Subgroups — C₁₃×#36625 #15722964

Order 3328.

3110 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2857	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2855	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2851	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2848	C₂	1	4	yes	maximal
7	C₄×C₁₃×C₂²⋊Q₈	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2296	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#533	—	2	8	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
15	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#117	C₂²	1	2	yes	—
20	C₂×C₁₃×#117	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	—	2	8	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	8	yes	complemented
29	C₁₃×#389	C₂²	1	8	yes	complemented
30	C₁₃×#389	C₂²	1	8	yes	complemented
31	C₁₃×#387	C₂²	1	16	yes	complemented
32	C₁₃×#385	C₂²	1	8	yes	—
33	C₁₃×#385	C₂²	1	16	yes	—
34	C₁₃×#384	C₂²	1	2	yes	complemented
35	C₁₃×#382	C₂²	1	2	yes	complemented
36	C₁₃×#381	C₂²	1	4	yes	—
37	C₁₃×#380	C₂²	1	8	yes	—
38	C₁₃×#380	C₂²	1	4	yes	—
39	C₁₃×#380	C₂²	1	8	yes	—
40	C₁₃×#379	C₂²	1	4	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	2	8	no	—
47	C₂³×C₄×C₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₃	—	2	16	no	—
49	C₂³×C₄×C₁₃	—	2	4	no	—
50	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	8	no	—
60	C₁₃×#125	—	2	8	no	—
61	C₁₃×C₂²⋊Q₈	—	2	16	no	—
62	C₁₃×C₂²⋊Q₈	—	2	32	no	—
63	C₄×Q₈×C₁₃	—	2	16	no	—
64	C₁₃×#117	—	2	8	no	—
65	C₁₃×#117	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₄²×C₁₃	—	2	8	no	—
76	C₂×C₄²×C₁₃	—	2	4	no	—
77	C₂×C₄²×C₁₃	—	2	16	no	—
78	C₂×C₄²×C₁₃	—	2	8	no	—
79	C₂×C₄²×C₁₃	—	2	8	no	—
80	C₂×C₄²×C₁₃	D₄	1	8	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#95	C₂³	1	16	yes	—
91	C₁₃×#95	C₂³	1	8	yes	—
92	C₁₃×#95	C₂³	1	16	yes	—
93	#36625	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	8	no	—
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	16	no	—
102	C₂²×C₄×C₁₃	—	2	64	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	8	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	32	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
122	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₁₃	#41	1	16	yes	—
125	C₂²×C₄×C₁₃	#41	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	16	no	—
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	16	no	—
139	C₁₃×C₄⋊C₄	—	2	32	no	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	8	no	—
142	C₁₃×C₂²⋊C₄	—	2	32	no	—
143	C₄²×C₁₃	—	2	8	no	—
144	C₄²×C₁₃	—	2	4	no	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	2	8	no	—
147	C₄²×C₁₃	—	2	8	no	—
148	C₄²×C₁₃	—	2	8	no	—
149	C₄²×C₁₃	C₂×D₄	1	8	yes	—
150	C₄²×C₁₃	C₂×D₄	1	4	yes	—
151	C₄²×C₁₃	C₂×D₄	1	4	yes	—
152	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₄²	C₂×C₁₃	1	1	yes	characteristic
154	#2857	C₂×C₁₃	1	4	yes	complemented
155	#2855	C₂×C₁₃	1	4	yes	complemented
156	#2851	C₂×C₁₃	1	4	yes	complemented
157	#2848	C₂×C₁₃	1	4	yes	—
158	C₄×C₂²⋊Q₈	C₂×C₁₃	1	8	yes	complemented
159	#2296	C₂×C₁₃	1	2	yes	complemented
160	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2280	C₂×C₁₃	1	2	yes	—
162	C₂³×C₁₃	—	2	16	no	—
163	C₂³×C₁₃	—	2	16	no	—
164	C₂³×C₁₃	—	2	8	no	—
165	C₂³×C₁₃	—	2	16	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	4	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
171	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
172	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
173	C₂³×C₁₃	C₂×#41	1	2	yes	—
174	C₂³×C₁₃	C₂×#41	1	8	yes	—
175	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	2	32	no	—
178	C₂×C₄×C₁₃	—	2	16	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	16	no	—
186	C₂×C₄×C₁₃	—	2	16	no	—
187	C₂×C₄×C₁₃	—	2	16	no	—
188	C₂×C₄×C₁₃	—	2	32	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	16	no	—
192	C₂×C₄×C₁₃	—	2	16	no	—
193	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
194	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
202	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
205	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
206	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
207	#533	—	2	8	no	—
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
209	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
210	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
211	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
212	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
213	C₂×#117	C₂²×C₁₃	1	2	yes	—
214	C₂×#117	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄²	—	2	8	no	—
216	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
221	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
222	#391	C₂²×C₁₃	1	8	yes	complemented
223	#389	C₂²×C₁₃	1	8	yes	complemented
224	#389	C₂²×C₁₃	1	8	yes	complemented
225	#387	C₂²×C₁₃	1	16	yes	complemented
226	#385	C₂²×C₁₃	1	16	yes	—
227	#385	C₂²×C₁₃	1	8	yes	—
228	#384	C₂²×C₁₃	1	2	yes	complemented
229	#382	C₂²×C₁₃	1	2	yes	complemented
230	#381	C₂²×C₁₃	1	4	yes	—
231	#380	C₂²×C₁₃	1	4	yes	—
232	#380	C₂²×C₁₃	1	8	yes	—
233	#380	C₂²×C₁₃	1	8	yes	—
234	#379	C₂²×C₁₃	1	4	yes	—
235	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
237	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
238	C₂²×C₁₃	—	2	32	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	8	no	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	8	no	—
246	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
247	C₂²×C₁₃	#533	1	8	yes	complemented
248	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
249	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
250	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×#41	1	4	yes	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	2	8	no	—
255	C₄×C₁₃	—	4	8	no	—
256	C₄×C₁₃	—	4	8	no	—
257	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
258	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
259	C₄×C₁₃	#525	1	8	yes	—
260	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	—	2	8	no	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	16	no	—
265	C₂³×C₄	—	2	4	no	—
266	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
267	C₂³×C₄	C₂³×C₁₃	1	2	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	2	yes	—
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	8	no	—
276	#125	—	2	8	no	—
277	C₂²⋊Q₈	—	2	16	no	—
278	C₂²⋊Q₈	—	2	32	no	—
279	C₄×Q₈	—	2	16	no	—
280	#117	—	2	8	no	—
281	#117	—	2	8	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	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	16	yes	—
291	C₂×C₄²	—	2	8	no	—
292	C₂×C₄²	—	2	4	no	—
293	C₂×C₄²	—	2	16	no	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	—	2	8	no	—
296	C₂×C₄²	D₄×C₁₃	1	8	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
301	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	#95	C₂³×C₁₃	1	16	yes	—
307	#95	C₂³×C₁₃	1	8	yes	—
308	#95	C₂³×C₁₃	1	16	yes	—
309	C₂×C₁₃	—	2	4	no	—
310	C₂×C₁₃	—	2	8	no	—
311	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
312	C₂×C₁₃	C₂×#525	1	2	yes	—
313	C₂×C₁₃	C₂×#533	1	2	yes	—
314	C₂×C₁₃	#3444	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	8	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
319	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
321	C₂×Q₈	—	2	8	no	—
322	C₂×Q₈	—	2	16	no	—
323	C₂²×C₄	—	2	64	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	32	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
341	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
343	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
344	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
345	C₂²×C₄	C₁₃×#41	1	16	yes	—
346	C₂²×C₄	C₁₃×#41	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	4	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	2	yes	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	16	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	16	no	—
360	C₄⋊C₄	—	2	32	no	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	32	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	8	no	—
368	C₄²	—	2	8	no	—
369	C₄²	—	2	8	no	—
370	C₄²	C₂×D₄×C₁₃	1	8	yes	—
371	C₄²	C₂×D₄×C₁₃	1	4	yes	—
372	C₄²	C₂×D₄×C₁₃	1	4	yes	—
373	C₁₃	#36625	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	16	no	—
375	C₂³	—	2	16	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	16	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
383	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
384	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
385	C₂³	C₂×C₁₃×#41	1	2	yes	—
386	C₂³	C₂×C₁₃×#41	1	8	yes	—
387	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
388	Q₈	—	4	16	no	—
389	C₂×C₄	—	2	32	no	—
390	C₂×C₄	—	2	16	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
406	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
411	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
412	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
413	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
414	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
415	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
416	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
417	C₂²	—	2	32	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	8	no	—
425	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
426	C₂²	C₁₃×#533	1	8	yes	complemented
427	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
428	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
429	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
430	C₂²	C₂²×C₁₃×#41	1	4	yes	—
431	C₄	—	2	4	no	—
432	C₄	—	2	4	no	—
433	C₄	—	2	8	no	—
434	C₄	—	4	8	no	—
435	C₄	—	4	8	no	—
436	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
437	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
438	C₄	C₁₃×#525	1	8	yes	—
439	C₂	—	2	4	no	—
440	C₂	—	2	8	no	—
441	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
442	C₂	C₂×C₁₃×#525	1	2	yes	—
443	C₂	C₂×C₁₃×#533	1	2	yes	—
444	C₂	C₁₃×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁵×C₁₃	C₂³
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×#533	C₂	semidirect
3. C₁₃×#2857	C₂	semidirect
4. C₁₃×#2855	C₂	semidirect
5. C₁₃×#2851	C₂	semidirect
7. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
8. C₁₃×#2296	C₂	semidirect
9. C₁₃×#2285	C₂	semidirect
14. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
15. C₂×C₁₃×#125	C₂²	semidirect
18. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#391	C₂²	semidirect
29. C₁₃×#389	C₂²	semidirect
30. C₁₃×#389	C₂²	semidirect
31. C₁₃×#387	C₂²	semidirect
34. C₁₃×#384	C₂²	semidirect
35. C₁₃×#382	C₂²	semidirect
41. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
50. C₂³×C₄×C₁₃	Q₈	semidirect
93. #36625	C₁₃	direct (N × H)
152. C₂×#533	C₂×C₁₃	semidirect
154. #2857	C₂×C₁₃	semidirect
155. #2855	C₂×C₁₃	semidirect
156. #2851	C₂×C₁₃	semidirect
158. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
159. #2296	C₂×C₁₃	semidirect
160. #2285	C₂×C₁₃	semidirect
193. C₂×C₄×C₁₃	C₂²⋊Q₈	semidirect
208. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
209. C₂×#125	C₂²×C₁₃	semidirect
212. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
222. #391	C₂²×C₁₃	semidirect
223. #389	C₂²×C₁₃	semidirect
224. #389	C₂²×C₁₃	semidirect
225. #387	C₂²×C₁₃	semidirect
228. #384	C₂²×C₁₃	semidirect
229. #382	C₂²×C₁₃	semidirect
235. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
236. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
247. C₂²×C₁₃	#533	semidirect
266. C₂³×C₄	Q₈×C₁₃	semidirect
373. C₁₃	#36625	direct (N × H)
405. C₂×C₄	C₁₃×C₂²⋊Q₈	semidirect
426. C₂²	C₁₃×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₂³×C₄²×C₁₃	2
C₁₃×#2857	2
C₁₃×#2855	2
C₁₃×#2851	2
C₁₃×#2848	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2296	2
C₁₃×#2285	2
C₁₃×#2280	2
#36625	13

Subgroups — C13×#36625 #15722964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36625 #15722964