Subgroups — C₁₃×#33833 #15720172

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2219	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2210	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×#2189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2177	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	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#547	—	2	1	no	—
21	C₁₃×#546	—	2	1	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₁₃×#508	—	2	4	no	—
24	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
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, complemented
31	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
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×#461	—	2	1	no	—
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#450	—	2	1	no	—
46	C₁₃×#449	—	2	1	no	—
47	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
49	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#367	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×#357	C₂²	1	1	yes	characteristic
56	C₁₃×#357	C₂²	1	1	yes	characteristic
57	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₁₃×#41	—	2	1	no	—
63	C₂×C₁₃×#41	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₁₃×#135	—	2	2	no	—
66	C₁₃×#135	—	2	2	no	—
67	C₁₃×#135	—	2	2	no	—
68	C₁₃×#135	—	4	1	no	—
69	C₁₃×#135	—	4	1	no	—
70	C₁₃×#135	—	4	1	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	2	no	—
80	C₂×C₁₃×D₈	—	2	1	no	—
81	C₂×C₁₃×D₈	—	4	1	no	—
82	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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×#124	—	2	1	no	—
89	C₁₃×#123	—	4	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×#123	—	4	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	4	1	no	—
97	C₁₃×#121	—	4	1	no	—
98	C₁₃×#120	—	4	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×Q₃₂	—	2	2	no	—
105	C₁₃×Q₃₂	—	4	1	no	—
106	C₁₃×SD₃₂	—	2	2	no	—
107	C₁₃×SD₃₂	—	2	2	no	—
108	C₁₃×SD₃₂	—	2	2	no	—
109	C₁₃×SD₃₂	—	2	2	no	—
110	C₁₃×SD₃₂	—	4	1	no	—
111	C₁₃×D₁₆	—	2	2	no	—
112	C₁₃×D₁₆	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×#102	—	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	#33833	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	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	—	8	1	no	—
137	C₁₃×#41	—	8	1	no	—
138	C₁₃×#41	—	8	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×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	—	4	1	no	—
147	C₂×D₄×C₁₃	—	4	1	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	—	4	1	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	8	1	no	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×SD₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×D₈	—	2	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	C₁₃×D₈	C₂×D₄	1	2	yes	—
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	1	no	—
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	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	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
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×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3280	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2219	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2217	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2210	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	#2189	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2186	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2177	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	—	4	1	no	—
227	C₂³×C₁₃	—	8	2	no	—
228	C₂³×C₁₃	—	8	2	no	—
229	C₂³×C₁₃	—	16	1	no	—
230	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
231	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
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	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	2	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	2	no	—
249	D₄×C₁₃	—	16	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	—	2	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	—	8	2	no	—
263	C₂×C₄×C₁₃	—	16	1	no	—
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	C₂×D₈	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
278	#547	—	2	1	no	—
279	#546	—	2	1	no	—
280	#509	—	2	4	no	—
281	#508	—	2	4	no	—
282	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
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, complemented
289	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#495	C₂²×C₁₃	1	1	yes	characteristic
294	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	#467	C₂²×C₁₃	1	1	yes	characteristic
296	#467	C₂²×C₁₃	1	1	yes	characteristic
297	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	#466	C₂²×C₁₃	1	1	yes	characteristic
299	#463	—	2	1	no	—
300	#461	—	2	1	no	—
301	#452	—	2	1	no	—
302	#452	—	2	1	no	—
303	#450	—	2	1	no	—
304	#449	—	2	1	no	—
305	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	#367	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₄⋊C₁₆	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	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
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	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	—	8	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	16	4	no	—
335	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	D₄²	1	1	yes	characteristic
346	C₄×C₁₃	#576	1	1	yes	characteristic
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂²×D₄	—	2	1	no	—
351	#135	—	2	2	no	—
352	#135	—	2	2	no	—
353	#135	—	2	2	no	—
354	#135	—	4	1	no	—
355	#135	—	4	1	no	—
356	#135	—	4	1	no	—
357	C₂×Q₁₆	—	2	1	no	—
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×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	2	1	no	—
367	C₂×D₈	—	4	1	no	—
368	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	1	no	—
374	#124	—	2	1	no	—
375	#123	—	4	1	no	—
376	#123	—	4	1	no	—
377	#123	—	4	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	4	1	no	—
383	#121	—	4	1	no	—
384	#120	—	4	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	—	4	1	no	—
389	C₂×C₂²⋊C₄	—	4	1	no	—
390	Q₃₂	—	2	2	no	—
391	Q₃₂	—	4	1	no	—
392	SD₃₂	—	2	2	no	—
393	SD₃₂	—	2	2	no	—
394	SD₃₂	—	2	2	no	—
395	SD₃₂	—	2	2	no	—
396	SD₃₂	—	4	1	no	—
397	D₁₆	—	2	2	no	—
398	D₁₆	D₄×C₁₃	1	4	yes	complemented
399	M₃₂	—	2	2	no	—
400	C₂×C₁₆	—	2	2	no	—
401	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
405	#107	C₂³×C₁₃	1	1	yes	characteristic
406	#107	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
415	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₁₃	—	4	1	no	—
418	C₂×C₁₃	—	4	1	no	—
419	C₂×C₁₃	—	8	2	no	—
420	C₂×C₁₃	—	8	2	no	—
421	C₂×C₁₃	—	16	1	no	—
422	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
423	C₂×C₁₃	#3414	1	1	yes	characteristic
424	C₂×C₁₃	#3416	1	1	yes	characteristic
425	C₂⁴	—	4	1	no	—
426	#41	—	4	2	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	#41	—	8	1	no	—
430	#41	—	8	1	no	—
431	#41	—	8	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	8	1	no	—
445	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	Q₁₆	—	2	1	no	—
454	Q₁₆	—	2	1	no	—
455	Q₁₆	—	2	1	no	—
456	Q₁₆	—	2	1	no	—
457	Q₁₆	—	2	1	no	—
458	Q₁₆	—	2	1	no	—
459	Q₁₆	—	8	1	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	8	1	no	—
464	D₈	—	2	1	no	—
465	D₈	—	2	1	no	—
466	D₈	—	2	1	no	—
467	D₈	—	2	1	no	—
468	D₈	—	4	2	no	—
469	D₈	C₂×D₄×C₁₃	1	2	yes	—
470	D₈	C₂×D₄×C₁₃	1	2	yes	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
496	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₁₆	—	2	1	no	—
499	C₁₆	—	2	1	no	—
500	C₁₆	—	2	1	no	—
501	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
502	C₁₃	#33833	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	8	2	no	—
507	C₂³	—	8	2	no	—
508	C₂³	—	16	1	no	—
509	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
510	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	D₄	—	2	2	no	—
518	D₄	—	2	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	2	no	—
525	D₄	—	8	2	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	16	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	16	1	no	—
543	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
544	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
545	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
546	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	16	4	no	—
569	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	D₄²×C₁₃	1	1	yes	characteristic
580	C₄	C₁₃×#576	1	1	yes	characteristic
581	C₂	—	4	1	no	—
582	C₂	—	4	1	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	2	no	—
585	C₂	—	16	1	no	—
586	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
587	C₂	C₁₃×#3414	1	1	yes	characteristic
588	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
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×#509	C₂	semidirect
2. C₂×C₁₃×#508	C₂	semidirect
3. C₁₃×#3283	C₂	semidirect
4. C₁₃×#3280	C₂	semidirect
5. C₁₃×#2251	C₂	semidirect
6. C₁₃×#2219	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2210	C₂	semidirect
9. C₁₃×#2208	C₂	semidirect
10. C₁₃×#2189	C₂	semidirect
11. C₁₃×#2189	C₂	semidirect
12. C₁₃×#2187	C₂	semidirect
13. C₁₃×#2186	C₂	semidirect
14. C₁₃×#2177	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
24. C₂×C₁₃×Q₃₂	C₂²	semidirect
25. C₂×C₁₃×Q₃₂	C₂²	semidirect
30. C₂×C₁₃×SD₃₂	C₂²	semidirect
34. C₂²×C₁₃×C₁₆	C₂²	semidirect
36. C₁₃×#494	C₂²	semidirect
39. C₁₃×#467	C₂²	semidirect
48. C₄×C₁₃×D₈	C₂²	semidirect
50. C₁₃×#367	C₂²	semidirect
51. C₁₃×C₄⋊C₁₆	C₂²	semidirect
52. C₁₃×#358	C₂²	semidirect
53. C₁₃×#358	C₂²	semidirect
54. C₁₃×#358	C₂²	semidirect
57. C₁₃×#357	C₂²	semidirect
59. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
60. C₁₃×#346	C₂²	semidirect
112. C₁₃×D₁₆	D₄	semidirect
131. #33833	C₁₃	direct (N × H)
209. C₂×#509	C₂×C₁₃	semidirect
210. C₂×#508	C₂×C₁₃	semidirect
211. #3283	C₂×C₁₃	semidirect
212. #3280	C₂×C₁₃	semidirect
213. #2251	C₂×C₁₃	semidirect
214. #2219	C₂×C₁₃	semidirect
215. #2217	C₂×C₁₃	semidirect
216. #2210	C₂×C₁₃	semidirect
217. #2208	C₂×C₁₃	semidirect
218. #2189	C₂×C₁₃	semidirect
219. #2189	C₂×C₁₃	semidirect
220. #2187	C₂×C₁₃	semidirect
221. #2186	C₂×C₁₃	semidirect
222. #2177	C₂×C₁₃	semidirect
223. #2168	C₂×C₁₃	semidirect
276. C₂×#135	C₂²×C₁₃	semidirect
282. C₂×Q₃₂	C₂²×C₁₃	semidirect
283. C₂×Q₃₂	C₂²×C₁₃	semidirect
288. C₂×SD₃₂	C₂²×C₁₃	semidirect
292. C₂²×C₁₆	C₂²×C₁₃	semidirect
294. #494	C₂²×C₁₃	semidirect
297. #467	C₂²×C₁₃	semidirect
306. C₄×D₈	C₂²×C₁₃	semidirect
308. #367	C₂²×C₁₃	semidirect
309. C₄⋊C₁₆	C₂²×C₁₃	semidirect
310. #358	C₂²×C₁₃	semidirect
311. #358	C₂²×C₁₃	semidirect
312. #358	C₂²×C₁₃	semidirect
315. #357	C₂²×C₁₃	semidirect
317. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
318. #346	C₂²×C₁₃	semidirect
398. D₁₆	D₄×C₁₃	semidirect
502. C₁₃	#33833	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₁₃×#3283	2
C₁₃×#3280	2
C₁₃×#2251	2
C₁₃×#2219	2
C₁₃×#2217	2
C₁₃×#2210	2
C₁₃×#2208	2
C₁₃×#2189	2
C₁₃×#2187	2
C₁₃×#2186	2
C₁₃×#2177	2
C₁₃×#2168	2
#33833	13

Subgroups — C13×#33833 #15720172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33833 #15720172