Subgroups — C₁₃×#60900 #15747239

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3250	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3248	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3247	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3076	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3050	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3035	C₂	1	4	yes	maximal, complemented
11	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	4	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	2	yes	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	—	2	2	no	—
23	C₁₃×#529	—	2	2	no	—
24	C₁₃×#529	C₂²	1	4	yes	—
25	C₁₃×#529	C₂²	1	4	yes	—
26	C₁₃×#525	—	2	2	no	—
27	C₁₃×#525	—	2	2	no	—
28	C₁₃×#525	C₂²	1	4	yes	—
29	C₄×C₁₃×#41	—	2	2	no	—
30	C₄×C₁₃×#41	—	2	2	no	—
31	C₄×C₁₃×#41	C₂²	1	4	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#479	C₂²	1	8	yes	complemented
34	C₁₃×#478	C₂²	1	8	yes	complemented
35	C₁₃×#477	C₂²	1	4	yes	complemented
36	C₁₃×#476	C₂²	1	4	yes	complemented
37	C₁₃×#475	C₂²	1	4	yes	complemented
38	C₁₃×#474	C₂²	1	4	yes	complemented
39	C₁₃×#467	C₂²	1	4	yes	—
40	C₁₃×#467	C₂²	1	4	yes	—
41	C₁₃×#466	C₂²	1	4	yes	—
42	C₁₃×#466	C₂²	1	4	yes	—
43	C₁₃×#465	C₂²	1	8	yes	—
44	C₁₃×#465	C₂²	1	8	yes	—
45	C₁₃×#464	C₂²	1	8	yes	complemented
46	C₁₃×#463	C₂²	1	8	yes	complemented
47	C₁₃×#462	C₂²	1	4	yes	complemented
48	C₁₃×#461	C₂²	1	4	yes	complemented
49	C₁₃×#460	C₂²	1	4	yes	complemented
50	C₁₃×#459	C₂²	1	4	yes	complemented
51	C₁₃×#427	C₂²	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
53	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
57	C₁₃×#416	C₂²	1	8	yes	—
58	C₂×C₁₃×#41	—	2	2	no	—
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#135	—	4	8	no	—
65	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
67	C₂×C₁₃×D₈	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₃	—	4	4	no	—
69	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₃×#127	C₂³	1	2	yes	—
77	C₁₃×#126	—	2	4	no	—
78	C₁₃×#126	—	2	4	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	C₂³	1	4	yes	—
85	C₁₃×#123	—	2	4	no	—
86	C₁₃×#123	—	2	4	no	—
87	C₁₃×#123	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	C₂³	1	4	yes	—
99	C₁₃×#121	C₂³	1	4	yes	—
100	C₁₃×#120	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	—	2	2	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	C₂³	1	4	yes	—
118	C₄×D₄×C₁₃	C₂³	1	4	yes	—
119	C₁₃×#117	—	2	2	no	—
120	C₁₃×#117	—	2	2	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	—	2	4	no	—
126	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	D₄	1	2	yes	—
128	C₂×C₄²×C₁₃	D₄	1	2	yes	—
129	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×#107	C₂³	1	4	yes	—
135	C₁₃×#107	C₂³	1	4	yes	—
136	C₁₃×#106	C₂³	1	8	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
140	C₁₃×#103	C₂³	1	8	yes	—
141	C₁₃×#103	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	8	yes	—
144	#60900	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×#41	—	2	8	no	—
147	C₁₃×#41	—	2	8	no	—
148	C₁₃×#41	—	4	8	no	—
149	C₁₃×#41	—	4	8	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×Q₁₆	—	4	4	no	—
181	C₁₃×SD₁₆	—	4	8	no	—
182	C₁₃×D₈	—	4	4	no	—
183	C₂×C₈×C₁₃	—	2	8	no	—
184	C₂×C₈×C₁₃	—	4	2	no	—
185	C₂×C₈×C₁₃	—	4	4	no	—
186	C₂×C₈×C₁₃	—	4	2	no	—
187	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
188	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂⁴	1	2	yes	—
220	C₄²×C₁₃	C₂⁴	1	2	yes	—
221	#3444	C₂×C₁₃	1	2	yes	complemented
222	#3250	C₂×C₁₃	1	4	yes	complemented
223	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#3248	C₂×C₁₃	1	4	yes	complemented
225	#3247	C₂×C₁₃	1	4	yes	complemented
226	#3246	C₂×C₁₃	1	2	yes	complemented
227	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3076	C₂×C₁₃	1	4	yes	complemented
229	#3050	C₂×C₁₃	1	4	yes	complemented
230	#3035	C₂×C₁₃	1	4	yes	complemented
231	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	2	4	no	—
241	Q₈×C₁₃	—	4	4	no	—
242	Q₈×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	8	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	#135	1	4	yes	complemented
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
279	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
281	C₈×C₁₃	—	2	4	no	—
282	C₈×C₁₃	—	2	4	no	—
283	C₂×#135	C₂²×C₁₃	1	4	yes	—
284	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
285	#533	C₂²×C₁₃	1	2	yes	—
286	#533	C₂²×C₁₃	1	2	yes	—
287	#533	C₂²×C₁₃	1	2	yes	—
288	#532	C₂²×C₁₃	1	2	yes	—
289	#532	C₂²×C₁₃	1	2	yes	—
290	#532	C₂²×C₁₃	1	2	yes	—
291	#529	—	2	2	no	—
292	#529	—	2	2	no	—
293	#529	—	2	2	no	—
294	#529	—	2	2	no	—
295	#529	C₂²×C₁₃	1	4	yes	—
296	#529	C₂²×C₁₃	1	4	yes	—
297	#525	—	2	2	no	—
298	#525	—	2	2	no	—
299	#525	C₂²×C₁₃	1	4	yes	—
300	C₄×#41	—	2	2	no	—
301	C₄×#41	—	2	2	no	—
302	C₄×#41	C₂²×C₁₃	1	4	yes	—
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#479	C₂²×C₁₃	1	8	yes	complemented
305	#478	C₂²×C₁₃	1	8	yes	complemented
306	#477	C₂²×C₁₃	1	4	yes	complemented
307	#476	C₂²×C₁₃	1	4	yes	complemented
308	#475	C₂²×C₁₃	1	4	yes	complemented
309	#474	C₂²×C₁₃	1	4	yes	complemented
310	#467	C₂²×C₁₃	1	4	yes	—
311	#467	C₂²×C₁₃	1	4	yes	—
312	#466	C₂²×C₁₃	1	4	yes	—
313	#466	C₂²×C₁₃	1	4	yes	—
314	#465	C₂²×C₁₃	1	8	yes	—
315	#465	C₂²×C₁₃	1	8	yes	—
316	#464	C₂²×C₁₃	1	8	yes	complemented
317	#463	C₂²×C₁₃	1	8	yes	complemented
318	#462	C₂²×C₁₃	1	4	yes	complemented
319	#461	C₂²×C₁₃	1	4	yes	complemented
320	#460	C₂²×C₁₃	1	4	yes	complemented
321	#459	C₂²×C₁₃	1	4	yes	complemented
322	#427	C₂²×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
324	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
327	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
328	#416	C₂²×C₁₃	1	8	yes	—
329	C₂²×C₁₃	—	2	8	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	4	4	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	#537	1	2	yes	—
340	C₂²×C₁₃	C₂×#135	1	2	yes	—
341	C₂²×C₁₃	#575	1	2	yes	—
342	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	4	4	no	—
349	C₄×C₁₃	—	4	4	no	—
350	C₄×C₁₃	—	4	4	no	—
351	C₄×C₁₃	#537	1	2	yes	—
352	C₄×C₁₃	C₂×#135	1	4	yes	—
353	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	C₂³×C₁₃	1	4	yes	—
358	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
361	#135	—	4	8	no	—
362	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
363	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
364	C₂×D₈	C₂³×C₁₃	1	4	yes	—
365	C₂²×C₈	—	4	4	no	—
366	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
367	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
368	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
369	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
371	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
372	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
373	#127	C₂³×C₁₃	1	2	yes	—
374	#126	—	2	4	no	—
375	#126	—	2	4	no	—
376	#125	—	2	2	no	—
377	#125	—	2	2	no	—
378	#125	C₂³×C₁₃	1	4	yes	—
379	#124	—	2	2	no	—
380	#124	—	2	2	no	—
381	#124	C₂³×C₁₃	1	4	yes	—
382	#123	—	2	4	no	—
383	#123	—	2	4	no	—
384	#123	—	2	4	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
390	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	2	no	—
394	#121	—	2	2	no	—
395	#121	C₂³×C₁₃	1	4	yes	—
396	#121	C₂³×C₁₃	1	4	yes	—
397	#120	—	2	4	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
403	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	2	4	no	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	—	2	4	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	C₂³×C₁₃	1	4	yes	—
415	C₄×D₄	C₂³×C₁₃	1	4	yes	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	#117	—	2	4	no	—
419	#117	—	2	4	no	—
420	#117	—	2	4	no	—
421	#117	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄²	—	2	4	no	—
423	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	D₄×C₁₃	1	2	yes	—
425	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	D₄×C₁₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	#107	C₂³×C₁₃	1	4	yes	—
432	#107	C₂³×C₁₃	1	4	yes	—
433	#106	C₂³×C₁₃	1	8	yes	—
434	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
435	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
436	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
437	#103	C₂³×C₁₃	1	8	yes	—
438	#103	C₂³×C₁₃	1	8	yes	—
439	#102	C₂³×C₁₃	1	8	yes	—
440	#102	C₂³×C₁₃	1	8	yes	—
441	C₂×C₁₃	—	2	2	no	—
442	C₂×C₁₃	—	2	2	no	—
443	C₂×C₁₃	—	2	2	no	—
444	C₂×C₁₃	—	8	4	no	—
445	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
446	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
447	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
448	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
449	#41	—	2	8	no	—
450	#41	—	2	8	no	—
451	#41	—	4	8	no	—
452	#41	—	4	8	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
483	Q₁₆	—	4	4	no	—
484	SD₁₆	—	4	8	no	—
485	D₈	—	4	4	no	—
486	C₂×C₈	—	2	8	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	4	4	no	—
489	C₂×C₈	—	4	2	no	—
490	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
491	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	C₂×D₄×C₁₃	1	2	yes	—
517	C₄²	C₂×D₄×C₁₃	1	2	yes	—
518	C₄²	C₂×D₄×C₁₃	1	2	yes	—
519	C₄²	C₂×D₄×C₁₃	1	2	yes	—
520	C₄²	C₂×D₄×C₁₃	1	2	yes	—
521	C₄²	C₂×D₄×C₁₃	1	2	yes	—
522	C₄²	C₂⁴×C₁₃	1	2	yes	—
523	C₄²	C₂⁴×C₁₃	1	2	yes	—
524	C₁₃	#60900	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	Q₈	—	2	4	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	4	4	no	—
535	Q₈	—	4	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	8	no	—
542	D₄	—	4	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	C₁₃×#135	1	4	yes	complemented
564	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
571	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
573	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
574	C₈	—	2	4	no	—
575	C₈	—	2	4	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	C₁₃×#537	1	2	yes	—
587	C₂²	C₂×C₁₃×#135	1	2	yes	—
588	C₂²	C₁₃×#575	1	2	yes	—
589	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	4	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	4	no	—
598	C₄	C₁₃×#537	1	2	yes	—
599	C₄	C₂×C₁₃×#135	1	4	yes	—
600	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
602	C₂	—	2	2	no	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	8	4	no	—
606	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
607	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
608	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3250	C₂	semidirect
3. C₁₃×#3249	C₂	semidirect
4. C₁₃×#3248	C₂	semidirect
5. C₁₃×#3247	C₂	semidirect
6. C₁₃×#3246	C₂	semidirect
7. C₁₃×#3245	C₂	semidirect
8. C₁₃×#3076	C₂	semidirect
9. C₁₃×#3050	C₂	semidirect
10. C₁₃×#3035	C₂	semidirect
11. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
33. C₁₃×#479	C₂²	semidirect
34. C₁₃×#478	C₂²	semidirect
35. C₁₃×#477	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
45. C₁₃×#464	C₂²	semidirect
46. C₁₃×#463	C₂²	semidirect
47. C₁₃×#462	C₂²	semidirect
48. C₁₃×#461	C₂²	semidirect
49. C₁₃×#460	C₂²	semidirect
50. C₁₃×#459	C₂²	semidirect
144. #60900	C₁₃	direct (N × H)
221. #3444	C₂×C₁₃	semidirect
222. #3250	C₂×C₁₃	semidirect
223. #3249	C₂×C₁₃	semidirect
224. #3248	C₂×C₁₃	semidirect
225. #3247	C₂×C₁₃	semidirect
226. #3246	C₂×C₁₃	semidirect
227. #3245	C₂×C₁₃	semidirect
228. #3076	C₂×C₁₃	semidirect
229. #3050	C₂×C₁₃	semidirect
230. #3035	C₂×C₁₃	semidirect
231. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
270. C₂×C₄×C₁₃	#135	semidirect
304. #479	C₂²×C₁₃	semidirect
305. #478	C₂²×C₁₃	semidirect
306. #477	C₂²×C₁₃	semidirect
307. #476	C₂²×C₁₃	semidirect
308. #475	C₂²×C₁₃	semidirect
309. #474	C₂²×C₁₃	semidirect
316. #464	C₂²×C₁₃	semidirect
317. #463	C₂²×C₁₃	semidirect
318. #462	C₂²×C₁₃	semidirect
319. #461	C₂²×C₁₃	semidirect
320. #460	C₂²×C₁₃	semidirect
321. #459	C₂²×C₁₃	semidirect
524. C₁₃	#60900	direct (N × H)
563. 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×#3444	2
C₁₃×#3250	2
C₁₃×#3249	2
C₁₃×#3248	2
C₁₃×#3247	2
C₁₃×#3246	2
C₁₃×#3245	2
C₁₃×#3076	2
C₁₃×#3050	2
C₁₃×#3035	2
C₂²×C₁₃×C₄⋊C₈	2
#60900	13

Subgroups — C13×#60900 #15747239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60900 #15747239