Subgroups — C₁₃×#34274 #15720613

Order 3328.

3154 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2363	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2362	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2360	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₁₃×#537	C₄	1	16	yes	complemented
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₁₃×#121	C₂²	1	4	yes	—
16	C₂×C₁₃×#121	C₂²	1	4	yes	—
17	C₁₃×#520	—	2	16	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	4	yes	—
34	C₁₃×#389	C₂²	1	4	yes	—
35	C₁₃×#389	C₂²	1	4	yes	—
36	C₁₃×#389	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	8	yes	—
38	C₁₃×#388	C₂²	1	8	yes	—
39	C₁₃×#387	C₂²	1	8	yes	—
40	C₁₃×#386	C₂²	1	4	yes	—
41	C₁₃×#386	C₂²	1	4	yes	—
42	C₁₃×#386	C₂²	1	8	yes	—
43	C₁₃×#385	C₂²	1	8	yes	—
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
51	C₂×C₁₃×#95	C₂²	1	2	yes	—
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	—	2	8	no	—
54	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	8	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	1	yes	characteristic
66	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
67	C₁₃×#121	C₂×C₄	1	32	yes	complemented
68	C₁₃×#121	C₂×C₄	1	32	yes	complemented
69	C₄×Q₈×C₁₃	—	2	16	no	—
70	C₄×D₄×C₁₃	—	2	32	no	—
71	C₄×D₄×C₁₃	—	2	16	no	—
72	C₄×D₄×C₁₃	—	4	8	no	—
73	C₁₃×#117	—	2	8	no	—
74	C₁₃×#117	—	2	16	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
77	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
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	8	yes	—
93	C₂×C₄²×C₁₃	—	2	4	no	—
94	C₂×C₄²×C₁₃	—	4	4	no	—
95	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	#34274	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×#41	—	2	64	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	4	4	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	16	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	1	no	—
135	C₂²×C₄×C₁₃	—	4	1	no	—
136	C₂²×C₄×C₁₃	—	4	8	no	—
137	C₂²×C₄×C₁₃	—	4	8	no	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	#41	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	16	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	4	4	no	—
157	C₁₃×C₄⋊C₄	—	4	4	no	—
158	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
159	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	16	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	4	4	no	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
168	C₄²×C₁₃	—	2	16	no	—
169	C₄²×C₁₃	—	2	8	no	—
170	C₄²×C₁₃	—	2	4	no	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	4	4	no	—
174	C₂×#537	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#520	C₂×C₁₃	1	2	yes	complemented
176	#2363	C₂×C₁₃	1	4	yes	complemented
177	#2362	C₂×C₁₃	1	4	yes	complemented
178	#2361	C₂×C₁₃	1	4	yes	complemented
179	#2360	C₂×C₁₃	1	4	yes	complemented
180	#2325	C₂×C₁₃	1	4	yes	complemented
181	#2316	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₄×#121	C₂×C₁₃	1	4	yes	complemented
183	#2297	C₂×C₁₃	1	2	yes	complemented
184	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
196	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
197	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂³×C₁₃	C₂×#41	1	2	yes	—
199	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	16	no	—
201	D₄×C₁₃	—	2	32	no	—
202	D₄×C₁₃	—	2	16	no	—
203	D₄×C₁₃	—	4	16	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	32	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	8	16	no	—
229	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
230	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
231	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
238	C₂²×#41	C₂²×C₁₃	1	2	yes	—
239	#537	C₄×C₁₃	1	16	yes	complemented
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
241	C₂×#121	C₂²×C₁₃	1	4	yes	—
242	C₂×#121	C₂²×C₁₃	1	4	yes	—
243	#520	—	2	16	no	—
244	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
245	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
246	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
247	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
248	C₂×#117	C₂²×C₁₃	1	2	yes	—
249	C₂×#117	C₂²×C₁₃	1	4	yes	—
250	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
255	#391	C₂²×C₁₃	1	2	yes	—
256	#391	C₂²×C₁₃	1	2	yes	—
257	#390	C₂²×C₁₃	1	2	yes	—
258	#390	C₂²×C₁₃	1	2	yes	—
259	#390	C₂²×C₁₃	1	4	yes	—
260	#389	C₂²×C₁₃	1	4	yes	—
261	#389	C₂²×C₁₃	1	4	yes	—
262	#389	C₂²×C₁₃	1	4	yes	—
263	#388	C₂²×C₁₃	1	8	yes	—
264	#388	C₂²×C₁₃	1	8	yes	—
265	#387	C₂²×C₁₃	1	8	yes	—
266	#386	C₂²×C₁₃	1	4	yes	—
267	#386	C₂²×C₁₃	1	8	yes	—
268	#386	C₂²×C₁₃	1	4	yes	—
269	#385	C₂²×C₁₃	1	8	yes	—
270	#380	C₂²×C₁₃	1	4	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
272	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
273	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
276	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
277	C₂×#95	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	8	no	—
285	C₂²×C₁₃	—	2	8	no	—
286	C₂²×C₁₃	—	2	8	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
292	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
293	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
294	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
295	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
297	C₂²×C₁₃	#585	1	1	yes	characteristic
298	C₂²×C₁₃	#585	1	1	yes	characteristic
299	C₄×C₁₃	—	2	8	no	—
300	C₄×C₁₃	—	2	8	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	8	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	C₂×C₄×D₄	1	8	yes	—
308	C₂×#41	—	2	8	no	—
309	C₂×#41	—	2	8	no	—
310	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
311	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
312	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
313	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
323	#121	C₂×C₄×C₁₃	1	32	yes	complemented
324	#121	C₂×C₄×C₁₃	1	32	yes	complemented
325	C₄×Q₈	—	2	16	no	—
326	C₄×D₄	—	2	32	no	—
327	C₄×D₄	—	2	16	no	—
328	C₄×D₄	—	4	8	no	—
329	#117	—	2	8	no	—
330	#117	—	2	16	no	—
331	C₂×C₄⋊C₄	—	2	16	no	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
333	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₄²	—	2	4	no	—
350	C₂×C₄²	—	4	4	no	—
351	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
353	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
357	#95	C₂³×C₁₃	1	8	yes	—
358	#95	C₂³×C₁₃	1	4	yes	—
359	#95	C₂³×C₁₃	1	4	yes	—
360	#95	C₂³×C₁₃	1	8	yes	—
361	#95	C₂³×C₁₃	1	4	yes	—
362	#95	C₂³×C₁₃	1	4	yes	—
363	C₂×C₁₃	—	2	4	no	—
364	C₂×C₁₃	—	4	8	no	—
365	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
366	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂×C₁₃	#3492	1	1	yes	characteristic
369	C₂×C₁₃	#3493	1	1	yes	characteristic
370	C₂×C₁₃	#3496	1	1	yes	characteristic
371	C₂×C₁₃	#3497	1	1	yes	characteristic
372	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
373	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
374	#41	—	2	64	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
385	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
386	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	16	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
403	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
407	C₂²×C₄	C₁₃×#41	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	16	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	4	4	no	—
422	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
423	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
432	C₄²	—	2	16	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	8	no	—
437	C₄²	—	4	4	no	—
438	C₁₃	#34274	1	1	yes	characteristic, direct product factor, Sylow
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
450	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
451	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂³	C₂×C₁₃×#41	1	2	yes	—
453	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
454	Q₈	—	2	16	no	—
455	D₄	—	2	32	no	—
456	D₄	—	2	16	no	—
457	D₄	—	4	16	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	32	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	8	16	no	—
483	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
484	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
485	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
486	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
489	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
490	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
491	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
506	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
507	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
509	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂²	C₁₃×#585	1	1	yes	characteristic
512	C₂²	C₁₃×#585	1	1	yes	characteristic
513	C₄	—	2	8	no	—
514	C₄	—	2	8	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	8	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	C₂×C₄×D₄×C₁₃	1	8	yes	—
522	C₂	—	2	4	no	—
523	C₂	—	4	8	no	—
524	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
525	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂	C₁₃×#3492	1	1	yes	characteristic
528	C₂	C₁₃×#3493	1	1	yes	characteristic
529	C₂	C₁₃×#3496	1	1	yes	characteristic
530	C₂	C₁₃×#3497	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×#537	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×#2363	C₂	semidirect
4. C₁₃×#2362	C₂	semidirect
5. C₁₃×#2361	C₂	semidirect
6. C₁₃×#2360	C₂	semidirect
7. C₁₃×#2325	C₂	semidirect
8. C₁₃×#2316	C₂	semidirect
9. C₄×C₁₃×#121	C₂	semidirect
10. C₁₃×#2297	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₁₃×#537	C₄	semidirect
54. C₂×C₁₃×#41	C₂×C₄	semidirect
66. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
67. C₁₃×#121	C₂×C₄	semidirect
68. C₁₃×#121	C₂×C₄	semidirect
76. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
77. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
107. #34274	C₁₃	direct (N × H)
175. C₂×#520	C₂×C₁₃	semidirect
176. #2363	C₂×C₁₃	semidirect
177. #2362	C₂×C₁₃	semidirect
178. #2361	C₂×C₁₃	semidirect
179. #2360	C₂×C₁₃	semidirect
180. #2325	C₂×C₁₃	semidirect
181. #2316	C₂×C₁₃	semidirect
182. C₄×#121	C₂×C₁₃	semidirect
183. #2297	C₂×C₁₃	semidirect
184. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
229. C₂×C₄×C₁₃	C₄×D₄	semidirect
239. #537	C₄×C₁₃	semidirect
310. C₂×#41	C₂×C₄×C₁₃	semidirect
322. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
323. #121	C₂×C₄×C₁₃	semidirect
324. #121	C₂×C₄×C₁₃	semidirect
332. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
333. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
438. C₁₃	#34274	direct (N × H)
483. C₂×C₄	C₄×D₄×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#537	2
C₂×C₁₃×#520	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2325	2
C₁₃×#2316	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34274	13

Subgroups — C13×#34274 #15720613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34274 #15720613