Subgroups — C₁₃×#24147 #15710486

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	2	yes	maximal
6	C₁₃×#2005	C₂	1	2	yes	maximal
7	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1886	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1857	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#556	—	2	1	no	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#552	—	2	2	no	—
19	C₁₃×#541	—	2	2	no	—
20	C₁₃×#536	C₂²	1	2	yes	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	—	2	1	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×#519	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#479	—	2	2	no	—
30	C₁₃×#477	—	2	1	no	—
31	C₁₃×#475	—	2	1	no	—
32	C₁₃×#441	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×Q₁₆	—	2	1	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₁₃×#428	C₂²	1	2	yes	—
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	2	yes	—
40	C₁₃×#419	C₂²	1	2	yes	—
41	C₁₃×#419	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#101	C₂²	1	2	yes	—
44	C₂×C₁₃×#101	C₂²	1	2	yes	—
45	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
46	C₁₃×#398	—	2	2	no	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#389	—	2	2	no	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₁₃×#339	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×#137	—	2	2	no	—
57	C₁₃×#137	—	2	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	1	no	—
59	C₂×C₁₃×SD₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	—	4	2	no	—
70	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	—	2	2	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	4	no	—
78	C₁₃×#125	D₄	1	2	yes	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	2	1	no	—
109	C₁₃×#117	C₂³	1	1	yes	characteristic
110	C₁₃×#117	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	—	2	1	no	—
118	C₂×C₄²×C₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	—	2	1	no	—
122	C₁₃×#107	—	2	2	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	2	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×#104	—	4	2	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#101	—	2	4	no	—
135	C₁₃×#101	—	4	2	no	—
136	C₁₃×#97	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	4	no	—
140	#24147	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	2	1	no	—
142	C₁₃×#41	—	2	1	no	—
143	C₁₃×#41	—	2	1	no	—
144	C₁₃×#41	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	2	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₃	#41	1	2	yes	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×Q₁₆	—	2	4	no	—
173	C₁₃×SD₁₆	—	2	4	no	—
174	C₁₃×M₁₆	—	2	1	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	1	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	—	2	1	no	—
179	C₁₃×M₁₆	#41	1	2	yes	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	4	8	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₄⋊C₄	—	4	1	no	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₁₃×C₂²⋊C₄	—	2	1	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	2	1	no	—
218	C₄²×C₁₃	—	2	2	no	—
219	C₄²×C₁₃	—	2	2	no	—
220	C₄²×C₁₃	—	2	2	no	—
221	C₄²×C₁₃	—	4	1	no	—
222	C₄²×C₁₃	—	4	1	no	—
223	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	#3509	C₂×C₁₃	1	1	yes	characteristic
228	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
230	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2038	C₂×C₁₃	1	2	yes	—
232	#2005	C₂×C₁₃	1	2	yes	—
233	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1886	C₂×C₁₃	1	2	yes	complemented
236	#1857	C₂×C₁₃	1	2	yes	complemented
237	#1806	C₂×C₁₃	1	1	yes	characteristic
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	2	no	—
241	Q₈×C₁₃	—	2	1	no	—
242	Q₈×C₁₃	—	2	1	no	—
243	Q₈×C₁₃	—	2	2	no	—
244	Q₈×C₁₃	—	4	2	no	—
245	Q₈×C₁₃	—	4	2	no	—
246	Q₈×C₁₃	—	4	2	no	—
247	Q₈×C₁₃	—	4	1	no	—
248	Q₈×C₁₃	—	4	2	no	—
249	Q₈×C₁₃	—	4	2	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	—	4	2	no	—
252	D₄×C₁₃	—	2	1	no	—
253	D₄×C₁₃	—	2	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
280	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
281	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₁₃	—	2	2	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	2	no	—
291	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
292	#557	—	2	1	no	—
293	#557	—	2	1	no	—
294	#556	—	2	1	no	—
295	#556	—	2	1	no	—
296	#552	—	2	2	no	—
297	#552	—	2	2	no	—
298	#541	—	2	2	no	—
299	#536	C₂²×C₁₃	1	2	yes	—
300	#533	—	2	1	no	—
301	#533	—	2	1	no	—
302	#533	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
304	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	#519	C₂²×C₁₃	1	2	yes	—
306	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	#479	—	2	2	no	—
309	#477	—	2	1	no	—
310	#475	—	2	1	no	—
311	#441	—	2	1	no	—
312	#440	—	2	1	no	—
313	C₄×Q₁₆	—	2	1	no	—
314	C₄×SD₁₆	—	2	1	no	—
315	#428	C₂²×C₁₃	1	2	yes	—
316	#428	C₂²×C₁₃	1	1	yes	characteristic
317	#423	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#104	C₂²×C₁₃	1	2	yes	—
319	#419	C₂²×C₁₃	1	2	yes	—
320	#419	C₂²×C₁₃	1	1	yes	characteristic
321	#417	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#101	C₂²×C₁₃	1	2	yes	—
323	C₂×#101	C₂²×C₁₃	1	2	yes	—
324	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
325	#398	—	2	2	no	—
326	#391	C₂²×C₁₃	1	2	yes	—
327	#389	—	2	2	no	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	#339	C₂²×C₁₃	1	2	yes	—
330	#339	C₂²×C₁₃	1	2	yes	—
331	#339	C₂²×C₁₃	1	2	yes	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
338	C₂²×C₁₃	#546	1	1	yes	characteristic
339	C₂²×C₁₃	#547	1	1	yes	characteristic
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	#456	1	2	yes	—
353	C₄×C₁₃	#525	1	1	yes	characteristic
354	C₄×C₁₃	#537	1	1	yes	characteristic
355	C₄×C₁₃	#548	1	1	yes	characteristic
356	C₄×C₁₃	#550	1	1	yes	characteristic
357	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
360	#137	—	2	2	no	—
361	#137	—	2	2	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
366	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	—	2	4	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	—	4	2	no	—
374	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
375	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
376	#126	—	2	4	no	—
377	#126	—	2	4	no	—
378	#125	—	2	2	no	—
379	#125	—	2	2	no	—
380	#125	—	2	4	no	—
381	#125	—	2	4	no	—
382	#125	D₄×C₁₃	1	2	yes	—
383	#124	—	2	2	no	—
384	#123	—	2	4	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
404	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
408	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	4	no	—
412	#117	—	2	1	no	—
413	#117	C₂³×C₁₃	1	1	yes	characteristic
414	#117	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	4	no	—
418	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
419	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	#107	—	2	1	no	—
426	#107	—	2	2	no	—
427	#106	—	2	1	no	—
428	#106	—	2	2	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	#104	—	4	2	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#103	—	2	1	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#102	—	2	1	no	—
438	#101	—	2	4	no	—
439	#101	—	4	2	no	—
440	#97	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	4	no	—
444	C₂×C₁₃	—	2	1	no	—
445	C₂×C₁₃	—	2	1	no	—
446	C₂×C₁₃	—	8	1	no	—
447	C₂×C₁₃	#2407	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
449	C₂×C₁₃	#3020	1	1	yes	characteristic
450	#41	—	2	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂×Q₈	C₁₃×#41	1	2	yes	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
481	Q₁₆	—	2	4	no	—
482	SD₁₆	—	2	4	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	1	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	C₁₃×#41	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	2	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	8	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	4	1	no	—
531	C₄²	—	4	1	no	—
532	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₁₃	#24147	1	1	yes	characteristic, direct product factor, Sylow
537	C₂³	—	2	1	no	—
538	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	4	2	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	1	no	—
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
578	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
579	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
580	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
584	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
585	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
587	C₈	—	2	2	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	2	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
596	C₂²	C₁₃×#546	1	1	yes	characteristic
597	C₂²	C₁₃×#547	1	1	yes	characteristic
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	4	4	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	4	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	8	1	no	—
610	C₄	C₁₃×#456	1	2	yes	—
611	C₄	C₁₃×#525	1	1	yes	characteristic
612	C₄	C₁₃×#537	1	1	yes	characteristic
613	C₄	C₁₃×#548	1	1	yes	characteristic
614	C₄	C₁₃×#550	1	1	yes	characteristic
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	8	1	no	—
618	C₂	C₁₃×#2407	1	1	yes	characteristic
619	C₂	C₂×C₁₃×#456	1	1	yes	characteristic
620	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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×#2546	C₂	semidirect
7. C₁₃×#1986	C₂	semidirect
8. C₁₃×#1966	C₂	semidirect
9. C₁₃×#1886	C₂	semidirect
10. C₁₃×#1857	C₂	semidirect
140. #24147	C₁₃	direct (N × H)
228. #3078	C₂×C₁₃	semidirect
230. #2546	C₂×C₁₃	semidirect
233. #1986	C₂×C₁₃	semidirect
234. #1966	C₂×C₁₃	semidirect
235. #1886	C₂×C₁₃	semidirect
236. #1857	C₂×C₁₃	semidirect
536. C₁₃	#24147	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×#3509	2
C₁₃×#3078	2
C₄×C₁₃×#137	2
C₁₃×#2546	2
C₁₃×#2038	2
C₁₃×#2005	2
C₁₃×#1986	2
C₁₃×#1966	2
C₁₃×#1886	2
C₁₃×#1857	2
C₁₃×#1806	2
#24147	13

Subgroups — C13×#24147 #15710486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24147 #15710486