Subgroups — C₁₃×#33830 #15720169

Order 3328.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 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	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2218	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×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2184	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, complemented
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#546	—	2	1	no	—
21	D₄²×C₁₃	—	2	1	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×D₁₆	—	2	4	no	—
27	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#466	C₂²	1	1	yes	characteristic
39	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#463	—	2	1	no	—
42	C₁₃×#459	—	2	1	no	—
43	C₁₃×#450	—	2	1	no	—
44	C₁₃×#449	—	2	1	no	—
45	C₁₃×#447	—	2	1	no	—
46	C₁₃×#447	—	2	1	no	—
47	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
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×#357	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
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×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	4	1	no	—
66	C₁₃×#135	—	2	2	no	—
67	C₁₃×#135	—	4	1	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂×C₁₃×D₈	—	2	2	no	—
73	C₂×C₁₃×D₈	—	2	2	no	—
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×D₈	—	2	1	no	—
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	4	1	no	—
79	C₂×C₁₃×D₈	—	4	1	no	—
80	C₂×C₁₃×D₈	—	4	1	no	—
81	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#127	—	2	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₁₃×#121	—	4	1	no	—
97	C₁₃×#120	—	4	1	no	—
98	C₁₃×#120	—	4	1	no	—
99	C₁₃×#120	—	4	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×SD₃₂	—	2	2	no	—
105	C₁₃×SD₃₂	—	2	2	no	—
106	C₁₃×SD₃₂	—	4	1	no	—
107	C₁₃×D₁₆	—	2	2	no	—
108	C₁₃×D₁₆	—	2	2	no	—
109	C₁₃×D₁₆	—	2	2	no	—
110	C₁₃×D₁₆	—	2	2	no	—
111	C₁₃×D₁₆	—	4	1	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×#102	—	2	1	no	—
124	C₁₃×#102	—	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	#33830	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	4	1	no	—
133	C₂⁴×C₁₃	—	4	1	no	—
134	C₂⁴×C₁₃	—	4	1	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	—	8	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	4	2	no	—
144	C₂×D₄×C₁₃	—	4	2	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	—	4	1	no	—
152	C₂×D₄×C₁₃	—	4	1	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	—	4	1	no	—
155	C₂×D₄×C₁₃	—	8	1	no	—
156	C₂×D₄×C₁₃	—	8	1	no	—
157	C₂×D₄×C₁₃	—	8	1	no	—
158	C₂×D₄×C₁₃	—	8	4	no	—
159	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₁₃×Q₁₆	—	2	1	no	—
166	C₁₃×Q₁₆	—	2	1	no	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×SD₁₆	—	8	1	no	—
169	C₁₃×D₈	—	2	1	no	—
170	C₁₃×D₈	—	2	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	—	2	1	no	—
176	C₁₃×D₈	—	2	1	no	—
177	C₁₃×D₈	—	4	2	no	—
178	C₁₃×D₈	—	4	2	no	—
179	C₁₃×D₈	—	4	2	no	—
180	C₁₃×D₈	—	8	1	no	—
181	C₁₃×D₈	C₂×D₄	1	2	yes	—
182	C₁₃×D₈	C₂×D₄	1	2	yes	complemented
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
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	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₁₆	—	2	1	no	—
207	C₁₃×C₁₆	—	2	1	no	—
208	C₁₃×C₁₆	—	2	1	no	—
209	C₁₃×C₁₆	C₂×D₄	1	2	yes	complemented
210	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3280	C₂×C₁₃	1	1	yes	characteristic, complemented
213	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2218	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2217	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2210	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2186	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2184	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2184	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2177	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2168	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	8	2	no	—
231	C₂³×C₁₃	—	8	2	no	—
232	C₂³×C₁₃	—	8	2	no	—
233	C₂³×C₁₃	—	8	2	no	—
234	C₂³×C₁₃	—	8	2	no	—
235	C₂³×C₁₃	—	8	2	no	—
236	C₂³×C₁₃	—	16	1	no	—
237	C₂³×C₁₃	—	16	1	no	—
238	C₂³×C₁₃	—	16	1	no	—
239	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
240	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	8	2	no	—
255	D₄×C₁₃	—	8	2	no	—
256	D₄×C₁₃	—	8	2	no	—
257	D₄×C₁₃	—	8	2	no	—
258	D₄×C₁₃	—	8	2	no	—
259	D₄×C₁₃	—	8	2	no	—
260	D₄×C₁₃	—	8	2	no	—
261	D₄×C₁₃	—	16	1	no	—
262	D₄×C₁₃	—	16	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	8	2	no	—
271	C₂×C₄×C₁₃	—	8	2	no	—
272	C₂×C₄×C₁₃	—	16	1	no	—
273	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
284	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#546	—	2	1	no	—
288	D₄²	—	2	1	no	—
289	#509	—	2	4	no	—
290	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	C₂×D₁₆	—	2	4	no	—
294	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
301	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	#466	C₂²×C₁₃	1	1	yes	characteristic
306	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#463	—	2	1	no	—
309	#459	—	2	1	no	—
310	#450	—	2	1	no	—
311	#449	—	2	1	no	—
312	#447	—	2	1	no	—
313	#447	—	2	1	no	—
314	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	#367	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
323	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	16	4	no	—
349	C₂²×C₁₃	—	16	4	no	—
350	C₂²×C₁₃	—	16	4	no	—
351	C₂²×C₁₃	#509	1	2	yes	complemented
352	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	—	8	1	no	—
360	C₄×C₁₃	D₄²	1	1	yes	characteristic
361	C₄×C₁₃	#576	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	4	1	no	—
367	#135	—	2	2	no	—
368	#135	—	4	1	no	—
369	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×D₈	—	2	2	no	—
373	C₂×D₈	—	2	2	no	—
374	C₂×D₈	—	2	2	no	—
375	C₂×D₈	—	2	1	no	—
376	C₂×D₈	—	2	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	4	1	no	—
380	C₂×D₈	—	4	1	no	—
381	C₂×D₈	—	4	1	no	—
382	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	#127	—	2	1	no	—
390	#124	—	2	1	no	—
391	#123	—	4	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	4	1	no	—
397	#121	—	4	1	no	—
398	#120	—	4	1	no	—
399	#120	—	4	1	no	—
400	#120	—	4	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	—	4	1	no	—
405	SD₃₂	—	2	2	no	—
406	SD₃₂	—	2	2	no	—
407	SD₃₂	—	4	1	no	—
408	D₁₆	—	2	2	no	—
409	D₁₆	—	2	2	no	—
410	D₁₆	—	2	2	no	—
411	D₁₆	—	2	2	no	—
412	D₁₆	—	4	1	no	—
413	D₁₆	D₄×C₁₃	1	4	yes	complemented
414	M₃₂	—	2	2	no	—
415	C₂×C₁₆	—	2	2	no	—
416	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
420	#107	C₂³×C₁₃	1	1	yes	characteristic
421	#107	C₂³×C₁₃	1	1	yes	characteristic
422	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
423	#103	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
430	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₁₃	—	2	2	no	—
433	C₂×C₁₃	—	4	1	no	—
434	C₂×C₁₃	—	8	2	no	—
435	C₂×C₁₃	—	8	2	no	—
436	C₂×C₁₃	—	16	1	no	—
437	C₂×C₁₃	—	16	1	no	—
438	C₂×C₁₃	—	16	1	no	—
439	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
440	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
441	C₂×C₁₃	#3415	1	1	yes	characteristic
442	C₂⁴	—	4	1	no	—
443	C₂⁴	—	4	1	no	—
444	C₂⁴	—	4	1	no	—
445	#41	—	4	2	no	—
446	#41	—	8	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	8	1	no	—
466	C₂×D₄	—	8	1	no	—
467	C₂×D₄	—	8	1	no	—
468	C₂×D₄	—	8	4	no	—
469	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	Q₁₆	—	2	1	no	—
476	Q₁₆	—	2	1	no	—
477	SD₁₆	—	4	2	no	—
478	SD₁₆	—	8	1	no	—
479	D₈	—	2	1	no	—
480	D₈	—	2	1	no	—
481	D₈	—	2	1	no	—
482	D₈	—	2	1	no	—
483	D₈	—	2	1	no	—
484	D₈	—	2	1	no	—
485	D₈	—	2	1	no	—
486	D₈	—	2	1	no	—
487	D₈	—	4	2	no	—
488	D₈	—	4	2	no	—
489	D₈	—	4	2	no	—
490	D₈	—	8	1	no	—
491	D₈	C₂×D₄×C₁₃	1	2	yes	—
492	D₈	C₂×D₄×C₁₃	1	2	yes	complemented
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
514	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₁₆	—	2	1	no	—
517	C₁₆	—	2	1	no	—
518	C₁₆	—	2	1	no	—
519	C₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
520	C₁₃	#33830	1	1	yes	characteristic, direct product factor, Sylow
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	8	2	no	—
527	C₂³	—	8	2	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	8	2	no	—
530	C₂³	—	8	2	no	—
531	C₂³	—	8	2	no	—
532	C₂³	—	16	1	no	—
533	C₂³	—	16	1	no	—
534	C₂³	—	16	1	no	—
535	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
536	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	2	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	—	8	2	no	—
557	D₄	—	16	1	no	—
558	D₄	—	16	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	—	16	1	no	—
569	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
570	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
571	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
572	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₈	—	2	1	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	16	4	no	—
600	C₂²	—	16	4	no	—
601	C₂²	—	16	4	no	—
602	C₂²	C₁₃×#509	1	2	yes	complemented
603	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	D₄²×C₁₃	1	1	yes	characteristic
612	C₄	C₁₃×#576	1	1	yes	characteristic
613	C₂	—	2	2	no	—
614	C₂	—	4	1	no	—
615	C₂	—	8	2	no	—
616	C₂	—	8	2	no	—
617	C₂	—	16	1	no	—
618	C₂	—	16	1	no	—
619	C₂	—	16	1	no	—
620	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
621	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
622	C₂	C₁₃×#3415	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. C₂²×C₁₃×D₁₆	C₂	semidirect
3. C₁₃×#3280	C₂	semidirect
4. D₄×C₁₃×D₈	C₂	semidirect
5. C₁₃×#2250	C₂	semidirect
6. C₁₃×#2218	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2210	C₂	semidirect
9. C₁₃×#2206	C₂	semidirect
10. C₁₃×#2187	C₂	semidirect
11. C₁₃×#2186	C₂	semidirect
12. C₁₃×#2184	C₂	semidirect
13. C₁₃×#2184	C₂	semidirect
14. C₁₃×#2177	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂×C₁₃×SD₃₂	C₂²	semidirect
24. C₂×C₁₃×SD₃₂	C₂²	semidirect
25. C₂×C₁₃×SD₃₂	C₂²	semidirect
29. C₂×C₁₃×D₁₆	C₂²	semidirect
30. C₂×C₁₃×D₁₆	C₂²	semidirect
31. C₂×C₁₃×D₁₆	C₂²	semidirect
32. C₂×C₁₃×D₁₆	C₂²	semidirect
33. C₂×C₁₃×M₃₂	C₂²	semidirect
34. C₂²×C₁₃×C₁₆	C₂²	semidirect
35. C₁₃×#495	C₂²	semidirect
36. C₁₃×#493	C₂²	semidirect
37. C₁₃×#467	C₂²	semidirect
39. C₁₃×#466	C₂²	semidirect
40. C₁₃×#466	C₂²	semidirect
47. C₄×C₁₃×D₈	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×#357	C₂²	semidirect
54. C₁₃×#357	C₂²	semidirect
55. C₁₃×#357	C₂²	semidirect
56. C₁₃×#357	C₂²	semidirect
57. C₁₃×#357	C₂²	semidirect
58. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
59. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
60. C₁₃×#346	C₂²	semidirect
112. C₁₃×D₁₆	D₄	semidirect
131. #33830	C₁₃	direct (N × H)
182. C₁₃×D₈	C₂×D₄	semidirect
209. C₁₃×C₁₆	C₂×D₄	semidirect
210. C₂×#509	C₂×C₁₃	semidirect
211. C₂²×D₁₆	C₂×C₁₃	semidirect
212. #3280	C₂×C₁₃	semidirect
213. D₄×D₈	C₂×C₁₃	semidirect
214. #2250	C₂×C₁₃	semidirect
215. #2218	C₂×C₁₃	semidirect
216. #2217	C₂×C₁₃	semidirect
217. #2210	C₂×C₁₃	semidirect
218. #2206	C₂×C₁₃	semidirect
219. #2187	C₂×C₁₃	semidirect
220. #2186	C₂×C₁₃	semidirect
221. #2184	C₂×C₁₃	semidirect
222. #2184	C₂×C₁₃	semidirect
223. #2177	C₂×C₁₃	semidirect
224. #2168	C₂×C₁₃	semidirect
283. C₂×#135	C₂²×C₁₃	semidirect
285. C₂²×D₈	C₂²×C₁₃	semidirect
286. C₂²×D₈	C₂²×C₁₃	semidirect
290. C₂×SD₃₂	C₂²×C₁₃	semidirect
291. C₂×SD₃₂	C₂²×C₁₃	semidirect
292. C₂×SD₃₂	C₂²×C₁₃	semidirect
296. C₂×D₁₆	C₂²×C₁₃	semidirect
297. C₂×D₁₆	C₂²×C₁₃	semidirect
298. C₂×D₁₆	C₂²×C₁₃	semidirect
299. C₂×D₁₆	C₂²×C₁₃	semidirect
300. C₂×M₃₂	C₂²×C₁₃	semidirect
301. C₂²×C₁₆	C₂²×C₁₃	semidirect
302. #495	C₂²×C₁₃	semidirect
303. #493	C₂²×C₁₃	semidirect
304. #467	C₂²×C₁₃	semidirect
306. #466	C₂²×C₁₃	semidirect
307. #466	C₂²×C₁₃	semidirect
314. C₄×D₈	C₂²×C₁₃	semidirect
315. C₄×D₈	C₂²×C₁₃	semidirect
317. #367	C₂²×C₁₃	semidirect
318. C₄⋊C₁₆	C₂²×C₁₃	semidirect
319. #358	C₂²×C₁₃	semidirect
320. #357	C₂²×C₁₃	semidirect
321. #357	C₂²×C₁₃	semidirect
322. #357	C₂²×C₁₃	semidirect
323. #357	C₂²×C₁₃	semidirect
324. #357	C₂²×C₁₃	semidirect
325. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
326. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
327. #346	C₂²×C₁₃	semidirect
351. C₂²×C₁₃	#509	semidirect
413. D₁₆	D₄×C₁₃	semidirect
492. D₈	C₂×D₄×C₁₃	semidirect
519. C₁₆	C₂×D₄×C₁₃	semidirect
520. C₁₃	#33830	direct (N × H)
602. C₂²	C₁₃×#509	semidirect

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
C₂²×C₁₃×D₁₆	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#2250	2
C₁₃×#2218	2
C₁₃×#2217	2
C₁₃×#2210	2
C₁₃×#2206	2
C₁₃×#2187	2
C₁₃×#2186	2
C₁₃×#2184	2
C₁₃×#2177	2
C₁₃×#2168	2
#33830	13

Subgroups — C13×#33830 #15720169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33830 #15720169