Subgroups — C₁₃×#26084 #15712423

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3084	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1765	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
17	C₁₃×#544	C₂²	1	1	yes	characteristic
18	C₁₃×#544	C₂²	1	1	yes	characteristic
19	C₁₃×#520	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#501	—	2	1	no	—
22	C₁₃×#501	—	2	1	no	—
23	C₁₃×#500	—	2	1	no	—
24	C₁₃×#499	—	2	1	no	—
25	C₁₃×#479	—	2	1	no	—
26	C₁₃×#479	—	2	1	no	—
27	C₁₃×#478	—	2	1	no	—
28	C₁₃×#478	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	—	2	1	no	—
32	C₁₃×#474	—	2	1	no	—
33	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
34	C₁₃×#428	—	2	1	no	—
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	—	2	1	no	—
43	C₁₃×#427	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#106	—	2	1	no	—
47	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
49	C₁₃×#424	C₂²	1	1	yes	characteristic
50	C₁₃×#424	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₁₃×#417	C₂²	1	1	yes	characteristic
54	C₁₃×#416	C₂²	1	1	yes	characteristic
55	C₁₃×#405	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
57	C₁₃×#384	C₂²	1	1	yes	characteristic
58	C₁₃×#382	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₁₃×#131	—	2	2	no	—
69	C₁₃×#131	Q₈	1	4	yes	complemented
70	C₂×C₁₃×M₁₆	—	2	1	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×#125	—	2	1	no	—
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#125	—	2	1	no	—
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	4	1	no	—
87	C₁₃×C₂²⋊Q₈	—	4	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	4	1	no	—
93	C₄×D₄×C₁₃	—	4	1	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	C₂³	1	1	yes	characteristic
97	C₁₃×#117	C₂³	1	1	yes	characteristic
98	C₁₃×#117	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#108	—	2	2	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	D₄	1	1	yes	characteristic
119	C₁₃×#107	D₄	1	1	yes	characteristic
120	C₁₃×#106	—	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×#106	—	2	1	no	—
126	C₁₃×#106	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	—	2	1	no	—
130	C₁₃×#106	D₄	1	1	yes	characteristic
131	C₁₃×#106	D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×C₄⋊C₈	—	2	1	no	—
135	C₁₃×C₄⋊C₈	—	2	1	no	—
136	C₁₃×#104	Q₈	1	4	yes	complemented
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	D₄	1	1	yes	characteristic
140	C₁₃×#103	D₄	1	1	yes	characteristic
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	D₄	1	1	yes	characteristic
144	C₁₃×#102	D₄	1	1	yes	characteristic
145	C₁₃×#97	—	2	1	no	—
146	C₁₃×#97	—	2	2	no	—
147	C₄×C₈×C₁₃	—	2	1	no	—
148	C₁₃×#95	—	4	1	no	—
149	#26084	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃×#41	—	2	1	no	—
151	C₁₃×#41	—	2	1	no	—
152	C₁₃×#41	C₂×Q₈	1	2	yes	—
153	C₁₃×#41	C₂×Q₈	1	2	yes	—
154	C₂×Q₈×C₁₃	—	4	1	no	—
155	C₂×Q₈×C₁₃	—	4	1	no	—
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×M₁₆	—	2	1	no	—
169	C₁₃×M₁₆	—	2	1	no	—
170	C₁₃×M₁₆	—	2	4	no	—
171	C₁₃×M₁₆	—	2	1	no	—
172	C₁₃×M₁₆	—	2	1	no	—
173	C₁₃×M₁₆	—	2	1	no	—
174	C₁₃×M₁₆	—	2	1	no	—
175	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
176	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	4	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
189	C₂×C₈×C₁₃	#41	1	2	yes	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₄⋊C₄	—	4	1	no	—
203	C₁₃×C₄⋊C₄	—	4	1	no	—
204	C₁₃×C₄⋊C₄	—	4	1	no	—
205	C₁₃×C₄⋊C₄	—	4	1	no	—
206	C₁₃×C₄⋊C₄	—	8	2	no	—
207	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₁₃×C₂²⋊C₄	—	2	1	no	—
214	C₁₃×C₂²⋊C₄	—	2	1	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	4	1	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	4	1	no	—
223	C₄²×C₁₃	—	4	1	no	—
224	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
225	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#3084	C₂×C₁₃	1	1	yes	characteristic
227	#3083	C₂×C₁₃	1	1	yes	characteristic
228	#2912	C₂×C₁₃	1	1	yes	characteristic
229	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1946	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1860	C₂×C₁₃	1	1	yes	characteristic
236	#1859	C₂×C₁₃	1	1	yes	characteristic
237	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1816	C₂×C₁₃	1	1	yes	characteristic
239	#1765	C₂×C₁₃	1	1	yes	characteristic
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
242	Q₈×C₁₃	—	2	1	no	—
243	Q₈×C₁₃	—	16	1	no	—
244	Q₈×C₁₃	—	16	1	no	—
245	Q₈×C₁₃	C₄⋊Q₈	1	2	yes	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	1	no	—
249	D₄×C₁₃	C₄⋊Q₈	1	2	yes	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	8	1	no	—
267	C₂×C₄×C₁₃	—	8	1	no	—
268	C₂×C₄×C₁₃	—	8	1	no	—
269	C₂×C₄×C₁₃	—	8	1	no	—
270	C₂×C₄×C₁₃	—	16	1	no	—
271	C₂×C₄×C₁₃	—	16	1	no	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₁₃	—	2	2	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
285	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
286	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
287	#544	C₂²×C₁₃	1	1	yes	characteristic
288	#544	C₂²×C₁₃	1	1	yes	characteristic
289	#520	C₂²×C₁₃	1	1	yes	characteristic
290	#520	C₂²×C₁₃	1	1	yes	characteristic
291	#501	—	2	1	no	—
292	#501	—	2	1	no	—
293	#500	—	2	1	no	—
294	#499	—	2	1	no	—
295	#479	—	2	1	no	—
296	#479	—	2	1	no	—
297	#478	—	2	1	no	—
298	#478	—	2	1	no	—
299	#477	—	2	1	no	—
300	#476	—	2	1	no	—
301	#475	—	2	1	no	—
302	#474	—	2	1	no	—
303	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
304	#428	—	2	1	no	—
305	#428	—	2	1	no	—
306	#428	C₂²×C₁₃	1	1	yes	characteristic
307	#428	C₂²×C₁₃	1	1	yes	characteristic
308	#428	C₂²×C₁₃	1	1	yes	characteristic
309	#428	C₂²×C₁₃	1	1	yes	characteristic
310	#428	C₂²×C₁₃	1	1	yes	characteristic
311	#428	C₂²×C₁₃	1	1	yes	characteristic
312	#427	—	2	1	no	—
313	#427	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#106	—	2	1	no	—
317	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
319	#424	C₂²×C₁₃	1	1	yes	characteristic
320	#424	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
322	#417	C₂²×C₁₃	1	1	yes	characteristic
323	#417	C₂²×C₁₃	1	1	yes	characteristic
324	#416	C₂²×C₁₃	1	1	yes	characteristic
325	#405	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
327	#384	C₂²×C₁₃	1	1	yes	characteristic
328	#382	C₂²×C₁₃	1	1	yes	characteristic
329	#343	C₂²×C₁₃	1	1	yes	characteristic
330	#343	C₂²×C₁₃	1	1	yes	characteristic
331	#343	C₂²×C₁₃	1	1	yes	characteristic
332	#343	C₂²×C₁₃	1	1	yes	characteristic
333	#341	C₂²×C₁₃	1	1	yes	characteristic
334	#339	C₂²×C₁₃	1	1	yes	characteristic
335	#339	C₂²×C₁₃	1	1	yes	characteristic
336	#339	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	#544	1	1	yes	characteristic
343	C₂²×C₁₃	D₄²	1	1	yes	characteristic
344	C₂²×C₁₃	#554	1	1	yes	characteristic
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
359	C₄×C₁₃	#547	1	1	yes	characteristic
360	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
361	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
362	#131	—	2	2	no	—
363	#131	Q₈×C₁₃	1	4	yes	complemented
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	C₂²⋊Q₈	—	4	1	no	—
381	C₂²⋊Q₈	—	4	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	4	1	no	—
387	C₄×D₄	—	4	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	C₂³×C₁₃	1	1	yes	characteristic
391	#117	C₂³×C₁₃	1	1	yes	characteristic
392	#117	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	4	1	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	#108	—	2	2	no	—
402	#107	—	2	1	no	—
403	#107	—	2	1	no	—
404	#107	—	2	1	no	—
405	#107	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#107	—	2	1	no	—
409	#107	—	2	1	no	—
410	#107	—	2	1	no	—
411	#107	—	2	1	no	—
412	#107	D₄×C₁₃	1	1	yes	characteristic
413	#107	D₄×C₁₃	1	1	yes	characteristic
414	#106	—	2	1	no	—
415	#106	—	2	1	no	—
416	#106	—	2	1	no	—
417	#106	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	—	2	1	no	—
420	#106	—	2	1	no	—
421	#106	—	2	1	no	—
422	#106	—	2	1	no	—
423	#106	—	2	1	no	—
424	#106	D₄×C₁₃	1	1	yes	characteristic
425	#106	D₄×C₁₃	1	1	yes	characteristic
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	1	no	—
430	#104	Q₈×C₁₃	1	4	yes	complemented
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#103	D₄×C₁₃	1	1	yes	characteristic
434	#103	D₄×C₁₃	1	1	yes	characteristic
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	D₄×C₁₃	1	1	yes	characteristic
438	#102	D₄×C₁₃	1	1	yes	characteristic
439	#97	—	2	1	no	—
440	#97	—	2	2	no	—
441	C₄×C₈	—	2	1	no	—
442	#95	—	4	1	no	—
443	C₂×C₁₃	—	2	1	no	—
444	C₂×C₁₃	—	2	1	no	—
445	C₂×C₁₃	—	4	2	no	—
446	C₂×C₁₃	#2440	1	1	yes	characteristic
447	C₂×C₁₃	#3288	1	1	yes	characteristic
448	C₂×C₁₃	#3289	1	1	yes	characteristic
449	#41	—	2	1	no	—
450	#41	—	2	1	no	—
451	#41	C₂×Q₈×C₁₃	1	2	yes	—
452	#41	C₂×Q₈×C₁₃	1	2	yes	—
453	C₂×Q₈	—	4	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
467	M₁₆	—	2	1	no	—
468	M₁₆	—	2	1	no	—
469	M₁₆	—	2	4	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	1	no	—
472	M₁₆	—	2	1	no	—
473	M₁₆	—	2	1	no	—
474	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
475	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
488	C₂×C₈	C₁₃×#41	1	2	yes	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	8	2	no	—
506	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	4	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
524	C₁₃	#26084	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	1	no	—
526	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
527	Q₈	—	2	1	no	—
528	Q₈	—	16	1	no	—
529	Q₈	—	16	1	no	—
530	Q₈	C₁₃×C₄⋊Q₈	1	2	yes	—
531	D₄	—	2	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	1	no	—
534	D₄	C₁₃×C₄⋊Q₈	1	2	yes	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	8	1	no	—
552	C₂×C₄	—	8	1	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	1	no	—
555	C₂×C₄	—	16	1	no	—
556	C₂×C₄	—	16	1	no	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
562	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
563	C₈	—	2	2	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	2	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
570	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	C₁₃×#544	1	1	yes	characteristic
577	C₂²	D₄²×C₁₃	1	1	yes	characteristic
578	C₂²	C₁₃×#554	1	1	yes	characteristic
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
592	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
593	C₄	C₁₃×#547	1	1	yes	characteristic
594	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	4	2	no	—
598	C₂	C₁₃×#2440	1	1	yes	characteristic
599	C₂	C₁₃×#3288	1	1	yes	characteristic
600	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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×#3164	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2061	C₂	semidirect
8. C₁₃×#2060	C₂	semidirect
9. C₁₃×#1951	C₂	semidirect
10. C₁₃×#1946	C₂	semidirect
13. C₁₃×#1847	C₂	semidirect
69. C₁₃×#131	Q₈	semidirect
136. C₁₃×#104	Q₈	semidirect
149. #26084	C₁₃	direct (N × H)
225. #3164	C₂×C₁₃	semidirect
229. #2090	C₂×C₁₃	semidirect
230. #2089	C₂×C₁₃	semidirect
231. #2061	C₂×C₁₃	semidirect
232. #2060	C₂×C₁₃	semidirect
233. #1951	C₂×C₁₃	semidirect
234. #1946	C₂×C₁₃	semidirect
237. #1847	C₂×C₁₃	semidirect
363. #131	Q₈×C₁₃	semidirect
430. #104	Q₈×C₁₃	semidirect
524. C₁₃	#26084	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×#3164	2
C₁₃×#3084	2
C₁₃×#3083	2
C₁₃×#2912	2
C₁₃×#2090	2
C₁₃×#2089	2
C₁₃×#2061	2
C₁₃×#2060	2
C₁₃×#1951	2
C₁₃×#1946	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1847	2
C₁₃×#1816	2
C₁₃×#1765	2
#26084	13

Subgroups — C13×#26084 #15712423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26084 #15712423