Subgroups — C₁₃×#23992 #15710331

Order 3328.

1128 conjugacy classes of subgroups.

The subgroup lattice has 556 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, complemented
2	C₁₃×#3028	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3022	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2901	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2031	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2005	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1915	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1912	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1909	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1905	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1827	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₁₃×#568	C₂²	1	1	yes	characteristic
15	C₁₃×#557	—	2	2	no	—
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#552	—	2	4	no	—
18	C₁₃×#541	—	2	2	no	—
19	C₁₃×#536	C₂²	1	1	yes	characteristic
20	C₁₃×#536	C₂²	1	1	yes	characteristic
21	C₁₃×#536	C₂²	1	2	yes	—
22	C₁₃×#533	—	2	2	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₁₃×#458	—	2	4	no	—
29	C₁₃×#456	—	2	2	no	—
30	C₁₃×#455	—	2	2	no	—
31	C₁₃×#421	—	2	2	no	—
32	C₁₃×#421	C₂²	1	2	yes	—
33	C₁₃×#421	C₂²	1	2	yes	—
34	C₂×C₁₃×#104	—	2	2	no	—
35	C₂×C₁₃×#104	C₂²	1	2	yes	—
36	C₁₃×#419	C₂²	1	2	yes	complemented
37	C₁₃×#413	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
39	C₁₃×#410	C₂²	1	2	yes	—
40	C₁₃×#410	C₂²	1	1	yes	characteristic
41	C₁₃×#344	C₂²	1	2	yes	complemented
42	C₁₃×#339	C₂²	1	2	yes	complemented
43	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
44	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	C₁₃×2₋¹⁺⁴	—	2	2	no	—
46	C₁₃×2₋¹⁺⁴	—	2	1	no	—
47	C₁₃×H(5,𝔽₂)	—	2	2	no	—
48	C₁₃×H(5,𝔽₂)	—	2	2	no	—
49	C₁₃×H(5,𝔽₂)	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	4	2	no	—
52	C₂×C₁₃×#41	C₂³	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	1	yes	characteristic
56	C₁₃×#137	—	2	4	no	—
57	C₁₃×#137	—	4	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₁₃×#131	—	4	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	—	2	1	no	—
70	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×#125	—	2	4	no	—
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	—	2	1	no	—
77	C₁₃×#124	—	2	1	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	D₄	1	2	yes	—
80	C₁₃×#123	—	2	2	no	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×#123	D₄	1	4	yes	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	4	2	no	—
88	C₄×Q₈×C₁₃	—	2	4	no	—
89	C₄×Q₈×C₁₃	—	2	1	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	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₁₃×#117	—	2	4	no	—
98	C₁₃×#117	—	2	2	no	—
99	C₁₃×#117	—	2	2	no	—
100	C₁₃×#117	D₄	1	2	yes	—
101	C₁₃×#117	C₂³	1	2	yes	—
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄²×C₁₃	D₄	1	2	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#104	—	2	2	no	—
109	C₁₃×#104	—	2	4	no	—
110	C₁₃×#104	—	2	2	no	—
111	C₁₃×#104	—	2	4	no	—
112	C₁₃×#103	—	4	2	no	—
113	C₁₃×#101	—	2	1	no	—
114	C₁₃×#101	—	4	2	no	—
115	C₁₃×#100	—	2	1	no	—
116	C₁₃×#99	—	2	2	no	—
117	C₁₃×#99	—	2	4	no	—
118	#23992	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	4	4	no	—
127	C₁₃×#41	—	4	2	no	—
128	C₁₃×#41	—	4	2	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₁₃×#41	—	4	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	4	2	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₁₃	#41	1	2	yes	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	4	2	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	—	4	2	no	—
149	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₃	#41	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	4	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	4	2	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	4	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	4	4	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	—	2	4	no	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	2	no	—
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂×D₄	1	2	yes	—
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	2	yes	—
203	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3028	C₂×C₁₃	1	1	yes	characteristic
205	#3022	C₂×C₁₃	1	1	yes	characteristic
206	#2901	C₂×C₁₃	1	1	yes	characteristic
207	#2031	C₂×C₁₃	1	2	yes	complemented
208	#2005	C₂×C₁₃	1	2	yes	complemented
209	#1915	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1912	C₂×C₁₃	1	2	yes	complemented
211	#1909	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1905	C₂×C₁₃	1	2	yes	complemented
213	#1827	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	#120	1	2	yes	—
217	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	4	4	no	—
223	Q₈×C₁₃	—	4	2	no	—
224	Q₈×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	2	2	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	#120	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
261	C₈×C₁₃	—	4	2	no	—
262	C₈×C₁₃	—	4	2	no	—
263	#585	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#137	C₂²×C₁₃	1	2	yes	—
265	#568	C₂²×C₁₃	1	1	yes	characteristic
266	#557	—	2	2	no	—
267	#556	—	2	2	no	—
268	#552	—	2	4	no	—
269	#541	—	2	2	no	—
270	#536	C₂²×C₁₃	1	1	yes	characteristic
271	#536	C₂²×C₁₃	1	1	yes	characteristic
272	#536	C₂²×C₁₃	1	2	yes	—
273	#533	—	2	2	no	—
274	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
279	#458	—	2	4	no	—
280	#456	—	2	2	no	—
281	#455	—	2	2	no	—
282	#421	—	2	2	no	—
283	#421	C₂²×C₁₃	1	2	yes	—
284	#421	C₂²×C₁₃	1	2	yes	—
285	C₂×#104	—	2	2	no	—
286	C₂×#104	C₂²×C₁₃	1	2	yes	—
287	#419	C₂²×C₁₃	1	2	yes	complemented
288	#413	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
290	#410	C₂²×C₁₃	1	1	yes	characteristic
291	#410	C₂²×C₁₃	1	2	yes	—
292	#344	C₂²×C₁₃	1	2	yes	complemented
293	#339	C₂²×C₁₃	1	2	yes	complemented
294	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	complemented
295	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	complemented
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	8	2	no	—
301	C₂²×C₁₃	—	16	2	no	—
302	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
303	C₂²×C₁₃	#546	1	2	yes	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	1	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	#525	1	1	yes	characteristic
315	C₄×C₁₃	#535	1	1	yes	characteristic
316	C₄×C₁₃	#546	1	2	yes	—
317	2₋¹⁺⁴	—	2	2	no	—
318	2₋¹⁺⁴	—	2	1	no	—
319	H(5,𝔽₂)	—	2	2	no	—
320	H(5,𝔽₂)	—	2	2	no	—
321	H(5,𝔽₂)	—	2	1	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	4	2	no	—
324	C₂×#41	C₂³×C₁₃	1	2	yes	—
325	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	#137	—	2	4	no	—
329	#137	—	4	2	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×SD₁₆	—	2	2	no	—
332	#131	—	4	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
335	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
343	#126	—	2	4	no	—
344	#126	—	2	4	no	—
345	#125	—	2	4	no	—
346	#125	—	2	4	no	—
347	#125	—	2	4	no	—
348	#125	—	2	1	no	—
349	#124	—	2	1	no	—
350	#124	—	2	2	no	—
351	#124	D₄×C₁₃	1	2	yes	—
352	#123	—	2	2	no	—
353	#123	—	2	4	no	—
354	#123	D₄×C₁₃	1	4	yes	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	4	2	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	#117	—	2	4	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	D₄×C₁₃	1	2	yes	—
373	#117	C₂³×C₁₃	1	2	yes	—
374	#117	C₂³×C₁₃	1	1	yes	characteristic
375	#117	C₂³×C₁₃	1	1	yes	characteristic
376	#117	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄²	D₄×C₁₃	1	2	yes	—
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	#104	—	2	2	no	—
381	#104	—	2	4	no	—
382	#104	—	2	2	no	—
383	#104	—	2	4	no	—
384	#103	—	4	2	no	—
385	#101	—	2	1	no	—
386	#101	—	4	2	no	—
387	#100	—	2	1	no	—
388	#99	—	2	2	no	—
389	#99	—	2	4	no	—
390	C₂×C₁₃	—	2	1	no	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	4	2	no	—
393	C₂×C₁₃	—	8	2	no	—
394	C₂×C₁₃	#2404	1	1	yes	characteristic
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	4	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	4	4	no	—
403	#41	—	4	2	no	—
404	#41	—	4	2	no	—
405	#41	—	4	2	no	—
406	#41	—	4	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	4	2	no	—
417	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
418	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂×Q₈	C₁₃×#41	1	2	yes	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂×D₄	C₁₃×#41	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	Q₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	4	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₄²	—	2	4	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₃	1	2	yes	—
477	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₁₃	1	2	yes	—
479	C₁₃	#23992	1	1	yes	characteristic, direct product factor, Sylow
480	C₂³	—	2	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	C₁₃×#120	1	2	yes	—
483	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	2	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	C₁₃×#120	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
525	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
526	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
527	C₈	—	4	2	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	16	2	no	—
535	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
536	C₂²	C₁₃×#546	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	2	no	—
547	C₄	C₁₃×#525	1	1	yes	characteristic
548	C₄	C₁₃×#535	1	1	yes	characteristic
549	C₄	C₁₃×#546	1	2	yes	—
550	C₂	—	2	1	no	—
551	C₂	—	2	2	no	—
552	C₂	—	4	2	no	—
553	C₂	—	8	2	no	—
554	C₂	C₁₃×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
5. C₁₃×#2031	C₂	semidirect
6. C₁₃×#2005	C₂	semidirect
7. C₁₃×#1915	C₂	semidirect
8. C₁₃×#1912	C₂	semidirect
9. C₁₃×#1909	C₂	semidirect
10. C₁₃×#1905	C₂	semidirect
11. C₁₃×#1827	C₂	semidirect
23. C₁₃×#533	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₁₃×#519	C₂²	semidirect
26. C₁₃×#519	C₂²	semidirect
36. C₁₃×#419	C₂²	semidirect
38. C₂×C₁₃×#101	C₂²	semidirect
41. C₁₃×#344	C₂²	semidirect
42. C₁₃×#339	C₂²	semidirect
43. C₁₃×H(3,ℤ/4)	C₂²	semidirect
44. C₁₃×H(3,ℤ/4)	C₂²	semidirect
118. #23992	C₁₃	direct (N × H)
203. #3509	C₂×C₁₃	semidirect
207. #2031	C₂×C₁₃	semidirect
208. #2005	C₂×C₁₃	semidirect
209. #1915	C₂×C₁₃	semidirect
210. #1912	C₂×C₁₃	semidirect
211. #1909	C₂×C₁₃	semidirect
212. #1905	C₂×C₁₃	semidirect
213. #1827	C₂×C₁₃	semidirect
274. #533	C₂²×C₁₃	semidirect
275. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
276. #519	C₂²×C₁₃	semidirect
277. #519	C₂²×C₁₃	semidirect
287. #419	C₂²×C₁₃	semidirect
289. C₂×#101	C₂²×C₁₃	semidirect
292. #344	C₂²×C₁₃	semidirect
293. #339	C₂²×C₁₃	semidirect
294. H(3,ℤ/4)	C₂²×C₁₃	semidirect
295. H(3,ℤ/4)	C₂²×C₁₃	semidirect
479. C₁₃	#23992	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×#3028	2
C₁₃×#3022	2
C₁₃×#2901	2
C₁₃×#2031	2
C₁₃×#2005	2
C₁₃×#1915	2
C₁₃×#1912	2
C₁₃×#1909	2
C₁₃×#1905	2
C₁₃×#1827	2
#23992	13

Subgroups — C13×#23992 #15710331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23992 #15710331