Subgroups — C₁₃×#34633 #15720972

Order 3328.

3166 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2621	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2620	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2619	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2618	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2617	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2392	C₂	1	8	yes	maximal, complemented
10	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#532	—	2	8	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
18	C₁₃×#525	—	2	16	no	—
19	C₂×C₁₃×#123	C₂²	1	4	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₁₃×#121	C₂²	1	4	yes	—
22	C₂×C₁₃×#121	C₂²	1	4	yes	—
23	C₂×C₁₃×#120	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#117	—	2	8	no	—
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	4	yes	—
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#398	C₂²	1	8	yes	complemented
36	C₁₃×#397	C₂²	1	8	yes	—
37	C₁₃×#396	C₂²	1	16	yes	complemented
38	C₁₃×#394	C₂²	1	16	yes	—
39	C₁₃×#394	C₂²	1	8	yes	complemented
40	C₁₃×#392	C₂²	1	8	yes	—
41	C₁₃×#391	C₂²	1	4	yes	complemented
42	C₁₃×#390	C₂²	1	4	yes	complemented
43	C₁₃×#386	C₂²	1	8	yes	—
44	C₁₃×#384	C₂²	1	2	yes	complemented
45	C₁₃×#382	C₂²	1	2	yes	complemented
46	C₁₃×#380	C₂²	1	4	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
49	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×#41	—	2	8	no	—
51	C₂×C₁₃×#41	—	2	8	no	—
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	—	2	4	no	—
59	C₂³×C₄×C₁₃	—	2	4	no	—
60	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	—	2	4	no	—
69	C₁₃×#127	—	2	4	no	—
70	C₁₃×#124	—	2	8	no	—
71	C₁₃×#123	—	2	16	no	—
72	C₁₃×C₂²⋊Q₈	—	2	16	no	—
73	C₁₃×#121	—	2	16	no	—
74	C₁₃×#121	—	2	16	no	—
75	C₁₃×#120	—	2	16	no	—
76	C₄×D₄×C₁₃	—	2	32	no	—
77	C₄×D₄×C₁₃	—	2	16	no	—
78	C₁₃×#117	—	2	8	no	—
79	C₁₃×#117	—	2	16	no	—
80	C₁₃×#117	—	2	8	no	—
81	C₁₃×#117	—	2	8	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
97	C₂×C₄²×C₁₃	—	2	4	no	—
98	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₁₃×#95	C₂³	1	16	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	#34633	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	4	4	no	—
111	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×#41	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	16	no	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	—	4	16	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	32	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	4	4	no	—
141	C₂²×C₄×C₁₃	—	4	4	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃	#41	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	16	no	—
162	C₁₃×C₄⋊C₄	—	4	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	16	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	16	no	—
168	C₁₃×C₂²⋊C₄	—	2	16	no	—
169	C₁₃×C₂²⋊C₄	—	4	16	no	—
170	C₄²×C₁₃	—	2	4	no	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	C₂×D₄	1	8	yes	—
174	C₄²×C₁₃	C₂×D₄	1	4	yes	—
175	C₄²×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂×#525	C₂×C₁₃	1	2	yes	complemented
178	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2621	C₂×C₁₃	1	2	yes	complemented
180	#2620	C₂×C₁₃	1	4	yes	complemented
181	#2619	C₂×C₁₃	1	2	yes	complemented
182	#2618	C₂×C₁₃	1	4	yes	complemented
183	#2617	C₂×C₁₃	1	4	yes	complemented
184	#2392	C₂×C₁₃	1	8	yes	complemented
185	#2297	C₂×C₁₃	1	2	yes	complemented
186	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	4	no	—
188	C₂³×C₁₃	—	2	8	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	2	16	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
200	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂³×C₁₃	C₂×#41	1	2	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃	—	4	8	no	—
205	D₄×C₁₃	—	4	16	no	—
206	D₄×C₁₃	—	4	32	no	—
207	D₄×C₁₃	—	4	16	no	—
208	D₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	16	no	—
215	C₂×C₄×C₁₃	—	2	16	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	16	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	8	no	—
225	C₂×C₄×C₁₃	—	4	16	no	—
226	C₂×C₄×C₁₃	#121	1	16	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂²×#41	C₂²×C₁₃	1	2	yes	—
237	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
238	#532	—	2	8	no	—
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
242	#525	—	2	16	no	—
243	C₂×#123	C₂²×C₁₃	1	4	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
245	C₂×#121	C₂²×C₁₃	1	4	yes	—
246	C₂×#121	C₂²×C₁₃	1	4	yes	—
247	C₂×#120	C₂²×C₁₃	1	4	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
249	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
250	C₂×#117	—	2	8	no	—
251	C₂×#117	C₂²×C₁₃	1	2	yes	—
252	C₂×#117	C₂²×C₁₃	1	2	yes	—
253	C₂×#117	C₂²×C₁₃	1	4	yes	—
254	C₂×#117	C₂²×C₁₃	1	2	yes	—
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
256	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
257	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
259	#398	C₂²×C₁₃	1	8	yes	complemented
260	#397	C₂²×C₁₃	1	8	yes	—
261	#396	C₂²×C₁₃	1	16	yes	complemented
262	#394	C₂²×C₁₃	1	16	yes	—
263	#394	C₂²×C₁₃	1	8	yes	complemented
264	#392	C₂²×C₁₃	1	8	yes	—
265	#391	C₂²×C₁₃	1	4	yes	complemented
266	#390	C₂²×C₁₃	1	4	yes	complemented
267	#386	C₂²×C₁₃	1	8	yes	—
268	#384	C₂²×C₁₃	1	2	yes	complemented
269	#382	C₂²×C₁₃	1	2	yes	complemented
270	#380	C₂²×C₁₃	1	4	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
272	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	2	8	no	—
278	C₂²×C₁₃	—	4	16	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	4	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	8	no	—
283	C₂²×C₁₃	—	4	8	no	—
284	C₂²×C₁₃	—	4	8	no	—
285	C₂²×C₁₃	C₂×#121	1	4	yes	—
286	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
289	C₂²×C₁₃	#585	1	4	yes	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	4	no	—
292	C₄×C₁₃	—	2	4	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	4	8	no	—
296	C₄×C₁₃	C₂×#121	1	4	yes	—
297	C₄×C₁₃	C₂×#121	1	4	yes	—
298	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	2	8	no	—
301	C₂×#41	—	2	8	no	—
302	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
304	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
305	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
306	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	2	4	no	—
309	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
310	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	4	no	—
318	#127	—	2	4	no	—
319	#124	—	2	8	no	—
320	#123	—	2	16	no	—
321	C₂²⋊Q₈	—	2	16	no	—
322	#121	—	2	16	no	—
323	#121	—	2	16	no	—
324	#120	—	2	16	no	—
325	C₄×D₄	—	2	32	no	—
326	C₄×D₄	—	2	16	no	—
327	#117	—	2	8	no	—
328	#117	—	2	16	no	—
329	#117	—	2	8	no	—
330	#117	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	8	no	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
338	C₂×C₂²⋊C₄	—	2	8	no	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
346	C₂×C₄²	—	2	4	no	—
347	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
348	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
349	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
351	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	#95	C₂³×C₁₃	1	16	yes	—
355	#95	C₂³×C₁₃	1	8	yes	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	—	4	4	no	—
358	C₂×C₁₃	—	8	4	no	—
359	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
360	C₂×C₁₃	#3449	1	2	yes	—
361	C₂×C₁₃	#3449	1	2	yes	—
362	C₂×C₁₃	#3455	1	2	yes	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
367	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
368	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
369	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
370	#41	—	4	32	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	16	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	32	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₂²×C₄	C₁₃×#41	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	16	no	—
417	C₄⋊C₄	—	4	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	16	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	4	16	no	—
425	C₄²	—	2	4	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	8	no	—
428	C₄²	C₂×D₄×C₁₃	1	8	yes	—
429	C₄²	C₂×D₄×C₁₃	1	4	yes	—
430	C₄²	C₂×D₄×C₁₃	1	4	yes	—
431	C₁₃	#34633	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	4	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	8	no	—
444	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
445	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
447	C₂³	C₂×C₁₃×#41	1	2	yes	—
448	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
449	Q₈	—	4	8	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	32	no	—
452	D₄	—	4	16	no	—
453	D₄	—	4	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	16	no	—
460	C₂×C₄	—	2	16	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	C₁₃×#121	1	16	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
480	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	8	no	—
493	C₂²	C₂×C₁₃×#121	1	4	yes	—
494	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
495	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
496	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
497	C₂²	C₁₃×#585	1	4	yes	—
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	4	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	8	no	—
504	C₄	C₂×C₁₃×#121	1	4	yes	—
505	C₄	C₂×C₁₃×#121	1	4	yes	—
506	C₂	—	2	4	no	—
507	C₂	—	4	4	no	—
508	C₂	—	8	4	no	—
509	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
510	C₂	C₁₃×#3449	1	2	yes	—
511	C₂	C₁₃×#3449	1	2	yes	—
512	C₂	C₁₃×#3455	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₂²×C₁₃×#117	C₂	semidirect
4. C₁₃×#2621	C₂	semidirect
5. C₁₃×#2620	C₂	semidirect
6. C₁₃×#2619	C₂	semidirect
7. C₁₃×#2618	C₂	semidirect
8. C₁₃×#2617	C₂	semidirect
9. C₁₃×#2392	C₂	semidirect
10. C₁₃×#2297	C₂	semidirect
11. C₁₃×#2285	C₂	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₁₃×#127	C₂²	semidirect
17. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₁₃×#398	C₂²	semidirect
37. C₁₃×#396	C₂²	semidirect
39. C₁₃×#394	C₂²	semidirect
41. C₁₃×#391	C₂²	semidirect
42. C₁₃×#390	C₂²	semidirect
44. C₁₃×#384	C₂²	semidirect
45. C₁₃×#382	C₂²	semidirect
47. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
60. C₂³×C₄×C₁₃	D₄	semidirect
98. C₂×C₄²×C₁₃	D₄	semidirect
107. #34633	C₁₃	direct (N × H)
176. C₂×#532	C₂×C₁₃	semidirect
177. C₂×#525	C₂×C₁₃	semidirect
178. C₂²×#117	C₂×C₁₃	semidirect
179. #2621	C₂×C₁₃	semidirect
180. #2620	C₂×C₁₃	semidirect
181. #2619	C₂×C₁₃	semidirect
182. #2618	C₂×C₁₃	semidirect
183. #2617	C₂×C₁₃	semidirect
184. #2392	C₂×C₁₃	semidirect
185. #2297	C₂×C₁₃	semidirect
186. #2285	C₂×C₁₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
240. C₂×#127	C₂²×C₁₃	semidirect
241. C₂×#124	C₂²×C₁₃	semidirect
249. C₂×C₄×D₄	C₂²×C₁₃	semidirect
259. #398	C₂²×C₁₃	semidirect
261. #396	C₂²×C₁₃	semidirect
263. #394	C₂²×C₁₃	semidirect
265. #391	C₂²×C₁₃	semidirect
266. #390	C₂²×C₁₃	semidirect
268. #384	C₂²×C₁₃	semidirect
269. #382	C₂²×C₁₃	semidirect
271. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
272. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
309. C₂³×C₄	D₄×C₁₃	semidirect
347. C₂×C₄²	D₄×C₁₃	semidirect
431. C₁₃	#34633	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#117	2
C₁₃×#2621	2
C₁₃×#2620	2
C₁₃×#2619	2
C₁₃×#2618	2
C₁₃×#2617	2
C₁₃×#2392	2
C₁₃×#2297	2
C₁₃×#2285	2
#34633	13

Subgroups — C13×#34633 #15720972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34633 #15720972