Subgroups — C₁₃×#17685 #15704024

Order 3328.

1152 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1533	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1530	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1527	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#329	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×2₋¹⁺⁴	C₄	1	1	yes	characteristic
10	C₂×C₁₃×H(5,𝔽₂)	C₄	1	1	yes	characteristic
11	C₁₃×#548	—	2	2	no	—
12	C₁₃×#546	—	2	2	no	—
13	C₁₃×#546	—	2	4	no	—
14	C₁₃×#536	C₄	1	1	yes	characteristic
15	C₁₃×#536	C₄	1	2	yes	—
16	C₁₃×#535	C₄	1	1	yes	characteristic
17	C₁₃×#535	C₄	1	2	yes	—
18	C₁₃×#532	C₂²	1	1	yes	characteristic
19	C₁₃×#532	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₁₃×#446	—	2	2	no	—
24	C₁₃×#435	—	2	4	no	—
25	C₈×D₄×C₁₃	—	2	2	no	—
26	C₁₃×#432	C₂²	1	2	yes	complemented
27	C₁₃×#432	C₂²	1	4	yes	complemented
28	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#97	C₂²	1	4	yes	complemented
30	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#329	C₂²	1	4	yes	complemented
32	C₁₃×#329	C₂²	1	2	yes	complemented
33	C₁₃×#329	C₂²	1	2	yes	complemented
34	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#329	C₂²	1	4	yes	complemented
36	C₁₃×#329	C₂²	1	2	yes	complemented
37	C₁₃×2₋¹⁺⁴	—	4	4	no	—
38	C₁₃×H(5,𝔽₂)	—	4	4	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	2	4	no	—
56	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
58	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
59	C₁₃×#127	C₂×C₄	1	2	yes	—
60	C₁₃×#124	—	2	2	no	—
61	C₁₃×#124	—	2	4	no	—
62	C₁₃×#124	C₂×C₄	1	2	yes	—
63	C₁₃×#124	C₂×C₄	1	2	yes	—
64	C₁₃×#124	C₂×C₄	1	2	yes	—
65	C₁₃×#124	C₂³	1	1	yes	characteristic
66	C₁₃×#124	C₂³	1	2	yes	—
67	C₁₃×#124	C₂³	1	1	yes	characteristic
68	C₁₃×#123	—	2	2	no	—
69	C₁₃×#123	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	4	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#120	—	2	2	no	—
77	C₁₃×#120	—	2	4	no	—
78	C₄×Q₈×C₁₃	D₄	1	2	yes	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	4	no	—
81	C₄×D₄×C₁₃	D₄	1	2	yes	—
82	C₄×D₄×C₁₃	D₄	1	4	yes	—
83	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#117	C₂×C₄	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊C₈	—	2	2	no	—
90	C₁₃×C₄⋊C₈	—	2	4	no	—
91	C₁₃×C₂²⋊C₈	—	2	4	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×#97	—	2	4	no	—
94	C₁₃×#97	C₂³	1	2	yes	—
95	C₁₃×#97	C₂³	1	4	yes	—
96	C₁₃×#97	C₂³	1	2	yes	—
97	C₄×C₈×C₁₃	—	2	2	no	—
98	#17685	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₁₃×#41	—	2	4	no	—
102	C₁₃×#41	—	4	4	no	—
103	C₁₃×#41	—	4	4	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₁₃×#41	—	4	8	no	—
107	C₁₃×#41	—	4	4	no	—
108	C₁₃×#41	—	4	4	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	4	4	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	4	8	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₁₃×M₁₆	—	4	4	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	4	no	—
149	C₂×C₈×C₁₃	—	4	8	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	4	no	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
161	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
162	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂×D₄	1	4	yes	—
166	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
167	#3500	C₂×C₁₃	1	1	yes	characteristic
168	#2970	C₂×C₁₃	1	2	yes	complemented
169	#1536	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1533	C₂×C₁₃	1	2	yes	complemented
171	#1530	C₂×C₁₃	1	4	yes	complemented
172	#1527	C₂×C₁₃	1	2	yes	complemented
173	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#329	C₂×C₁₃	1	2	yes	complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	4	no	—
180	C₂³×C₁₃	—	8	4	no	—
181	C₂³×C₁₃	—	8	2	no	—
182	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
184	Q₈×C₁₃	—	2	2	no	—
185	Q₈×C₁₃	—	4	4	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	1	no	—
188	Q₈×C₁₃	—	4	1	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	2	4	no	—
191	D₄×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	4	1	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	4	1	no	—
195	D₄×C₁₃	—	4	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	8	4	no	—
201	D₄×C₁₃	—	8	2	no	—
202	D₄×C₁₃	#100	1	4	yes	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	4	4	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₈×C₁₃	—	2	4	no	—
223	C₈×C₁₃	—	4	4	no	—
224	C₈×C₁₃	—	4	2	no	—
225	C₂×2₋¹⁺⁴	C₄×C₁₃	1	1	yes	characteristic
226	C₂×H(5,𝔽₂)	C₄×C₁₃	1	1	yes	characteristic
227	#548	—	2	2	no	—
228	#546	—	2	2	no	—
229	#546	—	2	4	no	—
230	#536	C₄×C₁₃	1	1	yes	characteristic
231	#536	C₄×C₁₃	1	2	yes	—
232	#535	C₄×C₁₃	1	1	yes	characteristic
233	#535	C₄×C₁₃	1	2	yes	—
234	#532	C₂²×C₁₃	1	1	yes	characteristic
235	#532	C₂²×C₁₃	1	2	yes	—
236	C₂×#124	C₂²×C₁₃	1	2	yes	—
237	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
238	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
239	#446	—	2	2	no	—
240	#435	—	2	4	no	—
241	C₈×D₄	—	2	2	no	—
242	#432	C₂²×C₁₃	1	2	yes	complemented
243	#432	C₂²×C₁₃	1	4	yes	complemented
244	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
245	C₂×#97	C₂²×C₁₃	1	4	yes	complemented
246	#329	C₂²×C₁₃	1	2	yes	complemented
247	#329	C₂²×C₁₃	1	2	yes	complemented
248	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	#329	C₂²×C₁₃	1	4	yes	complemented
250	#329	C₂²×C₁₃	1	2	yes	complemented
251	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
252	#329	C₂²×C₁₃	1	4	yes	complemented
253	C₂²×C₁₃	—	2	4	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	16	4	no	—
263	C₂²×C₁₃	—	16	2	no	—
264	C₂²×C₁₃	C₂×#100	1	4	yes	—
265	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	C₂×#100	1	2	yes	—
275	2₋¹⁺⁴	—	4	4	no	—
276	H(5,𝔽₂)	—	4	4	no	—
277	C₂×#41	—	2	1	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	1	no	—
280	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
281	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
282	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
283	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
284	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
291	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
292	C₂×M₁₆	—	2	2	no	—
293	C₂²×C₈	—	2	4	no	—
294	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
296	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
297	#127	C₂×C₄×C₁₃	1	2	yes	—
298	#124	—	2	2	no	—
299	#124	—	2	4	no	—
300	#124	C₂×C₄×C₁₃	1	2	yes	—
301	#124	C₂×C₄×C₁₃	1	2	yes	—
302	#124	C₂×C₄×C₁₃	1	2	yes	—
303	#124	C₂³×C₁₃	1	1	yes	characteristic
304	#124	C₂³×C₁₃	1	2	yes	—
305	#124	C₂³×C₁₃	1	1	yes	characteristic
306	#123	—	2	2	no	—
307	#123	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	#121	—	2	4	no	—
311	#121	—	2	2	no	—
312	#121	—	2	4	no	—
313	#121	—	2	2	no	—
314	#120	—	2	2	no	—
315	#120	—	2	4	no	—
316	C₄×Q₈	D₄×C₁₃	1	2	yes	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	D₄×C₁₃	1	2	yes	—
320	C₄×D₄	D₄×C₁₃	1	4	yes	—
321	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
322	#117	C₂×C₄×C₁₃	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	4	no	—
329	C₂²⋊C₈	—	2	4	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	#97	—	2	4	no	—
332	#97	C₂³×C₁₃	1	2	yes	—
333	#97	C₂³×C₁₃	1	4	yes	—
334	#97	C₂³×C₁₃	1	2	yes	—
335	C₄×C₈	—	2	2	no	—
336	C₂×C₁₃	—	2	4	no	—
337	C₂×C₁₃	—	4	1	no	—
338	C₂×C₁₃	—	8	1	no	—
339	C₂×C₁₃	—	8	1	no	—
340	C₂×C₁₃	—	8	2	no	—
341	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
342	C₂×C₁₃	#2901	1	2	yes	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	2	2	no	—
345	#41	—	2	4	no	—
346	#41	—	4	4	no	—
347	#41	—	4	4	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	#41	—	4	8	no	—
351	#41	—	4	4	no	—
352	#41	—	4	4	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
361	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
375	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
376	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
377	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
378	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	M₁₆	—	4	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	4	8	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
397	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
405	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
406	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
407	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₁₃	1	2	yes	—
409	C₄²	C₂×D₄×C₁₃	1	4	yes	—
410	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₁₃	#17685	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	8	4	no	—
418	C₂³	—	8	2	no	—
419	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
420	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
421	Q₈	—	2	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	4	no	—
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	1	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	4	no	—
438	D₄	—	8	2	no	—
439	D₄	C₁₃×#100	1	4	yes	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
454	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
455	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
456	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
459	C₈	—	2	4	no	—
460	C₈	—	4	4	no	—
461	C₈	—	4	2	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	16	4	no	—
472	C₂²	—	16	2	no	—
473	C₂²	C₂×C₁₃×#100	1	4	yes	—
474	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	1	no	—
483	C₄	C₂×C₁₃×#100	1	2	yes	—
484	C₂	—	2	4	no	—
485	C₂	—	4	1	no	—
486	C₂	—	8	1	no	—
487	C₂	—	8	2	no	—
488	C₂	—	8	1	no	—
489	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
490	C₂	C₁₃×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#1536	C₂	semidirect
4. C₁₃×#1533	C₂	semidirect
5. C₁₃×#1530	C₂	semidirect
6. C₁₃×#1527	C₂	semidirect
7. C₁₃×#1525	C₂	semidirect
8. C₂×C₁₃×#329	C₂	semidirect
26. C₁₃×#432	C₂²	semidirect
27. C₁₃×#432	C₂²	semidirect
28. C₄×C₁₃×M₁₆	C₂²	semidirect
29. C₂×C₁₃×#97	C₂²	semidirect
30. C₁₃×#329	C₂²	semidirect
31. C₁₃×#329	C₂²	semidirect
32. C₁₃×#329	C₂²	semidirect
33. C₁₃×#329	C₂²	semidirect
34. C₁₃×#329	C₂²	semidirect
35. C₁₃×#329	C₂²	semidirect
36. C₁₃×#329	C₂²	semidirect
98. #17685	C₁₃	direct (N × H)
168. #2970	C₂×C₁₃	semidirect
169. #1536	C₂×C₁₃	semidirect
170. #1533	C₂×C₁₃	semidirect
171. #1530	C₂×C₁₃	semidirect
172. #1527	C₂×C₁₃	semidirect
173. #1525	C₂×C₁₃	semidirect
174. C₂×#329	C₂×C₁₃	semidirect
242. #432	C₂²×C₁₃	semidirect
243. #432	C₂²×C₁₃	semidirect
244. C₄×M₁₆	C₂²×C₁₃	semidirect
245. C₂×#97	C₂²×C₁₃	semidirect
246. #329	C₂²×C₁₃	semidirect
247. #329	C₂²×C₁₃	semidirect
248. #329	C₂²×C₁₃	semidirect
249. #329	C₂²×C₁₃	semidirect
250. #329	C₂²×C₁₃	semidirect
251. #329	C₂²×C₁₃	semidirect
252. #329	C₂²×C₁₃	semidirect
411. C₁₃	#17685	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×#3500	2
C₁₃×#2970	2
C₁₃×#1536	2
C₁₃×#1533	2
C₁₃×#1530	2
C₁₃×#1527	2
C₁₃×#1525	2
C₂×C₁₃×#329	2
#17685	13

Subgroups — C13×#17685 #15704024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17685 #15704024