Subgroups — C₁₃×#60800 #15747139

Order 3328.

2134 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3218	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3209	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3206	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3152	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3139	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3039	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3004	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×#137	C₂²	1	8	yes	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	1	yes	characteristic
15	C₁₃×#532	C₂²	1	1	yes	characteristic
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
18	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
19	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₁₃×#529	—	2	2	no	—
25	C₁₃×#529	—	2	2	no	—
26	C₁₃×#529	C₂²	1	4	yes	—
27	C₁₃×#525	—	2	2	no	—
28	C₁₃×#525	C₂²	1	2	yes	—
29	C₄×C₁₃×#41	—	2	2	no	—
30	C₄×C₁₃×#41	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#497	C₂²	1	8	yes	complemented
34	C₁₃×#494	C₂²	1	4	yes	complemented
35	C₁₃×#492	C₂²	1	4	yes	complemented
36	C₁₃×#491	C₂²	1	8	yes	complemented
37	C₁₃×#487	C₂²	1	8	yes	complemented
38	C₁₃×#462	C₂²	1	16	yes	complemented
39	C₁₃×#461	C₂²	1	16	yes	complemented
40	C₁₃×#451	C₂²	1	16	yes	—
41	C₁₃×#448	C₂²	1	16	yes	—
42	C₁₃×#432	C₂²	1	4	yes	—
43	C₁₃×#431	C₂²	1	4	yes	—
44	C₁₃×#423	C₂²	1	2	yes	—
45	C₁₃×#419	C₂²	1	8	yes	—
46	C₁₃×#407	C₂²	1	2	yes	—
47	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	2	no	—
52	C₂²×Q₈×C₁₃	—	4	8	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	D₄	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#137	—	4	16	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	—	2	4	no	—
66	C₁₃×C₄⋊Q₈	—	2	4	no	—
67	C₁₃×C₄⋊Q₈	—	2	4	no	—
68	C₁₃×C₄⋊Q₈	—	2	4	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×#127	C₂³	1	1	yes	characteristic
75	C₁₃×#126	—	2	4	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	C₂³	1	2	yes	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	C₂³	1	2	yes	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×#123	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	C₂³	1	4	yes	—
88	C₁₃×#120	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	—	2	4	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	C₂³	1	4	yes	—
98	C₁₃×#117	—	2	2	no	—
99	C₁₃×#117	—	2	4	no	—
100	C₁₃×#117	—	2	2	no	—
101	C₁₃×#117	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₄²×C₁₃	—	2	2	no	—
109	C₂×C₄²×C₁₃	D₄	1	2	yes	—
110	C₂×C₄²×C₁₃	D₄	1	2	yes	—
111	C₂×C₄²×C₁₃	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#103	C₂³	1	32	yes	—
118	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
119	C₁₃×#97	C₂³	1	4	yes	—
120	C₄×C₈×C₁₃	C₂³	1	4	yes	—
121	#60800	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₁₃×#41	—	2	8	no	—
124	C₁₃×#41	—	4	8	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	8	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	16	no	—
129	C₂×Q₈×C₁₃	—	4	16	no	—
130	C₂×Q₈×C₁₃	—	4	8	no	—
131	C₂×Q₈×C₁₃	—	4	16	no	—
132	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	8	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×Q₁₆	—	4	16	no	—
156	C₁₃×SD₁₆	—	4	16	no	—
157	C₁₃×M₁₆	—	2	8	no	—
158	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₄²×C₁₃	—	2	4	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	C₄²×C₁₃	C₂×D₄	1	2	yes	—
182	C₄²×C₁₃	C₂×D₄	1	2	yes	—
183	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₄²×C₁₃	C₂⁴	1	2	yes	—
186	#3444	C₂×C₁₃	1	1	yes	characteristic
187	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3218	C₂×C₁₃	1	8	yes	complemented
189	#3209	C₂×C₁₃	1	4	yes	complemented
190	#3206	C₂×C₁₃	1	4	yes	complemented
191	#3152	C₂×C₁₃	1	2	yes	complemented
192	#3139	C₂×C₁₃	1	2	yes	complemented
193	#3039	C₂×C₁₃	1	4	yes	complemented
194	#3004	C₂×C₁₃	1	4	yes	complemented
195	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
201	Q₈×C₁₃	—	2	16	no	—
202	Q₈×C₁₃	—	2	4	no	—
203	Q₈×C₁₃	—	4	16	no	—
204	Q₈×C₁₃	—	4	8	no	—
205	Q₈×C₁₃	—	4	4	no	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	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	8	no	—
221	C₂×C₄×C₁₃	—	4	16	no	—
222	C₂×C₄×C₁₃	—	4	8	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	8	no	—
225	C₂×C₄×C₁₃	#137	1	8	yes	complemented
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₈×C₁₃	—	2	8	no	—
235	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
236	C₂×#137	C₂²×C₁₃	1	8	yes	—
237	#533	C₂²×C₁₃	1	2	yes	—
238	#533	C₂²×C₁₃	1	1	yes	characteristic
239	#532	C₂²×C₁₃	1	1	yes	characteristic
240	#532	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄⋊Q₈	—	2	2	no	—
242	C₂×C₄⋊Q₈	—	2	2	no	—
243	C₂×C₄⋊Q₈	—	2	2	no	—
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
248	#529	—	2	2	no	—
249	#529	—	2	2	no	—
250	#529	C₂²×C₁₃	1	4	yes	—
251	#525	—	2	2	no	—
252	#525	C₂²×C₁₃	1	2	yes	—
253	C₄×#41	—	2	2	no	—
254	C₄×#41	C₂²×C₁₃	1	2	yes	—
255	C₂²×C₄⋊C₄	—	2	2	no	—
256	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
257	#497	C₂²×C₁₃	1	8	yes	complemented
258	#494	C₂²×C₁₃	1	4	yes	complemented
259	#492	C₂²×C₁₃	1	4	yes	complemented
260	#491	C₂²×C₁₃	1	8	yes	complemented
261	#487	C₂²×C₁₃	1	8	yes	complemented
262	#462	C₂²×C₁₃	1	16	yes	complemented
263	#461	C₂²×C₁₃	1	16	yes	complemented
264	#451	C₂²×C₁₃	1	16	yes	—
265	#448	C₂²×C₁₃	1	16	yes	—
266	#432	C₂²×C₁₃	1	4	yes	—
267	#431	C₂²×C₁₃	1	4	yes	—
268	#423	C₂²×C₁₃	1	2	yes	—
269	#419	C₂²×C₁₃	1	8	yes	—
270	#407	C₂²×C₁₃	1	2	yes	—
271	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	2	8	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	#535	1	2	yes	—
279	C₂²×C₁₃	C₂×#137	1	4	yes	—
280	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	8	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	4	no	—
287	C₄×C₁₃	#535	1	2	yes	—
288	C₄×C₁₃	C₂×#137	1	4	yes	—
289	C₄×C₁₃	C₂×#137	1	4	yes	—
290	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
291	C₂×#41	—	2	2	no	—
292	C₂×#41	C₂³×C₁₃	1	2	yes	—
293	C₂²×Q₈	—	2	4	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	—	4	8	no	—
296	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
297	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	D₄×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
301	#137	—	4	16	no	—
302	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
303	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
304	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	C₄⋊Q₈	—	2	4	no	—
310	C₄⋊Q₈	—	2	4	no	—
311	C₄⋊Q₈	—	2	4	no	—
312	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
317	#127	C₂³×C₁₃	1	1	yes	characteristic
318	#126	—	2	4	no	—
319	#125	—	2	2	no	—
320	#125	C₂³×C₁₃	1	2	yes	—
321	#124	—	2	2	no	—
322	#124	C₂³×C₁₃	1	2	yes	—
323	#123	—	2	4	no	—
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
328	#121	—	2	2	no	—
329	#121	—	2	2	no	—
330	#121	C₂³×C₁₃	1	4	yes	—
331	#120	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂³×C₁₃	1	4	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	4	no	—
343	#117	—	2	2	no	—
344	#117	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	D₄×C₁₃	1	2	yes	—
353	C₂×C₄²	D₄×C₁₃	1	2	yes	—
354	C₂×C₄²	D₄×C₁₃	1	2	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
359	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
360	#103	C₂³×C₁₃	1	32	yes	—
361	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
362	#97	C₂³×C₁₃	1	4	yes	—
363	C₄×C₈	C₂³×C₁₃	1	4	yes	—
364	C₂×C₁₃	—	2	2	no	—
365	C₂×C₁₃	—	2	4	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
368	C₂×C₁₃	C₂²×#137	1	2	yes	—
369	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
370	#41	—	2	8	no	—
371	#41	—	4	8	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	16	no	—
376	C₂×Q₈	—	4	16	no	—
377	C₂×Q₈	—	4	8	no	—
378	C₂×Q₈	—	4	16	no	—
379	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
380	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	4	8	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	Q₁₆	—	4	16	no	—
403	SD₁₆	—	4	16	no	—
404	M₁₆	—	2	8	no	—
405	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₁₃	1	2	yes	—
425	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₃	1	2	yes	—
427	C₄²	C₂×D₄×C₁₃	1	2	yes	—
428	C₄²	C₂×D₄×C₁₃	1	2	yes	—
429	C₄²	C₂×D₄×C₁₃	1	2	yes	—
430	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
431	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
432	C₄²	C₂⁴×C₁₃	1	2	yes	—
433	C₁₃	#60800	1	1	yes	characteristic, direct product factor, Sylow
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
439	Q₈	—	2	16	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	4	16	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	4	16	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	C₁₃×#137	1	8	yes	complemented
464	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
471	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
472	C₈	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	C₁₃×#535	1	2	yes	—
480	C₂²	C₂×C₁₃×#137	1	4	yes	—
481	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	8	no	—
487	C₄	—	4	2	no	—
488	C₄	C₁₃×#535	1	2	yes	—
489	C₄	C₂×C₁₃×#137	1	4	yes	—
490	C₄	C₂×C₁₃×#137	1	4	yes	—
491	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	2	4	no	—
494	C₂	—	8	2	no	—
495	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
496	C₂	C₂²×C₁₃×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#3218	C₂	semidirect
4. C₁₃×#3209	C₂	semidirect
5. C₁₃×#3206	C₂	semidirect
6. C₁₃×#3152	C₂	semidirect
7. C₁₃×#3139	C₂	semidirect
8. C₁₃×#3039	C₂	semidirect
9. C₁₃×#3004	C₂	semidirect
10. C₁₃×#2920	C₂	semidirect
33. C₁₃×#497	C₂²	semidirect
34. C₁₃×#494	C₂²	semidirect
35. C₁₃×#492	C₂²	semidirect
36. C₁₃×#491	C₂²	semidirect
37. C₁₃×#487	C₂²	semidirect
38. C₁₃×#462	C₂²	semidirect
39. C₁₃×#461	C₂²	semidirect
121. #60800	C₁₃	direct (N × H)
187. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
188. #3218	C₂×C₁₃	semidirect
189. #3209	C₂×C₁₃	semidirect
190. #3206	C₂×C₁₃	semidirect
191. #3152	C₂×C₁₃	semidirect
192. #3139	C₂×C₁₃	semidirect
193. #3039	C₂×C₁₃	semidirect
194. #3004	C₂×C₁₃	semidirect
195. #2920	C₂×C₁₃	semidirect
225. C₂×C₄×C₁₃	#137	semidirect
257. #497	C₂²×C₁₃	semidirect
258. #494	C₂²×C₁₃	semidirect
259. #492	C₂²×C₁₃	semidirect
260. #491	C₂²×C₁₃	semidirect
261. #487	C₂²×C₁₃	semidirect
262. #462	C₂²×C₁₃	semidirect
263. #461	C₂²×C₁₃	semidirect
433. C₁₃	#60800	direct (N × H)
463. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3444	2
C₂²×C₁₃×C₄⋊Q₈	2
C₁₃×#3218	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3152	2
C₁₃×#3139	2
C₁₃×#3039	2
C₁₃×#3004	2
C₁₃×#2920	2
#60800	13

Subgroups — C13×#60800 #15747139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60800 #15747139