Subgroups — C₁₃×#25984 #15712323

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2897	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2897	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2027	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1792	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#478	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#477	—	2	1	no	—
27	C₁₃×#476	—	2	1	no	—
28	C₁₃×#475	—	2	1	no	—
29	C₁₃×#474	—	2	1	no	—
30	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
40	C₁₃×#418	—	2	1	no	—
41	C₁₃×#418	—	2	1	no	—
42	C₁₃×#418	C₂²	1	1	yes	characteristic
43	C₁₃×#418	C₂²	1	1	yes	characteristic
44	C₁₃×#417	—	2	1	no	—
45	C₁₃×#417	—	2	1	no	—
46	C₁₃×#417	C₂²	1	1	yes	characteristic
47	C₁₃×#417	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	—	2	1	no	—
51	C₁₃×#416	—	2	1	no	—
52	C₁₃×#416	C₂²	1	1	yes	characteristic
53	C₁₃×#416	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#102	—	2	1	no	—
55	C₂×C₁₃×#102	—	2	1	no	—
56	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×H(5,𝔽₂)	—	2	2	no	—
68	C₁₃×H(5,𝔽₂)	—	2	2	no	—
69	C₁₃×H(5,𝔽₂)	—	4	1	no	—
70	C₁₃×H(5,𝔽₂)	Q₈	1	4	yes	complemented
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	4	1	no	—
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#131	—	2	2	no	—
80	C₁₃×#131	—	2	2	no	—
81	C₁₃×#131	—	4	1	no	—
82	C₁₃×#131	—	4	1	no	—
83	C₂×C₁₃×M₁₆	—	2	1	no	—
84	C₂×C₁₃×M₁₆	—	2	1	no	—
85	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	—	2	1	no	—
90	C₂²×C₈×C₁₃	—	2	1	no	—
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	—	2	1	no	—
94	C₁₃×C₄⋊Q₈	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×C₂²⋊Q₈	—	4	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	4	1	no	—
103	C₄×D₄×C₁₃	—	4	1	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	C₂³	1	1	yes	characteristic
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#108	—	4	1	no	—
116	C₁₃×#108	—	4	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×#104	—	2	2	no	—
130	C₁₃×#104	—	2	2	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	D₄	1	1	yes	characteristic
136	C₁₃×#103	D₄	1	1	yes	characteristic
137	C₁₃×#103	D₄	1	1	yes	characteristic
138	C₁₃×#103	D₄	1	1	yes	characteristic
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	—	2	1	no	—
150	C₁₃×#102	—	2	1	no	—
151	C₁₃×#102	D₄	1	1	yes	characteristic
152	C₁₃×#102	D₄	1	1	yes	characteristic
153	C₁₃×#102	D₄	1	1	yes	characteristic
154	C₁₃×#102	D₄	1	1	yes	characteristic
155	C₁₃×#100	—	4	1	no	—
156	C₁₃×#95	—	4	1	no	—
157	#25984	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	1	no	—
159	C₂⁴×C₁₃	—	4	1	no	—
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	1	no	—
163	C₁₃×#41	—	2	1	no	—
164	C₁₃×#41	—	2	4	no	—
165	C₁₃×#41	—	2	4	no	—
166	C₁₃×#41	—	4	2	no	—
167	C₁₃×#41	—	4	2	no	—
168	C₁₃×#41	C₂×Q₈	1	2	yes	—
169	C₁₃×#41	C₂×Q₈	1	2	yes	—
170	C₁₃×#41	#41	1	2	yes	—
171	C₁₃×#41	#41	1	2	yes	—
172	C₂×Q₈×C₁₃	—	4	1	no	—
173	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	1	no	—
187	C₂×D₄×C₁₃	—	4	1	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	4	1	no	—
200	C₂²×C₄×C₁₃	—	4	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×M₁₆	—	2	1	no	—
204	C₁₃×M₁₆	—	2	1	no	—
205	C₁₃×M₁₆	—	2	1	no	—
206	C₁₃×M₁₆	—	2	1	no	—
207	C₁₃×M₁₆	—	2	1	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	2	1	no	—
211	C₁₃×M₁₆	—	4	2	no	—
212	C₁₃×M₁₆	—	4	2	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	4	2	no	—
222	C₂×C₈×C₁₃	—	4	2	no	—
223	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	4	1	no	—
234	C₁₃×C₄⋊C₄	—	4	1	no	—
235	C₁₃×C₄⋊C₄	—	4	1	no	—
236	C₁₃×C₄⋊C₄	—	4	1	no	—
237	C₁₃×C₄⋊C₄	—	4	1	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₁₃×C₂²⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	4	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	1	no	—
246	C₁₃×C₂²⋊C₄	—	8	2	no	—
247	C₄²×C₁₃	—	2	1	no	—
248	C₄²×C₁₃	—	2	1	no	—
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	4	1	no	—
252	C₄²×C₁₃	—	4	1	no	—
253	#3084	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#3083	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2897	C₂×C₁₃	1	1	yes	characteristic
256	#2897	C₂×C₁₃	1	1	yes	characteristic
257	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2027	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1792	C₂×C₁₃	1	1	yes	characteristic
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	4	4	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	8	1	no	—
275	C₂³×C₁₃	—	8	1	no	—
276	C₂³×C₁₃	—	16	1	no	—
277	C₂³×C₁₃	—	16	1	no	—
278	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
279	Q₈×C₁₃	—	2	1	no	—
280	Q₈×C₁₃	—	2	1	no	—
281	Q₈×C₁₃	—	16	1	no	—
282	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
283	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
284	D₄×C₁₃	—	2	2	no	—
285	D₄×C₁₃	—	2	2	no	—
286	D₄×C₁₃	—	2	2	no	—
287	D₄×C₁₃	—	2	2	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	1	no	—
291	D₄×C₁₃	—	2	1	no	—
292	D₄×C₁₃	—	4	4	no	—
293	D₄×C₁₃	—	4	4	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
297	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	4	4	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	8	1	no	—
316	C₂×C₄×C₁₃	—	8	1	no	—
317	C₂×C₄×C₁₃	—	8	1	no	—
318	C₂×C₄×C₁₃	—	16	1	no	—
319	C₂×C₄×C₁₃	—	16	1	no	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
326	C₈×C₁₃	—	2	1	no	—
327	C₈×C₁₃	—	2	1	no	—
328	C₈×C₁₃	—	2	1	no	—
329	C₈×C₁₃	—	2	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₈×C₁₃	—	4	1	no	—
332	C₈×C₁₃	—	4	1	no	—
333	C₈×C₁₃	—	4	1	no	—
334	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
337	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	#520	C₂²×C₁₃	1	1	yes	characteristic
339	#520	C₂²×C₁₃	1	1	yes	characteristic
340	#479	—	2	1	no	—
341	#479	—	2	1	no	—
342	#478	—	2	1	no	—
343	#478	—	2	1	no	—
344	#477	—	2	1	no	—
345	#476	—	2	1	no	—
346	#475	—	2	1	no	—
347	#474	—	2	1	no	—
348	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
349	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
350	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
351	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
354	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
355	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
358	#418	—	2	1	no	—
359	#418	—	2	1	no	—
360	#418	C₂²×C₁₃	1	1	yes	characteristic
361	#418	C₂²×C₁₃	1	1	yes	characteristic
362	#417	—	2	1	no	—
363	#417	—	2	1	no	—
364	#417	C₂²×C₁₃	1	1	yes	characteristic
365	#417	C₂²×C₁₃	1	1	yes	characteristic
366	#417	C₂²×C₁₃	1	1	yes	characteristic
367	#417	C₂²×C₁₃	1	1	yes	characteristic
368	#416	—	2	1	no	—
369	#416	—	2	1	no	—
370	#416	C₂²×C₁₃	1	1	yes	characteristic
371	#416	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#102	—	2	1	no	—
373	C₂×#102	—	2	1	no	—
374	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
377	#390	C₂²×C₁₃	1	1	yes	characteristic
378	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	2	1	no	—
387	C₂²×C₁₃	—	2	2	no	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	—	4	1	no	—
391	C₂²×C₁₃	—	4	1	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	8	2	no	—
395	C₂²×C₁₃	—	8	1	no	—
396	C₂²×C₁₃	—	8	1	no	—
397	C₂²×C₁₃	—	16	1	no	—
398	C₂²×C₁₃	—	16	4	no	—
399	C₂²×C₁₃	#543	1	1	yes	characteristic
400	C₂²×C₁₃	D₄²	1	1	yes	characteristic
401	C₂²×C₁₃	#551	1	1	yes	characteristic
402	C₄×C₁₃	—	2	2	no	—
403	C₄×C₁₃	—	2	2	no	—
404	C₄×C₁₃	—	4	1	no	—
405	C₄×C₁₃	—	4	1	no	—
406	C₄×C₁₃	—	4	1	no	—
407	C₄×C₁₃	—	4	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	—	8	1	no	—
411	C₄×C₁₃	—	8	1	no	—
412	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
413	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
414	C₄×C₁₃	#546	1	1	yes	characteristic
415	C₄×C₁₃	#546	1	1	yes	characteristic
416	H(5,𝔽₂)	—	2	2	no	—
417	H(5,𝔽₂)	—	2	2	no	—
418	H(5,𝔽₂)	—	4	1	no	—
419	H(5,𝔽₂)	Q₈×C₁₃	1	4	yes	complemented
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	1	no	—
422	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	4	1	no	—
427	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
428	#131	—	2	2	no	—
429	#131	—	2	2	no	—
430	#131	—	4	1	no	—
431	#131	—	4	1	no	—
432	C₂×M₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₄⋊Q₈	—	2	1	no	—
443	C₄⋊Q₈	—	2	1	no	—
444	#125	—	2	1	no	—
445	#125	—	2	1	no	—
446	C₂²⋊Q₈	—	4	1	no	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	4	1	no	—
452	C₄×D₄	—	4	1	no	—
453	#117	—	2	1	no	—
454	#117	—	2	1	no	—
455	#117	C₂³×C₁₃	1	1	yes	characteristic
456	#117	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	4	1	no	—
463	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
464	#108	—	4	1	no	—
465	#108	—	4	1	no	—
466	#107	—	2	1	no	—
467	#107	—	2	1	no	—
468	#107	—	2	1	no	—
469	#107	—	2	1	no	—
470	#106	—	2	1	no	—
471	#106	—	2	1	no	—
472	#106	—	2	1	no	—
473	#106	—	2	1	no	—
474	C₄⋊C₈	—	2	1	no	—
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	—	2	1	no	—
478	#104	—	2	2	no	—
479	#104	—	2	2	no	—
480	#103	—	2	1	no	—
481	#103	—	2	1	no	—
482	#103	—	2	1	no	—
483	#103	—	2	1	no	—
484	#103	D₄×C₁₃	1	1	yes	characteristic
485	#103	D₄×C₁₃	1	1	yes	characteristic
486	#103	D₄×C₁₃	1	1	yes	characteristic
487	#103	D₄×C₁₃	1	1	yes	characteristic
488	#102	—	2	1	no	—
489	#102	—	2	1	no	—
490	#102	—	2	1	no	—
491	#102	—	2	1	no	—
492	#102	—	2	1	no	—
493	#102	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#102	—	2	1	no	—
500	#102	D₄×C₁₃	1	1	yes	characteristic
501	#102	D₄×C₁₃	1	1	yes	characteristic
502	#102	D₄×C₁₃	1	1	yes	characteristic
503	#102	D₄×C₁₃	1	1	yes	characteristic
504	#100	—	4	1	no	—
505	#95	—	4	1	no	—
506	C₂×C₁₃	—	2	1	no	—
507	C₂×C₁₃	—	2	1	no	—
508	C₂×C₁₃	—	4	2	no	—
509	C₂×C₁₃	—	4	2	no	—
510	C₂×C₁₃	—	8	2	no	—
511	C₂×C₁₃	#2437	1	1	yes	characteristic
512	C₂×C₁₃	#3288	1	1	yes	characteristic
513	C₂×C₁₃	#3290	1	1	yes	characteristic
514	C₂⁴	—	2	1	no	—
515	C₂⁴	—	4	1	no	—
516	#41	—	2	1	no	—
517	#41	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	4	no	—
521	#41	—	2	4	no	—
522	#41	—	4	2	no	—
523	#41	—	4	2	no	—
524	#41	C₂×Q₈×C₁₃	1	2	yes	—
525	#41	C₂×Q₈×C₁₃	1	2	yes	—
526	#41	C₁₃×#41	1	2	yes	—
527	#41	C₁₃×#41	1	2	yes	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	M₁₆	—	2	1	no	—
560	M₁₆	—	2	1	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	—	2	1	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	2	1	no	—
565	M₁₆	—	2	1	no	—
566	M₁₆	—	2	1	no	—
567	M₁₆	—	4	2	no	—
568	M₁₆	—	4	2	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	4	2	no	—
578	C₂×C₈	—	4	2	no	—
579	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	—	4	1	no	—
593	C₄⋊C₄	—	4	1	no	—
594	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	8	2	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	4	1	no	—
608	C₄²	—	4	1	no	—
609	C₁₃	#25984	1	1	yes	characteristic, direct product factor, Sylow
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	4	4	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	8	1	no	—
617	C₂³	—	8	1	no	—
618	C₂³	—	16	1	no	—
619	C₂³	—	16	1	no	—
620	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	16	1	no	—
624	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
625	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	2	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	2	no	—
632	D₄	—	2	1	no	—
633	D₄	—	2	1	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
639	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	8	1	no	—
658	C₂×C₄	—	8	1	no	—
659	C₂×C₄	—	8	1	no	—
660	C₂×C₄	—	16	1	no	—
661	C₂×C₄	—	16	1	no	—
662	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
666	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
667	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
668	C₈	—	2	1	no	—
669	C₈	—	2	1	no	—
670	C₈	—	2	1	no	—
671	C₈	—	2	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	16	1	no	—
689	C₂²	—	16	4	no	—
690	C₂²	C₁₃×#543	1	1	yes	characteristic
691	C₂²	D₄²×C₁₃	1	1	yes	characteristic
692	C₂²	C₁₃×#551	1	1	yes	characteristic
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
704	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
705	C₄	C₁₃×#546	1	1	yes	characteristic
706	C₄	C₁₃×#546	1	1	yes	characteristic
707	C₂	—	2	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	8	2	no	—
712	C₂	C₁₃×#2437	1	1	yes	characteristic
713	C₂	C₁₃×#3288	1	1	yes	characteristic
714	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3084	C₂	semidirect
2. C₁₃×#3083	C₂	semidirect
5. C₁₃×#2092	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2027	C₂	semidirect
9. C₁₃×#1866	C₂	semidirect
10. C₁₃×#1866	C₂	semidirect
11. C₁₃×#1860	C₂	semidirect
12. C₁₃×#1860	C₂	semidirect
13. C₁₃×#1816	C₂	semidirect
14. C₁₃×#1815	C₂	semidirect
19. C₁₃×#544	C₂²	semidirect
30. C₂×C₁₃×#108	C₂²	semidirect
31. C₂×C₁₃×#108	C₂²	semidirect
32. C₁₃×#428	C₂²	semidirect
33. C₁₃×#428	C₂²	semidirect
34. C₂×C₁₃×#107	C₂²	semidirect
35. C₂×C₁₃×#106	C₂²	semidirect
36. C₁₃×#424	C₂²	semidirect
37. C₁₃×#424	C₂²	semidirect
60. C₁₃×#382	C₂²	semidirect
61. C₁₃×#343	C₂²	semidirect
62. C₁₃×#343	C₂²	semidirect
63. C₁₃×#343	C₂²	semidirect
64. C₁₃×#339	C₂²	semidirect
65. C₁₃×#339	C₂²	semidirect
66. C₁₃×#336	C₂²	semidirect
70. C₁₃×H(5,𝔽₂)	Q₈	semidirect
157. #25984	C₁₃	direct (N × H)
253. #3084	C₂×C₁₃	semidirect
254. #3083	C₂×C₁₃	semidirect
257. #2092	C₂×C₁₃	semidirect
258. #2063	C₂×C₁₃	semidirect
259. #2063	C₂×C₁₃	semidirect
260. #2027	C₂×C₁₃	semidirect
261. #1866	C₂×C₁₃	semidirect
262. #1866	C₂×C₁₃	semidirect
263. #1860	C₂×C₁₃	semidirect
264. #1860	C₂×C₁₃	semidirect
265. #1816	C₂×C₁₃	semidirect
266. #1815	C₂×C₁₃	semidirect
337. #544	C₂²×C₁₃	semidirect
348. C₂×#108	C₂²×C₁₃	semidirect
349. C₂×#108	C₂²×C₁₃	semidirect
350. #428	C₂²×C₁₃	semidirect
351. #428	C₂²×C₁₃	semidirect
352. C₂×#107	C₂²×C₁₃	semidirect
353. C₂×#106	C₂²×C₁₃	semidirect
354. #424	C₂²×C₁₃	semidirect
355. #424	C₂²×C₁₃	semidirect
378. #382	C₂²×C₁₃	semidirect
379. #343	C₂²×C₁₃	semidirect
380. #343	C₂²×C₁₃	semidirect
381. #343	C₂²×C₁₃	semidirect
382. #339	C₂²×C₁₃	semidirect
383. #339	C₂²×C₁₃	semidirect
384. #336	C₂²×C₁₃	semidirect
419. H(5,𝔽₂)	Q₈×C₁₃	semidirect
609. C₁₃	#25984	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×#3084	2
C₁₃×#3083	2
C₁₃×#2897	2
C₁₃×#2092	2
C₁₃×#2063	2
C₁₃×#2027	2
C₁₃×#1866	2
C₁₃×#1860	2
C₁₃×#1816	2
C₁₃×#1815	2
C₁₃×#1792	2
#25984	13

Subgroups — C13×#25984 #15712323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25984 #15712323