Subgroups — C₁₃×#24183 #15710522

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2005	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1963	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₁₃×#559	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#554	—	2	1	no	—
18	C₁₃×#552	—	2	2	no	—
19	C₁₃×#539	—	2	2	no	—
20	C₁₃×#536	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#529	—	2	2	no	—
25	C₁₃×#520	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#479	—	2	2	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#475	—	2	1	no	—
31	C₁₃×#464	—	2	2	no	—
32	C₁₃×#462	—	2	1	no	—
33	C₁₃×#460	—	2	1	no	—
34	C₁₃×#428	C₂²	1	2	yes	—
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#104	C₂²	1	2	yes	—
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₁₃×#419	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#101	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#387	—	2	2	no	—
45	C₁₃×#387	—	2	2	no	—
46	C₁₃×#382	C₂²	1	1	yes	characteristic
47	C₁₃×#376	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#339	C₂²	1	2	yes	—
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	C₂³	1	2	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#137	—	2	4	no	—
55	C₁₃×#137	—	4	2	no	—
56	C₂×C₁₃×Q₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₃×#127	D₄	1	1	yes	characteristic
67	C₁₃×#126	—	2	4	no	—
68	C₁₃×#126	—	2	4	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	4	no	—
71	C₁₃×#125	D₄	1	2	yes	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	2	no	—
74	C₁₃×#124	D₄	1	2	yes	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×#123	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	4	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₁₃×#117	—	2	4	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#107	—	2	2	no	—
116	C₁₃×#106	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	—	2	1	no	—
119	C₁₃×C₄⋊C₈	—	2	1	no	—
120	C₁₃×C₄⋊C₈	—	2	1	no	—
121	C₁₃×#104	—	2	4	no	—
122	C₁₃×#104	—	4	2	no	—
123	C₁₃×#103	—	2	2	no	—
124	C₁₃×#103	—	2	2	no	—
125	C₁₃×#103	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#101	—	4	2	no	—
128	C₁₃×#95	—	2	2	no	—
129	C₁₃×#95	—	2	2	no	—
130	C₁₃×#95	—	2	2	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	#24183	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₁₃×#41	—	2	2	no	—
135	C₁₃×#41	—	2	2	no	—
136	C₁₃×#41	—	2	2	no	—
137	C₁₃×#41	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
152	C₂×Q₈×C₁₃	#41	1	2	yes	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×Q₁₆	—	4	4	no	—
169	C₁₃×SD₁₆	—	4	4	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₄²×C₁₃	—	2	4	no	—
203	C₄²×C₁₃	—	2	2	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	2	2	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	—	4	1	no	—
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	#41	1	2	yes	—
216	#3507	C₂×C₁₃	1	1	yes	characteristic
217	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3037	C₂×C₁₃	1	1	yes	characteristic
219	#2327	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2038	C₂×C₁₃	1	2	yes	complemented
221	#2005	C₂×C₁₃	1	2	yes	complemented
222	#1995	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1963	C₂×C₁₃	1	1	yes	characteristic
224	#1882	C₂×C₁₃	1	2	yes	complemented
225	#1860	C₂×C₁₃	1	2	yes	complemented
226	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	2	no	—
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	2	2	no	—
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	4	2	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	8	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	8	4	no	—
271	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
281	C₈×C₁₃	—	4	2	no	—
282	C₈×C₁₃	—	4	2	no	—
283	C₂×#137	C₂²×C₁₃	1	2	yes	—
284	#559	—	2	1	no	—
285	#557	—	2	1	no	—
286	#556	—	2	1	no	—
287	#556	—	2	2	no	—
288	#554	—	2	1	no	—
289	#552	—	2	2	no	—
290	#539	—	2	2	no	—
291	#536	C₂²×C₁₃	1	2	yes	—
292	#533	C₂²×C₁₃	1	1	yes	characteristic
293	#532	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
295	#529	—	2	2	no	—
296	#520	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	#479	—	2	2	no	—
300	#477	—	2	1	no	—
301	#475	—	2	1	no	—
302	#464	—	2	2	no	—
303	#462	—	2	1	no	—
304	#460	—	2	1	no	—
305	#428	C₂²×C₁₃	1	2	yes	—
306	#423	C₂²×C₁₃	1	1	yes	characteristic
307	#423	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#104	C₂²×C₁₃	1	2	yes	—
309	C₂×#104	C₂²×C₁₃	1	2	yes	—
310	#419	C₂²×C₁₃	1	2	yes	—
311	#417	C₂²×C₁₃	1	2	yes	—
312	C₂×#101	C₂²×C₁₃	1	2	yes	—
313	#391	C₂²×C₁₃	1	1	yes	characteristic
314	#391	C₂²×C₁₃	1	1	yes	characteristic
315	#387	—	2	2	no	—
316	#387	—	2	2	no	—
317	#382	C₂²×C₁₃	1	1	yes	characteristic
318	#376	C₂²×C₁₃	1	1	yes	characteristic
319	#343	C₂²×C₁₃	1	2	yes	—
320	#339	C₂²×C₁₃	1	2	yes	—
321	#339	C₂²×C₁₃	1	2	yes	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
328	C₂²×C₁₃	#525	1	1	yes	characteristic
329	C₂²×C₁₃	#537	1	1	yes	characteristic
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	#546	1	1	yes	characteristic
344	C₄×C₁₃	#547	1	1	yes	characteristic
345	C₄×C₁₃	#548	1	1	yes	characteristic
346	C₄×C₁₃	#550	1	1	yes	characteristic
347	C₂×#41	C₂³×C₁₃	1	2	yes	—
348	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	#137	—	2	4	no	—
351	#137	—	4	2	no	—
352	C₂×Q₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	2	2	no	—
354	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
355	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	2	no	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
360	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
361	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
362	#127	D₄×C₁₃	1	1	yes	characteristic
363	#126	—	2	4	no	—
364	#126	—	2	4	no	—
365	#125	—	2	2	no	—
366	#125	—	2	4	no	—
367	#125	D₄×C₁₃	1	2	yes	—
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	D₄×C₁₃	1	2	yes	—
371	#123	—	2	4	no	—
372	#123	—	2	4	no	—
373	C₂²⋊Q₈	—	2	4	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	#117	—	2	4	no	—
398	#117	—	2	2	no	—
399	#117	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	D₄×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#106	—	2	2	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	—	2	1	no	—
417	#104	—	2	4	no	—
418	#104	—	4	2	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#102	—	2	2	no	—
423	#101	—	4	2	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	2	no	—
427	#95	—	2	2	no	—
428	#95	—	2	2	no	—
429	C₂×C₁₃	—	2	1	no	—
430	C₂×C₁₃	—	2	1	no	—
431	C₂×C₁₃	—	8	2	no	—
432	C₂×C₁₃	#2407	1	1	yes	characteristic
433	C₂×C₁₃	#3020	1	1	yes	characteristic
434	C₂×C₁₃	#3022	1	1	yes	characteristic
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
453	C₂×Q₈	C₁₃×#41	1	2	yes	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	Q₁₆	—	4	4	no	—
470	SD₁₆	—	4	4	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
496	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₄²	C₁₃×#41	1	2	yes	—
517	C₁₃	#24183	1	1	yes	characteristic, direct product factor, Sylow
518	C₂³	—	2	2	no	—
519	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	8	1	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	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	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
563	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
564	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
565	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
570	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
580	C₂²	C₁₃×#525	1	1	yes	characteristic
581	C₂²	C₁₃×#537	1	1	yes	characteristic
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	C₁₃×#546	1	1	yes	characteristic
596	C₄	C₁₃×#547	1	1	yes	characteristic
597	C₄	C₁₃×#548	1	1	yes	characteristic
598	C₄	C₁₃×#550	1	1	yes	characteristic
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	8	2	no	—
602	C₂	C₁₃×#2407	1	1	yes	characteristic
603	C₂	C₁₃×#3020	1	1	yes	characteristic
604	C₂	C₁₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3078	C₂	semidirect
4. C₁₃×#2327	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#2005	C₂	semidirect
7. C₁₃×#1995	C₂	semidirect
9. C₁₃×#1882	C₂	semidirect
10. C₁₃×#1860	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
133. #24183	C₁₃	direct (N × H)
217. #3078	C₂×C₁₃	semidirect
219. #2327	C₂×C₁₃	semidirect
220. #2038	C₂×C₁₃	semidirect
221. #2005	C₂×C₁₃	semidirect
222. #1995	C₂×C₁₃	semidirect
224. #1882	C₂×C₁₃	semidirect
225. #1860	C₂×C₁₃	semidirect
226. #1801	C₂×C₁₃	semidirect
517. C₁₃	#24183	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×#3507	2
C₁₃×#3078	2
C₁₃×#3037	2
C₁₃×#2327	2
C₁₃×#2038	2
C₁₃×#2005	2
C₁₃×#1995	2
C₁₃×#1963	2
C₁₃×#1882	2
C₁₃×#1860	2
C₁₃×#1801	2
#24183	13

Subgroups — C13×#24183 #15710522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24183 #15710522