Subgroups — C₁₃×#61014 #15747353

Order 3328.

1768 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3262	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3230	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3226	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3203	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3182	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3124	C₂	1	8	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#556	—	2	2	no	—
14	C₁₃×#555	—	2	2	no	—
15	C₁₃×#554	—	2	2	no	—
16	C₁₃×#553	—	2	2	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#548	—	2	2	no	—
19	C₁₃×#548	—	2	2	no	—
20	C₁₃×#547	—	2	2	no	—
21	C₁₃×#542	C₂²	1	4	yes	—
22	C₁₃×#542	C₂²	1	4	yes	—
23	C₁₃×#537	C₂²	1	4	yes	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	2	yes	—
26	C₁₃×#532	C₂²	1	2	yes	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₁₃×#520	C₂²	1	4	yes	—
31	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
32	C₁₃×#500	C₂²	1	1	yes	characteristic
33	C₁₃×#500	C₂²	1	1	yes	characteristic
34	C₁₃×#500	C₂²	1	2	yes	—
35	C₁₃×#494	C₂²	1	1	yes	characteristic
36	C₁₃×#493	C₂²	1	1	yes	characteristic
37	C₁₃×#492	C₂²	1	2	yes	—
38	C₁₃×#487	C₂²	1	2	yes	—
39	C₁₃×#487	C₂²	1	2	yes	—
40	C₁₃×#486	C₂²	1	2	yes	—
41	C₁₃×#486	C₂²	1	2	yes	—
42	C₁₃×#484	C₂²	1	8	yes	—
43	C₁₃×#480	C₂²	1	8	yes	—
44	C₁₃×#477	C₂²	1	8	yes	—
45	C₁₃×#474	C₂²	1	8	yes	—
46	C₁₃×#468	C₂²	1	8	yes	—
47	C₁₃×#467	C₂²	1	4	yes	—
48	C₁₃×#466	C₂²	1	4	yes	—
49	C₁₃×#464	C₂²	1	8	yes	—
50	C₁₃×#463	C₂²	1	8	yes	—
51	C₁₃×#452	C₂²	1	8	yes	—
52	C₁₃×#449	C₂²	1	8	yes	—
53	C₁₃×#440	C₂²	1	8	yes	—
54	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
55	C₄×C₁₃×D₈	C₂²	1	4	yes	—
56	C₁₃×#433	C₂²	1	4	yes	—
57	C₁₃×#431	C₂²	1	2	yes	—
58	C₁₃×#431	C₂²	1	2	yes	—
59	C₁₃×#424	C₂²	1	2	yes	—
60	C₁₃×#408	C₂²	1	2	yes	—
61	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×D₈	C₂³	1	4	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	—	2	2	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₃×#127	C₂³	1	2	yes	—
80	C₁₃×#126	—	2	4	no	—
81	C₁₃×#126	—	2	4	no	—
82	C₁₃×#125	—	2	2	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	—	2	2	no	—
87	C₁₃×#124	—	2	2	no	—
88	C₁₃×#124	C₂³	1	4	yes	—
89	C₁₃×#123	—	2	4	no	—
90	C₁₃×#123	—	2	4	no	—
91	C₁₃×C₂²⋊Q₈	—	2	4	no	—
92	C₁₃×C₂²⋊Q₈	—	2	2	no	—
93	C₁₃×C₂²⋊Q₈	—	2	2	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	C₂³	1	4	yes	—
106	C₁₃×#121	C₂³	1	4	yes	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	—	2	2	no	—
109	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
110	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
112	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₄×D₄×C₁₃	—	2	4	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	D₄	1	2	yes	—
120	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
121	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
122	C₄×D₄×C₁₃	D₄	1	2	yes	—
123	C₄×D₄×C₁₃	C₂³	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₁₃×#117	—	2	2	no	—
126	C₁₃×#117	—	2	2	no	—
127	C₁₃×#117	—	2	4	no	—
128	C₁₃×#117	C₂³	1	1	yes	characteristic
129	C₁₃×#117	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₁₃×#107	C₂³	1	4	yes	—
136	C₁₃×#107	C₂³	1	4	yes	—
137	C₁₃×#107	C₂³	1	8	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
140	C₁₃×#103	C₂³	1	8	yes	—
141	C₁₃×#103	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	8	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
146	C₁₃×#97	C₂³	1	2	yes	—
147	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×C₈×C₁₃	C₂³	1	2	yes	—
150	C₄×C₈×C₁₃	C₂³	1	2	yes	—
151	#61014	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₁₃×#41	—	4	2	no	—
153	C₁₃×#41	—	4	8	no	—
154	C₁₃×#41	—	8	4	no	—
155	C₁₃×#41	—	8	4	no	—
156	C₂×Q₈×C₁₃	—	2	2	no	—
157	C₂×Q₈×C₁₃	—	2	2	no	—
158	C₂×Q₈×C₁₃	—	2	4	no	—
159	C₂×Q₈×C₁₃	—	8	4	no	—
160	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×Q₁₆	—	4	4	no	—
181	C₁₃×SD₁₆	—	4	8	no	—
182	C₁₃×D₈	—	4	4	no	—
183	C₁₃×M₁₆	—	4	2	no	—
184	C₂×C₈×C₁₃	—	4	2	no	—
185	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
186	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
187	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
213	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
214	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	—	2	4	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	#3511	C₂×C₁₃	1	2	yes	complemented
225	#3262	C₂×C₁₃	1	4	yes	complemented
226	#3230	C₂×C₁₃	1	2	yes	complemented
227	#3226	C₂×C₁₃	1	2	yes	complemented
228	#3210	C₂×C₁₃	1	2	yes	complemented
229	#3207	C₂×C₁₃	1	2	yes	complemented
230	#3203	C₂×C₁₃	1	4	yes	complemented
231	#3182	C₂×C₁₃	1	2	yes	complemented
232	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3124	C₂×C₁₃	1	8	yes	complemented
235	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
239	Q₈×C₁₃	—	2	8	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	4	no	—
242	Q₈×C₁₃	—	4	4	no	—
243	Q₈×C₁₃	—	8	4	no	—
244	D₄×C₁₃	—	2	8	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	4	4	no	—
249	D₄×C₁₃	—	4	4	no	—
250	D₄×C₁₃	—	8	4	no	—
251	D₄×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	8	4	no	—
263	C₂×C₄×C₁₃	—	8	4	no	—
264	C₂×C₄×C₁₃	—	8	4	no	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	—	2	4	no	—
277	#556	—	2	2	no	—
278	#555	—	2	2	no	—
279	#554	—	2	2	no	—
280	#553	—	2	2	no	—
281	#553	—	2	2	no	—
282	#548	—	2	2	no	—
283	#548	—	2	2	no	—
284	#547	—	2	2	no	—
285	#542	C₂²×C₁₃	1	4	yes	—
286	#542	C₂²×C₁₃	1	4	yes	—
287	#537	C₂²×C₁₃	1	4	yes	—
288	#533	C₂²×C₁₃	1	2	yes	—
289	#533	C₂²×C₁₃	1	2	yes	—
290	#532	C₂²×C₁₃	1	2	yes	—
291	#532	C₂²×C₁₃	1	2	yes	—
292	#532	C₂²×C₁₃	1	2	yes	—
293	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
294	#520	C₂²×C₁₃	1	4	yes	—
295	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
296	#500	C₂²×C₁₃	1	1	yes	characteristic
297	#500	C₂²×C₁₃	1	1	yes	characteristic
298	#500	C₂²×C₁₃	1	2	yes	—
299	#494	C₂²×C₁₃	1	1	yes	characteristic
300	#493	C₂²×C₁₃	1	1	yes	characteristic
301	#492	C₂²×C₁₃	1	2	yes	—
302	#487	C₂²×C₁₃	1	2	yes	—
303	#487	C₂²×C₁₃	1	2	yes	—
304	#486	C₂²×C₁₃	1	2	yes	—
305	#486	C₂²×C₁₃	1	2	yes	—
306	#484	C₂²×C₁₃	1	8	yes	—
307	#480	C₂²×C₁₃	1	8	yes	—
308	#477	C₂²×C₁₃	1	8	yes	—
309	#474	C₂²×C₁₃	1	8	yes	—
310	#468	C₂²×C₁₃	1	8	yes	—
311	#467	C₂²×C₁₃	1	4	yes	—
312	#466	C₂²×C₁₃	1	4	yes	—
313	#464	C₂²×C₁₃	1	8	yes	—
314	#463	C₂²×C₁₃	1	8	yes	—
315	#452	C₂²×C₁₃	1	8	yes	—
316	#449	C₂²×C₁₃	1	8	yes	—
317	#440	C₂²×C₁₃	1	8	yes	—
318	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
319	C₄×D₈	C₂²×C₁₃	1	4	yes	—
320	#433	C₂²×C₁₃	1	4	yes	—
321	#431	C₂²×C₁₃	1	2	yes	—
322	#431	C₂²×C₁₃	1	2	yes	—
323	#424	C₂²×C₁₃	1	2	yes	—
324	#408	C₂²×C₁₃	1	2	yes	—
325	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	—	4	4	no	—
346	C₄×C₁₃	#576	1	2	yes	—
347	C₄×C₁₃	#578	1	2	yes	—
348	C₄×C₁₃	#585	1	2	yes	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	C₂³×C₁₃	1	4	yes	—
352	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×Q₈	—	2	2	no	—
354	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
355	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
356	C₂×D₈	C₂³×C₁₃	1	4	yes	—
357	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
358	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
362	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
364	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
365	#127	C₂³×C₁₃	1	2	yes	—
366	#126	—	2	4	no	—
367	#126	—	2	4	no	—
368	#125	—	2	2	no	—
369	#125	—	2	2	no	—
370	#124	—	2	4	no	—
371	#124	—	2	4	no	—
372	#124	—	2	2	no	—
373	#124	—	2	2	no	—
374	#124	C₂³×C₁₃	1	4	yes	—
375	#123	—	2	4	no	—
376	#123	—	2	4	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
383	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
384	#121	—	2	4	no	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	C₂³×C₁₃	1	4	yes	—
392	#121	C₂³×C₁₃	1	4	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
396	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
397	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
398	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	D₄×C₁₃	1	2	yes	—
406	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
407	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
408	C₄×D₄	D₄×C₁₃	1	2	yes	—
409	C₄×D₄	C₂³×C₁₃	1	4	yes	—
410	C₄×D₄	C₂³×C₁₃	1	4	yes	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	4	no	—
414	#117	C₂³×C₁₃	1	2	yes	—
415	#117	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	4	no	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
421	#107	C₂³×C₁₃	1	4	yes	—
422	#107	C₂³×C₁₃	1	4	yes	—
423	#107	C₂³×C₁₃	1	8	yes	—
424	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
425	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
426	#103	C₂³×C₁₃	1	8	yes	—
427	#103	C₂³×C₁₃	1	8	yes	—
428	#102	C₂³×C₁₃	1	8	yes	—
429	#102	C₂³×C₁₃	1	8	yes	—
430	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
431	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
432	#97	C₂³×C₁₃	1	2	yes	—
433	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	2	yes	—
436	C₄×C₈	C₂³×C₁₃	1	2	yes	—
437	C₂×C₁₃	—	4	2	no	—
438	C₂×C₁₃	—	4	1	no	—
439	C₂×C₁₃	—	8	4	no	—
440	C₂×C₁₃	#3449	1	1	yes	characteristic
441	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
442	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
443	#41	—	4	2	no	—
444	#41	—	4	8	no	—
445	#41	—	8	4	no	—
446	#41	—	8	4	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	8	4	no	—
451	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
471	Q₁₆	—	4	4	no	—
472	SD₁₆	—	4	8	no	—
473	D₈	—	4	4	no	—
474	M₁₆	—	4	2	no	—
475	C₂×C₈	—	4	2	no	—
476	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
477	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
478	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
491	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
504	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
505	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₁₃	1	2	yes	—
510	C₄²	C₂×D₄×C₁₃	1	2	yes	—
511	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₄²	C₂⁴×C₁₃	1	2	yes	—
515	C₁₃	#61014	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	4	no	—
517	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
519	Q₈	—	2	8	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	4	no	—
522	Q₈	—	4	4	no	—
523	Q₈	—	8	4	no	—
524	D₄	—	2	8	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	8	no	—
542	C₂×C₄	—	8	4	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	—	8	4	no	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	2	4	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	C₁₃×#576	1	2	yes	—
577	C₄	C₁₃×#578	1	2	yes	—
578	C₄	C₁₃×#585	1	2	yes	—
579	C₂	—	4	2	no	—
580	C₂	—	4	1	no	—
581	C₂	—	8	4	no	—
582	C₂	C₁₃×#3449	1	1	yes	characteristic
583	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
584	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3262	C₂	semidirect
3. C₁₃×#3230	C₂	semidirect
4. C₁₃×#3226	C₂	semidirect
5. C₁₃×#3210	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3203	C₂	semidirect
8. C₁₃×#3182	C₂	semidirect
9. C₁₃×#3170	C₂	semidirect
10. C₁₃×#3169	C₂	semidirect
11. C₁₃×#3124	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
151. #61014	C₁₃	direct (N × H)
224. #3511	C₂×C₁₃	semidirect
225. #3262	C₂×C₁₃	semidirect
226. #3230	C₂×C₁₃	semidirect
227. #3226	C₂×C₁₃	semidirect
228. #3210	C₂×C₁₃	semidirect
229. #3207	C₂×C₁₃	semidirect
230. #3203	C₂×C₁₃	semidirect
231. #3182	C₂×C₁₃	semidirect
232. #3170	C₂×C₁₃	semidirect
233. #3169	C₂×C₁₃	semidirect
234. #3124	C₂×C₁₃	semidirect
235. #2922	C₂×C₁₃	semidirect
515. C₁₃	#61014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3262	2
C₁₃×#3230	2
C₁₃×#3226	2
C₁₃×#3210	2
C₁₃×#3207	2
C₁₃×#3203	2
C₁₃×#3182	2
C₁₃×#3170	2
C₁₃×#3169	2
C₁₃×#3124	2
C₁₃×#2922	2
#61014	13

Subgroups — C13×#61014 #15747353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61014 #15747353