Subgroups — C₁₃×#60824 #15747163

Order 3328.

2058 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3046	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
16	C₂×C₁₃×#137	C₂²	1	4	yes	—
17	C₂×C₁₃×#135	C₂²	1	4	yes	—
18	C₁₃×#556	—	2	1	no	—
19	C₁₃×#555	—	2	1	no	—
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#553	—	2	2	no	—
22	D₄×Q₈×C₁₃	—	2	1	no	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	C₁₃×#548	—	2	2	no	—
25	C₁₃×#547	—	2	1	no	—
26	C₁₃×#547	—	2	2	no	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#542	C₂²	1	4	yes	—
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#536	C₂²	1	2	yes	—
33	C₁₃×#536	C₂²	1	4	yes	—
34	C₁₃×#533	C₂²	1	2	yes	—
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	2	yes	—
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#497	C₂²	1	4	yes	—
45	C₁₃×#495	C₂²	1	4	yes	—
46	C₁₃×#494	C₂²	1	1	yes	characteristic
47	C₁₃×#494	C₂²	1	2	yes	—
48	C₁₃×#493	C₂²	1	1	yes	characteristic
49	C₁₃×#492	C₂²	1	1	yes	characteristic
50	C₁₃×#492	C₂²	1	1	yes	characteristic
51	C₁₃×#492	C₂²	1	2	yes	—
52	C₁₃×#489	C₂²	1	4	yes	—
53	C₁₃×#487	C₂²	1	2	yes	—
54	C₁₃×#487	C₂²	1	2	yes	—
55	C₁₃×#487	C₂²	1	4	yes	—
56	C₁₃×#487	C₂²	1	2	yes	—
57	C₁₃×#486	C₂²	1	2	yes	—
58	C₁₃×#464	C₂²	1	8	yes	—
59	C₁₃×#463	C₂²	1	8	yes	—
60	C₁₃×#462	C₂²	1	8	yes	—
61	C₁₃×#461	C₂²	1	8	yes	—
62	C₁₃×#452	C₂²	1	8	yes	—
63	C₁₃×#451	C₂²	1	8	yes	—
64	C₁₃×#449	C₂²	1	8	yes	—
65	C₁₃×#448	C₂²	1	8	yes	—
66	C₁₃×#433	C₂²	1	4	yes	—
67	C₁₃×#431	C₂²	1	2	yes	—
68	C₁₃×#431	C₂²	1	2	yes	—
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#417	C₂²	1	4	yes	—
71	C₂×C₁₃×#103	C₂²	1	4	yes	—
72	C₁₃×#408	C₂²	1	2	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
75	C₁₃×2₋¹⁺⁴	—	4	8	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
77	C₂×C₁₃×#41	—	2	4	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	C₂³	1	2	yes	—
80	C₂×C₁₃×#41	C₂³	1	2	yes	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃	—	2	2	no	—
84	C₂²×Q₈×C₁₃	—	2	1	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
87	C₁₃×#137	—	4	8	no	—
88	C₁₃×#135	—	4	8	no	—
89	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
91	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×D₈	C₂³	1	4	yes	—
95	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	—	2	1	no	—
99	C₁₃×C₄⋊Q₈	—	2	1	no	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	—	2	1	no	—
102	C₁₃×C₄⋊Q₈	—	2	1	no	—
103	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#127	C₂³	1	1	yes	characteristic
111	C₁₃×#127	C₂³	1	1	yes	characteristic
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#125	—	2	2	no	—
114	C₁₃×#124	—	2	4	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#124	C₂³	1	2	yes	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	4	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	C₂³	1	4	yes	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
143	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
144	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	2	no	—
147	C₄×D₄×C₁₃	—	2	1	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
154	C₄×D₄×C₁₃	D₄	1	2	yes	—
155	C₄×D₄×C₁₃	D₄	1	2	yes	—
156	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
157	C₄×D₄×C₁₃	C₂³	1	4	yes	—
158	C₁₃×#117	—	2	2	no	—
159	C₁₃×#117	—	2	2	no	—
160	C₁₃×#117	C₂³	1	1	yes	characteristic
161	C₁₃×#117	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	8	yes	—
174	C₁₃×#103	C₂³	1	8	yes	—
175	C₁₃×#103	C₂³	1	8	yes	—
176	C₁₃×#102	C₂³	1	8	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₁₃×#97	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	C₄×C₈×C₁₃	C₂³	1	2	yes	—
184	#60824	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃×#41	—	2	4	no	—
186	C₁₃×#41	—	2	8	no	—
187	C₁₃×#41	—	2	8	no	—
188	C₁₃×#41	—	4	8	no	—
189	C₁₃×#41	—	4	16	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₁₃×#41	—	8	4	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	4	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	2	2	no	—
196	C₂×Q₈×C₁₃	—	2	8	no	—
197	C₂×Q₈×C₁₃	—	4	8	no	—
198	C₂×Q₈×C₁₃	—	4	8	no	—
199	C₂×Q₈×C₁₃	—	8	2	no	—
200	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
202	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×Q₁₆	—	4	4	no	—
230	C₁₃×Q₁₆	—	4	8	no	—
231	C₁₃×SD₁₆	—	4	4	no	—
232	C₁₃×SD₁₆	—	4	4	no	—
233	C₁₃×SD₁₆	—	4	8	no	—
234	C₁₃×D₈	—	4	4	no	—
235	C₁₃×M₁₆	—	2	4	no	—
236	C₂×C₈×C₁₃	—	2	4	no	—
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
256	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
270	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
272	C₄²×C₁₃	—	2	4	no	—
273	C₄²×C₁₃	C₂×D₄	1	2	yes	—
274	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₃	C₂×D₄	1	2	yes	—
277	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₄²×C₁₃	C₂⁴	1	2	yes	—
280	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#3225	C₂×C₁₃	1	8	yes	complemented
283	#3210	C₂×C₁₃	1	2	yes	complemented
284	#3209	C₂×C₁₃	1	2	yes	complemented
285	#3207	C₂×C₁₃	1	2	yes	complemented
286	#3206	C₂×C₁₃	1	2	yes	complemented
287	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3046	C₂×C₁₃	1	4	yes	complemented
292	#3013	C₂×C₁₃	1	4	yes	complemented
293	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
297	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₁₃	—	2	2	no	—
299	Q₈×C₁₃	—	2	4	no	—
300	Q₈×C₁₃	—	2	8	no	—
301	Q₈×C₁₃	—	2	4	no	—
302	Q₈×C₁₃	—	4	8	no	—
303	Q₈×C₁₃	—	4	4	no	—
304	Q₈×C₁₃	—	4	4	no	—
305	Q₈×C₁₃	—	8	2	no	—
306	D₄×C₁₃	—	2	4	no	—
307	D₄×C₁₃	—	2	2	no	—
308	D₄×C₁₃	—	2	4	no	—
309	D₄×C₁₃	—	2	4	no	—
310	D₄×C₁₃	—	4	8	no	—
311	D₄×C₁₃	—	4	4	no	—
312	D₄×C₁₃	—	4	4	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	4	2	no	—
315	D₄×C₁₃	—	4	2	no	—
316	D₄×C₁₃	—	4	2	no	—
317	D₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	4	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	4	8	no	—
328	C₂×C₄×C₁₃	—	4	8	no	—
329	C₂×C₄×C₁₃	—	4	4	no	—
330	C₂×C₄×C₁₃	—	4	4	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	8	4	no	—
333	C₂×C₄×C₁₃	—	8	2	no	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
343	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
344	C₈×C₁₃	—	2	2	no	—
345	C₈×C₁₃	—	2	2	no	—
346	C₈×C₁₃	—	2	4	no	—
347	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
348	C₂×#137	C₂²×C₁₃	1	4	yes	—
349	C₂×#135	C₂²×C₁₃	1	4	yes	—
350	#556	—	2	1	no	—
351	#555	—	2	1	no	—
352	#554	—	2	1	no	—
353	#553	—	2	2	no	—
354	D₄×Q₈	—	2	1	no	—
355	D₄×Q₈	—	2	1	no	—
356	#548	—	2	2	no	—
357	#547	—	2	1	no	—
358	#547	—	2	2	no	—
359	#547	—	2	2	no	—
360	#547	—	2	1	no	—
361	#547	—	2	1	no	—
362	#542	C₂²×C₁₃	1	4	yes	—
363	#537	C₂²×C₁₃	1	2	yes	—
364	#536	C₂²×C₁₃	1	4	yes	—
365	#536	C₂²×C₁₃	1	2	yes	—
366	#533	C₂²×C₁₃	1	2	yes	—
367	#532	C₂²×C₁₃	1	1	yes	characteristic
368	#532	C₂²×C₁₃	1	1	yes	characteristic
369	#532	C₂²×C₁₃	1	2	yes	—
370	#532	C₂²×C₁₃	1	2	yes	—
371	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
373	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	#520	C₂²×C₁₃	1	2	yes	—
375	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
376	#497	C₂²×C₁₃	1	4	yes	—
377	#495	C₂²×C₁₃	1	4	yes	—
378	#494	C₂²×C₁₃	1	1	yes	characteristic
379	#494	C₂²×C₁₃	1	2	yes	—
380	#493	C₂²×C₁₃	1	1	yes	characteristic
381	#492	C₂²×C₁₃	1	1	yes	characteristic
382	#492	C₂²×C₁₃	1	1	yes	characteristic
383	#492	C₂²×C₁₃	1	2	yes	—
384	#489	C₂²×C₁₃	1	4	yes	—
385	#487	C₂²×C₁₃	1	2	yes	—
386	#487	C₂²×C₁₃	1	2	yes	—
387	#487	C₂²×C₁₃	1	4	yes	—
388	#487	C₂²×C₁₃	1	2	yes	—
389	#486	C₂²×C₁₃	1	2	yes	—
390	#464	C₂²×C₁₃	1	8	yes	—
391	#463	C₂²×C₁₃	1	8	yes	—
392	#462	C₂²×C₁₃	1	8	yes	—
393	#461	C₂²×C₁₃	1	8	yes	—
394	#452	C₂²×C₁₃	1	8	yes	—
395	#451	C₂²×C₁₃	1	8	yes	—
396	#449	C₂²×C₁₃	1	8	yes	—
397	#448	C₂²×C₁₃	1	8	yes	—
398	#433	C₂²×C₁₃	1	4	yes	—
399	#431	C₂²×C₁₃	1	2	yes	—
400	#431	C₂²×C₁₃	1	2	yes	—
401	#424	C₂²×C₁₃	1	2	yes	—
402	#417	C₂²×C₁₃	1	4	yes	—
403	C₂×#103	C₂²×C₁₃	1	4	yes	—
404	#408	C₂²×C₁₃	1	2	yes	—
405	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₁₃	—	2	1	no	—
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	4	2	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	#535	1	2	yes	—
419	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	2	no	—
422	C₄×C₁₃	—	2	1	no	—
423	C₄×C₁₃	—	2	2	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	4	4	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	4	no	—
429	C₄×C₁₃	#535	1	2	yes	—
430	C₄×C₁₃	#577	1	2	yes	—
431	C₄×C₁₃	#578	1	2	yes	—
432	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
433	2₋¹⁺⁴	—	4	8	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	4	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	C₂³×C₁₃	1	2	yes	—
438	C₂×#41	C₂³×C₁₃	1	2	yes	—
439	C₂×#41	C₂³×C₁₃	1	4	yes	—
440	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×Q₈	—	2	2	no	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
444	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
445	#137	—	4	8	no	—
446	#135	—	4	8	no	—
447	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
448	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
449	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
450	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
451	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
452	C₂×D₈	C₂³×C₁₃	1	4	yes	—
453	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
454	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
455	C₄⋊Q₈	—	2	2	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	—	2	1	no	—
458	C₄⋊Q₈	—	2	2	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	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
464	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
468	#127	C₂³×C₁₃	1	1	yes	characteristic
469	#127	C₂³×C₁₃	1	1	yes	characteristic
470	#126	—	2	4	no	—
471	#125	—	2	2	no	—
472	#124	—	2	4	no	—
473	#124	—	2	2	no	—
474	#124	C₂³×C₁₃	1	4	yes	—
475	#124	C₂³×C₁₃	1	2	yes	—
476	#124	C₂³×C₁₃	1	2	yes	—
477	#123	—	2	4	no	—
478	#123	—	2	4	no	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
489	#121	—	2	2	no	—
490	#121	—	2	4	no	—
491	#121	—	2	1	no	—
492	#121	—	2	2	no	—
493	#121	—	2	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	—	2	2	no	—
498	#121	C₂³×C₁₃	1	4	yes	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
501	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
502	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
512	C₄×D₄	D₄×C₁₃	1	2	yes	—
513	C₄×D₄	D₄×C₁₃	1	2	yes	—
514	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
515	C₄×D₄	C₂³×C₁₃	1	4	yes	—
516	#117	—	2	2	no	—
517	#117	—	2	2	no	—
518	#117	C₂³×C₁₃	1	1	yes	characteristic
519	#117	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	2	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
529	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
530	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
531	#103	C₂³×C₁₃	1	8	yes	—
532	#103	C₂³×C₁₃	1	8	yes	—
533	#103	C₂³×C₁₃	1	8	yes	—
534	#102	C₂³×C₁₃	1	8	yes	—
535	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
536	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
537	#97	C₂³×C₁₃	1	2	yes	—
538	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄×C₈	C₂³×C₁₃	1	2	yes	—
541	C₄×C₈	C₂³×C₁₃	1	2	yes	—
542	C₂×C₁₃	—	2	2	no	—
543	C₂×C₁₃	—	4	2	no	—
544	C₂×C₁₃	—	8	2	no	—
545	C₂×C₁₃	—	8	2	no	—
546	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
547	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
548	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
549	#41	—	2	4	no	—
550	#41	—	2	8	no	—
551	#41	—	2	8	no	—
552	#41	—	4	8	no	—
553	#41	—	4	16	no	—
554	#41	—	4	8	no	—
555	#41	—	8	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	8	no	—
561	C₂×Q₈	—	4	8	no	—
562	C₂×Q₈	—	4	8	no	—
563	C₂×Q₈	—	8	2	no	—
564	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
566	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
567	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
577	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
579	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
589	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
593	Q₁₆	—	4	4	no	—
594	Q₁₆	—	4	8	no	—
595	SD₁₆	—	4	4	no	—
596	SD₁₆	—	4	4	no	—
597	SD₁₆	—	4	8	no	—
598	D₈	—	4	4	no	—
599	M₁₆	—	2	4	no	—
600	C₂×C₈	—	2	4	no	—
601	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
602	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
603	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
622	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₄²	—	2	4	no	—
637	C₄²	C₂×D₄×C₁₃	1	2	yes	—
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₁₃	1	2	yes	—
641	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
642	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₄²	C₂⁴×C₁₃	1	2	yes	—
644	C₁₃	#60824	1	1	yes	characteristic, direct product factor, Sylow
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
648	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	Q₈	—	2	2	no	—
650	Q₈	—	2	4	no	—
651	Q₈	—	2	8	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	4	8	no	—
654	Q₈	—	4	4	no	—
655	Q₈	—	4	4	no	—
656	Q₈	—	8	2	no	—
657	D₄	—	2	4	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	4	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	8	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	8	no	—
679	C₂×C₄	—	4	8	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
694	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	—	2	4	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	C₁₃×#535	1	2	yes	—
710	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	C₁₃×#535	1	2	yes	—
721	C₄	C₁₃×#577	1	2	yes	—
722	C₄	C₁₃×#578	1	2	yes	—
723	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	4	2	no	—
726	C₂	—	8	2	no	—
727	C₂	—	8	2	no	—
728	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
729	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
730	C₂	C₂×C₁₃×#578	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3210	C₂	semidirect
5. C₁₃×#3209	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3206	C₂	semidirect
8. C₁₃×#3152	C₂	semidirect
9. C₁₃×#3147	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₂×C₁₃×#487	C₂	semidirect
12. C₁₃×#3046	C₂	semidirect
13. C₁₃×#3013	C₂	semidirect
14. C₁₃×#2922	C₂	semidirect
184. #60824	C₁₃	direct (N × H)
280. #3511	C₂×C₁₃	semidirect
281. #3499	C₂×C₁₃	semidirect
282. #3225	C₂×C₁₃	semidirect
283. #3210	C₂×C₁₃	semidirect
284. #3209	C₂×C₁₃	semidirect
285. #3207	C₂×C₁₃	semidirect
286. #3206	C₂×C₁₃	semidirect
287. #3152	C₂×C₁₃	semidirect
288. #3147	C₂×C₁₃	semidirect
289. #3141	C₂×C₁₃	semidirect
290. C₂×#487	C₂×C₁₃	semidirect
291. #3046	C₂×C₁₃	semidirect
292. #3013	C₂×C₁₃	semidirect
293. #2922	C₂×C₁₃	semidirect
644. C₁₃	#60824	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3499	2
C₁₃×#3225	2
C₁₃×#3210	2
C₁₃×#3209	2
C₁₃×#3207	2
C₁₃×#3206	2
C₁₃×#3152	2
C₁₃×#3147	2
C₁₃×#3141	2
C₂×C₁₃×#487	2
C₁₃×#3046	2
C₁₃×#3013	2
C₁₃×#2922	2
#60824	13

Subgroups — C13×#60824 #15747163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60824 #15747163