Subgroups — C₁₃×#36626 #15722965

Order 3328.

3250 conjugacy classes of subgroups.

The subgroup lattice has 436 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	1	yes	maximal, characteristic
2	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2854	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2853	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2849	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₃×#123	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2296	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#525	—	2	8	no	—
15	C₂×C₁₃×#123	C₂²	1	8	yes	—
16	C₂×C₁₃×#123	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#120	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₁₃×#117	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	—	2	8	no	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
28	C₁₃×#391	C₂²	1	4	yes	complemented
29	C₁₃×#390	C₂²	1	4	yes	complemented
30	C₁₃×#389	C₂²	1	8	yes	complemented
31	C₁₃×#388	C₂²	1	16	yes	complemented
32	C₁₃×#387	C₂²	1	16	yes	complemented
33	C₁₃×#386	C₂²	1	8	yes	—
34	C₁₃×#386	C₂²	1	8	yes	—
35	C₁₃×#385	C₂²	1	8	yes	—
36	C₁₃×#385	C₂²	1	8	yes	—
37	C₁₃×#381	C₂²	1	2	yes	—
38	C₁₃×#381	C₂²	1	8	yes	—
39	C₁₃×#380	C₂²	1	4	yes	—
40	C₁₃×#379	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
42	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×#41	—	2	4	no	—
46	C₂×C₁₃×#41	—	2	8	no	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	8	no	—
52	C₂³×C₄×C₁₃	—	2	8	no	—
53	C₂³×C₄×C₁₃	—	2	16	no	—
54	C₂³×C₄×C₁₃	D₄	1	8	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#123	—	2	8	no	—
64	C₁₃×#123	—	2	32	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×#121	—	2	8	no	—
67	C₁₃×#120	—	2	8	no	—
68	C₄×D₄×C₁₃	—	2	16	no	—
69	C₁₃×#117	—	2	4	no	—
70	C₁₃×#117	—	2	8	no	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	—	2	16	no	—
82	C₂×C₄²×C₁₃	—	2	16	no	—
83	C₂×C₄²×C₁₃	—	2	8	no	—
84	C₂×C₄²×C₁₃	—	2	8	no	—
85	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₁₃×#95	C₂³	1	16	yes	—
92	C₁₃×#95	C₂³	1	16	yes	—
93	#36626	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	8	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
100	C₁₃×#41	—	4	16	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	16	no	—
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	64	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	32	no	—
116	C₂²×C₄×C₁₃	—	2	16	no	—
117	C₂²×C₄×C₁₃	—	2	16	no	—
118	C₂²×C₄×C₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₃	#41	1	8	yes	—
127	C₂²×C₄×C₁₃	#41	1	16	yes	complemented
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	32	no	—
139	C₁₃×C₂²⋊C₄	—	2	4	no	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	8	no	—
142	C₁₃×C₂²⋊C₄	—	2	16	no	—
143	C₁₃×C₂²⋊C₄	—	2	8	no	—
144	C₁₃×C₂²⋊C₄	—	2	32	no	—
145	C₄²×C₁₃	—	2	16	no	—
146	C₄²×C₁₃	—	2	8	no	—
147	C₄²×C₁₃	—	2	8	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	—	2	8	no	—
150	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
151	C₂³×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2855	C₂×C₁₃	1	4	yes	complemented
153	#2854	C₂×C₁₃	1	4	yes	complemented
154	#2853	C₂×C₁₃	1	4	yes	complemented
155	#2849	C₂×C₁₃	1	4	yes	complemented
156	C₄×#123	C₂×C₁₃	1	8	yes	complemented
157	#2297	C₂×C₁₃	1	2	yes	complemented
158	#2296	C₂×C₁₃	1	2	yes	complemented
159	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	32	no	—
161	C₂³×C₁₃	—	2	8	no	—
162	C₂³×C₁₃	—	2	16	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	8	no	—
168	C₂³×C₁₃	—	2	4	no	—
169	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
171	C₂³×C₁₃	C₂×#41	1	4	yes	—
172	C₂³×C₁₃	C₂×#41	1	8	yes	—
173	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
174	Q₈×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	4	8	no	—
176	D₄×C₁₃	—	4	16	no	—
177	D₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	2	32	no	—
179	C₂×C₄×C₁₃	—	2	32	no	—
180	C₂×C₄×C₁₃	—	2	8	no	—
181	C₂×C₄×C₁₃	—	2	32	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	16	no	—
186	C₂×C₄×C₁₃	—	2	16	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	16	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	#123	1	16	yes	complemented
195	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
199	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
200	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
201	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
203	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
204	#525	—	2	8	no	—
205	C₂×#123	C₂²×C₁₃	1	8	yes	—
206	C₂×#123	C₂²×C₁₃	1	2	yes	—
207	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
208	C₂×#121	C₂²×C₁₃	1	2	yes	—
209	C₂×#120	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
211	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#117	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₄²	—	2	8	no	—
214	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
216	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
218	#391	C₂²×C₁₃	1	4	yes	complemented
219	#390	C₂²×C₁₃	1	4	yes	complemented
220	#389	C₂²×C₁₃	1	8	yes	complemented
221	#388	C₂²×C₁₃	1	16	yes	complemented
222	#387	C₂²×C₁₃	1	16	yes	complemented
223	#386	C₂²×C₁₃	1	8	yes	—
224	#386	C₂²×C₁₃	1	8	yes	—
225	#385	C₂²×C₁₃	1	8	yes	—
226	#385	C₂²×C₁₃	1	8	yes	—
227	#381	C₂²×C₁₃	1	8	yes	—
228	#381	C₂²×C₁₃	1	2	yes	—
229	#380	C₂²×C₁₃	1	4	yes	—
230	#379	C₂²×C₁₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
232	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
233	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
234	C₂²×C₁₃	—	2	32	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	2	8	no	—
239	C₂²×C₁₃	—	2	16	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	8	no	—
243	C₂²×C₁₃	C₂×#123	1	4	yes	—
244	C₂²×C₁₃	#525	1	8	yes	—
245	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
246	C₂²×C₁₃	C₂²×#41	1	2	yes	—
247	C₂²×C₁₃	C₂²×#41	1	4	yes	—
248	C₄×C₁₃	—	2	4	no	—
249	C₄×C₁₃	—	2	16	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	4	no	—
252	C₄×C₁₃	—	4	8	no	—
253	C₄×C₁₃	C₂×#123	1	4	yes	—
254	C₄×C₁₃	C₂×#123	1	4	yes	—
255	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×#41	—	2	4	no	—
257	C₂×#41	—	2	8	no	—
258	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
260	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
261	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	8	no	—
263	C₂³×C₄	—	2	8	no	—
264	C₂³×C₄	—	2	16	no	—
265	C₂³×C₄	D₄×C₁₃	1	8	yes	—
266	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
268	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
269	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
273	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
274	#123	—	2	8	no	—
275	#123	—	2	32	no	—
276	C₂²⋊Q₈	—	2	8	no	—
277	#121	—	2	8	no	—
278	#120	—	2	8	no	—
279	C₄×D₄	—	2	16	no	—
280	#117	—	2	4	no	—
281	#117	—	2	8	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
292	C₂×C₄²	—	2	16	no	—
293	C₂×C₄²	—	2	16	no	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	—	2	8	no	—
296	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
300	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
301	#95	C₂³×C₁₃	1	8	yes	—
302	#95	C₂³×C₁₃	1	16	yes	—
303	#95	C₂³×C₁₃	1	16	yes	—
304	C₂×C₁₃	—	2	4	no	—
305	C₂×C₁₃	—	2	8	no	—
306	C₂×C₁₃	—	8	2	no	—
307	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
308	C₂×C₁₃	C₂×#525	1	2	yes	—
309	C₂×C₁₃	#3444	1	4	yes	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	8	no	—
312	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
313	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
314	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
315	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
316	#41	—	4	16	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	16	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂²×C₄	—	2	64	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	32	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	16	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₁₃×#41	1	8	yes	—
343	C₂²×C₄	C₁₃×#41	1	16	yes	complemented
344	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	32	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	2	16	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	32	no	—
361	C₄²	—	2	16	no	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	8	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	8	no	—
366	C₁₃	#36626	1	1	yes	characteristic, direct product factor, Sylow
367	C₂³	—	2	32	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	4	no	—
376	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
377	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
378	C₂³	C₂×C₁₃×#41	1	4	yes	—
379	C₂³	C₂×C₁₃×#41	1	8	yes	—
380	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
381	Q₈	—	4	4	no	—
382	D₄	—	4	8	no	—
383	D₄	—	4	16	no	—
384	D₄	—	4	4	no	—
385	C₂×C₄	—	2	32	no	—
386	C₂×C₄	—	2	32	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	32	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	C₁₃×#123	1	16	yes	complemented
402	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
405	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
406	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
407	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
408	C₂²	—	2	32	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	16	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	8	no	—
417	C₂²	C₂×C₁₃×#123	1	4	yes	—
418	C₂²	C₁₃×#525	1	8	yes	—
419	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
420	C₂²	C₂²×C₁₃×#41	1	2	yes	—
421	C₂²	C₂²×C₁₃×#41	1	4	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	16	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	C₂×C₁₃×#123	1	4	yes	—
428	C₄	C₂×C₁₃×#123	1	4	yes	—
429	C₂	—	2	4	no	—
430	C₂	—	2	8	no	—
431	C₂	—	8	2	no	—
432	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
433	C₂	C₂×C₁₃×#525	1	2	yes	—
434	C₂	C₁₃×#3444	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#525	C₂
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
2. C₂³×C₄²×C₁₃	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
4. C₁₃×#2854	C₂	semidirect
5. C₁₃×#2853	C₂	semidirect
6. C₁₃×#2849	C₂	semidirect
7. C₄×C₁₃×#123	C₂	semidirect
8. C₁₃×#2297	C₂	semidirect
9. C₁₃×#2296	C₂	semidirect
10. C₁₃×#2280	C₂	semidirect
28. C₁₃×#391	C₂²	semidirect
29. C₁₃×#390	C₂²	semidirect
30. C₁₃×#389	C₂²	semidirect
31. C₁₃×#388	C₂²	semidirect
32. C₁₃×#387	C₂²	semidirect
41. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
93. #36626	C₁₃	direct (N × H)
127. C₂²×C₄×C₁₃	#41	semidirect
151. C₂³×C₄²	C₂×C₁₃	semidirect
152. #2855	C₂×C₁₃	semidirect
153. #2854	C₂×C₁₃	semidirect
154. #2853	C₂×C₁₃	semidirect
155. #2849	C₂×C₁₃	semidirect
156. C₄×#123	C₂×C₁₃	semidirect
157. #2297	C₂×C₁₃	semidirect
158. #2296	C₂×C₁₃	semidirect
159. #2280	C₂×C₁₃	semidirect
194. C₂×C₄×C₁₃	#123	semidirect
218. #391	C₂²×C₁₃	semidirect
219. #390	C₂²×C₁₃	semidirect
220. #389	C₂²×C₁₃	semidirect
221. #388	C₂²×C₁₃	semidirect
222. #387	C₂²×C₁₃	semidirect
231. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
233. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
343. C₂²×C₄	C₁₃×#41	semidirect
366. C₁₃	#36626	direct (N × H)
401. C₂×C₄	C₁₃×#123	semidirect

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
C₂³×C₄²×C₁₃	2
C₁₃×#2855	2
C₁₃×#2854	2
C₁₃×#2853	2
C₁₃×#2849	2
C₄×C₁₃×#123	2
C₁₃×#2297	2
C₁₃×#2296	2
C₁₃×#2280	2
#36626	13

Subgroups — C13×#36626 #15722965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36626 #15722965