Subgroups — C₁₃×#34313 #15720652

Order 3328.

3276 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2366	C₂	1	3	yes	maximal, complemented
4	C₁₃×#2361	C₂	1	6	yes	maximal, complemented
5	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₁₃×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
7	C₁₃×#2341	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2324	C₂	1	6	yes	maximal, complemented
9	C₄×C₁₃×#127	C₂	1	3	yes	maximal, complemented
10	C₁₃×#2293	C₂	1	3	yes	maximal, complemented
11	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₁₃×#550	C₄	1	16	yes	complemented
14	C₂×C₁₃×#127	C₂²	1	3	yes	—
15	C₂×C₁₃×#121	C₂²	1	6	yes	—
16	C₁₃×#520	—	2	16	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
26	C₂×C₁₃×#117	C₂²	1	6	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
28	C₁₃×#390	C₂²	1	3	yes	—
29	C₁₃×#390	C₂²	1	3	yes	—
30	C₁₃×#390	C₂²	1	6	yes	—
31	C₁₃×#390	C₂²	1	6	yes	—
32	C₁₃×#390	C₂²	1	6	yes	—
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	3	yes	—
35	C₁₃×#389	C₂²	1	6	yes	—
36	C₁₃×#388	C₂²	1	6	yes	—
37	C₁₃×#388	C₂²	1	6	yes	—
38	C₁₃×#386	C₂²	1	12	yes	—
39	C₁₃×#385	C₂²	1	12	yes	—
40	C₁₃×#384	C₂²	1	3	yes	—
41	C₁₃×#380	C₂²	1	6	yes	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	—
47	C₄³×C₁₃	C₂²	1	3	yes	—
48	C₂×C₁₃×#41	—	2	8	no	—
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
57	C₁₃×#127	C₂×C₄	1	24	yes	complemented
58	C₁₃×#121	C₂×C₄	1	48	yes	complemented
59	C₄×Q₈×C₁₃	—	2	8	no	—
60	C₄×Q₈×C₁₃	—	2	4	no	—
61	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
62	C₄×Q₈×C₁₃	D₄	1	8	yes	complemented
63	C₄×D₄×C₁₃	—	2	24	no	—
64	C₄×D₄×C₁₃	—	2	24	no	—
65	C₄×D₄×C₁₃	—	4	12	no	—
66	C₄×D₄×C₁₃	—	4	12	no	—
67	C₄×D₄×C₁₃	C₂×C₄	1	24	yes	complemented
68	C₁₃×#117	—	2	24	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	24	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
94	C₁₃×#95	C₂³	1	2	yes	—
95	C₁₃×#95	C₂³	1	6	yes	—
96	C₁₃×#95	C₂³	1	6	yes	—
97	C₁₃×#95	C₂³	1	6	yes	—
98	#34313	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
100	C₁₃×#41	—	2	64	no	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₁₃	#41	1	4	yes	—
104	C₂×D₄×C₁₃	—	2	12	no	—
105	C₂×D₄×C₁₃	—	2	12	no	—
106	C₂×D₄×C₁₃	—	2	6	no	—
107	C₂×D₄×C₁₃	—	2	6	no	—
108	C₂×D₄×C₁₃	—	4	6	no	—
109	C₂×D₄×C₁₃	—	4	6	no	—
110	C₂×D₄×C₁₃	C₂²×C₄	1	12	yes	—
111	C₂×D₄×C₁₃	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	24	yes	—
113	C₂²×C₄×C₁₃	—	2	12	no	—
114	C₂²×C₄×C₁₃	—	2	12	no	—
115	C₂²×C₄×C₁₃	—	2	24	no	—
116	C₂²×C₄×C₁₃	—	4	12	no	—
117	C₂²×C₄×C₁₃	—	4	12	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	24	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	12	no	—
130	C₁₃×C₄⋊C₄	—	2	12	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	6	no	—
133	C₁₃×C₄⋊C₄	—	2	6	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	6	no	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	12	yes	—
139	C₁₃×C₂²⋊C₄	—	2	12	no	—
140	C₁₃×C₂²⋊C₄	—	2	12	no	—
141	C₁₃×C₂²⋊C₄	—	2	12	no	—
142	C₁₃×C₂²⋊C₄	—	4	6	no	—
143	C₁₃×C₂²⋊C₄	—	4	12	no	—
144	C₁₃×C₂²⋊C₄	C₂²×C₄	1	24	yes	—
145	C₄²×C₁₃	—	2	12	no	—
146	C₄²×C₁₃	—	2	6	no	—
147	C₄²×C₁₃	—	2	6	no	—
148	C₄²×C₁₃	—	2	6	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	4	3	no	—
151	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
152	C₄²×C₁₃	C₂×D₄	1	12	yes	—
153	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
154	C₂×#520	C₂×C₁₃	1	2	yes	complemented
155	#2366	C₂×C₁₃	1	3	yes	complemented
156	#2361	C₂×C₁₃	1	6	yes	complemented
157	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
158	D₄×C₄⋊C₄	C₂×C₁₃	1	3	yes	complemented
159	#2341	C₂×C₁₃	1	2	yes	complemented
160	#2324	C₂×C₁₃	1	6	yes	complemented
161	C₄×#127	C₂×C₁₃	1	3	yes	complemented
162	#2293	C₂×C₁₃	1	3	yes	complemented
163	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	6	no	—
165	C₂³×C₁₃	—	2	6	no	—
166	C₂³×C₁₃	—	2	6	no	—
167	C₂³×C₁₃	—	2	6	no	—
168	C₂³×C₁₃	—	2	6	no	—
169	C₂³×C₁₃	—	2	6	no	—
170	C₂³×C₁₃	C₂³×C₄	1	12	yes	—
171	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
172	Q₈×C₁₃	C₄×D₄	1	16	yes	complemented
173	D₄×C₁₃	—	2	48	no	—
174	D₄×C₁₃	—	2	24	no	—
175	D₄×C₁₃	—	4	24	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	3	no	—
180	C₂×C₄×C₁₃	—	2	3	no	—
181	C₂×C₄×C₁₃	—	2	3	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	3	no	—
186	C₂×C₄×C₁₃	—	2	48	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	6	no	—
189	C₂×C₄×C₁₃	—	2	3	no	—
190	C₂×C₄×C₁₃	—	2	3	no	—
191	C₂×C₄×C₁₃	—	2	6	no	—
192	C₂×C₄×C₁₃	—	2	6	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	3	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	8	24	no	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
205	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
208	C₂²×#41	C₂²×C₁₃	1	2	yes	—
209	#550	C₄×C₁₃	1	16	yes	complemented
210	C₂×#127	C₂²×C₁₃	1	3	yes	—
211	C₂×#121	C₂²×C₁₃	1	6	yes	—
212	#520	—	2	16	no	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
218	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
219	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
220	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
221	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
222	C₂×#117	C₂²×C₁₃	1	6	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
224	#390	C₂²×C₁₃	1	3	yes	—
225	#390	C₂²×C₁₃	1	6	yes	—
226	#390	C₂²×C₁₃	1	6	yes	—
227	#390	C₂²×C₁₃	1	6	yes	—
228	#390	C₂²×C₁₃	1	3	yes	—
229	#389	C₂²×C₁₃	1	6	yes	—
230	#389	C₂²×C₁₃	1	3	yes	—
231	#389	C₂²×C₁₃	1	1	yes	characteristic
232	#388	C₂²×C₁₃	1	6	yes	—
233	#388	C₂²×C₁₃	1	6	yes	—
234	#386	C₂²×C₁₃	1	12	yes	—
235	#385	C₂²×C₁₃	1	12	yes	—
236	#384	C₂²×C₁₃	1	3	yes	—
237	#380	C₂²×C₁₃	1	6	yes	—
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	—
243	C₄³	C₂²×C₁₃	1	3	yes	—
244	C₂²×C₁₃	—	2	12	no	—
245	C₂²×C₁₃	—	2	12	no	—
246	C₂²×C₁₃	—	2	12	no	—
247	C₂²×C₁₃	—	4	6	no	—
248	C₂²×C₁₃	—	4	6	no	—
249	C₂²×C₁₃	—	4	6	no	—
250	C₂²×C₁₃	—	4	6	no	—
251	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
252	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
253	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
257	C₂²×C₁₃	#585	1	1	yes	characteristic
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	6	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	6	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	6	no	—
265	C₄×C₁₃	—	4	3	no	—
266	C₄×C₁₃	C₂×C₄×D₄	1	12	yes	—
267	C₄×C₁₃	#520	1	4	yes	complemented
268	C₂×#41	—	2	8	no	—
269	C₂×#41	—	2	8	no	—
270	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
271	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
274	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
276	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
277	#127	C₂×C₄×C₁₃	1	24	yes	complemented
278	#121	C₂×C₄×C₁₃	1	48	yes	complemented
279	C₄×Q₈	—	2	8	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
282	C₄×Q₈	D₄×C₁₃	1	8	yes	complemented
283	C₄×D₄	—	2	24	no	—
284	C₄×D₄	—	2	24	no	—
285	C₄×D₄	—	4	12	no	—
286	C₄×D₄	—	4	12	no	—
287	C₄×D₄	C₂×C₄×C₁₃	1	24	yes	complemented
288	#117	—	2	24	no	—
289	C₂×C₄⋊C₄	—	2	24	no	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
307	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
308	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
309	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
312	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
314	#95	C₂³×C₁₃	1	2	yes	—
315	#95	C₂³×C₁₃	1	6	yes	—
316	#95	C₂³×C₁₃	1	6	yes	—
317	#95	C₂³×C₁₃	1	6	yes	—
318	C₂×C₁₃	—	4	12	no	—
319	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
321	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₁₃	#3497	1	1	yes	characteristic
323	C₂×C₁₃	#3498	1	1	yes	characteristic
324	C₂×C₁₃	#3517	1	1	yes	characteristic
325	C₂×C₁₃	#3522	1	1	yes	characteristic
326	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
327	#41	—	2	64	no	—
328	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
329	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
330	C₂×Q₈	C₁₃×#41	1	4	yes	—
331	C₂×D₄	—	2	12	no	—
332	C₂×D₄	—	2	12	no	—
333	C₂×D₄	—	2	6	no	—
334	C₂×D₄	—	2	6	no	—
335	C₂×D₄	—	4	6	no	—
336	C₂×D₄	—	4	6	no	—
337	C₂×D₄	C₂²×C₄×C₁₃	1	12	yes	—
338	C₂×D₄	C₂²×C₄×C₁₃	1	24	yes	—
339	C₂×D₄	C₂²×C₄×C₁₃	1	24	yes	—
340	C₂²×C₄	—	2	12	no	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	2	24	no	—
343	C₂²×C₄	—	4	12	no	—
344	C₂²×C₄	—	4	12	no	—
345	C₂²×C₄	C₂²×C₄×C₁₃	1	24	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	12	no	—
357	C₄⋊C₄	—	2	12	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	6	no	—
360	C₄⋊C₄	—	2	6	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	6	no	—
363	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
364	C₄⋊C₄	C₂²×C₄×C₁₃	1	12	yes	—
365	C₄⋊C₄	C₂×D₄×C₁₃	1	12	yes	—
366	C₂²⋊C₄	—	2	12	no	—
367	C₂²⋊C₄	—	2	12	no	—
368	C₂²⋊C₄	—	2	12	no	—
369	C₂²⋊C₄	—	4	12	no	—
370	C₂²⋊C₄	—	4	6	no	—
371	C₂²⋊C₄	C₂²×C₄×C₁₃	1	24	yes	—
372	C₄²	—	2	12	no	—
373	C₄²	—	2	6	no	—
374	C₄²	—	2	6	no	—
375	C₄²	—	2	6	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	3	no	—
378	C₄²	C₂²×C₄×C₁₃	1	12	yes	—
379	C₄²	C₂×D₄×C₁₃	1	12	yes	—
380	C₁₃	#34313	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	6	no	—
382	C₂³	—	2	6	no	—
383	C₂³	—	2	6	no	—
384	C₂³	—	2	6	no	—
385	C₂³	—	2	6	no	—
386	C₂³	—	2	6	no	—
387	C₂³	C₂³×C₄×C₁₃	1	12	yes	—
388	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
389	Q₈	C₄×D₄×C₁₃	1	16	yes	complemented
390	D₄	—	2	48	no	—
391	D₄	—	2	24	no	—
392	D₄	—	4	24	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	3	no	—
397	C₂×C₄	—	2	3	no	—
398	C₂×C₄	—	2	3	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	3	no	—
403	C₂×C₄	—	2	48	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	6	no	—
406	C₂×C₄	—	2	3	no	—
407	C₂×C₄	—	2	3	no	—
408	C₂×C₄	—	2	6	no	—
409	C₂×C₄	—	2	6	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	3	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	8	24	no	—
414	C₂×C₄	C₂³×C₄×C₁₃	1	6	yes	—
415	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
416	C₂×C₄	C₂³×C₄×C₁₃	1	6	yes	—
417	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
421	C₂×C₄	C₂×C₁₃×#41	1	6	yes	—
422	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
425	C₂²	—	2	12	no	—
426	C₂²	—	2	12	no	—
427	C₂²	—	2	12	no	—
428	C₂²	—	4	6	no	—
429	C₂²	—	4	6	no	—
430	C₂²	—	4	6	no	—
431	C₂²	—	4	6	no	—
432	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
433	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
434	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
435	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂²	C₁₃×#585	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	6	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	6	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	6	no	—
446	C₄	—	4	3	no	—
447	C₄	C₂×C₄×D₄×C₁₃	1	12	yes	—
448	C₄	C₁₃×#520	1	4	yes	complemented
449	C₂	—	4	12	no	—
450	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
451	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
452	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂	C₁₃×#3497	1	1	yes	characteristic
454	C₂	C₁₃×#3498	1	1	yes	characteristic
455	C₂	C₁₃×#3517	1	1	yes	characteristic
456	C₂	C₁₃×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#520	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. C₁₃×#2361	C₂	semidirect
5. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
6. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
7. C₁₃×#2341	C₂	semidirect
8. C₁₃×#2324	C₂	semidirect
9. C₄×C₁₃×#127	C₂	semidirect
10. C₁₃×#2293	C₂	semidirect
11. C₄²×Q₈×C₁₃	C₂	semidirect
13. C₁₃×#550	C₄	semidirect
50. C₂×C₁₃×#41	C₂×C₄	semidirect
57. C₁₃×#127	C₂×C₄	semidirect
58. C₁₃×#121	C₂×C₄	semidirect
61. C₄×Q₈×C₁₃	C₂×C₄	semidirect
62. C₄×Q₈×C₁₃	D₄	semidirect
67. C₄×D₄×C₁₃	C₂×C₄	semidirect
98. #34313	C₁₃	direct (N × H)
154. C₂×#520	C₂×C₁₃	semidirect
155. #2366	C₂×C₁₃	semidirect
156. #2361	C₂×C₁₃	semidirect
157. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
158. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
159. #2341	C₂×C₁₃	semidirect
160. #2324	C₂×C₁₃	semidirect
161. C₄×#127	C₂×C₁₃	semidirect
162. #2293	C₂×C₁₃	semidirect
163. C₄²×Q₈	C₂×C₁₃	semidirect
172. Q₈×C₁₃	C₄×D₄	semidirect
209. #550	C₄×C₁₃	semidirect
267. C₄×C₁₃	#520	semidirect
270. C₂×#41	C₂×C₄×C₁₃	semidirect
277. #127	C₂×C₄×C₁₃	semidirect
278. #121	C₂×C₄×C₁₃	semidirect
281. C₄×Q₈	C₂×C₄×C₁₃	semidirect
282. C₄×Q₈	D₄×C₁₃	semidirect
287. C₄×D₄	C₂×C₄×C₁₃	semidirect
380. C₁₃	#34313	direct (N × H)
389. Q₈	C₄×D₄×C₁₃	semidirect
448. C₄	C₁₃×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#550	2
C₂×C₁₃×#520	2
C₁₃×#2366	2
C₁₃×#2361	2
Q₈×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2341	2
C₁₃×#2324	2
C₄×C₁₃×#127	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
#34313	13

Subgroups — C13×#34313 #15720652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34313 #15720652