Subgroups — C₁₃×#22452 #15708791

Order 3328.

1368 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#444	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2880	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1975	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1876	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1789	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	2	yes	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₃×#135	C₄	1	2	yes	complemented
13	C₂×C₁₃×#135	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₃×#135	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×SD₁₆	C₄	1	2	yes	complemented
19	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#131	C₂²	1	4	yes	complemented
21	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#444	—	2	8	no	—
23	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
26	C₁₃×#408	—	2	4	no	—
27	C₁₃×#408	C₂²	1	4	yes	complemented
28	C₁₃×#407	—	2	2	no	—
29	C₁₃×#407	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
33	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#341	C₂²	1	2	yes	complemented
35	C₁₃×#336	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	2	8	no	—
39	C₂×C₁₃×#41	—	4	4	no	—
40	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#135	—	2	8	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	8	no	—
52	C₁₃×#135	—	2	4	no	—
53	C₁₃×#135	—	2	4	no	—
54	C₁₃×#135	D₄	1	8	yes	—
55	C₂×C₁₃×Q₁₆	—	2	4	no	—
56	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×SD₁₆	—	2	8	no	—
60	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×D₈	—	2	4	no	—
65	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
68	C₁₃×#131	—	2	8	no	—
69	C₁₃×#131	—	4	4	no	—
70	C₂×C₁₃×M₁₆	—	2	4	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₃	—	2	4	no	—
73	C₂²×C₈×C₁₃	—	2	4	no	—
74	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#108	—	2	4	no	—
84	C₁₃×#104	—	2	8	no	—
85	C₁₃×#104	—	4	4	no	—
86	C₁₃×C₂²⋊C₈	—	2	2	no	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₃×#97	—	2	4	no	—
93	C₁₃×#95	—	2	1	no	—
94	#22452	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	4	no	—
100	C₁₃×#41	—	2	4	no	—
101	C₁₃×#41	—	2	4	no	—
102	C₁₃×#41	—	4	8	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	8	no	—
106	C₁₃×#41	C₂×D₄	1	8	yes	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	4	2	no	—
110	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	4	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	8	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	4	8	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	2	4	no	—
138	C₁₃×Q₁₆	—	2	2	no	—
139	C₁₃×Q₁₆	C₂²⋊C₄	1	4	yes	complemented
140	C₁₃×SD₁₆	—	2	4	no	—
141	C₁₃×SD₁₆	—	2	4	no	—
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×SD₁₆	C₂²⋊C₄	1	8	yes	complemented
144	C₁₃×D₈	—	2	4	no	—
145	C₁₃×D₈	—	2	2	no	—
146	C₁₃×D₈	C₂²⋊C₄	1	4	yes	complemented
147	C₁₃×M₁₆	—	2	4	no	—
148	C₁₃×M₁₆	—	2	4	no	—
149	C₁₃×M₁₆	—	4	8	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	4	no	—
158	C₂×C₈×C₁₃	—	4	8	no	—
159	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
164	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic
169	C₂×#444	C₂×C₁₃	1	2	yes	complemented
170	#2880	C₂×C₁₃	1	2	yes	complemented
171	#1975	C₂×C₁₃	1	2	yes	complemented
172	#1876	C₂×C₁₃	1	4	yes	complemented
173	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1789	C₂×C₁₃	1	2	yes	complemented
175	#1752	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	4	no	—
182	C₂³×C₁₃	—	4	4	no	—
183	C₂³×C₁₃	—	8	2	no	—
184	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
192	D₄×C₁₃	—	2	8	no	—
193	D₄×C₁₃	—	2	2	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	4	4	no	—
197	D₄×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	4	4	no	—
200	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	—	2	4	no	—
227	C₈×C₁₃	—	4	4	no	—
228	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
229	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂²×#41	C₂²×C₁₃	1	2	yes	—
231	C₂×#135	—	2	8	no	—
232	C₂×#135	C₄×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#135	C₄×C₁₃	1	2	yes	complemented
234	C₂×#135	C₄×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#135	C₂²×C₁₃	1	2	yes	—
236	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×Q₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
239	C₂²×SD₁₆	C₄×C₁₃	1	2	yes	complemented
240	C₂²×D₈	C₄×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#131	C₂²×C₁₃	1	4	yes	complemented
242	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
243	#444	—	2	8	no	—
244	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
245	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
246	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
247	#408	—	2	4	no	—
248	#408	C₂²×C₁₃	1	4	yes	complemented
249	#407	—	2	2	no	—
250	#407	C₂²×C₁₃	1	2	yes	—
251	C₂×C₂²⋊C₈	—	2	2	no	—
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
254	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	#341	C₂²×C₁₃	1	2	yes	complemented
256	#336	C₂²×C₁₃	1	2	yes	complemented
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	8	8	no	—
272	C₂²×C₁₃	#444	1	2	yes	complemented
273	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₁₃	#546	1	2	yes	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₄×C₁₃	#518	1	1	yes	characteristic
282	C₄×C₁₃	D₄²	1	2	yes	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	8	no	—
286	C₂×#41	—	4	4	no	—
287	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
288	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
289	C₂×#41	C₂³×C₁₃	1	2	yes	—
290	C₂×#41	C₂³×C₁₃	1	2	yes	—
291	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	#135	—	2	8	no	—
297	#135	—	2	4	no	—
298	#135	—	2	8	no	—
299	#135	—	2	4	no	—
300	#135	—	2	4	no	—
301	#135	D₄×C₁₃	1	8	yes	—
302	C₂×Q₁₆	—	2	4	no	—
303	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
304	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₂×SD₁₆	—	2	8	no	—
307	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
308	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
309	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
310	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
313	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
314	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
315	#131	—	2	8	no	—
316	#131	—	4	4	no	—
317	C₂×M₁₆	—	2	4	no	—
318	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
319	C₂²×C₈	—	2	4	no	—
320	C₂²×C₈	—	2	4	no	—
321	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
330	#108	—	2	4	no	—
331	#104	—	2	8	no	—
332	#104	—	4	4	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	4	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
338	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
339	#97	—	2	4	no	—
340	#95	—	2	1	no	—
341	C₂×C₁₃	—	2	2	no	—
342	C₂×C₁₃	—	2	2	no	—
343	C₂×C₁₃	—	4	1	no	—
344	C₂×C₁₃	—	4	4	no	—
345	C₂×C₁₃	—	8	2	no	—
346	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
348	C₂×C₁₃	#2957	1	1	yes	characteristic
349	C₂⁴	—	2	2	no	—
350	C₂⁴	C₁₃×#41	1	1	yes	characteristic
351	#41	—	2	4	no	—
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	2	4	no	—
355	#41	—	2	4	no	—
356	#41	—	4	8	no	—
357	#41	—	4	2	no	—
358	#41	—	4	2	no	—
359	#41	—	4	8	no	—
360	#41	C₂×D₄×C₁₃	1	8	yes	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
365	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
375	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
391	Q₁₆	—	2	4	no	—
392	Q₁₆	—	2	2	no	—
393	Q₁₆	C₁₃×C₂²⋊C₄	1	4	yes	complemented
394	SD₁₆	—	2	4	no	—
395	SD₁₆	—	2	4	no	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	C₁₃×C₂²⋊C₄	1	8	yes	complemented
398	D₈	—	2	4	no	—
399	D₈	—	2	2	no	—
400	D₈	C₁₃×C₂²⋊C₄	1	4	yes	complemented
401	M₁₆	—	2	4	no	—
402	M₁₆	—	2	4	no	—
403	M₁₆	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	—	4	8	no	—
413	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
414	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
415	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
416	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
417	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
418	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₁₃	#22452	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	2	no	—
431	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
432	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
433	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
434	Q₈	—	2	2	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	4	4	no	—
438	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
439	D₄	—	2	8	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	4	no	—
474	C₈	—	4	4	no	—
475	C₈	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
476	C₈	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	8	no	—
492	C₂²	C₁₃×#444	1	2	yes	complemented
493	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
494	C₂²	C₁₃×#546	1	2	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	2	no	—
500	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
501	C₄	C₁₃×#518	1	1	yes	characteristic
502	C₄	D₄²×C₁₃	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	4	1	no	—
506	C₂	—	4	4	no	—
507	C₂	—	8	2	no	—
508	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
509	C₂	C₂×C₁₃×#444	1	1	yes	characteristic
510	C₂	C₁₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#444	C₂	semidirect
3. C₁₃×#2880	C₂	semidirect
4. C₁₃×#1975	C₂	semidirect
5. C₁₃×#1876	C₂	semidirect
6. C₁₃×#1810	C₂	semidirect
7. C₁₃×#1789	C₂	semidirect
8. C₁₃×#1752	C₂	semidirect
11. C₂×C₁₃×#135	C₄	semidirect
12. C₂×C₁₃×#135	C₄	semidirect
13. C₂×C₁₃×#135	C₄	semidirect
17. C₂²×C₁₃×Q₁₆	C₄	semidirect
18. C₂²×C₁₃×SD₁₆	C₄	semidirect
19. C₂²×C₁₃×D₈	C₄	semidirect
20. C₂×C₁₃×#131	C₂²	semidirect
23. C₂×C₁₃×#108	C₂²	semidirect
24. C₂×C₁₃×#104	C₂²	semidirect
25. C₂×C₁₃×#104	C₂²	semidirect
27. C₁₃×#408	C₂²	semidirect
32. C₂×C₁₃×#97	C₂²	semidirect
34. C₁₃×#341	C₂²	semidirect
35. C₁₃×#336	C₂²	semidirect
94. #22452	C₁₃	direct (N × H)
139. C₁₃×Q₁₆	C₂²⋊C₄	semidirect
143. C₁₃×SD₁₆	C₂²⋊C₄	semidirect
146. C₁₃×D₈	C₂²⋊C₄	semidirect
169. C₂×#444	C₂×C₁₃	semidirect
170. #2880	C₂×C₁₃	semidirect
171. #1975	C₂×C₁₃	semidirect
172. #1876	C₂×C₁₃	semidirect
173. #1810	C₂×C₁₃	semidirect
174. #1789	C₂×C₁₃	semidirect
175. #1752	C₂×C₁₃	semidirect
232. C₂×#135	C₄×C₁₃	semidirect
233. C₂×#135	C₄×C₁₃	semidirect
234. C₂×#135	C₄×C₁₃	semidirect
238. C₂²×Q₁₆	C₄×C₁₃	semidirect
239. C₂²×SD₁₆	C₄×C₁₃	semidirect
240. C₂²×D₈	C₄×C₁₃	semidirect
241. C₂×#131	C₂²×C₁₃	semidirect
244. C₂×#108	C₂²×C₁₃	semidirect
245. C₂×#104	C₂²×C₁₃	semidirect
246. C₂×#104	C₂²×C₁₃	semidirect
248. #408	C₂²×C₁₃	semidirect
253. C₂×#97	C₂²×C₁₃	semidirect
255. #341	C₂²×C₁₃	semidirect
256. #336	C₂²×C₁₃	semidirect
272. C₂²×C₁₃	#444	semidirect
393. Q₁₆	C₁₃×C₂²⋊C₄	semidirect
397. SD₁₆	C₁₃×C₂²⋊C₄	semidirect
400. D₈	C₁₃×C₂²⋊C₄	semidirect
422. C₁₃	#22452	direct (N × H)
492. C₂²	C₁₃×#444	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#444	2
C₁₃×#2880	2
C₁₃×#1975	2
C₁₃×#1876	2
C₁₃×#1810	2
C₁₃×#1789	2
C₁₃×#1752	2
#22452	13

Subgroups — C13×#22452 #15708791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22452 #15708791