Subgroups — C₁₃×#61573 #15747912

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3316	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3270	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3195	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3113	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	4	yes	complemented
18	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
19	C₁₃×#548	—	2	4	no	—
20	C₁₃×#548	C₂²	1	8	yes	—
21	C₁₃×#544	—	2	1	no	—
22	C₁₃×#543	—	2	1	no	—
23	C₁₃×#543	—	2	1	no	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	—	2	1	no	—
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₁₃×#518	—	2	1	no	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	—	2	1	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	4	yes	complemented
38	C₁₃×#489	C₂²	1	4	yes	complemented
39	C₁₃×#483	C₂²	1	4	yes	—
40	C₁₃×#483	C₂²	1	4	yes	complemented
41	C₁₃×#481	C₂²	1	4	yes	complemented
42	C₁₃×#475	C₂²	1	4	yes	complemented
43	C₁₃×#470	C₂²	1	8	yes	complemented
44	C₁₃×#465	C₂²	1	8	yes	complemented
45	C₁₃×#464	C₂²	1	8	yes	complemented
46	C₁₃×#462	C₂²	1	4	yes	complemented
47	C₁₃×#452	C₂²	1	8	yes	complemented
48	C₁₃×#451	C₂²	1	4	yes	—
49	C₁₃×#451	C₂²	1	4	yes	—
50	C₁₃×#451	C₂²	1	4	yes	complemented
51	C₁₃×#451	C₂²	1	8	yes	complemented
52	C₁₃×#450	C₂²	1	4	yes	—
53	C₁₃×#448	C₂²	1	4	yes	complemented
54	C₁₃×#441	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#432	C₂²	1	2	yes	—
57	C₁₃×#417	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	—
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	4	4	no	—
63	C₂×C₁₃×#41	C₂³	1	4	yes	—
64	C₂²×Q₈×C₁₃	—	2	1	no	—
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	—	4	4	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#137	—	4	8	no	—
81	C₂×C₁₃×Q₁₆	—	4	8	no	—
82	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
83	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
87	C₁₃×C₄⋊Q₈	—	2	4	no	—
88	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₃×#125	—	2	4	no	—
91	C₁₃×#125	—	2	2	no	—
92	C₁₃×#124	—	2	8	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×C₂²⋊Q₈	—	2	2	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	8	no	—
102	C₁₃×C₂²⋊Q₈	—	2	4	no	—
103	C₁₃×C₂²⋊Q₈	—	2	4	no	—
104	C₁₃×C₂²⋊Q₈	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×#121	—	2	8	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	C₂³	1	4	yes	—
113	C₄×Q₈×C₁₃	—	2	2	no	—
114	C₄×Q₈×C₁₃	—	2	2	no	—
115	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	—	2	8	no	—
120	C₄×D₄×C₁₃	D₄	1	4	yes	—
121	C₄×D₄×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#117	—	2	2	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	—	2	1	no	—
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×#106	C₂³	1	8	yes	—
142	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
143	C₁₃×#103	C₂³	1	8	yes	—
144	C₁₃×#103	C₂³	1	8	yes	—
145	C₁₃×#103	C₂³	1	8	yes	—
146	C₁₃×#102	C₂³	1	8	yes	—
147	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
150	C₁₃×#97	C₂³	1	4	yes	—
151	#61573	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₁₃×#41	—	2	8	no	—
156	C₁₃×#41	—	4	4	no	—
157	C₁₃×#41	—	4	8	no	—
158	C₂×Q₈×C₁₃	—	2	4	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	4	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	2	no	—
163	C₂×Q₈×C₁₃	—	2	2	no	—
164	C₂×Q₈×C₁₃	—	2	2	no	—
165	C₂×Q₈×C₁₃	—	2	8	no	—
166	C₂×Q₈×C₁₃	—	4	4	no	—
167	C₂×Q₈×C₁₃	—	4	2	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂×Q₈×C₁₃	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	4	4	no	—
171	C₂×Q₈×C₁₃	—	4	8	no	—
172	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
173	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	—	4	4	no	—
181	C₂×D₄×C₁₃	—	4	4	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	4	2	no	—
195	C₂²×C₄×C₁₃	—	4	4	no	—
196	C₂²×C₄×C₁₃	—	4	4	no	—
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₁₃×Q₁₆	—	2	16	no	—
207	C₁₃×Q₁₆	—	4	8	no	—
208	C₁₃×SD₁₆	—	4	8	no	—
209	C₁₃×M₁₆	—	4	4	no	—
210	C₂×C₈×C₁₃	—	4	4	no	—
211	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	4	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	4	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
225	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
235	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	C₂×D₄	1	2	yes	—
239	C₄²×C₁₃	C₂⁴	1	2	yes	—
240	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#548	C₂×C₁₃	1	1	yes	characteristic
242	#3316	C₂×C₁₃	1	8	yes	complemented
243	#3270	C₂×C₁₃	1	8	yes	complemented
244	#3215	C₂×C₁₃	1	2	yes	complemented
245	#3195	C₂×C₁₃	1	2	yes	complemented
246	#3187	C₂×C₁₃	1	2	yes	complemented
247	#3113	C₂×C₁₃	1	2	yes	complemented
248	#3007	C₂×C₁₃	1	2	yes	complemented
249	C₂×#451	C₂×C₁₃	1	2	yes	complemented
250	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	2	no	—
258	C₂³×C₁₃	—	4	2	no	—
259	C₂³×C₁₃	—	4	2	no	—
260	C₂³×C₁₃	#137	1	4	yes	complemented
261	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
264	Q₈×C₁₃	—	2	4	no	—
265	Q₈×C₁₃	—	2	2	no	—
266	Q₈×C₁₃	—	2	8	no	—
267	Q₈×C₁₃	—	2	4	no	—
268	Q₈×C₁₃	—	4	8	no	—
269	Q₈×C₁₃	—	4	2	no	—
270	Q₈×C₁₃	—	8	2	no	—
271	Q₈×C₁₃	—	8	2	no	—
272	Q₈×C₁₃	—	8	2	no	—
273	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
274	D₄×C₁₃	—	2	8	no	—
275	D₄×C₁₃	—	2	4	no	—
276	D₄×C₁₃	—	4	8	no	—
277	D₄×C₁₃	—	4	2	no	—
278	D₄×C₁₃	—	4	8	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	4	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	2	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	8	no	—
295	C₂×C₄×C₁₃	—	4	8	no	—
296	C₂×C₄×C₁₃	—	4	2	no	—
297	C₂×C₄×C₁₃	—	4	2	no	—
298	C₂×C₄×C₁₃	—	8	2	no	—
299	C₂×C₄×C₁₃	—	8	2	no	—
300	C₂×C₄×C₁₃	—	8	2	no	—
301	C₂×C₄×C₁₃	—	8	2	no	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
308	C₈×C₁₃	—	2	8	no	—
309	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
310	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
312	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
313	#554	—	2	4	no	—
314	#554	C₂²×C₁₃	1	4	yes	complemented
315	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
316	#548	—	2	4	no	—
317	#548	C₂²×C₁₃	1	8	yes	—
318	#544	—	2	1	no	—
319	#543	—	2	1	no	—
320	#543	—	2	1	no	—
321	#533	C₂²×C₁₃	1	2	yes	—
322	C₂×#124	—	2	1	no	—
323	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
328	C₂×#121	—	2	1	no	—
329	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
330	#518	—	2	1	no	—
331	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄×D₄	—	2	1	no	—
333	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
334	#497	C₂²×C₁₃	1	4	yes	complemented
335	#489	C₂²×C₁₃	1	4	yes	complemented
336	#483	C₂²×C₁₃	1	4	yes	—
337	#483	C₂²×C₁₃	1	4	yes	complemented
338	#481	C₂²×C₁₃	1	4	yes	complemented
339	#475	C₂²×C₁₃	1	4	yes	complemented
340	#470	C₂²×C₁₃	1	8	yes	complemented
341	#465	C₂²×C₁₃	1	8	yes	complemented
342	#464	C₂²×C₁₃	1	8	yes	complemented
343	#462	C₂²×C₁₃	1	4	yes	complemented
344	#452	C₂²×C₁₃	1	8	yes	complemented
345	#451	C₂²×C₁₃	1	4	yes	—
346	#451	C₂²×C₁₃	1	4	yes	—
347	#451	C₂²×C₁₃	1	4	yes	complemented
348	#451	C₂²×C₁₃	1	8	yes	complemented
349	#450	C₂²×C₁₃	1	4	yes	—
350	#448	C₂²×C₁₃	1	4	yes	complemented
351	#441	C₂²×C₁₃	1	8	yes	complemented
352	#435	C₂²×C₁₃	1	8	yes	complemented
353	#432	C₂²×C₁₃	1	2	yes	—
354	#417	C₂²×C₁₃	1	4	yes	complemented
355	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
356	#407	C₂²×C₁₃	1	2	yes	—
357	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	2	1	no	—
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	2	no	—
364	C₂²×C₁₃	—	2	2	no	—
365	C₂²×C₁₃	—	4	4	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	—	8	2	no	—
370	C₂²×C₁₃	—	8	4	no	—
371	C₂²×C₁₃	C₂×#137	1	2	yes	—
372	C₂²×C₁₃	C₂×#137	1	4	yes	—
373	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₁₃	—	2	2	no	—
375	C₄×C₁₃	—	2	4	no	—
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	2	1	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	4	4	no	—
381	C₄×C₁₃	—	4	2	no	—
382	C₄×C₁₃	—	4	4	no	—
383	C₄×C₁₃	—	4	2	no	—
384	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
385	C₂×#41	—	2	2	no	—
386	C₂×#41	—	4	4	no	—
387	C₂×#41	C₂³×C₁₃	1	4	yes	—
388	C₂²×Q₈	—	2	1	no	—
389	C₂²×Q₈	—	2	2	no	—
390	C₂²×Q₈	—	4	4	no	—
391	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
393	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
395	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
404	#137	—	4	8	no	—
405	C₂×Q₁₆	—	4	8	no	—
406	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
407	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
408	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
409	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
410	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
411	C₄⋊Q₈	—	2	4	no	—
412	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
413	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
414	#125	—	2	4	no	—
415	#125	—	2	2	no	—
416	#124	—	2	8	no	—
417	#124	—	2	2	no	—
418	#124	C₂³×C₁₃	1	4	yes	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	8	no	—
426	C₂²⋊Q₈	—	2	4	no	—
427	C₂²⋊Q₈	—	2	4	no	—
428	C₂²⋊Q₈	—	2	4	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
431	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
432	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
433	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
434	#121	—	2	8	no	—
435	#121	—	2	2	no	—
436	#121	C₂³×C₁₃	1	4	yes	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
440	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	4	no	—
443	C₄×D₄	—	2	8	no	—
444	C₄×D₄	D₄×C₁₃	1	4	yes	—
445	C₄×D₄	C₂³×C₁₃	1	4	yes	—
446	#117	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	2	no	—
450	C₂×C₄⋊C₄	—	2	2	no	—
451	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	—	2	2	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
465	#106	C₂³×C₁₃	1	8	yes	—
466	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
467	#103	C₂³×C₁₃	1	8	yes	—
468	#103	C₂³×C₁₃	1	8	yes	—
469	#103	C₂³×C₁₃	1	8	yes	—
470	#102	C₂³×C₁₃	1	8	yes	—
471	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
472	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
474	#97	C₂³×C₁₃	1	4	yes	—
475	C₂×C₁₃	—	2	2	no	—
476	C₂×C₁₃	—	2	4	no	—
477	C₂×C₁₃	—	4	2	no	—
478	C₂×C₁₃	—	8	2	no	—
479	C₂×C₁₃	#3484	1	1	yes	characteristic
480	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
481	C₂×C₁₃	#3586	1	1	yes	characteristic
482	C₂⁴	—	2	1	no	—
483	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
485	#41	—	2	8	no	—
486	#41	—	4	4	no	—
487	#41	—	4	8	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	8	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	—	4	4	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	—	4	8	no	—
502	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
503	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
504	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	4	4	no	—
512	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
513	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
536	Q₁₆	—	2	16	no	—
537	Q₁₆	—	4	8	no	—
538	SD₁₆	—	4	8	no	—
539	M₁₆	—	4	4	no	—
540	C₂×C₈	—	4	4	no	—
541	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
555	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
556	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
565	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	4	no	—
568	C₄²	C₂×D₄×C₁₃	1	2	yes	—
569	C₄²	C₂⁴×C₁₃	1	2	yes	—
570	C₁₃	#61573	1	1	yes	characteristic, direct product factor, Sylow
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	2	no	—
580	C₂³	C₁₃×#137	1	4	yes	complemented
581	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
582	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
584	Q₈	—	2	4	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	2	8	no	—
587	Q₈	—	2	4	no	—
588	Q₈	—	4	8	no	—
589	Q₈	—	4	2	no	—
590	Q₈	—	8	2	no	—
591	Q₈	—	8	2	no	—
592	Q₈	—	8	2	no	—
593	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
594	D₄	—	2	8	no	—
595	D₄	—	2	4	no	—
596	D₄	—	4	8	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	8	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	8	2	no	—
619	C₂×C₄	—	8	2	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
627	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
628	C₈	—	2	8	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	4	no	—
642	C₂²	C₂×C₁₃×#137	1	2	yes	—
643	C₂²	C₂×C₁₃×#137	1	4	yes	—
644	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	4	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	4	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	4	no	—
655	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
656	C₂	—	2	2	no	—
657	C₂	—	2	4	no	—
658	C₂	—	4	2	no	—
659	C₂	—	8	2	no	—
660	C₂	C₁₃×#3484	1	1	yes	characteristic
661	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
662	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#548	C₂
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×#3501	C₂	semidirect
3. C₁₃×#3316	C₂	semidirect
4. C₁₃×#3270	C₂	semidirect
5. C₁₃×#3215	C₂	semidirect
6. C₁₃×#3195	C₂	semidirect
7. C₁₃×#3187	C₂	semidirect
8. C₁₃×#3113	C₂	semidirect
9. C₁₃×#3007	C₂	semidirect
10. C₂×C₁₃×#451	C₂	semidirect
11. C₁₃×#2973	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
17. C₁₃×#554	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
40. C₁₃×#483	C₂²	semidirect
41. C₁₃×#481	C₂²	semidirect
42. C₁₃×#475	C₂²	semidirect
43. C₁₃×#470	C₂²	semidirect
44. C₁₃×#465	C₂²	semidirect
45. C₁₃×#464	C₂²	semidirect
46. C₁₃×#462	C₂²	semidirect
47. C₁₃×#452	C₂²	semidirect
50. C₁₃×#451	C₂²	semidirect
51. C₁₃×#451	C₂²	semidirect
53. C₁₃×#448	C₂²	semidirect
54. C₁₃×#441	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
57. C₁₃×#417	C₂²	semidirect
58. C₂×C₁₃×#103	C₂²	semidirect
151. #61573	C₁₃	direct (N × H)
240. #3501	C₂×C₁₃	semidirect
242. #3316	C₂×C₁₃	semidirect
243. #3270	C₂×C₁₃	semidirect
244. #3215	C₂×C₁₃	semidirect
245. #3195	C₂×C₁₃	semidirect
246. #3187	C₂×C₁₃	semidirect
247. #3113	C₂×C₁₃	semidirect
248. #3007	C₂×C₁₃	semidirect
249. C₂×#451	C₂×C₁₃	semidirect
250. #2973	C₂×C₁₃	semidirect
260. C₂³×C₁₃	#137	semidirect
311. C₂×#137	C₂²×C₁₃	semidirect
312. C₂²×Q₁₆	C₂²×C₁₃	semidirect
314. #554	C₂²×C₁₃	semidirect
315. D₄×Q₈	C₂²×C₁₃	semidirect
334. #497	C₂²×C₁₃	semidirect
335. #489	C₂²×C₁₃	semidirect
337. #483	C₂²×C₁₃	semidirect
338. #481	C₂²×C₁₃	semidirect
339. #475	C₂²×C₁₃	semidirect
340. #470	C₂²×C₁₃	semidirect
341. #465	C₂²×C₁₃	semidirect
342. #464	C₂²×C₁₃	semidirect
343. #462	C₂²×C₁₃	semidirect
344. #452	C₂²×C₁₃	semidirect
347. #451	C₂²×C₁₃	semidirect
348. #451	C₂²×C₁₃	semidirect
350. #448	C₂²×C₁₃	semidirect
351. #441	C₂²×C₁₃	semidirect
352. #435	C₂²×C₁₃	semidirect
354. #417	C₂²×C₁₃	semidirect
355. C₂×#103	C₂²×C₁₃	semidirect
570. C₁₃	#61573	direct (N × H)
580. C₂³	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3501	2
C₂×C₁₃×#548	2
C₁₃×#3316	2
C₁₃×#3270	2
C₁₃×#3215	2
C₁₃×#3195	2
C₁₃×#3187	2
C₁₃×#3113	2
C₁₃×#3007	2
C₂×C₁₃×#451	2
C₁₃×#2973	2
#61573	13

Subgroups — C13×#61573 #15747912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61573 #15747912