Subgroups — C₁₃×#61566 #15747905

Order 3328.

2194 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3305	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3304	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3287	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3284	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3188	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3002	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#556	C₂²	1	2	yes	complemented
18	C₁₃×#555	C₂²	1	2	yes	complemented
19	C₁₃×#553	—	2	2	no	—
20	C₁₃×#550	—	2	2	no	—
21	C₁₃×#550	—	2	2	no	—
22	C₁₃×#550	C₂²	1	4	yes	—
23	C₁₃×#550	C₂²	1	4	yes	—
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#547	C₂²	1	2	yes	complemented
26	C₁₃×#538	—	2	2	no	—
27	C₁₃×#535	—	2	1	no	—
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#127	—	2	1	no	—
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#525	C₂²	1	4	yes	—
33	C₂×C₁₃×#121	—	2	2	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₁₃×#520	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#493	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#486	C₂²	1	2	yes	complemented
43	C₁₃×#484	C₂²	1	2	yes	—
44	C₁₃×#482	C₂²	1	8	yes	complemented
45	C₁₃×#481	C₂²	1	2	yes	—
46	C₁₃×#477	C₂²	1	2	yes	complemented
47	C₁₃×#475	C₂²	1	2	yes	complemented
48	C₁₃×#466	C₂²	1	8	yes	complemented
49	C₁₃×#465	C₂²	1	8	yes	complemented
50	C₁₃×#462	C₂²	1	2	yes	complemented
51	C₁₃×#460	C₂²	1	2	yes	complemented
52	C₁₃×#460	C₂²	1	4	yes	complemented
53	C₁₃×#459	C₂²	1	4	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#451	C₂²	1	2	yes	—
56	C₁₃×#450	C₂²	1	4	yes	—
57	C₁₃×#449	C₂²	1	8	yes	complemented
58	C₁₃×#449	C₂²	1	8	yes	complemented
59	C₁₃×#448	C₂²	1	2	yes	—
60	C₁₃×#447	C₂²	1	4	yes	—
61	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
62	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
64	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
65	C₁₃×#431	C₂²	1	1	yes	characteristic
66	C₁₃×#431	C₂²	1	1	yes	characteristic
67	C₁₃×#416	C₂²	1	8	yes	complemented
68	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	—	2	4	no	—
71	C₂×C₁₃×#41	—	4	8	no	—
72	C₂×C₁₃×#41	C₂³	1	8	yes	—
73	C₂×C₁₃×#41	C₂³	1	4	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	2	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	—	2	2	no	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#135	—	4	16	no	—
84	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
87	C₂×C₁₃×D₈	C₂³	1	8	yes	—
88	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₃×#127	—	2	4	no	—
93	C₁₃×#127	—	2	4	no	—
94	C₁₃×#127	—	2	2	no	—
95	C₁₃×#127	—	2	1	no	—
96	C₁₃×#127	—	2	1	no	—
97	C₁₃×#127	C₂³	1	2	yes	—
98	C₁₃×#127	C₂³	1	2	yes	—
99	C₁₃×#127	C₂³	1	1	yes	characteristic
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#125	—	2	1	no	—
102	C₁₃×#124	—	2	2	no	—
103	C₁₃×#124	—	2	4	no	—
104	C₁₃×#124	—	2	1	no	—
105	C₁₃×#123	—	2	4	no	—
106	C₁₃×#123	—	2	4	no	—
107	C₁₃×C₂²⋊Q₈	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	4	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	8	no	—
115	C₁₃×#121	—	2	8	no	—
116	C₁₃×#121	—	2	4	no	—
117	C₁₃×#121	C₂³	1	2	yes	—
118	C₁₃×#121	C₂³	1	4	yes	—
119	C₁₃×#121	C₂³	1	8	yes	—
120	C₁₃×#120	—	2	4	no	—
121	C₄×Q₈×C₁₃	—	2	2	no	—
122	C₄×Q₈×C₁₃	—	2	1	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	4	no	—
130	C₄×D₄×C₁₃	—	2	4	no	—
131	C₄×D₄×C₁₃	—	2	4	no	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	D₄	1	2	yes	—
135	C₄×D₄×C₁₃	D₄	1	2	yes	—
136	C₄×D₄×C₁₃	C₂³	1	2	yes	—
137	C₄×D₄×C₁₃	C₂³	1	2	yes	—
138	C₄×D₄×C₁₃	C₂³	1	2	yes	—
139	C₁₃×#117	—	2	1	no	—
140	C₁₃×#117	—	2	2	no	—
141	C₁₃×#117	C₂³	1	4	yes	—
142	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
148	C₂×C₄²×C₁₃	—	2	1	no	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₁₃×#107	C₂³	1	4	yes	—
151	C₁₃×#106	C₂³	1	4	yes	—
152	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	4	yes	—
156	C₁₃×#103	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	8	yes	—
158	C₁₃×#102	C₂³	1	8	yes	—
159	C₁₃×#102	C₂³	1	4	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
163	C₄×C₈×C₁₃	C₂³	1	2	yes	—
164	C₄×C₈×C₁₃	C₂³	1	2	yes	—
165	#61566	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
168	C₁₃×#41	—	2	16	no	—
169	C₁₃×#41	—	4	8	no	—
170	C₁₃×#41	—	4	8	no	—
171	C₁₃×#41	—	4	16	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₂×Q₈×C₁₃	—	2	4	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	8	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	8	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	2	2	no	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	8	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	8	2	no	—
196	C₂×D₄×C₁₃	—	8	4	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	8	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	—	4	8	no	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
214	C₁₃×Q₁₆	—	2	8	no	—
215	C₁₃×SD₁₆	—	2	8	no	—
216	C₁₃×SD₁₆	—	4	8	no	—
217	C₁₃×D₈	—	4	8	no	—
218	C₂×C₈×C₁₃	—	4	8	no	—
219	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
220	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
235	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
236	C₁₃×C₂²⋊C₄	—	2	2	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	8	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	2	2	no	—
243	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
244	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
245	C₄²×C₁₃	—	2	2	no	—
246	C₄²×C₁₃	—	2	2	no	—
247	C₄²×C₁₃	—	2	4	no	—
248	C₄²×C₁₃	—	2	2	no	—
249	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
253	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#3305	C₂×C₁₃	1	4	yes	complemented
256	#3304	C₂×C₁₃	1	4	yes	complemented
257	#3287	C₂×C₁₃	1	4	yes	complemented
258	#3284	C₂×C₁₃	1	4	yes	complemented
259	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#3188	C₂×C₁₃	1	4	yes	complemented
262	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3002	C₂×C₁₃	1	4	yes	complemented
265	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂³×C₁₃	—	2	4	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	4	no	—
269	C₂³×C₁₃	—	4	2	no	—
270	C₂³×C₁₃	—	4	2	no	—
271	C₂³×C₁₃	—	4	4	no	—
272	C₂³×C₁₃	—	4	4	no	—
273	C₂³×C₁₃	—	4	4	no	—
274	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
275	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₁₃	—	2	4	no	—
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	—	2	4	no	—
279	Q₈×C₁₃	—	4	2	no	—
280	Q₈×C₁₃	—	8	1	no	—
281	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
282	D₄×C₁₃	—	2	4	no	—
283	D₄×C₁₃	—	2	4	no	—
284	D₄×C₁₃	—	2	4	no	—
285	D₄×C₁₃	—	2	8	no	—
286	D₄×C₁₃	—	4	16	no	—
287	D₄×C₁₃	—	4	4	no	—
288	D₄×C₁₃	—	4	4	no	—
289	D₄×C₁₃	—	4	4	no	—
290	D₄×C₁₃	—	4	4	no	—
291	D₄×C₁₃	—	4	2	no	—
292	D₄×C₁₃	—	8	1	no	—
293	D₄×C₁₃	—	8	2	no	—
294	D₄×C₁₃	—	8	2	no	—
295	D₄×C₁₃	—	8	4	no	—
296	D₄×C₁₃	—	8	8	no	—
297	D₄×C₁₃	—	8	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	8	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	4	2	no	—
307	C₂×C₄×C₁₃	—	4	4	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	16	no	—
310	C₂×C₄×C₁₃	—	4	2	no	—
311	C₂×C₄×C₁₃	—	4	4	no	—
312	C₂×C₄×C₁₃	—	8	4	no	—
313	C₂×C₄×C₁₃	#135	1	4	yes	complemented
314	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
321	C₈×C₁₃	—	2	4	no	—
322	C₈×C₁₃	—	2	4	no	—
323	C₂²×#41	C₂²×C₁₃	1	2	yes	—
324	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
325	#559	—	2	2	no	—
326	#556	C₂²×C₁₃	1	2	yes	complemented
327	#555	C₂²×C₁₃	1	2	yes	complemented
328	#553	—	2	2	no	—
329	#550	—	2	2	no	—
330	#550	—	2	2	no	—
331	#550	C₂²×C₁₃	1	4	yes	—
332	#550	C₂²×C₁₃	1	4	yes	—
333	#550	C₂²×C₁₃	1	2	yes	complemented
334	#547	C₂²×C₁₃	1	2	yes	complemented
335	#538	—	2	2	no	—
336	#535	—	2	1	no	—
337	#533	C₂²×C₁₃	1	1	yes	characteristic
338	#532	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#127	—	2	1	no	—
340	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
341	#525	C₂²×C₁₃	1	4	yes	—
342	C₂×#121	—	2	2	no	—
343	C₂×#121	C₂²×C₁₃	1	2	yes	—
344	#520	—	2	1	no	—
345	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₄×D₄	—	2	1	no	—
347	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
348	#493	C₂²×C₁₃	1	2	yes	complemented
349	#492	C₂²×C₁₃	1	2	yes	complemented
350	#486	C₂²×C₁₃	1	2	yes	complemented
351	#486	C₂²×C₁₃	1	2	yes	complemented
352	#484	C₂²×C₁₃	1	2	yes	—
353	#482	C₂²×C₁₃	1	8	yes	complemented
354	#481	C₂²×C₁₃	1	2	yes	—
355	#477	C₂²×C₁₃	1	2	yes	complemented
356	#475	C₂²×C₁₃	1	2	yes	complemented
357	#466	C₂²×C₁₃	1	8	yes	complemented
358	#465	C₂²×C₁₃	1	8	yes	complemented
359	#462	C₂²×C₁₃	1	2	yes	complemented
360	#460	C₂²×C₁₃	1	2	yes	complemented
361	#460	C₂²×C₁₃	1	4	yes	complemented
362	#459	C₂²×C₁₃	1	4	yes	complemented
363	#452	C₂²×C₁₃	1	8	yes	complemented
364	#451	C₂²×C₁₃	1	2	yes	—
365	#450	C₂²×C₁₃	1	4	yes	—
366	#449	C₂²×C₁₃	1	8	yes	complemented
367	#449	C₂²×C₁₃	1	8	yes	complemented
368	#448	C₂²×C₁₃	1	2	yes	—
369	#447	C₂²×C₁₃	1	4	yes	—
370	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
371	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
372	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
373	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
374	#431	C₂²×C₁₃	1	1	yes	characteristic
375	#431	C₂²×C₁₃	1	1	yes	characteristic
376	#416	C₂²×C₁₃	1	8	yes	complemented
377	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
378	C₂²×C₁₃	—	2	1	no	—
379	C₂²×C₁₃	—	2	1	no	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	4	no	—
389	C₂²×C₁₃	—	8	4	no	—
390	C₂²×C₁₃	—	8	8	no	—
391	C₂²×C₁₃	C₂×#135	1	2	yes	—
392	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₁₃	—	2	1	no	—
394	C₄×C₁₃	—	2	1	no	—
395	C₄×C₁₃	—	2	4	no	—
396	C₄×C₁₃	—	2	4	no	—
397	C₄×C₁₃	—	2	1	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	C₂×#135	1	2	yes	—
403	C₄×C₁₃	C₂×#135	1	2	yes	—
404	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	4	no	—
407	C₂×#41	—	4	8	no	—
408	C₂×#41	C₂³×C₁₃	1	8	yes	—
409	C₂×#41	C₂³×C₁₃	1	4	yes	—
410	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×D₄	—	2	2	no	—
412	C₂²×D₄	—	2	2	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
417	C₂³×C₄	—	2	2	no	—
418	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
419	#135	—	4	16	no	—
420	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
421	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
422	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
423	C₂×D₈	C₂³×C₁₃	1	8	yes	—
424	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
425	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	#127	—	2	4	no	—
429	#127	—	2	4	no	—
430	#127	—	2	2	no	—
431	#127	—	2	1	no	—
432	#127	—	2	1	no	—
433	#127	C₂³×C₁₃	1	2	yes	—
434	#127	C₂³×C₁₃	1	2	yes	—
435	#127	C₂³×C₁₃	1	1	yes	characteristic
436	#126	—	2	4	no	—
437	#125	—	2	1	no	—
438	#124	—	2	2	no	—
439	#124	—	2	4	no	—
440	#124	—	2	1	no	—
441	#123	—	2	4	no	—
442	#123	—	2	4	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
445	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
446	#121	—	2	2	no	—
447	#121	—	2	2	no	—
448	#121	—	2	4	no	—
449	#121	—	2	1	no	—
450	#121	—	2	8	no	—
451	#121	—	2	8	no	—
452	#121	—	2	4	no	—
453	#121	C₂³×C₁₃	1	8	yes	—
454	#121	C₂³×C₁₃	1	2	yes	—
455	#121	C₂³×C₁₃	1	4	yes	—
456	#120	—	2	4	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	1	no	—
459	C₄×Q₈	—	2	1	no	—
460	C₄×Q₈	—	2	1	no	—
461	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
462	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
463	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	—	2	4	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	4	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	D₄×C₁₃	1	2	yes	—
471	C₄×D₄	D₄×C₁₃	1	2	yes	—
472	C₄×D₄	C₂³×C₁₃	1	2	yes	—
473	C₄×D₄	C₂³×C₁₃	1	2	yes	—
474	C₄×D₄	C₂³×C₁₃	1	2	yes	—
475	#117	—	2	1	no	—
476	#117	—	2	2	no	—
477	#117	C₂³×C₁₃	1	4	yes	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	2	no	—
480	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	—	2	2	no	—
483	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
484	C₂×C₄²	—	2	1	no	—
485	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
486	#107	C₂³×C₁₃	1	4	yes	—
487	#106	C₂³×C₁₃	1	4	yes	—
488	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
489	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
490	#103	C₂³×C₁₃	1	4	yes	—
491	#103	C₂³×C₁₃	1	4	yes	—
492	#103	C₂³×C₁₃	1	4	yes	—
493	#102	C₂³×C₁₃	1	8	yes	—
494	#102	C₂³×C₁₃	1	8	yes	—
495	#102	C₂³×C₁₃	1	4	yes	—
496	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
497	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
499	C₄×C₈	C₂³×C₁₃	1	2	yes	—
500	C₄×C₈	C₂³×C₁₃	1	2	yes	—
501	C₂×C₁₃	—	2	2	no	—
502	C₂×C₁₃	—	4	4	no	—
503	C₂×C₁₃	—	8	2	no	—
504	C₂×C₁₃	—	8	4	no	—
505	C₂×C₁₃	#3484	1	1	yes	characteristic
506	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
507	C₂×C₁₃	#3585	1	1	yes	characteristic
508	C₂⁴	—	2	2	no	—
509	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
510	#41	—	2	16	no	—
511	#41	—	4	8	no	—
512	#41	—	4	8	no	—
513	#41	—	4	16	no	—
514	#41	—	4	4	no	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
520	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	8	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	4	4	no	—
535	C₂×D₄	—	4	8	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	8	2	no	—
538	C₂×D₄	—	8	4	no	—
539	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
540	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
541	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
542	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	8	no	—
550	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
556	Q₁₆	—	2	8	no	—
557	SD₁₆	—	2	8	no	—
558	SD₁₆	—	4	8	no	—
559	D₈	—	4	8	no	—
560	C₂×C₈	—	4	8	no	—
561	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
562	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
574	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
575	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
576	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
577	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
586	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
592	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₁₃	#61566	1	1	yes	characteristic, direct product factor, Sylow
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	4	no	—
604	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
605	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
606	Q₈	—	2	4	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	4	no	—
609	Q₈	—	4	2	no	—
610	Q₈	—	8	1	no	—
611	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
612	D₄	—	2	4	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	4	no	—
615	D₄	—	2	8	no	—
616	D₄	—	4	16	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	4	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	2	no	—
622	D₄	—	8	2	no	—
623	D₄	—	8	2	no	—
624	D₄	—	8	1	no	—
625	D₄	—	8	8	no	—
626	D₄	—	8	4	no	—
627	D₄	—	8	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	16	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	C₁₃×#135	1	4	yes	complemented
644	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
645	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
651	C₈	—	2	4	no	—
652	C₈	—	2	4	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	8	4	no	—
665	C₂²	—	8	8	no	—
666	C₂²	C₂×C₁₃×#135	1	2	yes	—
667	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	2	no	—
677	C₄	C₂×C₁₃×#135	1	2	yes	—
678	C₄	C₂×C₁₃×#135	1	2	yes	—
679	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	4	4	no	—
682	C₂	—	8	4	no	—
683	C₂	—	8	2	no	—
684	C₂	C₁₃×#3484	1	1	yes	characteristic
685	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
686	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×#3506	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3305	C₂	semidirect
4. C₁₃×#3304	C₂	semidirect
5. C₁₃×#3287	C₂	semidirect
6. C₁₃×#3284	C₂	semidirect
7. C₁₃×#3208	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3188	C₂	semidirect
10. C₁₃×#3104	C₂	semidirect
11. C₁₃×#3103	C₂	semidirect
12. C₁₃×#3002	C₂	semidirect
13. C₁₃×#2972	C₂	semidirect
15. C₂×C₁₃×#135	C₂²	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#555	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
39. C₁₃×#493	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
46. C₁₃×#477	C₂²	semidirect
47. C₁₃×#475	C₂²	semidirect
48. C₁₃×#466	C₂²	semidirect
49. C₁₃×#465	C₂²	semidirect
50. C₁₃×#462	C₂²	semidirect
51. C₁₃×#460	C₂²	semidirect
52. C₁₃×#460	C₂²	semidirect
53. C₁₃×#459	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
57. C₁₃×#449	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
61. C₄×C₁₃×Q₁₆	C₂²	semidirect
62. C₄×C₁₃×SD₁₆	C₂²	semidirect
63. C₈×D₄×C₁₃	C₂²	semidirect
64. C₈×D₄×C₁₃	C₂²	semidirect
67. C₁₃×#416	C₂²	semidirect
165. #61566	C₁₃	direct (N × H)
253. #3506	C₂×C₁₃	semidirect
254. C₂×#550	C₂×C₁₃	semidirect
255. #3305	C₂×C₁₃	semidirect
256. #3304	C₂×C₁₃	semidirect
257. #3287	C₂×C₁₃	semidirect
258. #3284	C₂×C₁₃	semidirect
259. #3208	C₂×C₁₃	semidirect
260. #3205	C₂×C₁₃	semidirect
261. #3188	C₂×C₁₃	semidirect
262. #3104	C₂×C₁₃	semidirect
263. #3103	C₂×C₁₃	semidirect
264. #3002	C₂×C₁₃	semidirect
265. #2972	C₂×C₁₃	semidirect
313. C₂×C₄×C₁₃	#135	semidirect
324. C₂×#135	C₂²×C₁₃	semidirect
326. #556	C₂²×C₁₃	semidirect
327. #555	C₂²×C₁₃	semidirect
333. #550	C₂²×C₁₃	semidirect
334. #547	C₂²×C₁₃	semidirect
348. #493	C₂²×C₁₃	semidirect
349. #492	C₂²×C₁₃	semidirect
350. #486	C₂²×C₁₃	semidirect
351. #486	C₂²×C₁₃	semidirect
353. #482	C₂²×C₁₃	semidirect
355. #477	C₂²×C₁₃	semidirect
356. #475	C₂²×C₁₃	semidirect
357. #466	C₂²×C₁₃	semidirect
358. #465	C₂²×C₁₃	semidirect
359. #462	C₂²×C₁₃	semidirect
360. #460	C₂²×C₁₃	semidirect
361. #460	C₂²×C₁₃	semidirect
362. #459	C₂²×C₁₃	semidirect
363. #452	C₂²×C₁₃	semidirect
366. #449	C₂²×C₁₃	semidirect
367. #449	C₂²×C₁₃	semidirect
370. C₄×Q₁₆	C₂²×C₁₃	semidirect
371. C₄×SD₁₆	C₂²×C₁₃	semidirect
372. C₈×D₄	C₂²×C₁₃	semidirect
373. C₈×D₄	C₂²×C₁₃	semidirect
376. #416	C₂²×C₁₃	semidirect
595. C₁₃	#61566	direct (N × H)
643. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3506	2
C₂×C₁₃×#550	2
C₁₃×#3305	2
C₁₃×#3304	2
C₁₃×#3287	2
C₁₃×#3284	2
C₁₃×#3208	2
C₁₃×#3205	2
C₁₃×#3188	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#3002	2
C₁₃×#2972	2
#61566	13

Subgroups — C13×#61566 #15747905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61566 #15747905