Subgroups — C₁₃×#36652 #15722991

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 476 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×#2817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2816	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2814	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2813	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2812	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2280	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×#525	—	2	16	no	—
15	C₂×C₁₃×#123	C₂²	1	4	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₁₃×#120	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₁₃×#400	C₂²	1	4	yes	complemented
27	C₁₃×#399	C₂²	1	4	yes	complemented
28	C₁₃×#398	C₂²	1	4	yes	complemented
29	C₁₃×#398	C₂²	1	4	yes	complemented
30	C₁₃×#397	C₂²	1	8	yes	—
31	C₁₃×#397	C₂²	1	4	yes	—
32	C₁₃×#397	C₂²	1	4	yes	complemented
33	C₁₃×#396	C₂²	1	8	yes	complemented
34	C₁₃×#395	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	8	yes	—
36	C₁₃×#394	C₂²	1	8	yes	—
37	C₁₃×#394	C₂²	1	8	yes	—
38	C₁₃×#394	C₂²	1	4	yes	complemented
39	C₁₃×#394	C₂²	1	4	yes	complemented
40	C₁₃×#393	C₂²	1	4	yes	complemented
41	C₁₃×#392	C₂²	1	8	yes	—
42	C₁₃×#392	C₂²	1	4	yes	—
43	C₁₃×#392	C₂²	1	4	yes	complemented
44	C₁₃×#381	C₂²	1	1	yes	characteristic
45	C₁₃×#381	C₂²	1	1	yes	characteristic
46	C₁₃×#380	C₂²	1	4	yes	—
47	C₁₃×#379	C₂²	1	2	yes	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	—	4	8	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	—	4	4	no	—
61	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#123	—	2	16	no	—
68	C₁₃×C₂²⋊Q₈	—	2	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	8	no	—
70	C₁₃×#121	—	2	8	no	—
71	C₁₃×#121	—	2	8	no	—
72	C₁₃×#120	—	2	16	no	—
73	C₄×D₄×C₁₃	—	2	16	no	—
74	C₄×D₄×C₁₃	—	2	16	no	—
75	C₄×D₄×C₁₃	—	4	8	no	—
76	C₁₃×#117	—	2	8	no	—
77	C₁₃×#117	—	4	4	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊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	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₁₃×#95	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	#36652	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	—	4	2	no	—
106	C₂⁴×C₁₃	—	4	4	no	—
107	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
111	C₁₃×#41	—	4	32	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	8	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	—	4	8	no	—
121	C₂×D₄×C₁₃	—	4	8	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	8	no	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	2	16	no	—
129	C₂²×C₄×C₁₃	—	4	16	no	—
130	C₂²×C₄×C₁₃	—	4	4	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	4	8	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	4	8	no	—
157	C₁₃×C₂²⋊C₄	—	4	8	no	—
158	C₁₃×C₂²⋊C₄	—	4	8	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	8	no	—
162	C₄²×C₁₃	—	2	8	no	—
163	C₄²×C₁₃	—	2	8	no	—
164	C₂×#525	C₂×C₁₃	1	2	yes	complemented
165	#2817	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2816	C₂×C₁₃	1	2	yes	complemented
167	#2815	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2814	C₂×C₁₃	1	4	yes	complemented
169	#2813	C₂×C₁₃	1	4	yes	complemented
170	#2812	C₂×C₁₃	1	4	yes	complemented
171	#2395	C₂×C₁₃	1	4	yes	complemented
172	#2392	C₂×C₁₃	1	4	yes	complemented
173	#2388	C₂×C₁₃	1	4	yes	complemented
174	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	2	8	no	—
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	4	16	no	—
188	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
190	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	8	no	—
192	D₄×C₁₃	—	4	8	no	—
193	D₄×C₁₃	—	4	16	no	—
194	D₄×C₁₃	—	4	16	no	—
195	D₄×C₁₃	—	4	16	no	—
196	D₄×C₁₃	—	4	16	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	2	16	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	16	no	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
219	C₂²×#41	C₂²×C₁₃	1	2	yes	—
220	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
221	#525	—	2	16	no	—
222	C₂×#123	C₂²×C₁₃	1	4	yes	—
223	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
224	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
225	C₂×#121	C₂²×C₁₃	1	2	yes	—
226	C₂×#121	C₂²×C₁₃	1	2	yes	—
227	C₂×#120	C₂²×C₁₃	1	4	yes	—
228	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
229	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
230	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
231	C₂×#117	C₂²×C₁₃	1	2	yes	—
232	C₂×#117	C₂²×C₁₃	1	2	yes	—
233	#400	C₂²×C₁₃	1	4	yes	complemented
234	#399	C₂²×C₁₃	1	4	yes	complemented
235	#398	C₂²×C₁₃	1	4	yes	complemented
236	#398	C₂²×C₁₃	1	4	yes	complemented
237	#397	C₂²×C₁₃	1	4	yes	—
238	#397	C₂²×C₁₃	1	8	yes	—
239	#397	C₂²×C₁₃	1	4	yes	complemented
240	#396	C₂²×C₁₃	1	8	yes	complemented
241	#395	C₂²×C₁₃	1	4	yes	complemented
242	#394	C₂²×C₁₃	1	8	yes	—
243	#394	C₂²×C₁₃	1	8	yes	—
244	#394	C₂²×C₁₃	1	8	yes	—
245	#394	C₂²×C₁₃	1	4	yes	complemented
246	#394	C₂²×C₁₃	1	4	yes	complemented
247	#393	C₂²×C₁₃	1	4	yes	complemented
248	#392	C₂²×C₁₃	1	8	yes	—
249	#392	C₂²×C₁₃	1	4	yes	—
250	#392	C₂²×C₁₃	1	4	yes	complemented
251	#381	C₂²×C₁₃	1	1	yes	characteristic
252	#381	C₂²×C₁₃	1	1	yes	characteristic
253	#380	C₂²×C₁₃	1	4	yes	—
254	#379	C₂²×C₁₃	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
256	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	2	no	—
260	C₂²×C₁₃	—	2	4	no	—
261	C₂²×C₁₃	—	2	4	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	4	16	no	—
264	C₂²×C₁₃	—	4	4	no	—
265	C₂²×C₁₃	—	4	8	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	8	no	—
270	C₂²×C₁₃	—	4	8	no	—
271	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
272	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
273	C₂²×C₁₃	#585	1	4	yes	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	4	no	—
276	C₄×C₁₃	—	4	4	no	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	#534	1	4	yes	—
282	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×#41	—	2	8	no	—
284	C₂×#41	—	4	8	no	—
285	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
286	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
287	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
288	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
289	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
290	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
291	C₂³×C₄	—	4	4	no	—
292	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
293	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
294	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
298	#123	—	2	16	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	#121	—	2	8	no	—
302	#121	—	2	8	no	—
303	#120	—	2	16	no	—
304	C₄×D₄	—	2	16	no	—
305	C₄×D₄	—	2	16	no	—
306	C₄×D₄	—	4	8	no	—
307	#117	—	2	8	no	—
308	#117	—	4	4	no	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
327	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
328	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
329	#95	C₂³×C₁₃	1	4	yes	—
330	#95	C₂³×C₁₃	1	4	yes	—
331	#95	C₂³×C₁₃	1	8	yes	—
332	#95	C₂³×C₁₃	1	8	yes	—
333	#95	C₂³×C₁₃	1	4	yes	—
334	#95	C₂³×C₁₃	1	4	yes	—
335	C₂×C₁₃	—	4	4	no	—
336	C₂×C₁₃	—	4	2	no	—
337	C₂×C₁₃	—	8	4	no	—
338	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
339	C₂×C₁₃	#3449	1	2	yes	—
340	C₂×C₁₃	#3529	1	4	yes	—
341	C₂⁴	—	4	2	no	—
342	C₂⁴	—	4	4	no	—
343	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
344	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
345	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
346	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
347	#41	—	4	32	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	—	4	8	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	16	no	—
365	C₂²×C₄	—	4	16	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	4	8	no	—
396	C₂²⋊C₄	—	4	8	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	8	no	—
400	C₁₃	#36652	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	8	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	8	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	16	no	—
414	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
415	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
416	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
417	Q₈	—	4	8	no	—
418	D₄	—	4	8	no	—
419	D₄	—	4	16	no	—
420	D₄	—	4	16	no	—
421	D₄	—	4	16	no	—
422	D₄	—	4	16	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	16	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
444	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	16	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	8	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
459	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
460	C₂²	C₁₃×#585	1	4	yes	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	4	no	—
468	C₄	C₁₃×#534	1	4	yes	—
469	C₂	—	4	4	no	—
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
473	C₂	C₁₃×#3449	1	2	yes	—
474	C₂	C₁₃×#3529	1	4	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×#525	C₂	semidirect
2. C₁₃×#2817	C₂	semidirect
3. C₁₃×#2816	C₂	semidirect
4. C₁₃×#2815	C₂	semidirect
5. C₁₃×#2814	C₂	semidirect
6. C₁₃×#2813	C₂	semidirect
7. C₁₃×#2812	C₂	semidirect
8. C₁₃×#2395	C₂	semidirect
9. C₁₃×#2392	C₂	semidirect
10. C₁₃×#2388	C₂	semidirect
11. C₁₃×#2280	C₂	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#399	C₂²	semidirect
28. C₁₃×#398	C₂²	semidirect
29. C₁₃×#398	C₂²	semidirect
32. C₁₃×#397	C₂²	semidirect
33. C₁₃×#396	C₂²	semidirect
34. C₁₃×#395	C₂²	semidirect
38. C₁₃×#394	C₂²	semidirect
39. C₁₃×#394	C₂²	semidirect
40. C₁₃×#393	C₂²	semidirect
43. C₁₃×#392	C₂²	semidirect
48. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
50. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
61. C₂³×C₄×C₁₃	D₄	semidirect
104. #36652	C₁₃	direct (N × H)
164. C₂×#525	C₂×C₁₃	semidirect
165. #2817	C₂×C₁₃	semidirect
166. #2816	C₂×C₁₃	semidirect
167. #2815	C₂×C₁₃	semidirect
168. #2814	C₂×C₁₃	semidirect
169. #2813	C₂×C₁₃	semidirect
170. #2812	C₂×C₁₃	semidirect
171. #2395	C₂×C₁₃	semidirect
172. #2392	C₂×C₁₃	semidirect
173. #2388	C₂×C₁₃	semidirect
174. #2280	C₂×C₁₃	semidirect
230. C₂×C₄×D₄	C₂²×C₁₃	semidirect
233. #400	C₂²×C₁₃	semidirect
234. #399	C₂²×C₁₃	semidirect
235. #398	C₂²×C₁₃	semidirect
236. #398	C₂²×C₁₃	semidirect
239. #397	C₂²×C₁₃	semidirect
240. #396	C₂²×C₁₃	semidirect
241. #395	C₂²×C₁₃	semidirect
245. #394	C₂²×C₁₃	semidirect
246. #394	C₂²×C₁₃	semidirect
247. #393	C₂²×C₁₃	semidirect
250. #392	C₂²×C₁₃	semidirect
255. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
257. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
292. C₂³×C₄	D₄×C₁₃	semidirect
400. C₁₃	#36652	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×#2817	2
C₁₃×#2816	2
C₁₃×#2815	2
C₁₃×#2814	2
C₁₃×#2813	2
C₁₃×#2812	2
C₁₃×#2395	2
C₁₃×#2392	2
C₁₃×#2388	2
C₁₃×#2280	2
#36652	13

Subgroups — C13×#36652 #15722991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36652 #15722991