Subgroups — C₁₃×#35032 #15721371

Order 3328.

2778 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2850	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2617	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2602	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2500	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2499	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2432	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2431	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
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	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#120	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#397	C₂²	1	8	yes	—
33	C₁₃×#394	C₂²	1	8	yes	—
34	C₁₃×#394	C₂²	1	8	yes	—
35	C₁₃×#392	C₂²	1	8	yes	—
36	C₁₃×#391	C₂²	1	2	yes	complemented
37	C₁₃×#391	C₂²	1	2	yes	complemented
38	C₁₃×#390	C₂²	1	2	yes	complemented
39	C₁₃×#390	C₂²	1	2	yes	complemented
40	C₁₃×#390	C₂²	1	4	yes	complemented
41	C₁₃×#389	C₂²	1	4	yes	complemented
42	C₁₃×#388	C₂²	1	8	yes	complemented
43	C₁₃×#388	C₂²	1	8	yes	complemented
44	C₁₃×#387	C₂²	1	8	yes	complemented
45	C₁₃×#386	C₂²	1	8	yes	—
46	C₁₃×#386	C₂²	1	8	yes	complemented
47	C₁₃×#385	C₂²	1	8	yes	complemented
48	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#382	C₂²	1	2	yes	complemented
51	C₁₃×#380	C₂²	1	4	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
55	C₂×C₁₃×#95	C₂²	1	2	yes	—
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×#41	—	2	8	no	—
58	C₂×C₁₃×#41	—	4	4	no	—
59	C₂×C₁₃×#41	—	4	4	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	—	4	2	no	—
67	C₂³×C₄×C₁₃	—	4	2	no	—
68	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	—	4	2	no	—
77	C₁₃×#127	—	4	2	no	—
78	C₁₃×#124	—	4	4	no	—
79	C₁₃×#123	—	2	16	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	8	no	—
84	C₁₃×#121	—	2	16	no	—
85	C₁₃×#120	—	2	16	no	—
86	C₄×D₄×C₁₃	—	2	16	no	—
87	C₄×D₄×C₁₃	—	2	16	no	—
88	C₁₃×#117	—	2	8	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₄²×C₁₃	—	4	2	no	—
108	C₂×C₄²×C₁₃	—	4	2	no	—
109	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₁₃×#95	C₂³	1	4	yes	—
116	C₁₃×#95	C₂³	1	4	yes	—
117	C₁₃×#95	C₂³	1	8	yes	—
118	C₁₃×#95	C₂³	1	8	yes	—
119	C₁₃×#95	C₂³	1	8	yes	—
120	#35032	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	4	1	no	—
123	C₂⁴×C₁₃	—	4	1	no	—
124	C₂⁴×C₁₃	—	4	2	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×#41	—	4	32	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	16	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	—	4	4	no	—
143	C₂×D₄×C₁₃	—	4	4	no	—
144	C₂×D₄×C₁₃	—	4	4	no	—
145	C₂×D₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	—	4	16	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	4	no	—
162	C₂²×C₄×C₁₃	—	4	4	no	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
167	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	4	4	no	—
183	C₁₃×C₄⋊C₄	—	4	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	16	no	—
192	C₁₃×C₂²⋊C₄	—	4	8	no	—
193	C₁₃×C₂²⋊C₄	—	4	8	no	—
194	C₄²×C₁₃	—	2	8	no	—
195	C₄²×C₁₃	—	2	4	no	—
196	C₄²×C₁₃	—	2	2	no	—
197	C₄²×C₁₃	—	2	2	no	—
198	C₄²×C₁₃	—	4	2	no	—
199	C₄²×C₁₃	—	4	2	no	—
200	C₂×#525	C₂×C₁₃	1	2	yes	complemented
201	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2856	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2850	C₂×C₁₃	1	2	yes	complemented
204	#2617	C₂×C₁₃	1	4	yes	complemented
205	#2602	C₂×C₁₃	1	8	yes	complemented
206	#2500	C₂×C₁₃	1	2	yes	complemented
207	#2499	C₂×C₁₃	1	2	yes	complemented
208	#2432	C₂×C₁₃	1	2	yes	complemented
209	#2431	C₂×C₁₃	1	2	yes	complemented
210	#2325	C₂×C₁₃	1	4	yes	complemented
211	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	8	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	8	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	2	8	no	—
225	C₂³×C₁₃	—	4	4	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	4	8	no	—
228	C₂³×C₁₃	—	4	8	no	—
229	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
230	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂³×C₁₃	C₂×#41	1	4	yes	—
232	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
233	Q₈×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	4	16	no	—
235	D₄×C₁₃	—	4	16	no	—
236	D₄×C₁₃	—	4	16	no	—
237	D₄×C₁₃	—	4	8	no	—
238	D₄×C₁₃	—	8	8	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	16	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	8	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	4	16	no	—
263	C₂×C₄×C₁₃	—	4	8	no	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
270	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
271	C₂²×#41	C₂²×C₁₃	1	2	yes	—
272	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
276	#525	—	2	16	no	—
277	C₂×#123	C₂²×C₁₃	1	4	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
280	C₂×#121	C₂²×C₁₃	1	4	yes	—
281	C₂×#121	C₂²×C₁₃	1	2	yes	—
282	C₂×#121	C₂²×C₁₃	1	2	yes	—
283	C₂×#120	C₂²×C₁₃	1	4	yes	—
284	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
286	C₂×#117	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#397	C₂²×C₁₃	1	8	yes	—
291	#394	C₂²×C₁₃	1	8	yes	—
292	#394	C₂²×C₁₃	1	8	yes	—
293	#392	C₂²×C₁₃	1	8	yes	—
294	#391	C₂²×C₁₃	1	2	yes	complemented
295	#391	C₂²×C₁₃	1	2	yes	complemented
296	#390	C₂²×C₁₃	1	2	yes	complemented
297	#390	C₂²×C₁₃	1	4	yes	complemented
298	#390	C₂²×C₁₃	1	2	yes	complemented
299	#389	C₂²×C₁₃	1	4	yes	complemented
300	#388	C₂²×C₁₃	1	8	yes	complemented
301	#388	C₂²×C₁₃	1	8	yes	complemented
302	#387	C₂²×C₁₃	1	8	yes	complemented
303	#386	C₂²×C₁₃	1	8	yes	—
304	#386	C₂²×C₁₃	1	8	yes	complemented
305	#385	C₂²×C₁₃	1	8	yes	complemented
306	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#382	C₂²×C₁₃	1	2	yes	complemented
309	#380	C₂²×C₁₃	1	4	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
313	C₂×#95	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	2	4	no	—
318	C₂²×C₁₃	—	2	4	no	—
319	C₂²×C₁₃	—	2	4	no	—
320	C₂²×C₁₃	—	2	4	no	—
321	C₂²×C₁₃	—	4	16	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	8	no	—
328	C₂²×C₁₃	—	4	8	no	—
329	C₂²×C₁₃	#532	1	4	yes	—
330	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
331	C₂²×C₁₃	C₂²×#41	1	2	yes	—
332	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²×C₁₃	#585	1	2	yes	—
335	C₄×C₁₃	—	2	4	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	4	no	—
338	C₄×C₁₃	—	2	4	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	—	4	4	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	#534	1	4	yes	—
344	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×#41	—	2	8	no	—
346	C₂×#41	—	4	4	no	—
347	C₂×#41	—	4	4	no	—
348	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
349	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
350	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
351	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
352	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
354	C₂³×C₄	—	4	2	no	—
355	C₂³×C₄	—	4	2	no	—
356	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
360	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
364	C₄⋊Q₈	—	4	2	no	—
365	#127	—	4	2	no	—
366	#124	—	4	4	no	—
367	#123	—	2	16	no	—
368	C₂²⋊Q₈	—	2	8	no	—
369	C₂²⋊Q₈	—	2	8	no	—
370	#121	—	2	8	no	—
371	#121	—	2	8	no	—
372	#121	—	2	16	no	—
373	#120	—	2	16	no	—
374	C₄×D₄	—	2	16	no	—
375	C₄×D₄	—	2	16	no	—
376	#117	—	2	8	no	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
395	C₂×C₄²	—	4	2	no	—
396	C₂×C₄²	—	4	2	no	—
397	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
398	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
403	#95	C₂³×C₁₃	1	4	yes	—
404	#95	C₂³×C₁₃	1	4	yes	—
405	#95	C₂³×C₁₃	1	8	yes	—
406	#95	C₂³×C₁₃	1	8	yes	—
407	#95	C₂³×C₁₃	1	8	yes	—
408	C₂×C₁₃	—	2	4	no	—
409	C₂×C₁₃	—	4	4	no	—
410	C₂×C₁₃	—	8	4	no	—
411	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
413	C₂×C₁₃	#3449	1	1	yes	characteristic
414	C₂×C₁₃	#3505	1	2	yes	—
415	C₂×C₁₃	#3506	1	2	yes	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	4	1	no	—
418	C₂⁴	—	4	1	no	—
419	C₂⁴	—	4	2	no	—
420	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
421	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
422	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
423	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
424	#41	—	4	32	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	8	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	4	16	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
459	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
462	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
463	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	16	no	—
487	C₂²⋊C₄	—	4	8	no	—
488	C₂²⋊C₄	—	4	8	no	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	2	no	—
495	C₁₃	#35032	1	1	yes	characteristic, direct product factor, Sylow
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	8	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	8	no	—
509	C₂³	—	4	4	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
514	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
515	C₂³	C₂×C₁₃×#41	1	4	yes	—
516	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
517	Q₈	—	4	8	no	—
518	D₄	—	4	16	no	—
519	D₄	—	4	16	no	—
520	D₄	—	4	16	no	—
521	D₄	—	4	8	no	—
522	D₄	—	8	8	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	16	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
552	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
553	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
554	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	4	16	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	8	no	—
569	C₂²	—	4	8	no	—
570	C₂²	C₁₃×#532	1	4	yes	—
571	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
572	C₂²	C₂²×C₁₃×#41	1	2	yes	—
573	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂²	C₁₃×#585	1	2	yes	—
576	C₄	—	2	4	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	4	no	—
579	C₄	—	2	4	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	4	no	—
584	C₄	C₁₃×#534	1	4	yes	—
585	C₂	—	2	4	no	—
586	C₂	—	4	4	no	—
587	C₂	—	8	4	no	—
588	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
589	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
590	C₂	C₁₃×#3449	1	1	yes	characteristic
591	C₂	C₁₃×#3505	1	2	yes	—
592	C₂	C₁₃×#3506	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2856	C₂	semidirect
4. C₁₃×#2850	C₂	semidirect
5. C₁₃×#2617	C₂	semidirect
6. C₁₃×#2602	C₂	semidirect
7. C₁₃×#2500	C₂	semidirect
8. C₁₃×#2499	C₂	semidirect
9. C₁₃×#2432	C₂	semidirect
10. C₁₃×#2431	C₂	semidirect
11. C₁₃×#2325	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₁₃×#127	C₂²	semidirect
17. C₂×C₁₃×#124	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#390	C₂²	semidirect
39. C₁₃×#390	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
43. C₁₃×#388	C₂²	semidirect
44. C₁₃×#387	C₂²	semidirect
46. C₁₃×#386	C₂²	semidirect
47. C₁₃×#385	C₂²	semidirect
48. C₁₃×#384	C₂²	semidirect
49. C₁₃×#384	C₂²	semidirect
50. C₁₃×#382	C₂²	semidirect
68. C₂³×C₄×C₁₃	D₄	semidirect
120. #35032	C₁₃	direct (N × H)
167. C₂²×C₄×C₁₃	#41	semidirect
200. C₂×#525	C₂×C₁₃	semidirect
201. #2857	C₂×C₁₃	semidirect
202. #2856	C₂×C₁₃	semidirect
203. #2850	C₂×C₁₃	semidirect
204. #2617	C₂×C₁₃	semidirect
205. #2602	C₂×C₁₃	semidirect
206. #2500	C₂×C₁₃	semidirect
207. #2499	C₂×C₁₃	semidirect
208. #2432	C₂×C₁₃	semidirect
209. #2431	C₂×C₁₃	semidirect
210. #2325	C₂×C₁₃	semidirect
211. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
273. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
274. C₂×#127	C₂²×C₁₃	semidirect
275. C₂×#124	C₂²×C₁₃	semidirect
294. #391	C₂²×C₁₃	semidirect
295. #391	C₂²×C₁₃	semidirect
296. #390	C₂²×C₁₃	semidirect
297. #390	C₂²×C₁₃	semidirect
298. #390	C₂²×C₁₃	semidirect
299. #389	C₂²×C₁₃	semidirect
300. #388	C₂²×C₁₃	semidirect
301. #388	C₂²×C₁₃	semidirect
302. #387	C₂²×C₁₃	semidirect
304. #386	C₂²×C₁₃	semidirect
305. #385	C₂²×C₁₃	semidirect
306. #384	C₂²×C₁₃	semidirect
307. #384	C₂²×C₁₃	semidirect
308. #382	C₂²×C₁₃	semidirect
356. C₂³×C₄	D₄×C₁₃	semidirect
462. C₂²×C₄	C₁₃×#41	semidirect
495. C₁₃	#35032	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×#525	2
C₁₃×#2857	2
C₁₃×#2856	2
C₁₃×#2850	2
C₁₃×#2617	2
C₁₃×#2602	2
C₁₃×#2500	2
C₁₃×#2499	2
C₁₃×#2432	2
C₁₃×#2431	2
C₁₃×#2325	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35032	13

Subgroups — C13×#35032 #15721371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35032 #15721371