Subgroups — C₁₃×#60907 #15747246

Order 3328.

1910 conjugacy classes of subgroups.

The subgroup lattice has 594 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×#3256	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3252	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3251	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3076	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3054	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3035	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	4	yes	—
13	C₂²×C₁₃×M₁₆	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×#470	C₂²	1	4	yes	—
40	C₁₃×#470	C₂²	1	4	yes	—
41	C₁₃×#469	C₂²	1	4	yes	—
42	C₁₃×#469	C₂²	1	4	yes	—
43	C₁₃×#468	C₂²	1	8	yes	—
44	C₁₃×#468	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	C₁₃×#423	C₂²	1	4	yes	—
53	C₁₃×#423	C₂²	1	1	yes	characteristic
54	C₁₃×#423	C₂²	1	1	yes	characteristic
55	C₁₃×#423	C₂²	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	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	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#135	—	4	8	no	—
64	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×D₈	C₂³	1	4	yes	—
67	C₂×C₁₃×M₁₆	—	4	4	no	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×#127	C₂³	1	2	yes	—
76	C₁₃×#126	—	2	4	no	—
77	C₁₃×#126	—	2	4	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	C₂³	1	4	yes	—
81	C₁₃×#124	—	2	2	no	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂³	1	4	yes	—
84	C₁₃×#123	—	2	4	no	—
85	C₁₃×#123	—	2	4	no	—
86	C₁₃×#123	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	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	C₂³	1	4	yes	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	C₂³	1	4	yes	—
98	C₁₃×#121	C₂³	1	4	yes	—
99	C₁₃×#120	—	2	4	no	—
100	C₄×Q₈×C₁₃	—	2	2	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	C₂³	1	4	yes	—
105	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
106	C₄×D₄×C₁₃	—	2	4	no	—
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	2	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	C₂³	1	4	yes	—
117	C₄×D₄×C₁₃	C₂³	1	4	yes	—
118	C₁₃×#117	—	2	2	no	—
119	C₁₃×#117	—	2	2	no	—
120	C₁₃×#117	—	2	4	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₁₃×#117	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃	—	2	4	no	—
125	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	D₄	1	2	yes	—
127	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
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	8	yes	—
135	C₁₃×#106	C₂³	1	4	yes	—
136	C₁₃×#106	C₂³	1	4	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	#60907	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	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×Q₁₆	—	4	4	no	—
178	C₁₃×SD₁₆	—	4	8	no	—
179	C₁₃×D₈	—	4	4	no	—
180	C₁₃×M₁₆	—	4	2	no	—
181	C₁₃×M₁₆	—	4	4	no	—
182	C₁₃×M₁₆	—	4	2	no	—
183	C₂×C₈×C₁₃	—	2	8	no	—
184	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	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	C₂⁴	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	2	yes	—
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	2	yes	—
219	C₄²×C₁₃	C₂⁴	1	2	yes	—
220	#3444	C₂×C₁₃	1	2	yes	complemented
221	#3256	C₂×C₁₃	1	4	yes	complemented
222	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3254	C₂×C₁₃	1	2	yes	complemented
224	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3252	C₂×C₁₃	1	4	yes	complemented
226	#3251	C₂×C₁₃	1	4	yes	complemented
227	#3076	C₂×C₁₃	1	4	yes	complemented
228	#3054	C₂×C₁₃	1	4	yes	complemented
229	#3035	C₂×C₁₃	1	4	yes	complemented
230	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	4	no	—
238	Q₈×C₁₃	—	2	4	no	—
239	Q₈×C₁₃	—	4	4	no	—
240	Q₈×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	8	no	—
245	D₄×C₁₃	—	4	8	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	4	8	no	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
277	C₈×C₁₃	—	2	4	no	—
278	C₈×C₁₃	—	2	4	no	—
279	C₂×#135	C₂²×C₁₃	1	4	yes	—
280	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
281	#533	C₂²×C₁₃	1	2	yes	—
282	#533	C₂²×C₁₃	1	2	yes	—
283	#533	C₂²×C₁₃	1	2	yes	—
284	#532	C₂²×C₁₃	1	2	yes	—
285	#532	C₂²×C₁₃	1	2	yes	—
286	#532	C₂²×C₁₃	1	2	yes	—
287	#529	—	2	2	no	—
288	#529	—	2	2	no	—
289	#529	—	2	2	no	—
290	#529	—	2	2	no	—
291	#529	C₂²×C₁₃	1	4	yes	—
292	#529	C₂²×C₁₃	1	4	yes	—
293	#525	—	2	2	no	—
294	#525	—	2	2	no	—
295	#525	C₂²×C₁₃	1	4	yes	—
296	C₄×#41	—	2	2	no	—
297	C₄×#41	—	2	2	no	—
298	C₄×#41	C₂²×C₁₃	1	4	yes	—
299	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
300	#479	C₂²×C₁₃	1	8	yes	complemented
301	#478	C₂²×C₁₃	1	8	yes	complemented
302	#477	C₂²×C₁₃	1	4	yes	complemented
303	#476	C₂²×C₁₃	1	4	yes	complemented
304	#475	C₂²×C₁₃	1	4	yes	complemented
305	#474	C₂²×C₁₃	1	4	yes	complemented
306	#470	C₂²×C₁₃	1	4	yes	—
307	#470	C₂²×C₁₃	1	4	yes	—
308	#469	C₂²×C₁₃	1	4	yes	—
309	#469	C₂²×C₁₃	1	4	yes	—
310	#468	C₂²×C₁₃	1	8	yes	—
311	#468	C₂²×C₁₃	1	8	yes	—
312	#464	C₂²×C₁₃	1	8	yes	complemented
313	#463	C₂²×C₁₃	1	8	yes	complemented
314	#462	C₂²×C₁₃	1	4	yes	complemented
315	#461	C₂²×C₁₃	1	4	yes	complemented
316	#460	C₂²×C₁₃	1	4	yes	complemented
317	#459	C₂²×C₁₃	1	4	yes	complemented
318	#427	C₂²×C₁₃	1	4	yes	—
319	#423	C₂²×C₁₃	1	4	yes	—
320	#423	C₂²×C₁₃	1	1	yes	characteristic
321	#423	C₂²×C₁₃	1	1	yes	characteristic
322	#423	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
324	#416	C₂²×C₁₃	1	8	yes	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	—	4	4	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	#537	1	2	yes	—
335	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	4	4	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	#537	1	2	yes	—
345	C₄×C₁₃	#575	1	4	yes	—
346	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	C₂³×C₁₃	1	4	yes	—
351	C₂³×C₄	D₄×C₁₃	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
353	#135	—	4	8	no	—
354	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
355	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
356	C₂×D₈	C₂³×C₁₃	1	4	yes	—
357	C₂×M₁₆	—	4	4	no	—
358	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
359	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
360	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
361	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
362	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
364	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
365	#127	C₂³×C₁₃	1	2	yes	—
366	#126	—	2	4	no	—
367	#126	—	2	4	no	—
368	#125	—	2	2	no	—
369	#125	—	2	2	no	—
370	#125	C₂³×C₁₃	1	4	yes	—
371	#124	—	2	2	no	—
372	#124	—	2	2	no	—
373	#124	C₂³×C₁₃	1	4	yes	—
374	#123	—	2	4	no	—
375	#123	—	2	4	no	—
376	#123	—	2	4	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
382	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	C₂³×C₁₃	1	4	yes	—
388	#121	C₂³×C₁₃	1	4	yes	—
389	#120	—	2	4	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
395	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
396	C₄×D₄	—	2	4	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	C₂³×C₁₃	1	4	yes	—
407	C₄×D₄	C₂³×C₁₃	1	4	yes	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	—	2	4	no	—
411	#117	—	2	4	no	—
412	#117	—	2	4	no	—
413	#117	C₂³×C₁₃	1	4	yes	—
414	C₂×C₄²	—	2	4	no	—
415	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	D₄×C₁₃	1	2	yes	—
417	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	#107	C₂³×C₁₃	1	8	yes	—
425	#106	C₂³×C₁₃	1	4	yes	—
426	#106	C₂³×C₁₃	1	4	yes	—
427	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
428	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
429	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
430	#103	C₂³×C₁₃	1	8	yes	—
431	#103	C₂³×C₁₃	1	8	yes	—
432	#102	C₂³×C₁₃	1	8	yes	—
433	#102	C₂³×C₁₃	1	8	yes	—
434	C₂×C₁₃	—	2	2	no	—
435	C₂×C₁₃	—	4	1	no	—
436	C₂×C₁₃	—	4	1	no	—
437	C₂×C₁₃	—	8	4	no	—
438	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
439	C₂×C₁₃	C₂×#575	1	2	yes	—
440	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
441	#41	—	2	8	no	—
442	#41	—	2	8	no	—
443	#41	—	4	8	no	—
444	#41	—	4	8	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
472	Q₁₆	—	4	4	no	—
473	SD₁₆	—	4	8	no	—
474	D₈	—	4	4	no	—
475	M₁₆	—	4	2	no	—
476	M₁₆	—	4	4	no	—
477	M₁₆	—	4	2	no	—
478	C₂×C₈	—	2	8	no	—
479	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
480	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
492	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	C₂×D₄×C₁₃	1	2	yes	—
506	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₁₃	1	2	yes	—
508	C₄²	C₂×D₄×C₁₃	1	2	yes	—
509	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	2	yes	—
511	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₃	1	2	yes	—
514	C₄²	C₂⁴×C₁₃	1	2	yes	—
515	C₁₃	#60907	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
521	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	2	4	no	—
524	Q₈	—	4	4	no	—
525	Q₈	—	4	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
560	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
561	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
562	C₈	—	2	4	no	—
563	C₈	—	2	4	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	C₁₃×#537	1	2	yes	—
574	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₄	C₁₃×#537	1	2	yes	—
584	C₄	C₁₃×#575	1	4	yes	—
585	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
586	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
587	C₂	—	2	2	no	—
588	C₂	—	4	1	no	—
589	C₂	—	4	1	no	—
590	C₂	—	8	4	no	—
591	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
592	C₂	C₂×C₁₃×#575	1	2	yes	—

	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×#3256	C₂	semidirect
3. C₁₃×#3255	C₂	semidirect
4. C₁₃×#3254	C₂	semidirect
5. C₁₃×#3253	C₂	semidirect
6. C₁₃×#3252	C₂	semidirect
7. C₁₃×#3251	C₂	semidirect
8. C₁₃×#3076	C₂	semidirect
9. C₁₃×#3054	C₂	semidirect
10. C₁₃×#3035	C₂	semidirect
11. C₂×C₁₃×#423	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. #60907	C₁₃	direct (N × H)
220. #3444	C₂×C₁₃	semidirect
221. #3256	C₂×C₁₃	semidirect
222. #3255	C₂×C₁₃	semidirect
223. #3254	C₂×C₁₃	semidirect
224. #3253	C₂×C₁₃	semidirect
225. #3252	C₂×C₁₃	semidirect
226. #3251	C₂×C₁₃	semidirect
227. #3076	C₂×C₁₃	semidirect
228. #3054	C₂×C₁₃	semidirect
229. #3035	C₂×C₁₃	semidirect
230. C₂×#423	C₂×C₁₃	semidirect
300. #479	C₂²×C₁₃	semidirect
301. #478	C₂²×C₁₃	semidirect
302. #477	C₂²×C₁₃	semidirect
303. #476	C₂²×C₁₃	semidirect
304. #475	C₂²×C₁₃	semidirect
305. #474	C₂²×C₁₃	semidirect
312. #464	C₂²×C₁₃	semidirect
313. #463	C₂²×C₁₃	semidirect
314. #462	C₂²×C₁₃	semidirect
315. #461	C₂²×C₁₃	semidirect
316. #460	C₂²×C₁₃	semidirect
317. #459	C₂²×C₁₃	semidirect
515. C₁₃	#60907	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×#3444	2
C₁₃×#3256	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3253	2
C₁₃×#3252	2
C₁₃×#3251	2
C₁₃×#3076	2
C₁₃×#3054	2
C₁₃×#3035	2
C₂×C₁₃×#423	2
#60907	13

Subgroups — C13×#60907 #15747246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60907 #15747246