Subgroups — C₁₃×#60884 #15747223

Order 3328.

1622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3242	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3237	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3236	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3097	C₂	1	4	yes	maximal
11	C₁₃×#3082	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#557	—	2	2	no	—
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#556	—	2	2	no	—
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	—	2	2	no	—
18	C₁₃×#552	—	2	4	no	—
19	C₁₃×#544	C₂²	1	2	yes	—
20	C₁₃×#544	C₂²	1	4	yes	—
21	C₁₃×#541	C₂²	1	4	yes	—
22	C₁₃×#536	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	4	yes	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₁₃×#533	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	2	yes	—
30	C₁₃×#520	C₂²	1	2	yes	—
31	C₁₃×#519	C₂²	1	2	yes	—
32	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
33	C₁₃×#501	C₂²	1	2	yes	—
34	C₁₃×#501	C₂²	1	2	yes	—
35	C₁₃×#501	C₂²	1	4	yes	—
36	C₁₃×#501	C₂²	1	4	yes	—
37	C₁₃×#499	C₂²	1	4	yes	—
38	C₁₃×#491	C₂²	1	4	yes	—
39	C₁₃×#491	C₂²	1	4	yes	—
40	C₁₃×#491	C₂²	1	2	yes	—
41	C₁₃×#491	C₂²	1	2	yes	—
42	C₁₃×#487	C₂²	1	4	yes	—
43	C₁₃×#485	C₂²	1	8	yes	—
44	C₁₃×#485	C₂²	1	8	yes	—
45	C₁₃×#484	C₂²	1	8	yes	—
46	C₁₃×#483	C₂²	1	8	yes	—
47	C₁₃×#479	C₂²	1	8	yes	—
48	C₁₃×#479	C₂²	1	8	yes	—
49	C₁₃×#477	C₂²	1	8	yes	—
50	C₁₃×#475	C₂²	1	8	yes	—
51	C₁₃×#433	C₂²	1	4	yes	—
52	C₁₃×#432	C₂²	1	4	yes	—
53	C₁₃×#428	C₂²	1	4	yes	—
54	C₁₃×#427	C₂²	1	4	yes	—
55	C₁₃×#424	C₂²	1	2	yes	—
56	C₁₃×#419	C₂²	1	4	yes	—
57	C₂×C₁₃×#103	C₂²	1	4	yes	—
58	C₁₃×#408	C₂²	1	2	yes	—
59	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	4	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×#126	—	2	8	no	—
75	C₁₃×#125	—	2	8	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	—	2	4	no	—
78	C₁₃×#125	—	2	4	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	—	2	4	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#125	C₂³	1	2	yes	—
83	C₁₃×#125	C₂³	1	2	yes	—
84	C₁₃×#125	C₂³	1	1	yes	characteristic
85	C₁₃×#125	C₂³	1	1	yes	characteristic
86	C₁₃×#125	C₂³	1	2	yes	—
87	C₁₃×#124	—	2	2	no	—
88	C₁₃×#123	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	4	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	—	2	4	no	—
93	C₁₃×C₂²⋊Q₈	—	2	4	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	4	no	—
99	C₄×Q₈×C₁₃	—	2	4	no	—
100	C₄×Q₈×C₁₃	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	D₄	1	2	yes	—
104	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	D₄	1	4	yes	—
108	C₄×D₄×C₁₃	D₄	1	2	yes	—
109	C₁₃×#117	—	2	4	no	—
110	C₁₃×#117	—	2	4	no	—
111	C₁₃×#117	C₂³	1	2	yes	—
112	C₁₃×#117	C₂³	1	2	yes	—
113	C₁₃×#117	C₂³	1	4	yes	—
114	C₁₃×#117	C₂³	1	1	yes	characteristic
115	C₁₃×#117	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#107	C₂³	1	4	yes	—
125	C₁₃×#107	C₂³	1	8	yes	—
126	C₁₃×#106	C₂³	1	4	yes	—
127	C₁₃×#106	C₂³	1	4	yes	—
128	C₁₃×#106	C₂³	1	8	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
130	C₁₃×#103	C₂³	1	8	yes	—
131	C₁₃×#103	C₂³	1	8	yes	—
132	C₁₃×#103	C₂³	1	8	yes	—
133	C₁₃×#103	C₂³	1	8	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₁₃×#97	C₂³	1	2	yes	—
136	C₁₃×#97	C₂³	1	2	yes	—
137	C₁₃×#97	C₂³	1	2	yes	—
138	C₄×C₈×C₁₃	C₂³	1	2	yes	—
139	#60884	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₁₃×#41	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	2	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	8	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×M₁₆	—	2	4	no	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
160	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
188	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	—	2	8	no	—
190	C₄²×C₁₃	—	2	4	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	—	2	2	no	—
193	C₄²×C₁₃	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃	C₂×D₄	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	2	yes	—
198	#3509	C₂×C₁₃	1	1	yes	characteristic
199	#3504	C₂×C₁₃	1	1	yes	characteristic
200	#3242	C₂×C₁₃	1	8	yes	complemented
201	#3237	C₂×C₁₃	1	4	yes	complemented
202	#3236	C₂×C₁₃	1	4	yes	complemented
203	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3097	C₂×C₁₃	1	4	yes	—
208	#3082	C₂×C₁₃	1	4	yes	complemented
209	#2923	C₂×C₁₃	1	1	yes	characteristic
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	8	no	—
214	Q₈×C₁₃	—	4	4	no	—
215	Q₈×C₁₃	—	4	4	no	—
216	Q₈×C₁₃	—	8	4	no	—
217	Q₈×C₁₃	—	8	2	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	8	2	no	—
230	C₂×C₄×C₁₃	—	8	4	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₁₃	—	2	4	no	—
239	C₈×C₁₃	—	2	4	no	—
240	#557	—	2	2	no	—
241	#557	—	2	2	no	—
242	#556	—	2	2	no	—
243	#554	—	2	4	no	—
244	#554	—	2	2	no	—
245	#552	—	2	4	no	—
246	#544	C₂²×C₁₃	1	2	yes	—
247	#544	C₂²×C₁₃	1	4	yes	—
248	#541	C₂²×C₁₃	1	4	yes	—
249	#536	C₂²×C₁₃	1	2	yes	—
250	#533	C₂²×C₁₃	1	4	yes	—
251	#533	C₂²×C₁₃	1	1	yes	characteristic
252	#533	C₂²×C₁₃	1	1	yes	characteristic
253	#533	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#125	C₂²×C₁₃	1	2	yes	—
257	#520	C₂²×C₁₃	1	2	yes	—
258	#519	C₂²×C₁₃	1	2	yes	—
259	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
260	#501	C₂²×C₁₃	1	2	yes	—
261	#501	C₂²×C₁₃	1	2	yes	—
262	#501	C₂²×C₁₃	1	4	yes	—
263	#501	C₂²×C₁₃	1	4	yes	—
264	#499	C₂²×C₁₃	1	4	yes	—
265	#491	C₂²×C₁₃	1	4	yes	—
266	#491	C₂²×C₁₃	1	4	yes	—
267	#491	C₂²×C₁₃	1	2	yes	—
268	#491	C₂²×C₁₃	1	2	yes	—
269	#487	C₂²×C₁₃	1	4	yes	—
270	#485	C₂²×C₁₃	1	8	yes	—
271	#485	C₂²×C₁₃	1	8	yes	—
272	#484	C₂²×C₁₃	1	8	yes	—
273	#483	C₂²×C₁₃	1	8	yes	—
274	#479	C₂²×C₁₃	1	8	yes	—
275	#479	C₂²×C₁₃	1	8	yes	—
276	#477	C₂²×C₁₃	1	8	yes	—
277	#475	C₂²×C₁₃	1	8	yes	—
278	#433	C₂²×C₁₃	1	4	yes	—
279	#432	C₂²×C₁₃	1	4	yes	—
280	#428	C₂²×C₁₃	1	4	yes	—
281	#427	C₂²×C₁₃	1	4	yes	—
282	#424	C₂²×C₁₃	1	2	yes	—
283	#419	C₂²×C₁₃	1	4	yes	—
284	C₂×#103	C₂²×C₁₃	1	4	yes	—
285	#408	C₂²×C₁₃	1	2	yes	—
286	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	4	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	#536	1	2	yes	—
292	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	4	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	#536	1	2	yes	—
303	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
304	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
306	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	—	2	4	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
316	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
317	#126	—	2	8	no	—
318	#125	—	2	8	no	—
319	#125	—	2	2	no	—
320	#125	—	2	4	no	—
321	#125	—	2	4	no	—
322	#125	—	2	2	no	—
323	#125	—	2	4	no	—
324	#125	C₂³×C₁₃	1	2	yes	—
325	#125	C₂³×C₁₃	1	1	yes	characteristic
326	#125	C₂³×C₁₃	1	4	yes	—
327	#125	C₂³×C₁₃	1	2	yes	—
328	#125	C₂³×C₁₃	1	1	yes	characteristic
329	#125	C₂³×C₁₃	1	2	yes	—
330	#124	—	2	2	no	—
331	#123	—	2	4	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	—	2	4	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	D₄×C₁₃	1	2	yes	—
347	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	D₄×C₁₃	1	4	yes	—
351	C₄×D₄	D₄×C₁₃	1	2	yes	—
352	#117	—	2	4	no	—
353	#117	—	2	4	no	—
354	#117	C₂³×C₁₃	1	2	yes	—
355	#117	C₂³×C₁₃	1	2	yes	—
356	#117	C₂³×C₁₃	1	4	yes	—
357	#117	C₂³×C₁₃	1	1	yes	characteristic
358	#117	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
366	#107	C₂³×C₁₃	1	4	yes	—
367	#107	C₂³×C₁₃	1	4	yes	—
368	#107	C₂³×C₁₃	1	8	yes	—
369	#106	C₂³×C₁₃	1	4	yes	—
370	#106	C₂³×C₁₃	1	4	yes	—
371	#106	C₂³×C₁₃	1	8	yes	—
372	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
373	#103	C₂³×C₁₃	1	8	yes	—
374	#103	C₂³×C₁₃	1	8	yes	—
375	#103	C₂³×C₁₃	1	8	yes	—
376	#103	C₂³×C₁₃	1	8	yes	—
377	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
378	#97	C₂³×C₁₃	1	2	yes	—
379	#97	C₂³×C₁₃	1	2	yes	—
380	#97	C₂³×C₁₃	1	2	yes	—
381	C₄×C₈	C₂³×C₁₃	1	2	yes	—
382	C₂×C₁₃	—	2	2	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
385	C₂×C₁₃	#3586	1	2	yes	—
386	#41	—	2	4	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
394	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	M₁₆	—	2	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
406	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₄²	—	2	8	no	—
436	C₄²	—	2	4	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	C₂×D₄×C₁₃	1	4	yes	—
440	C₄²	C₂×D₄×C₁₃	1	2	yes	—
441	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₄²	C₂⁴×C₁₃	1	2	yes	—
444	C₁₃	#60884	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	8	4	no	—
452	Q₈	—	8	2	no	—
453	D₄	—	2	4	no	—
454	D₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	—	8	4	no	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
472	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
473	C₈	—	2	4	no	—
474	C₈	—	2	4	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	2	no	—
478	C₂²	C₁₃×#536	1	2	yes	—
479	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	C₁₃×#536	1	2	yes	—
490	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
491	C₂	—	2	2	no	—
492	C₂	—	4	2	no	—
493	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
494	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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
3. C₁₃×#3242	C₂	semidirect
4. C₁₃×#3237	C₂	semidirect
5. C₁₃×#3236	C₂	semidirect
6. C₁₃×#3166	C₂	semidirect
7. C₁₃×#3162	C₂	semidirect
8. C₁₃×#3139	C₂	semidirect
9. C₂×C₁₃×#491	C₂	semidirect
11. C₁₃×#3082	C₂	semidirect
139. #60884	C₁₃	direct (N × H)
200. #3242	C₂×C₁₃	semidirect
201. #3237	C₂×C₁₃	semidirect
202. #3236	C₂×C₁₃	semidirect
203. #3166	C₂×C₁₃	semidirect
204. #3162	C₂×C₁₃	semidirect
205. #3139	C₂×C₁₃	semidirect
206. C₂×#491	C₂×C₁₃	semidirect
208. #3082	C₂×C₁₃	semidirect
444. C₁₃	#60884	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×#3509	2
C₁₃×#3504	2
C₁₃×#3242	2
C₁₃×#3237	2
C₁₃×#3236	2
C₁₃×#3166	2
C₁₃×#3162	2
C₁₃×#3139	2
C₂×C₁₃×#491	2
C₁₃×#3097	2
C₁₃×#3082	2
C₁₃×#2923	2
#60884	13

Subgroups — C13×#60884 #15747223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60884 #15747223