Subgroups — C₁₃×#33832 #15720171

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3280	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2220	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2216	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2211	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2175	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	—	2	1	no	—
21	C₁₃×#546	—	2	1	no	—
22	C₁₃×#510	—	2	4	no	—
23	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×SD₃₂	—	2	4	no	—
27	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
35	C₁₃×#495	C₂²	1	1	yes	characteristic
36	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#467	C₂²	1	1	yes	characteristic
38	C₁₃×#467	C₂²	1	1	yes	characteristic
39	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#466	C₂²	1	1	yes	characteristic
41	C₁₃×#463	—	2	1	no	—
42	C₁₃×#462	—	2	1	no	—
43	C₁₃×#451	—	2	1	no	—
44	C₁₃×#451	—	2	1	no	—
45	C₁₃×#450	—	2	1	no	—
46	C₁₃×#449	—	2	1	no	—
47	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#357	C₂²	1	1	yes	characteristic
57	C₁₃×#357	C₂²	1	1	yes	characteristic
58	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#41	—	2	1	no	—
62	C₂²×Q₈×C₁₃	—	2	1	no	—
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₁₃×#135	—	2	2	no	—
66	C₁₃×#135	—	4	1	no	—
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	2	2	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	4	1	no	—
73	C₂×C₁₃×Q₁₆	—	4	1	no	—
74	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	2	no	—
81	C₂×C₁₃×D₈	—	2	1	no	—
82	C₂×C₁₃×D₈	—	4	1	no	—
83	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	4	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	4	1	no	—
95	C₁₃×C₂²⋊Q₈	—	4	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	4	1	no	—
98	C₁₃×#120	—	4	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	4	1	no	—
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×Q₃₂	—	2	2	no	—
105	C₁₃×Q₃₂	—	2	2	no	—
106	C₁₃×Q₃₂	—	4	1	no	—
107	C₁₃×SD₃₂	—	2	2	no	—
108	C₁₃×SD₃₂	—	2	2	no	—
109	C₁₃×SD₃₂	—	2	2	no	—
110	C₁₃×SD₃₂	—	2	2	no	—
111	C₁₃×SD₃₂	—	4	1	no	—
112	C₁₃×SD₃₂	D₄	1	4	yes	complemented
113	C₁₃×M₃₂	—	2	2	no	—
114	C₂×C₁₃×C₁₆	—	2	2	no	—
115	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
119	C₁₃×#107	C₂³	1	1	yes	characteristic
120	C₁₃×#107	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	#33832	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	4	1	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	8	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	—	4	2	no	—
141	C₂×Q₈×C₁₃	—	4	1	no	—
142	C₂×Q₈×C₁₃	—	4	1	no	—
143	C₂×Q₈×C₁₃	—	8	1	no	—
144	C₂×Q₈×C₁₃	—	8	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	4	2	no	—
148	C₂×D₄×C₁₃	—	4	1	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	—	8	1	no	—
152	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	4	1	no	—
154	C₂²×C₄×C₁₃	—	4	1	no	—
155	C₂²×C₄×C₁₃	—	4	1	no	—
156	C₂²×C₄×C₁₃	—	4	1	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	1	no	—
160	C₁₃×Q₁₆	—	2	1	no	—
161	C₁₃×Q₁₆	—	2	1	no	—
162	C₁₃×Q₁₆	—	2	1	no	—
163	C₁₃×Q₁₆	—	2	1	no	—
164	C₁₃×Q₁₆	—	2	1	no	—
165	C₁₃×Q₁₆	—	2	1	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	—	4	2	no	—
168	C₁₃×Q₁₆	—	8	1	no	—
169	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
170	C₁₃×SD₁₆	—	4	2	no	—
171	C₁₃×SD₁₆	—	8	1	no	—
172	C₁₃×D₈	—	2	1	no	—
173	C₁₃×D₈	—	2	1	no	—
174	C₁₃×D₈	—	2	1	no	—
175	C₁₃×D₈	—	4	2	no	—
176	C₁₃×D₈	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	4	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	1	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
202	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
203	C₄²×C₁₃	—	4	1	no	—
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₁₆	—	2	1	no	—
206	C₁₃×C₁₆	—	2	1	no	—
207	C₁₃×C₁₆	—	2	1	no	—
208	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
209	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
211	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3280	C₂×C₁₃	1	1	yes	characteristic
213	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2220	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2216	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2211	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2189	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2185	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2175	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2168	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	—	8	2	no	—
227	C₂³×C₁₃	—	8	2	no	—
228	C₂³×C₁₃	—	16	1	no	—
229	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
230	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	2	no	—
232	Q₈×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	4	1	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	—	8	2	no	—
240	Q₈×C₁₃	—	8	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	8	2	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	16	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	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	—	8	2	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	—	8	2	no	—
262	C₂×C₄×C₁₃	—	16	1	no	—
263	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
277	D₄×Q₈	—	2	1	no	—
278	#546	—	2	1	no	—
279	#510	—	2	4	no	—
280	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	C₂×SD₃₂	—	2	4	no	—
284	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
292	#495	C₂²×C₁₃	1	1	yes	characteristic
293	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	#467	C₂²×C₁₃	1	1	yes	characteristic
295	#467	C₂²×C₁₃	1	1	yes	characteristic
296	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	#466	C₂²×C₁₃	1	1	yes	characteristic
298	#463	—	2	1	no	—
299	#462	—	2	1	no	—
300	#451	—	2	1	no	—
301	#451	—	2	1	no	—
302	#450	—	2	1	no	—
303	#449	—	2	1	no	—
304	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	#357	C₂²×C₁₃	1	1	yes	characteristic
314	#357	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	8	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	16	4	no	—
330	C₂²×C₁₃	#510	1	2	yes	complemented
331	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	D₄²	1	1	yes	characteristic
343	C₄×C₁₃	#576	1	1	yes	characteristic
344	C₂×#41	—	2	1	no	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	#135	—	2	2	no	—
349	#135	—	4	1	no	—
350	C₂×Q₁₆	—	2	2	no	—
351	C₂×Q₁₆	—	2	2	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×Q₁₆	—	4	1	no	—
356	C₂×Q₁₆	—	4	1	no	—
357	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×D₈	—	2	1	no	—
365	C₂×D₈	—	4	1	no	—
366	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	4	1	no	—
372	#124	—	2	1	no	—
373	#123	—	4	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	4	1	no	—
378	C₂²⋊Q₈	—	4	1	no	—
379	#121	—	2	1	no	—
380	#121	—	4	1	no	—
381	#120	—	4	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	4	1	no	—
385	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	—	4	1	no	—
387	Q₃₂	—	2	2	no	—
388	Q₃₂	—	2	2	no	—
389	Q₃₂	—	4	1	no	—
390	SD₃₂	—	2	2	no	—
391	SD₃₂	—	2	2	no	—
392	SD₃₂	—	2	2	no	—
393	SD₃₂	—	2	2	no	—
394	SD₃₂	—	4	1	no	—
395	SD₃₂	D₄×C₁₃	1	4	yes	complemented
396	M₃₂	—	2	2	no	—
397	C₂×C₁₆	—	2	2	no	—
398	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
402	#107	C₂³×C₁₃	1	1	yes	characteristic
403	#107	C₂³×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
412	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₁₃	—	2	2	no	—
415	C₂×C₁₃	—	4	1	no	—
416	C₂×C₁₃	—	8	2	no	—
417	C₂×C₁₃	—	16	1	no	—
418	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
419	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
420	C₂×C₁₃	#3416	1	1	yes	characteristic
421	C₂⁴	—	4	1	no	—
422	#41	—	4	2	no	—
423	#41	—	8	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	—	8	1	no	—
433	C₂×Q₈	—	8	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	8	1	no	—
441	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	Q₁₆	—	2	1	no	—
449	Q₁₆	—	2	1	no	—
450	Q₁₆	—	2	1	no	—
451	Q₁₆	—	2	1	no	—
452	Q₁₆	—	2	1	no	—
453	Q₁₆	—	2	1	no	—
454	Q₁₆	—	2	1	no	—
455	Q₁₆	—	4	2	no	—
456	Q₁₆	—	4	2	no	—
457	Q₁₆	—	8	1	no	—
458	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	8	1	no	—
461	D₈	—	2	1	no	—
462	D₈	—	2	1	no	—
463	D₈	—	2	1	no	—
464	D₈	—	4	2	no	—
465	D₈	C₂×D₄×C₁₃	1	2	yes	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
491	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
492	C₄²	—	4	1	no	—
493	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₁₆	—	2	1	no	—
495	C₁₆	—	2	1	no	—
496	C₁₆	—	2	1	no	—
497	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
498	C₁₃	#33832	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	16	1	no	—
504	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
505	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	8	2	no	—
515	Q₈	—	8	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	16	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	—	16	1	no	—
538	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
539	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	16	4	no	—
560	C₂²	C₁₃×#510	1	2	yes	complemented
561	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	D₄²×C₁₃	1	1	yes	characteristic
573	C₄	C₁₃×#576	1	1	yes	characteristic
574	C₂	—	2	2	no	—
575	C₂	—	4	1	no	—
576	C₂	—	8	2	no	—
577	C₂	—	16	1	no	—
578	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
579	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
580	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3280	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
2. C₂²×C₁₃×SD₃₂	C₂	semidirect
3. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#2251	C₂	semidirect
6. C₁₃×#2220	C₂	semidirect
7. C₁₃×#2216	C₂	semidirect
8. C₁₃×#2211	C₂	semidirect
9. C₁₃×#2208	C₂	semidirect
10. C₁₃×#2189	C₂	semidirect
11. C₁₃×#2188	C₂	semidirect
12. C₁₃×#2187	C₂	semidirect
13. C₁₃×#2185	C₂	semidirect
14. C₁₃×#2175	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
18. C₂²×C₁₃×Q₁₆	C₂²	semidirect
23. C₂×C₁₃×Q₃₂	C₂²	semidirect
24. C₂×C₁₃×Q₃₂	C₂²	semidirect
25. C₂×C₁₃×Q₃₂	C₂²	semidirect
33. C₂×C₁₃×M₃₂	C₂²	semidirect
36. C₁₃×#494	C₂²	semidirect
39. C₁₃×#467	C₂²	semidirect
47. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₁₃×#366	C₂²	semidirect
51. C₁₃×C₄⋊C₁₆	C₂²	semidirect
52. C₁₃×#358	C₂²	semidirect
53. C₁₃×#358	C₂²	semidirect
54. C₁₃×#358	C₂²	semidirect
55. C₁₃×#358	C₂²	semidirect
59. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
60. C₁₃×#346	C₂²	semidirect
112. C₁₃×SD₃₂	D₄	semidirect
131. #33832	C₁₃	direct (N × H)
209. C₂×#510	C₂×C₁₃	semidirect
210. C₂²×SD₃₂	C₂×C₁₃	semidirect
211. D₄×Q₁₆	C₂×C₁₃	semidirect
213. #2251	C₂×C₁₃	semidirect
214. #2220	C₂×C₁₃	semidirect
215. #2216	C₂×C₁₃	semidirect
216. #2211	C₂×C₁₃	semidirect
217. #2208	C₂×C₁₃	semidirect
218. #2189	C₂×C₁₃	semidirect
219. #2188	C₂×C₁₃	semidirect
220. #2187	C₂×C₁₃	semidirect
221. #2185	C₂×C₁₃	semidirect
222. #2175	C₂×C₁₃	semidirect
223. #2168	C₂×C₁₃	semidirect
275. C₂²×Q₁₆	C₂²×C₁₃	semidirect
280. C₂×Q₃₂	C₂²×C₁₃	semidirect
281. C₂×Q₃₂	C₂²×C₁₃	semidirect
282. C₂×Q₃₂	C₂²×C₁₃	semidirect
290. C₂×M₃₂	C₂²×C₁₃	semidirect
293. #494	C₂²×C₁₃	semidirect
296. #467	C₂²×C₁₃	semidirect
304. C₄×Q₁₆	C₂²×C₁₃	semidirect
307. #366	C₂²×C₁₃	semidirect
308. C₄⋊C₁₆	C₂²×C₁₃	semidirect
309. #358	C₂²×C₁₃	semidirect
310. #358	C₂²×C₁₃	semidirect
311. #358	C₂²×C₁₃	semidirect
312. #358	C₂²×C₁₃	semidirect
316. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
317. #346	C₂²×C₁₃	semidirect
330. C₂²×C₁₃	#510	semidirect
395. SD₃₂	D₄×C₁₃	semidirect
498. C₁₃	#33832	direct (N × H)
560. C₂²	C₁₃×#510	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#510	2
C₂²×C₁₃×SD₃₂	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3280	2
C₁₃×#2251	2
C₁₃×#2220	2
C₁₃×#2216	2
C₁₃×#2211	2
C₁₃×#2208	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2187	2
C₁₃×#2185	2
C₁₃×#2175	2
C₁₃×#2168	2
#33832	13

Subgroups — C13×#33832 #15720171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33832 #15720171