Subgroups — C₁₃×#61559 #15747898

Order 3328.

2854 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3294	C₂	1	8	yes	maximal, complemented
4	D₄×C₁₃×D₈	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3186	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#447	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₂³×D₄×C₁₃	—	2	1	no	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂²×C₁₃×D₈	C₂²	1	8	yes	complemented
14	C₁₃×#547	C₂²	1	4	yes	complemented
15	C₁₃×#546	—	2	4	no	—
16	D₄²×C₁₃	—	2	4	no	—
17	D₄²×C₁₃	C₂²	1	8	yes	complemented
18	D₄²×C₁₃	C₂²	1	4	yes	complemented
19	C₁₃×#537	—	2	1	no	—
20	C₁₃×#534	—	2	2	no	—
21	C₁₃×#532	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#120	—	2	2	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#493	C₂²	1	4	yes	complemented
30	C₁₃×#486	C₂²	1	4	yes	complemented
31	C₁₃×#480	C₂²	1	4	yes	complemented
32	C₁₃×#480	C₂²	1	8	yes	complemented
33	C₁₃×#474	C₂²	1	4	yes	complemented
34	C₁₃×#466	C₂²	1	16	yes	complemented
35	C₁₃×#459	C₂²	1	4	yes	complemented
36	C₁₃×#459	C₂²	1	8	yes	complemented
37	C₁₃×#447	C₂²	1	4	yes	complemented
38	C₁₃×#447	C₂²	1	8	yes	complemented
39	C₁₃×#447	C₂²	1	16	yes	complemented
40	C₁₃×#447	C₂²	1	8	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₂⁵×C₁₃	—	2	2	no	—
47	C₁₃×H(5,𝔽₂)	—	4	8	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	—	4	8	no	—
59	C₂²×D₄×C₁₃	—	4	8	no	—
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂×C₁₃×D₈	—	4	16	no	—
68	C₂×C₁₃×D₈	C₂³	1	8	yes	—
69	C₂×C₁₃×D₈	C₂³	1	16	yes	complemented
70	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
71	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
72	C₁₃×#127	—	2	2	no	—
73	C₁₃×#127	C₂³	1	4	yes	—
74	C₁₃×#127	C₂³	1	2	yes	complemented
75	C₁₃×#124	—	2	2	no	—
76	C₁₃×#123	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	4	no	—
84	C₁₃×#121	C₂³	1	4	yes	—
85	C₁₃×#121	C₂³	1	8	yes	—
86	C₁₃×#121	C₂³	1	8	yes	complemented
87	C₁₃×#120	—	2	16	no	—
88	C₁₃×#120	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	D₄	1	4	yes	—
92	C₄×D₄×C₁₃	C₂³	1	4	yes	—
93	C₄×D₄×C₁₃	C₂³	1	4	yes	—
94	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
95	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
101	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	C₂³	1	8	yes	complemented
104	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	16	yes	complemented
107	C₁₃×#102	C₂³	1	8	yes	complemented
108	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
110	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
111	#61559	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	1	no	—
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	4	8	no	—
117	C₂⁴×C₁₃	—	4	8	no	—
118	C₂⁴×C₁₃	—	8	4	no	—
119	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
120	C₁₃×#41	—	4	16	no	—
121	C₁₃×#41	—	4	8	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	16	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	4	8	no	—
137	C₂×D₄×C₁₃	—	4	4	no	—
138	C₂×D₄×C₁₃	—	4	8	no	—
139	C₂×D₄×C₁₃	—	4	16	no	—
140	C₂×D₄×C₁₃	—	4	8	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	—	4	16	no	—
143	C₂×D₄×C₁₃	—	4	32	no	—
144	C₂×D₄×C₁₃	—	4	16	no	—
145	C₂×D₄×C₁₃	—	4	4	no	—
146	C₂×D₄×C₁₃	—	8	2	no	—
147	C₂×D₄×C₁₃	D₈	1	8	yes	complemented
148	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
149	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₁₃×D₈	—	2	16	no	—
165	C₁₃×D₈	—	4	16	no	—
166	C₂×C₈×C₁₃	—	4	8	no	—
167	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	4	no	—
179	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	C₄²×C₁₃	C₂⁴	1	2	yes	—
182	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#3294	C₂×C₁₃	1	8	yes	complemented
185	D₄×D₈	C₂×C₁₃	1	8	yes	complemented
186	#3205	C₂×C₁₃	1	2	yes	complemented
187	#3186	C₂×C₁₃	1	4	yes	complemented
188	#3100	C₂×C₁₃	1	2	yes	complemented
189	C₂×#447	C₂×C₁₃	1	4	yes	complemented
190	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	16	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	16	no	—
203	C₂³×C₁₃	—	4	4	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	—	8	8	no	—
206	C₂³×C₁₃	—	8	4	no	—
207	C₂³×C₁₃	—	8	4	no	—
208	C₂³×C₁₃	—	8	32	no	—
209	C₂³×C₁₃	C₂×D₈	1	8	yes	complemented
210	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	4	4	no	—
213	D₄×C₁₃	—	2	4	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	8	no	—
216	D₄×C₁₃	—	2	8	no	—
217	D₄×C₁₃	—	4	16	no	—
218	D₄×C₁₃	—	4	4	no	—
219	D₄×C₁₃	—	4	16	no	—
220	D₄×C₁₃	—	4	8	no	—
221	D₄×C₁₃	—	4	16	no	—
222	D₄×C₁₃	—	4	8	no	—
223	D₄×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	8	2	no	—
225	D₄×C₁₃	—	8	4	no	—
226	D₄×C₁₃	—	8	4	no	—
227	D₄×C₁₃	C₂×D₈	1	16	yes	complemented
228	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	8	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	complemented
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
246	C₈×C₁₃	—	2	8	no	—
247	C₂×H(5,𝔽₂)	—	2	1	no	—
248	C₂³×D₄	—	2	1	no	—
249	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
250	C₂²×D₈	C₂²×C₁₃	1	8	yes	complemented
251	#547	C₂²×C₁₃	1	4	yes	complemented
252	#546	—	2	4	no	—
253	D₄²	—	2	4	no	—
254	D₄²	C₂²×C₁₃	1	8	yes	complemented
255	D₄²	C₂²×C₁₃	1	4	yes	complemented
256	#537	—	2	1	no	—
257	#534	—	2	2	no	—
258	#532	C₂²×C₁₃	1	2	yes	complemented
259	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#121	—	2	1	no	—
261	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
262	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
263	C₂×#120	—	2	2	no	—
264	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#493	C₂²×C₁₃	1	4	yes	complemented
267	#486	C₂²×C₁₃	1	4	yes	complemented
268	#480	C₂²×C₁₃	1	4	yes	complemented
269	#480	C₂²×C₁₃	1	8	yes	complemented
270	#474	C₂²×C₁₃	1	4	yes	complemented
271	#466	C₂²×C₁₃	1	16	yes	complemented
272	#459	C₂²×C₁₃	1	4	yes	complemented
273	#459	C₂²×C₁₃	1	8	yes	complemented
274	#447	C₂²×C₁₃	1	4	yes	complemented
275	#447	C₂²×C₁₃	1	8	yes	complemented
276	#447	C₂²×C₁₃	1	16	yes	complemented
277	#447	C₂²×C₁₃	1	8	yes	complemented
278	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
279	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
280	#431	C₂²×C₁₃	1	2	yes	complemented
281	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
282	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	4	no	—
288	C₂²×C₁₃	—	4	8	no	—
289	C₂²×C₁₃	—	4	8	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	4	4	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	4	no	—
297	C₂²×C₁₃	—	4	4	no	—
298	C₂²×C₁₃	—	8	32	no	—
299	C₂²×C₁₃	—	8	8	no	—
300	C₂²×C₁₃	—	16	8	no	—
301	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
302	C₂²×C₁₃	C₂²×D₈	1	8	yes	—
303	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	4	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	C₂²×D₈	1	4	yes	—
310	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
311	C₂⁵	—	2	2	no	—
312	H(5,𝔽₂)	—	4	8	no	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	4	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	4	8	no	—
324	C₂²×D₄	—	4	8	no	—
325	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
328	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
332	C₂×D₈	—	4	16	no	—
333	C₂×D₈	C₂³×C₁₃	1	8	yes	—
334	C₂×D₈	C₂³×C₁₃	1	16	yes	complemented
335	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
336	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
337	#127	—	2	2	no	—
338	#127	C₂³×C₁₃	1	4	yes	—
339	#127	C₂³×C₁₃	1	2	yes	complemented
340	#124	—	2	2	no	—
341	#123	—	2	8	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	#121	—	2	4	no	—
344	#121	—	2	4	no	—
345	#121	—	2	4	no	—
346	#121	—	2	2	no	—
347	#121	—	2	8	no	—
348	#121	—	2	4	no	—
349	#121	C₂³×C₁₃	1	4	yes	—
350	#121	C₂³×C₁₃	1	8	yes	—
351	#121	C₂³×C₁₃	1	8	yes	complemented
352	#120	—	2	16	no	—
353	#120	—	2	8	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	D₄×C₁₃	1	4	yes	—
357	C₄×D₄	C₂³×C₁₃	1	4	yes	—
358	C₄×D₄	C₂³×C₁₃	1	4	yes	—
359	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
360	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
368	#107	C₂³×C₁₃	1	8	yes	complemented
369	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
370	#102	C₂³×C₁₃	1	8	yes	—
371	#102	C₂³×C₁₃	1	16	yes	complemented
372	#102	C₂³×C₁₃	1	8	yes	complemented
373	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
374	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
375	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
376	C₂×C₁₃	—	2	2	no	—
377	C₂×C₁₃	—	2	8	no	—
378	C₂×C₁₃	—	4	4	no	—
379	C₂×C₁₃	—	8	4	no	—
380	C₂×C₁₃	—	8	4	no	—
381	C₂×C₁₃	#3484	1	1	yes	characteristic
382	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
383	C₂×C₁₃	#3585	1	1	yes	characteristic
384	C₂⁴	—	2	1	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	8	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	4	8	no	—
389	C₂⁴	—	4	8	no	—
390	C₂⁴	—	8	4	no	—
391	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
392	#41	—	4	16	no	—
393	#41	—	4	8	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	16	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	—	4	16	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	8	no	—
414	C₂×D₄	—	4	16	no	—
415	C₂×D₄	—	4	32	no	—
416	C₂×D₄	—	4	16	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	C₁₃×D₈	1	8	yes	complemented
420	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
421	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
422	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
436	D₈	—	2	16	no	—
437	D₈	—	4	16	no	—
438	C₂×C₈	—	4	8	no	—
439	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₄²	C₂⁴×C₁₃	1	2	yes	—
454	C₁₃	#61559	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	16	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	8	no	—
469	C₂³	—	8	8	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	32	no	—
473	C₂³	C₂×C₁₃×D₈	1	8	yes	complemented
474	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	Q₈	—	4	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	8	no	—
480	D₄	—	2	8	no	—
481	D₄	—	4	16	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	16	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	4	no	—
488	D₄	—	8	4	no	—
489	D₄	—	8	4	no	—
490	D₄	—	8	2	no	—
491	D₄	C₂×C₁₃×D₈	1	16	yes	complemented
492	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	complemented
505	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
509	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
510	C₈	—	2	8	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	4	8	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	8	32	no	—
527	C₂²	—	8	8	no	—
528	C₂²	—	16	8	no	—
529	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
530	C₂²	C₂²×C₁₃×D₈	1	8	yes	—
531	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	4	no	—
537	C₄	C₂²×C₁₃×D₈	1	4	yes	—
538	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
539	C₂	—	2	2	no	—
540	C₂	—	2	8	no	—
541	C₂	—	4	4	no	—
542	C₂	—	8	4	no	—
543	C₂	—	8	4	no	—
544	C₂	C₁₃×#3484	1	1	yes	characteristic
545	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
546	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. C₂×D₄²×C₁₃	C₂	semidirect
3. C₁₃×#3294	C₂	semidirect
4. D₄×C₁₃×D₈	C₂	semidirect
5. C₁₃×#3205	C₂	semidirect
6. C₁₃×#3186	C₂	semidirect
7. C₁₃×#3100	C₂	semidirect
8. C₂×C₁₃×#447	C₂	semidirect
9. C₁₃×#2972	C₂	semidirect
12. C₂³×D₄×C₁₃	C₂²	semidirect
13. C₂²×C₁₃×D₈	C₂²	semidirect
14. C₁₃×#547	C₂²	semidirect
17. D₄²×C₁₃	C₂²	semidirect
18. D₄²×C₁₃	C₂²	semidirect
21. C₁₃×#532	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₁₃×#493	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
31. C₁₃×#480	C₂²	semidirect
32. C₁₃×#480	C₂²	semidirect
33. C₁₃×#474	C₂²	semidirect
34. C₁₃×#466	C₂²	semidirect
35. C₁₃×#459	C₂²	semidirect
36. C₁₃×#459	C₂²	semidirect
37. C₁₃×#447	C₂²	semidirect
38. C₁₃×#447	C₂²	semidirect
39. C₁₃×#447	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₈×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
64. C₂²×D₄×C₁₃	C₂³	semidirect
69. C₂×C₁₃×D₈	C₂³	semidirect
70. C₂²×C₈×C₁₃	C₂³	semidirect
71. C₁₃×C₄⋊Q₈	C₂³	semidirect
74. C₁₃×#127	C₂³	semidirect
86. C₁₃×#121	C₂³	semidirect
94. C₄×D₄×C₁₃	C₂³	semidirect
97. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
103. C₁₃×#107	C₂³	semidirect
104. C₁₃×C₄⋊C₈	C₂³	semidirect
106. C₁₃×#102	C₂³	semidirect
107. C₁₃×#102	C₂³	semidirect
109. C₁₃×C₂²⋊C₈	C₂³	semidirect
110. C₄×C₈×C₁₃	C₂³	semidirect
111. #61559	C₁₃	direct (N × H)
147. C₂×D₄×C₁₃	D₈	semidirect
182. #3496	C₂×C₁₃	semidirect
183. C₂×D₄²	C₂×C₁₃	semidirect
184. #3294	C₂×C₁₃	semidirect
185. D₄×D₈	C₂×C₁₃	semidirect
186. #3205	C₂×C₁₃	semidirect
187. #3186	C₂×C₁₃	semidirect
188. #3100	C₂×C₁₃	semidirect
189. C₂×#447	C₂×C₁₃	semidirect
190. #2972	C₂×C₁₃	semidirect
209. C₂³×C₁₃	C₂×D₈	semidirect
227. D₄×C₁₃	C₂×D₈	semidirect
228. D₄×C₁₃	H(5,𝔽₂)	semidirect
240. C₂×C₄×C₁₃	C₂×D₈	semidirect
249. C₂³×D₄	C₂²×C₁₃	semidirect
250. C₂²×D₈	C₂²×C₁₃	semidirect
251. #547	C₂²×C₁₃	semidirect
254. D₄²	C₂²×C₁₃	semidirect
255. D₄²	C₂²×C₁₃	semidirect
258. #532	C₂²×C₁₃	semidirect
259. C₂×#127	C₂²×C₁₃	semidirect
261. C₂×#121	C₂²×C₁₃	semidirect
262. C₂×#121	C₂²×C₁₃	semidirect
265. C₂×C₄×D₄	C₂²×C₁₃	semidirect
266. #493	C₂²×C₁₃	semidirect
267. #486	C₂²×C₁₃	semidirect
268. #480	C₂²×C₁₃	semidirect
269. #480	C₂²×C₁₃	semidirect
270. #474	C₂²×C₁₃	semidirect
271. #466	C₂²×C₁₃	semidirect
272. #459	C₂²×C₁₃	semidirect
273. #459	C₂²×C₁₃	semidirect
274. #447	C₂²×C₁₃	semidirect
275. #447	C₂²×C₁₃	semidirect
276. #447	C₂²×C₁₃	semidirect
277. #447	C₂²×C₁₃	semidirect
278. C₄×D₈	C₂²×C₁₃	semidirect
279. C₈×D₄	C₂²×C₁₃	semidirect
280. #431	C₂²×C₁₃	semidirect
281. C₂×#102	C₂²×C₁₃	semidirect
282. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
329. C₂²×D₄	C₂³×C₁₃	semidirect
334. C₂×D₈	C₂³×C₁₃	semidirect
335. C₂²×C₈	C₂³×C₁₃	semidirect
336. C₄⋊Q₈	C₂³×C₁₃	semidirect
339. #127	C₂³×C₁₃	semidirect
351. #121	C₂³×C₁₃	semidirect
359. C₄×D₄	C₂³×C₁₃	semidirect
362. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
368. #107	C₂³×C₁₃	semidirect
369. C₄⋊C₈	C₂³×C₁₃	semidirect
371. #102	C₂³×C₁₃	semidirect
372. #102	C₂³×C₁₃	semidirect
374. C₂²⋊C₈	C₂³×C₁₃	semidirect
375. C₄×C₈	C₂³×C₁₃	semidirect
419. C₂×D₄	C₁₃×D₈	semidirect
454. C₁₃	#61559	direct (N × H)
473. C₂³	C₂×C₁₃×D₈	semidirect
491. D₄	C₂×C₁₃×D₈	semidirect
492. D₄	C₁₃×H(5,𝔽₂)	semidirect
504. C₂×C₄	C₂×C₁₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3496	2
C₂×D₄²×C₁₃	2
C₁₃×#3294	2
D₄×C₁₃×D₈	2
C₁₃×#3205	2
C₁₃×#3186	2
C₁₃×#3100	2
C₂×C₁₃×#447	2
C₁₃×#2972	2
#61559	13

Subgroups — C13×#61559 #15747898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61559 #15747898