Subgroups — C₁₃×#61560 #15747899

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3295	C₂	1	8	yes	maximal, complemented
4	D₄×C₁₃×SD₁₆	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3187	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#450	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	—	2	1	no	—
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#554	C₂²	1	4	yes	complemented
15	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
16	D₄²×C₁₃	—	2	4	no	—
17	D₄²×C₁₃	C₂²	1	8	yes	—
18	C₁₃×#544	—	2	1	no	—
19	C₁₃×#543	—	2	2	no	—
20	C₁₃×#533	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#120	—	2	2	no	—
26	C₁₃×#518	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#492	C₂²	1	4	yes	complemented
30	C₁₃×#486	C₂²	1	4	yes	complemented
31	C₁₃×#483	C₂²	1	4	yes	complemented
32	C₁₃×#481	C₂²	1	8	yes	complemented
33	C₁₃×#476	C₂²	1	4	yes	complemented
34	C₁₃×#465	C₂²	1	16	yes	complemented
35	C₁₃×#461	C₂²	1	4	yes	complemented
36	C₁₃×#460	C₂²	1	8	yes	complemented
37	C₁₃×#450	C₂²	1	4	yes	—
38	C₁₃×#450	C₂²	1	8	yes	complemented
39	C₁₃×#450	C₂²	1	16	yes	complemented
40	C₁₃×#448	C₂²	1	8	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₂⁵×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	8	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	4	8	no	—
55	C₂²×D₄×C₁₃	—	4	8	no	—
56	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂×C₁₃×SD₁₆	—	4	16	no	—
63	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
65	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
66	C₁₃×C₄⋊Q₈	—	2	4	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
69	C₁₃×#127	—	2	2	no	—
70	C₁₃×#127	C₂³	1	4	yes	—
71	C₁₃×#125	—	2	4	no	—
72	C₁₃×#125	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	—	2	2	no	—
76	C₁₃×C₂²⋊Q₈	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	8	no	—
78	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	8	no	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₁₃×#120	—	2	16	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	D₄	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₁₃×#117	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
97	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	C₂³	1	8	yes	complemented
103	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
104	C₁₃×#103	C₂³	1	8	yes	complemented
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	16	yes	complemented
107	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
109	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
110	#61560	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	1	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	8	no	—
114	C₂⁴×C₁₃	—	4	8	no	—
115	C₂⁴×C₁₃	—	4	8	no	—
116	C₂⁴×C₁₃	—	8	4	no	—
117	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	4	8	no	—
121	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	16	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	4	8	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	16	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	—	4	8	no	—
135	C₂×D₄×C₁₃	—	4	32	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	8	2	no	—
138	C₂×D₄×C₁₃	SD₁₆	1	8	yes	complemented
139	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	4	4	no	—
147	C₂²×C₄×C₁₃	—	4	4	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₁₃×SD₁₆	—	2	16	no	—
155	C₁₃×SD₁₆	—	4	16	no	—
156	C₂×C₈×C₁₃	—	4	8	no	—
157	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
174	C₄²×C₁₃	—	2	4	no	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂⁴	1	2	yes	—
177	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
179	#3295	C₂×C₁₃	1	8	yes	complemented
180	D₄×SD₁₆	C₂×C₁₃	1	8	yes	complemented
181	#3208	C₂×C₁₃	1	2	yes	complemented
182	#3187	C₂×C₁₃	1	4	yes	complemented
183	#3101	C₂×C₁₃	1	2	yes	complemented
184	C₂×#450	C₂×C₁₃	1	4	yes	complemented
185	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	16	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	16	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	8	8	no	—
199	C₂³×C₁₃	—	8	32	no	—
200	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	complemented
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
203	Q₈×C₁₃	—	2	8	no	—
204	Q₈×C₁₃	—	8	2	no	—
205	Q₈×C₁₃	—	8	4	no	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	8	no	—
209	D₄×C₁₃	—	4	16	no	—
210	D₄×C₁₃	—	4	4	no	—
211	D₄×C₁₃	—	4	16	no	—
212	D₄×C₁₃	—	4	8	no	—
213	D₄×C₁₃	—	8	4	no	—
214	D₄×C₁₃	C₂×SD₁₆	1	16	yes	complemented
215	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	8	no	—
226	C₂×C₄×C₁₃	—	8	4	no	—
227	C₂×C₄×C₁₃	—	8	4	no	—
228	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	complemented
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₈×C₁₃	—	2	8	no	—
235	C₂³×D₄	—	2	1	no	—
236	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
238	#554	—	2	4	no	—
239	#554	C₂²×C₁₃	1	4	yes	complemented
240	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
241	D₄²	—	2	4	no	—
242	D₄²	C₂²×C₁₃	1	8	yes	—
243	#544	—	2	1	no	—
244	#543	—	2	2	no	—
245	#533	C₂²×C₁₃	1	2	yes	complemented
246	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
248	C₂×#121	—	2	1	no	—
249	C₂×#121	C₂²×C₁₃	1	2	yes	—
250	C₂×#120	—	2	2	no	—
251	#518	—	2	1	no	—
252	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
254	#492	C₂²×C₁₃	1	4	yes	complemented
255	#486	C₂²×C₁₃	1	4	yes	complemented
256	#483	C₂²×C₁₃	1	4	yes	complemented
257	#481	C₂²×C₁₃	1	8	yes	complemented
258	#476	C₂²×C₁₃	1	4	yes	complemented
259	#465	C₂²×C₁₃	1	16	yes	complemented
260	#461	C₂²×C₁₃	1	4	yes	complemented
261	#460	C₂²×C₁₃	1	8	yes	complemented
262	#450	C₂²×C₁₃	1	4	yes	—
263	#450	C₂²×C₁₃	1	8	yes	complemented
264	#450	C₂²×C₁₃	1	16	yes	complemented
265	#448	C₂²×C₁₃	1	8	yes	complemented
266	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
267	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
268	#431	C₂²×C₁₃	1	2	yes	complemented
269	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
270	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	4	8	no	—
277	C₂²×C₁₃	—	4	8	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	4	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	8	32	no	—
284	C₂²×C₁₃	—	8	8	no	—
285	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
286	C₂²×C₁₃	C₂²×SD₁₆	1	8	yes	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	4	4	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
295	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
296	C₂⁵	—	2	2	no	—
297	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	8	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	4	8	no	—
305	C₂²×D₄	—	4	8	no	—
306	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
309	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
312	C₂×SD₁₆	—	4	16	no	—
313	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
314	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
315	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
318	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
319	#127	—	2	2	no	—
320	#127	C₂³×C₁₃	1	4	yes	—
321	#125	—	2	4	no	—
322	#125	—	2	2	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
329	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
330	#121	—	2	4	no	—
331	#121	—	2	8	no	—
332	#121	C₂³×C₁₃	1	8	yes	—
333	#120	—	2	16	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	D₄×C₁₃	1	4	yes	—
340	C₄×D₄	C₂³×C₁₃	1	4	yes	—
341	C₄×D₄	C₂³×C₁₃	1	4	yes	—
342	#117	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
351	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
352	#106	C₂³×C₁₃	1	8	yes	complemented
353	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
354	#103	C₂³×C₁₃	1	8	yes	complemented
355	#102	C₂³×C₁₃	1	8	yes	—
356	#102	C₂³×C₁₃	1	16	yes	complemented
357	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
358	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
359	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
360	C₂×C₁₃	—	2	2	no	—
361	C₂×C₁₃	—	2	8	no	—
362	C₂×C₁₃	—	4	4	no	—
363	C₂×C₁₃	—	8	4	no	—
364	C₂×C₁₃	#3484	1	1	yes	characteristic
365	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
366	C₂×C₁₃	#3585	1	1	yes	characteristic
367	C₂⁴	—	2	1	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	4	8	no	—
371	C₂⁴	—	4	8	no	—
372	C₂⁴	—	8	4	no	—
373	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	4	8	no	—
377	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	16	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	16	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	32	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	8	2	no	—
394	C₂×D₄	C₁₃×SD₁₆	1	8	yes	complemented
395	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
397	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	SD₁₆	—	2	16	no	—
411	SD₁₆	—	4	16	no	—
412	C₂×C₈	—	4	8	no	—
413	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
424	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
430	C₄²	—	2	4	no	—
431	C₄²	C₂×D₄×C₁₃	1	2	yes	—
432	C₄²	C₂⁴×C₁₃	1	2	yes	—
433	C₁₃	#61560	1	1	yes	characteristic, direct product factor, Sylow
434	C₂³	—	2	4	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	16	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	16	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	8	8	no	—
447	C₂³	—	8	32	no	—
448	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	complemented
449	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
451	Q₈	—	2	8	no	—
452	Q₈	—	8	4	no	—
453	Q₈	—	8	2	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	8	no	—
457	D₄	—	4	16	no	—
458	D₄	—	4	4	no	—
459	D₄	—	4	16	no	—
460	D₄	—	4	8	no	—
461	D₄	—	8	4	no	—
462	D₄	C₂×C₁₃×SD₁₆	1	16	yes	complemented
463	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	8	4	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	complemented
477	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
482	C₈	—	2	8	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	4	8	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	32	no	—
496	C₂²	—	8	8	no	—
497	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
498	C₂²	C₂²×C₁₃×SD₁₆	1	8	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
507	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
508	C₂	—	2	2	no	—
509	C₂	—	2	8	no	—
510	C₂	—	4	4	no	—
511	C₂	—	8	4	no	—
512	C₂	C₁₃×#3484	1	1	yes	characteristic
513	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
514	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×D₄²×C₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3295	C₂	semidirect
4. D₄×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3208	C₂	semidirect
6. C₁₃×#3187	C₂	semidirect
7. C₁₃×#3101	C₂	semidirect
8. C₂×C₁₃×#450	C₂	semidirect
9. C₁₃×#2972	C₂	semidirect
12. C₂²×C₁₃×SD₁₆	C₂²	semidirect
14. C₁₃×#554	C₂²	semidirect
15. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#533	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
31. C₁₃×#483	C₂²	semidirect
32. C₁₃×#481	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#465	C₂²	semidirect
35. C₁₃×#461	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
38. C₁₃×#450	C₂²	semidirect
39. C₁₃×#450	C₂²	semidirect
40. C₁₃×#448	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₈×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
47. C₂²×Q₈×C₁₃	C₂³	semidirect
64. C₂×C₁₃×SD₁₆	C₂³	semidirect
65. C₂²×C₈×C₁₃	C₂³	semidirect
67. C₁₃×C₄⋊Q₈	C₂³	semidirect
68. C₁₃×C₄⋊Q₈	C₂³	semidirect
79. C₁₃×C₂²⋊Q₈	C₂³	semidirect
85. C₄×Q₈×C₁₃	C₂³	semidirect
96. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
102. C₁₃×#106	C₂³	semidirect
103. C₁₃×C₄⋊C₈	C₂³	semidirect
104. C₁₃×#103	C₂³	semidirect
106. C₁₃×#102	C₂³	semidirect
108. C₁₃×C₂²⋊C₈	C₂³	semidirect
109. C₄×C₈×C₁₃	C₂³	semidirect
110. #61560	C₁₃	direct (N × H)
138. C₂×D₄×C₁₃	SD₁₆	semidirect
177. #3501	C₂×C₁₃	semidirect
179. #3295	C₂×C₁₃	semidirect
180. D₄×SD₁₆	C₂×C₁₃	semidirect
181. #3208	C₂×C₁₃	semidirect
182. #3187	C₂×C₁₃	semidirect
183. #3101	C₂×C₁₃	semidirect
184. C₂×#450	C₂×C₁₃	semidirect
185. #2972	C₂×C₁₃	semidirect
200. C₂³×C₁₃	C₂×SD₁₆	semidirect
214. D₄×C₁₃	C₂×SD₁₆	semidirect
228. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
237. C₂²×SD₁₆	C₂²×C₁₃	semidirect
239. #554	C₂²×C₁₃	semidirect
240. D₄×Q₈	C₂²×C₁₃	semidirect
245. #533	C₂²×C₁₃	semidirect
247. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
254. #492	C₂²×C₁₃	semidirect
255. #486	C₂²×C₁₃	semidirect
256. #483	C₂²×C₁₃	semidirect
257. #481	C₂²×C₁₃	semidirect
258. #476	C₂²×C₁₃	semidirect
259. #465	C₂²×C₁₃	semidirect
260. #461	C₂²×C₁₃	semidirect
261. #460	C₂²×C₁₃	semidirect
263. #450	C₂²×C₁₃	semidirect
264. #450	C₂²×C₁₃	semidirect
265. #448	C₂²×C₁₃	semidirect
266. C₄×SD₁₆	C₂²×C₁₃	semidirect
267. C₈×D₄	C₂²×C₁₃	semidirect
268. #431	C₂²×C₁₃	semidirect
269. C₂×#102	C₂²×C₁₃	semidirect
270. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
297. C₂²×Q₈	C₂³×C₁₃	semidirect
314. C₂×SD₁₆	C₂³×C₁₃	semidirect
315. C₂²×C₈	C₂³×C₁₃	semidirect
317. C₄⋊Q₈	C₂³×C₁₃	semidirect
318. C₄⋊Q₈	C₂³×C₁₃	semidirect
329. C₂²⋊Q₈	C₂³×C₁₃	semidirect
335. C₄×Q₈	C₂³×C₁₃	semidirect
346. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
352. #106	C₂³×C₁₃	semidirect
353. C₄⋊C₈	C₂³×C₁₃	semidirect
354. #103	C₂³×C₁₃	semidirect
356. #102	C₂³×C₁₃	semidirect
358. C₂²⋊C₈	C₂³×C₁₃	semidirect
359. C₄×C₈	C₂³×C₁₃	semidirect
394. C₂×D₄	C₁₃×SD₁₆	semidirect
433. C₁₃	#61560	direct (N × H)
448. C₂³	C₂×C₁₃×SD₁₆	semidirect
462. D₄	C₂×C₁₃×SD₁₆	semidirect
476. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3501	2
C₂×D₄²×C₁₃	2
C₁₃×#3295	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3208	2
C₁₃×#3187	2
C₁₃×#3101	2
C₂×C₁₃×#450	2
C₁₃×#2972	2
#61560	13

Subgroups — C13×#61560 #15747899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61560 #15747899