	—	4	8	no	—
276	C₂³×C₁₃	—	4	8	no	—
277	C₂³×C₁₃	—	4	16	no	—
278	C₂³×C₁₃	—	8	16	no	—
279	C₂³×C₁₃	C₂⁵	1	8	yes	—
280	C₂³×C₁₃	C₂⁵	1	8	yes	—
281	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
282	C₂³×C₁₃	C₂⁵	1	2	yes	—
283	Q₈×C₁₃	—	2	16	no	—
284	Q₈×C₁₃	—	2	8	no	—
285	Q₈×C₁₃	—	4	8	no	—
286	Q₈×C₁₃	—	4	8	no	—
287	Q₈×C₁₃	—	4	8	no	—
288	D₄×C₁₃	—	2	16	no	—
289	D₄×C₁₃	—	2	32	no	—
290	D₄×C₁₃	—	2	16	no	—
291	D₄×C₁₃	—	2	8	no	—
292	D₄×C₁₃	—	4	8	no	—
293	D₄×C₁₃	—	4	16	no	—
294	D₄×C₁₃	—	4	32	no	—
295	D₄×C₁₃	—	4	8	no	—
296	D₄×C₁₃	—	4	8	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	8	no	—
299	C₂×C₄×C₁₃	—	2	8	no	—
300	C₂×C₄×C₁₃	—	2	8	no	—
301	C₂×C₄×C₁₃	—	2	16	no	—
302	C₂×C₄×C₁₃	—	4	2	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	4	2	no	—
305	C₂×C₄×C₁₃	—	4	8	no	—
306	C₂×C₄×C₁₃	—	4	16	no	—
307	C₂×C₄×C₁₃	—	4	8	no	—
308	C₂×C₄×C₁₃	—	4	16	no	—
309	C₂×C₄×C₁₃	—	4	16	no	—
310	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
311	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
312	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
313	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
314	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
317	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
318	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
319	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
320	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	#563	C₂²×C₁₃	1	8	yes	complemented
323	#562	C₂²×C₁₃	1	16	yes	complemented
324	H(3,𝔽₄)	C₂²×C₁₃	1	8	yes	complemented
325	#559	C₂²×C₁₃	1	16	yes	complemented
326	#556	C₂²×C₁₃	1	16	yes	complemented
327	#555	C₂²×C₁₃	1	16	yes	complemented
328	#551	C₂²×C₁₃	1	32	yes	complemented
329	#551	C₂²×C₁₃	1	32	yes	complemented
330	#551	C₂²×C₁₃	1	16	yes	complemented
331	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
332	#548	C₂²×C₁₃	1	16	yes	complemented
333	#548	C₂²×C₁₃	1	16	yes	complemented
334	#546	C₂²×C₁₃	1	16	yes	complemented
335	#546	C₂²×C₁₃	1	32	yes	complemented
336	#546	C₂²×C₁₃	1	32	yes	complemented
337	#546	C₂²×C₁₃	1	16	yes	complemented
338	D₄²	C₂²×C₁₃	1	16	yes	complemented
339	#543	C₂²×C₁₃	1	8	yes	complemented
340	#542	C₂²×C₁₃	1	16	yes	complemented
341	#542	C₂²×C₁₃	1	32	yes	complemented
342	#538	C₂²×C₁₃	1	16	yes	complemented
343	#538	C₂²×C₁₃	1	16	yes	complemented
344	#538	C₂²×C₁₃	1	32	yes	complemented
345	#536	C₂²×C₁₃	1	4	yes	complemented
346	#536	C₂²×C₁₃	1	8	yes	complemented
347	#536	C₂²×C₁₃	1	8	yes	complemented
348	#535	C₂²×C₁₃	1	4	yes	—
349	#535	C₂²×C₁₃	1	8	yes	complemented
350	#534	C₂²×C₁₃	1	8	yes	complemented
351	#534	C₂²×C₁₃	1	8	yes	complemented
352	#533	C₂²×C₁₃	1	2	yes	complemented
353	#533	C₂²×C₁₃	1	4	yes	complemented
354	#532	C₂²×C₁₃	1	2	yes	complemented
355	#532	C₂²×C₁₃	1	4	yes	complemented
356	#532	C₂²×C₁₃	1	8	yes	complemented
357	#529	C₂²×C₁₃	1	8	yes	complemented
358	#529	C₂²×C₁₃	1	8	yes	complemented
359	#529	C₂²×C₁₃	1	8	yes	complemented
360	#529	C₂²×C₁₃	1	16	yes	complemented
361	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
362	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
363	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
364	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
365	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
366	#525	C₂²×C₁₃	1	4	yes	complemented
367	#525	C₂²×C₁₃	1	8	yes	complemented
368	#525	C₂²×C₁₃	1	8	yes	complemented
369	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
370	#519	C₂²×C₁₃	1	2	yes	complemented
371	#518	C₂²×C₁₃	1	2	yes	complemented
372	#518	C₂²×C₁₃	1	16	yes	complemented
373	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
374	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
376	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
377	C₂²×C₁₃	—	2	8	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	8	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	—	2	16	no	—
384	C₂²×C₁₃	—	2	16	no	—
385	C₂²×C₁₃	—	8	8	no	—
386	C₂²×C₁₃	—	8	16	no	—
387	C₂²×C₁₃	—	16	8	no	—
388	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
389	C₂²×C₁₃	#585	1	4	yes	—
390	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	2	8	no	—
393	C₄×C₁₃	—	2	8	no	—
394	C₄×C₁₃	—	2	4	no	—
395	C₄×C₁₃	—	2	4	no	—
396	C₄×C₁₃	—	2	16	no	—
397	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
398	C₂⁵	C₂³×C₁₃	1	2	yes	—
399	2₋¹⁺⁴	—	4	8	no	—
400	H(5,𝔽₂)	—	4	8	no	—
401	C₂×#41	C₂³×C₁₃	1	4	yes	—
402	C₂×#41	C₂³×C₁₃	1	8	yes	—
403	C₂×#41	C₂³×C₁₃	1	8	yes	—
404	C₂×#41	C₂³×C₁₃	1	8	yes	—
405	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
406	C₂²×Q₈	—	4	4	no	—
407	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
408	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
409	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
410	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
411	C₂²×D₄	—	4	4	no	—
412	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
413	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
414	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
415	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
416	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
417	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
418	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
421	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
422	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
423	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
424	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
425	#127	C₂³×C₁₃	1	8	yes	—
426	#127	C₂³×C₁₃	1	2	yes	complemented
427	#126	C₂³×C₁₃	1	16	yes	complemented
428	#126	C₂³×C₁₃	1	32	yes	complemented
429	#126	C₂³×C₁₃	1	32	yes	complemented
430	#125	C₂³×C₁₃	1	4	yes	complemented
431	#125	C₂³×C₁₃	1	8	yes	complemented
432	#124	C₂³×C₁₃	1	8	yes	—
433	#124	C₂³×C₁₃	1	8	yes	—
434	#124	C₂³×C₁₃	1	16	yes	—
435	#124	C₂³×C₁₃	1	16	yes	—
436	#124	C₂³×C₁₃	1	8	yes	—
437	#124	C₂³×C₁₃	1	8	yes	—
438	#124	C₂³×C₁₃	1	8	yes	—
439	#124	C₂³×C₁₃	1	4	yes	complemented
440	#124	C₂³×C₁₃	1	8	yes	complemented
441	#124	C₂³×C₁₃	1	32	yes	complemented
442	#124	C₂³×C₁₃	1	8	yes	complemented
443	#124	C₂³×C₁₃	1	16	yes	complemented
444	#124	C₂³×C₁₃	1	32	yes	complemented
445	#123	C₂³×C₁₃	1	8	yes	—
446	#123	C₂³×C₁₃	1	16	yes	—
447	#123	C₂³×C₁₃	1	16	yes	—
448	#123	C₂³×C₁₃	1	16	yes	—
449	#123	C₂³×C₁₃	1	32	yes	complemented
450	#123	C₂³×C₁₃	1	32	yes	complemented
451	#123	C₂³×C₁₃	1	32	yes	complemented
452	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
453	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
454	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
455	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
456	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
457	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
458	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
459	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
460	#121	C₂³×C₁₃	1	8	yes	—
461	#121	C₂³×C₁₃	1	8	yes	—
462	#121	C₂³×C₁₃	1	8	yes	—
463	#121	C₂³×C₁₃	1	16	yes	—
464	#121	C₂³×C₁₃	1	16	yes	—
465	#121	C₂³×C₁₃	1	32	yes	—
466	#121	C₂³×C₁₃	1	32	yes	complemented
467	#121	C₂³×C₁₃	1	32	yes	complemented
468	#120	C₂³×C₁₃	1	8	yes	—
469	#120	C₂³×C₁₃	1	16	yes	—
470	#120	C₂³×C₁₃	1	32	yes	—
471	#120	C₂³×C₁₃	1	16	yes	—
472	#120	C₂³×C₁₃	1	32	yes	complemented
473	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
474	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
475	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
476	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
477	C₄×D₄	C₂³×C₁₃	1	16	yes	—
478	C₄×D₄	C₂³×C₁₃	1	16	yes	—
479	C₄×D₄	C₂³×C₁₃	1	16	yes	—
480	C₄×D₄	C₂³×C₁₃	1	32	yes	—
481	C₄×D₄	C₂³×C₁₃	1	16	yes	—
482	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
483	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
484	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
485	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
486	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
487	#117	C₂³×C₁₃	1	4	yes	—
488	#117	C₂³×C₁₃	1	8	yes	—
489	#117	C₂³×C₁₃	1	8	yes	—
490	#117	C₂³×C₁₃	1	8	yes	complemented
491	#117	C₂³×C₁₃	1	16	yes	complemented
492	#117	C₂³×C₁₃	1	32	yes	complemented
493	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
500	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
501	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
504	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
505	C₂×C₁₃	—	2	2	no	—
506	C₂×C₁₃	—	2	4	no	—
507	C₂×C₁₃	—	4	8	no	—
508	C₂×C₁₃	—	4	8	no	—
509	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂×C₁₃	C₂×#585	1	2	yes	—
511	C₂⁴	—	4	4	no	—
512	C₂⁴	—	4	8	no	—
513	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
515	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
516	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
517	#41	—	2	16	no	—
518	#41	—	4	16	no	—
519	#41	—	4	16	no	—
520	#41	—	4	16	no	—
521	#41	—	4	16	no	—
522	C₂×Q₈	—	2	8	no	—
523	C₂×Q₈	—	4	4	no	—
524	C₂×Q₈	—	4	16	no	—
525	C₂×Q₈	—	4	16	no	—
526	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
527	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
528	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
529	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
530	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	4	16	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	4	no	—
535	C₂×D₄	—	4	16	no	—
536	C₂×D₄	—	4	32	no	—
537	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
538	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
539	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
540	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
541	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
542	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
543	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
544	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
545	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
559	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
560	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
561	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
562	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
564	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
565	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
566	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
567	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
571	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
572	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
573	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
574	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
575	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
576	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
577	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
578	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
579	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
580	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
581	C₄²	C₂⁴×C₁₃	1	2	yes	—
582	C₄²	C₂⁴×C₁₃	1	2	yes	—
583	C₄²	C₂⁴×C₁₃	1	2	yes	—
584	C₄²	C₂⁴×C₁₃	1	4	yes	—
585	C₄²	C₂⁴×C₁₃	1	4	yes	—
586	C₄²	C₂⁴×C₁₃	1	2	yes	—
587	C₄²	C₂⁴×C₁₃	1	16	yes	—
588	C₄²	C₂⁴×C₁₃	1	8	yes	—
589	C₄²	C₂⁴×C₁₃	1	16	yes	—
590	C₁₃	#62824	1	1	yes	characteristic, direct product factor, Sylow
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	8	no	—
594	C₂³	—	2	16	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	8	no	—
598	C₂³	—	4	8	no	—
599	C₂³	—	4	16	no	—
600	C₂³	—	8	16	no	—
601	C₂³	C₂⁵×C₁₃	1	8	yes	—
602	C₂³	C₂⁵×C₁₃	1	8	yes	—
603	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
604	C₂³	C₂⁵×C₁₃	1	2	yes	—
605	Q₈	—	2	16	no	—
606	Q₈	—	2	8	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	Q₈	—	4	8	no	—
610	D₄	—	2	16	no	—
611	D₄	—	2	32	no	—
612	D₄	—	2	16	no	—
613	D₄	—	2	8	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	16	no	—
616	D₄	—	4	32	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	16	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	—	4	16	no	—
629	C₂×C₄	—	4	8	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
633	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
634	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
635	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
636	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
637	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
638	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
639	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	2	16	no	—
648	C₂²	—	8	8	no	—
649	C₂²	—	8	16	no	—
650	C₂²	—	16	8	no	—
651	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
652	C₂²	C₁₃×#585	1	4	yes	—
653	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	16	no	—
660	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	8	no	—
665	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3561	C₂	semidirect
2. C₁₃×#3558	C₂	semidirect
3. C₁₃×#3545	C₂	semidirect
4. C₁₃×#3514	C₂	semidirect
5. C₁₃×#3510	C₂	semidirect
6. C₁₃×#3500	C₂	semidirect
7. C₁₃×#3490	C₂	semidirect
8. C₁₃×#3486	C₂	semidirect
9. C₁₃×#3484	C₂	semidirect
10. C₁₃×#3444	C₂	semidirect
11. C₂²×C₁₃×#124	C₂	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
16. C₁₃×#563	C₂²	semidirect
17. C₁₃×#562	C₂²	semidirect
18. C₁₃×H(3,𝔽₄)	C₂²	semidirect
19. C₁₃×#559	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#551	C₂²	semidirect
23. C₁₃×#551	C₂²	semidirect
24. C₁₃×#551	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#548	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
32. D₄²×C₁₃	C₂²	semidirect
33. C₁₃×#543	C₂²	semidirect
34. C₁₃×#542	C₂²	semidirect
35. C₁₃×#542	C₂²	semidirect
36. C₁₃×#538	C₂²	semidirect
37. C₁₃×#538	C₂²	semidirect
38. C₁₃×#538	C₂²	semidirect
39. C₁₃×#536	C₂²	semidirect
40. C₁₃×#536	C₂²	semidirect
41. C₁₃×#536	C₂²	semidirect
43. C₁₃×#535	C₂²	semidirect
44. C₁₃×#534	C₂²	semidirect
45. C₁₃×#534	C₂²	semidirect
46. C₁₃×#533	C₂²	semidirect
47. C₁₃×#533	C₂²	semidirect
48. C₁₃×#532	C₂²	semidirect
49. C₁₃×#532	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
51. C₁₃×#529	C₂²	semidirect
52. C₁₃×#529	C₂²	semidirect
53. C₁₃×#529	C₂²	semidirect
54. C₁₃×#529	C₂²	semidirect
55. C₂×C₁₃×#124	C₂²	semidirect
56. C₂×C₁₃×#124	C₂²	semidirect
57. C₂×C₁₃×#124	C₂²	semidirect
58. C₂×C₁₃×#124	C₂²	semidirect
59. C₂×C₁₃×#124	C₂²	semidirect
60. C₁₃×#525	C₂²	semidirect
61. C₁₃×#525	C₂²	semidirect
62. C₁₃×#525	C₂²	semidirect
63. C₂×C₁₃×#120	C₂²	semidirect
64. C₁₃×#519	C₂²	semidirect
65. C₁₃×#518	C₂²	semidirect
66. C₁₃×#518	C₂²	semidirect
67. C₄×C₁₃×#41	C₂²	semidirect
68. C₄×C₁₃×#41	C₂²	semidirect
69. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
70. C₂²×C₄²×C₁₃	C₂²	semidirect
78. C₂×C₁₃×#41	C₂³	semidirect
83. C₂²×Q₈×C₁₃	C₂³	semidirect
94. C₁₃×C₄⋊Q₈	C₂³	semidirect
95. C₁₃×C₄⋊Q₈	C₂³	semidirect
96. C₁₃×C₄⋊Q₈	C₂³	semidirect
97. C₁₃×C₄⋊Q₈	C₂³	semidirect
99. C₁₃×#127	C₂³	semidirect
100. C₁₃×#126	C₂³	semidirect
101. C₁₃×#126	C₂³	semidirect
102. C₁₃×#126	C₂³	semidirect
103. C₁₃×#125	C₂³	semidirect
104. C₁₃×#125	C₂³	semidirect
112. C₁₃×#124	C₂³	semidirect
113. C₁₃×#124	C₂³	semidirect
114. C₁₃×#124	C₂³	semidirect
115. C₁₃×#124	C₂³	semidirect
116. C₁₃×#124	C₂³	semidirect
117. C₁₃×#124	C₂³	semidirect
122. C₁₃×#123	C₂³	semidirect
123. C₁₃×#123	C₂³	semidirect
124. C₁₃×#123	C₂³	semidirect
129. C₁₃×C₂²⋊Q₈	C₂³	semidirect
130. C₁₃×C₂²⋊Q₈	C₂³	semidirect
131. C₁₃×C₂²⋊Q₈	C₂³	semidirect
132. C₁₃×C₂²⋊Q₈	C₂³	semidirect
139. C₁₃×#121	C₂³	semidirect
140. C₁₃×#121	C₂³	semidirect
145. C₁₃×#120	C₂³	semidirect
146. C₄×Q₈×C₁₃	C₂³	semidirect
147. C₄×Q₈×C₁₃	C₂³	semidirect
148. C₄×Q₈×C₁₃	C₂³	semidirect
149. C₄×Q₈×C₁₃	C₂³	semidirect
155. C₄×D₄×C₁₃	C₂³	semidirect
156. C₄×D₄×C₁₃	C₂³	semidirect
157. C₄×D₄×C₁₃	C₂³	semidirect
158. C₄×D₄×C₁₃	C₂³	semidirect
159. C₄×D₄×C₁₃	C₂³	semidirect
163. C₁₃×#117	C₂³	semidirect
164. C₁₃×#117	C₂³	semidirect
165. C₁₃×#117	C₂³	semidirect
172. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
177. C₂×C₄²×C₁₃	C₂³	semidirect
178. #62824	C₁₃	direct (N × H)
258. #3561	C₂×C₁₃	semidirect
259. #3558	C₂×C₁₃	semidirect
260. #3545	C₂×C₁₃	semidirect
261. #3514	C₂×C₁₃	semidirect
262. #3510	C₂×C₁₃	semidirect
263. #3500	C₂×C₁₃	semidirect
264. #3490	C₂×C₁₃	semidirect
265. #3486	C₂×C₁₃	semidirect
266. #3484	C₂×C₁₃	semidirect
267. #3444	C₂×C₁₃	semidirect
268. C₂²×#124	C₂×C₁₃	semidirect
318. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
319. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
320. C₂³×Q₈	C₂²×C₁₃	semidirect
322. #563	C₂²×C₁₃	semidirect
323. #562	C₂²×C₁₃	semidirect
324. H(3,𝔽₄)	C₂²×C₁₃	semidirect
325. #559	C₂²×C₁₃	semidirect
326. #556	C₂²×C₁₃	semidirect
327. #555	C₂²×C₁₃	semidirect
328. #551	C₂²×C₁₃	semidirect
329. #551	C₂²×C₁₃	semidirect
330. #551	C₂²×C₁₃	semidirect
331. D₄×Q₈	C₂²×C₁₃	semidirect
332. #548	C₂²×C₁₃	semidirect
333. #548	C₂²×C₁₃	semidirect
334. #546	C₂²×C₁₃	semidirect
335. #546	C₂²×C₁₃	semidirect
336. #546	C₂²×C₁₃	semidirect
337. #546	C₂²×C₁₃	semidirect
338. D₄²	C₂²×C₁₃	semidirect
339. #543	C₂²×C₁₃	semidirect
340. #542	C₂²×C₁₃	semidirect
341. #542	C₂²×C₁₃	semidirect
342. #538	C₂²×C₁₃	semidirect
343. #538	C₂²×C₁₃	semidirect
344. #538	C₂²×C₁₃	semidirect
345. #536	C₂²×C₁₃	semidirect
346. #536	C₂²×C₁₃	semidirect
347. #536	C₂²×C₁₃	semidirect
349. #535	C₂²×C₁₃	semidirect
350. #534	C₂²×C₁₃	semidirect
351. #534	C₂²×C₁₃	semidirect
352. #533	C₂²×C₁₃	semidirect
353. #533	C₂²×C₁₃	semidirect
354. #532	C₂²×C₁₃	semidirect
355. #532	C₂²×C₁₃	semidirect
356. #532	C₂²×C₁₃	semidirect
357. #529	C₂²×C₁₃	semidirect
358. #529	C₂²×C₁₃	semidirect
359. #529	C₂²×C₁₃	semidirect
360. #529	C₂²×C₁₃	semidirect
361. C₂×#124	C₂²×C₁₃	semidirect
362. C₂×#124	C₂²×C₁₃	semidirect
363. C₂×#124	C₂²×C₁₃	semidirect
364. C₂×#124	C₂²×C₁₃	semidirect
365. C₂×#124	C₂²×C₁₃	semidirect
366. #525	C₂²×C₁₃	semidirect
367. #525	C₂²×C₁₃	semidirect
368. #525	C₂²×C₁₃	semidirect
369. C₂×#120	C₂²×C₁₃	semidirect
370. #519	C₂²×C₁₃	semidirect
371. #518	C₂²×C₁₃	semidirect
372. #518	C₂²×C₁₃	semidirect
373. C₄×#41	C₂²×C₁₃	semidirect
374. C₄×#41	C₂²×C₁₃	semidirect
375. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
376. C₂²×C₄²	C₂²×C₁₃	semidirect
405. C₂×#41	C₂³×C₁₃	semidirect
410. C₂²×Q₈	C₂³×C₁₃	semidirect
421. C₄⋊Q₈	C₂³×C₁₃	semidirect
422. C₄⋊Q₈	C₂³×C₁₃	semidirect
423. C₄⋊Q₈	C₂³×C₁₃	semidirect
424. C₄⋊Q₈	C₂³×C₁₃	semidirect
426. #127	C₂³×C₁₃	semidirect
427. #126	C₂³×C₁₃	semidirect
428. #126	C₂³×C₁₃	semidirect
429. #126	C₂³×C₁₃	semidirect
430. #125	C₂³×C₁₃	semidirect
431. #125	C₂³×C₁₃	semidirect
439. #124	C₂³×C₁₃	semidirect
440. #124	C₂³×C₁₃	semidirect
441. #124	C₂³×C₁₃	semidirect
442. #124	C₂³×C₁₃	semidirect
443. #124	C₂³×C₁₃	semidirect
444. #124	C₂³×C₁₃	semidirect
449. #123	C₂³×C₁₃	semidirect
450. #123	C₂³×C₁₃	semidirect
451. #123	C₂³×C₁₃	semidirect
456. C₂²⋊Q₈	C₂³×C₁₃	semidirect
457. C₂²⋊Q₈	C₂³×C₁₃	semidirect
458. C₂²⋊Q₈	C₂³×C₁₃	semidirect
459. C₂²⋊Q₈	C₂³×C₁₃	semidirect
466. #121	C₂³×C₁₃	semidirect
467. #121	C₂³×C₁₃	semidirect
472. #120	C₂³×C₁₃	semidirect
473. C₄×Q₈	C₂³×C₁₃	semidirect
474. C₄×Q₈	C₂³×C₁₃	semidirect
475. C₄×Q₈	C₂³×C₁₃	semidirect
476. C₄×Q₈	C₂³×C₁₃	semidirect
482. C₄×D₄	C₂³×C₁₃	semidirect
483. C₄×D₄	C₂³×C₁₃	semidirect
484. C₄×D₄	C₂³×C₁₃	semidirect
485. C₄×D₄	C₂³×C₁₃	semidirect
486. C₄×D₄	C₂³×C₁₃	semidirect
490. #117	C₂³×C₁₃	semidirect
491. #117	C₂³×C₁₃	semidirect
492. #117	C₂³×C₁₃	semidirect
499. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
504. C₂×C₄²	C₂³×C₁₃	semidirect
590. C₁₃	#62824	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×#3561	2
C₁₃×#3558	2
C₁₃×#3545	2
C₁₃×#3514	2
C₁₃×#3510	2
C₁₃×#3500	2
C₁₃×#3490	2
C₁₃×#3486	2
C₁₃×#3484	2
C₁₃×#3444	2
C₂²×C₁₃×#124	2
#62824	13

Subgroups — C13×#62824 #15749163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62824 #15749163