Subgroups — C₁₃×#24803 #15711142

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1900	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#525	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₁₃×#472	—	2	4	no	—
20	C₁₃×#469	—	2	2	no	—
21	C₁₃×#468	—	2	2	no	—
22	C₁₃×#466	—	2	1	no	—
23	C₁₃×#466	—	2	1	no	—
24	C₁₃×#466	—	2	1	no	—
25	C₁₃×#466	—	2	1	no	—
26	C₁₃×#466	—	2	2	no	—
27	C₁₃×#465	—	2	2	no	—
28	C₁₃×#435	—	2	1	no	—
29	C₁₃×#435	—	2	1	no	—
30	C₈×D₄×C₁₃	—	2	1	no	—
31	C₈×D₄×C₁₃	—	2	1	no	—
32	C₂×C₁₃×#108	—	2	4	no	—
33	C₂×C₁₃×#108	C₂²	1	2	yes	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	2	yes	—
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
38	C₁₃×#424	C₂²	1	1	yes	characteristic
39	C₁₃×#418	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#102	C₂²	1	2	yes	—
42	C₂×C₁₃×#100	C₂²	1	2	yes	—
43	C₂×C₁₃×#100	C₂²	1	2	yes	—
44	C₁₃×#408	C₂²	1	1	yes	characteristic
45	C₁₃×#407	C₂²	1	1	yes	characteristic
46	C₁₃×#405	C₂²	1	1	yes	characteristic
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
54	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	—	2	1	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₁₃×#131	—	2	2	no	—
62	C₁₃×#131	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	2	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	4	no	—
66	C₂×C₁₃×M₁₆	—	4	2	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#123	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
83	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	D₄	1	1	yes	characteristic
89	C₁₃×#121	D₄	1	1	yes	characteristic
90	C₁₃×#120	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₁₃×#117	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₁₃×#108	—	2	4	no	—
97	C₁₃×#108	—	2	2	no	—
98	C₁₃×#108	D₄	1	4	yes	complemented
99	C₁₃×#107	—	2	1	no	—
100	C₁₃×#107	—	2	1	no	—
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#106	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#100	—	2	4	no	—
112	C₁₃×#100	—	4	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	1	no	—
114	C₁₃×C₂²⋊C₈	—	2	1	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₁₃×C₂²⋊C₈	—	2	1	no	—
117	C₁₃×#97	—	2	1	no	—
118	C₄×C₈×C₁₃	—	2	1	no	—
119	#24803	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	#41	1	1	yes	characteristic
122	C₁₃×#41	—	2	1	no	—
123	C₁₃×#41	—	2	1	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₁₃×#41	—	2	1	no	—
126	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	4	2	no	—
137	C₂×D₄×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	8	4	no	—
139	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×SD₁₆	—	4	4	no	—
153	C₁₃×D₈	—	4	4	no	—
154	C₁₃×D₈	—	4	2	no	—
155	C₁₃×D₈	—	4	2	no	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₁₃×M₁₆	—	2	1	no	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	—	2	1	no	—
160	C₁₃×M₁₆	—	2	1	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	2	1	no	—
163	C₁₃×M₁₆	—	4	4	no	—
164	C₁₃×M₁₆	—	4	2	no	—
165	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	4	4	no	—
177	C₂×C₈×C₁₃	—	4	2	no	—
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₁₃	#41	1	2	yes	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	2	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#3055	C₂×C₁₃	1	2	yes	complemented
200	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2063	C₂×C₁₃	1	2	yes	complemented
204	#2051	C₂×C₁₃	1	2	yes	complemented
205	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1900	C₂×C₁₃	1	2	yes	complemented
208	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	8	2	no	—
218	C₂³×C₁₃	—	8	2	no	—
219	C₂³×C₁₃	#121	1	1	yes	characteristic
220	C₂³×C₁₃	#121	1	1	yes	characteristic
221	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
222	Q₈×C₁₃	—	2	1	no	—
223	Q₈×C₁₃	—	2	1	no	—
224	D₄×C₁₃	—	2	1	no	—
225	D₄×C₁₃	—	2	1	no	—
226	D₄×C₁₃	—	4	2	no	—
227	D₄×C₁₃	—	4	1	no	—
228	D₄×C₁₃	—	4	1	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	8	4	no	—
235	D₄×C₁₃	—	8	4	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	8	2	no	—
253	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	4	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	2	no	—
267	C₈×C₁₃	#121	1	2	yes	—
268	C₈×C₁₃	#121	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
270	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
273	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
274	#525	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#121	C₂²×C₁₃	1	2	yes	—
276	#472	—	2	4	no	—
277	#469	—	2	2	no	—
278	#468	—	2	2	no	—
279	#466	—	2	1	no	—
280	#466	—	2	1	no	—
281	#466	—	2	1	no	—
282	#466	—	2	1	no	—
283	#466	—	2	2	no	—
284	#465	—	2	2	no	—
285	#435	—	2	1	no	—
286	#435	—	2	1	no	—
287	C₈×D₄	—	2	1	no	—
288	C₈×D₄	—	2	1	no	—
289	C₂×#108	—	2	4	no	—
290	C₂×#108	C₂²×C₁₃	1	2	yes	—
291	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
293	#428	C₂²×C₁₃	1	2	yes	—
294	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
295	#424	C₂²×C₁₃	1	1	yes	characteristic
296	#418	C₂²×C₁₃	1	2	yes	—
297	#417	C₂²×C₁₃	1	2	yes	—
298	C₂×#102	C₂²×C₁₃	1	2	yes	—
299	C₂×#100	C₂²×C₁₃	1	2	yes	—
300	C₂×#100	C₂²×C₁₃	1	2	yes	—
301	#408	C₂²×C₁₃	1	1	yes	characteristic
302	#407	C₂²×C₁₃	1	1	yes	characteristic
303	#405	C₂²×C₁₃	1	1	yes	characteristic
304	#343	C₂²×C₁₃	1	2	yes	—
305	#343	C₂²×C₁₃	1	2	yes	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	1	no	—
316	C₂²×C₁₃	—	4	1	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	8	2	no	—
319	C₂²×C₁₃	—	8	2	no	—
320	C₂²×C₁₃	—	8	2	no	—
321	C₂²×C₁₃	—	16	2	no	—
322	C₂²×C₁₃	—	16	2	no	—
323	C₂²×C₁₃	#472	1	2	yes	complemented
324	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
325	C₂²×C₁₃	#548	1	1	yes	characteristic
326	C₂²×C₁₃	#553	1	1	yes	characteristic
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	8	2	no	—
333	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
334	C₄×C₁₃	#537	1	1	yes	characteristic
335	C₄×C₁₃	D₄²	1	1	yes	characteristic
336	C₄×C₁₃	#547	1	1	yes	characteristic
337	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	AGL(1,ℤ/8)	—	2	4	no	—
342	AGL(1,ℤ/8)	—	4	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×D₈	—	2	2	no	—
345	C₂×D₈	—	2	1	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	2	2	no	—
348	C₂×D₈	—	2	2	no	—
349	#131	—	2	2	no	—
350	#131	—	2	2	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	4	2	no	—
355	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
356	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	#123	—	2	1	no	—
370	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
371	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	D₄×C₁₃	1	1	yes	characteristic
377	#121	D₄×C₁₃	1	1	yes	characteristic
378	#120	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	#117	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	#108	—	2	4	no	—
385	#108	—	2	2	no	—
386	#108	D₄×C₁₃	1	4	yes	complemented
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	2	2	no	—
390	#106	—	2	2	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	#103	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#100	—	2	4	no	—
400	#100	—	4	2	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	#97	—	2	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₂×C₁₃	—	2	1	no	—
408	C₂×C₁₃	—	2	1	no	—
409	C₂×C₁₃	—	2	2	no	—
410	C₂×C₁₃	—	4	1	no	—
411	C₂×C₁₃	—	8	1	no	—
412	C₂×C₁₃	—	16	2	no	—
413	C₂×C₁₃	#2416	1	1	yes	characteristic
414	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
415	C₂×C₁₃	#3067	1	1	yes	characteristic
416	C₂⁴	—	2	2	no	—
417	C₂⁴	C₁₃×#41	1	1	yes	characteristic
418	#41	—	2	1	no	—
419	#41	—	2	1	no	—
420	#41	—	2	1	no	—
421	#41	—	2	1	no	—
422	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	8	4	no	—
435	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
448	SD₁₆	—	4	4	no	—
449	D₈	—	4	4	no	—
450	D₈	—	4	2	no	—
451	D₈	—	4	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	1	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	4	4	no	—
460	M₁₆	—	4	2	no	—
461	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	4	4	no	—
473	C₂×C₈	—	4	2	no	—
474	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
479	C₂×C₈	C₁₃×#41	1	2	yes	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₄²	—	2	1	no	—
494	C₁₃	#24803	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	2	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	2	no	—
505	C₂³	C₁₃×#121	1	1	yes	characteristic
506	C₂³	C₁₃×#121	1	1	yes	characteristic
507	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	8	4	no	—
521	D₄	—	8	4	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
540	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
545	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	4	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	2	no	—
553	C₈	C₁₃×#121	1	2	yes	—
554	C₈	C₁₃×#121	1	2	yes	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	2	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	16	2	no	—
571	C₂²	—	16	2	no	—
572	C₂²	C₁₃×#472	1	2	yes	complemented
573	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
574	C₂²	C₁₃×#548	1	1	yes	characteristic
575	C₂²	C₁₃×#553	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	8	2	no	—
582	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
583	C₄	C₁₃×#537	1	1	yes	characteristic
584	C₄	D₄²×C₁₃	1	1	yes	characteristic
585	C₄	C₁₃×#547	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	4	1	no	—
590	C₂	—	8	1	no	—
591	C₂	—	16	2	no	—
592	C₂	C₁₃×#2416	1	1	yes	characteristic
593	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
594	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#472	C₂	semidirect
2. C₁₃×#3055	C₂	semidirect
3. C₂×C₁₃×#466	C₂	semidirect
4. C₁₃×#2929	C₂	semidirect
5. C₂²×C₁₃×#108	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
8. C₁₃×#1978	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1900	C₂	semidirect
11. C₁₃×#1816	C₂	semidirect
98. C₁₃×#108	D₄	semidirect
119. #24803	C₁₃	direct (N × H)
198. C₂×#472	C₂×C₁₃	semidirect
199. #3055	C₂×C₁₃	semidirect
200. C₂×#466	C₂×C₁₃	semidirect
201. #2929	C₂×C₁₃	semidirect
202. C₂²×#108	C₂×C₁₃	semidirect
203. #2063	C₂×C₁₃	semidirect
204. #2051	C₂×C₁₃	semidirect
205. #1978	C₂×C₁₃	semidirect
206. #1952	C₂×C₁₃	semidirect
207. #1900	C₂×C₁₃	semidirect
208. #1816	C₂×C₁₃	semidirect
323. C₂²×C₁₃	#472	semidirect
386. #108	D₄×C₁₃	semidirect
494. C₁₃	#24803	direct (N × H)
572. C₂²	C₁₃×#472	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#472	2
C₁₃×#3055	2
C₂×C₁₃×#466	2
C₁₃×#2929	2
C₂²×C₁₃×#108	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#1978	2
C₁₃×#1952	2
C₁₃×#1900	2
C₁₃×#1816	2
#24803	13

Subgroups — C13×#24803 #15711142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24803 #15711142