Subgroups — C₁₃×#61434 #15747773

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3340	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3304	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3303	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3284	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3167	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3107	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3106	C₂	1	3	yes	maximal, complemented
14	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#135	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₃×#135	C₂²	1	3	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	C₂²	1	1	yes	characteristic
19	C₁₃×#556	C₂²	1	3	yes	—
20	C₁₃×#555	—	2	3	no	—
21	C₁₃×#555	C₂²	1	3	yes	—
22	C₁₃×#552	—	2	3	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	C₂²	1	3	yes	—
25	C₁₃×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	1	no	—
28	C₁₃×#547	C₂²	1	3	yes	—
29	C₁₃×#533	C₂²	1	3	yes	—
30	C₁₃×#532	—	2	3	no	—
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#529	—	2	3	no	—
33	C₄×C₁₃×#41	—	2	1	no	—
34	C₄×C₁₃×#41	C₂²	1	3	yes	—
35	C₄×C₁₃×#41	C₂²	1	3	yes	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
38	C₁₃×#498	C₂²	1	3	yes	—
39	C₁₃×#492	C₂²	1	3	yes	—
40	C₁₃×#487	C₂²	1	3	yes	—
41	C₁₃×#486	C₂²	1	3	yes	—
42	C₁₃×#485	C₂²	1	6	yes	—
43	C₁₃×#482	C₂²	1	6	yes	—
44	C₁₃×#477	C₂²	1	3	yes	—
45	C₁₃×#476	C₂²	1	3	yes	—
46	C₁₃×#475	C₂²	1	3	yes	—
47	C₁₃×#474	C₂²	1	3	yes	—
48	C₁₃×#465	C₂²	1	6	yes	—
49	C₁₃×#465	C₂²	1	6	yes	—
50	C₁₃×#462	C₂²	1	3	yes	—
51	C₁₃×#461	C₂²	1	3	yes	—
52	C₁₃×#460	C₂²	1	3	yes	—
53	C₁₃×#459	C₂²	1	3	yes	—
54	C₁₃×#452	C₂²	1	6	yes	—
55	C₁₃×#449	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
59	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
60	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
61	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
62	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
63	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
64	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×D₈	C₂²	1	3	yes	—
66	C₄×C₁₃×D₈	C₂²	1	3	yes	—
67	C₈×D₄×C₁₃	C₂²	1	3	yes	—
68	C₈×D₄×C₁₃	C₂²	1	3	yes	—
69	C₁₃×#431	C₂²	1	3	yes	—
70	C₁₃×#427	C₂²	1	3	yes	—
71	C₁₃×#416	C₂²	1	3	yes	—
72	C₁₃×#416	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	3	no	—
76	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
77	C₂×C₁₃×#41	C₂³	1	3	yes	—
78	C₂×C₁₃×#41	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₃	—	2	1	no	—
80	C₁₃×#135	—	2	12	no	—
81	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×D₈	C₂³	1	3	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
87	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
88	C₁₃×C₄⋊Q₈	—	2	3	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₃×#127	—	2	3	no	—
93	C₁₃×#127	C₂³	1	3	yes	—
94	C₁₃×#126	—	2	6	no	—
95	C₁₃×#125	—	2	3	no	—
96	C₁₃×#125	—	2	3	no	—
97	C₁₃×#124	—	2	3	no	—
98	C₁₃×#124	—	2	6	no	—
99	C₁₃×#124	—	2	3	no	—
100	C₁₃×#123	—	2	6	no	—
101	C₁₃×C₂²⋊Q₈	—	2	3	no	—
102	C₁₃×C₂²⋊Q₈	—	2	3	no	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
104	C₁₃×#121	—	2	3	no	—
105	C₁₃×#121	—	2	3	no	—
106	C₁₃×#121	—	2	3	no	—
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	6	no	—
109	C₁₃×#121	C₂³	1	6	yes	—
110	C₄×Q₈×C₁₃	—	2	1	no	—
111	C₄×Q₈×C₁₃	—	2	1	no	—
112	C₄×Q₈×C₁₃	—	2	3	no	—
113	C₄×Q₈×C₁₃	—	2	3	no	—
114	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₁₃	—	2	3	no	—
121	C₄×D₄×C₁₃	—	2	3	no	—
122	C₄×D₄×C₁₃	—	2	3	no	—
123	C₄×D₄×C₁₃	—	2	3	no	—
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	D₄	1	3	yes	—
127	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₁₃	C₂³	1	3	yes	—
129	C₄×D₄×C₁₃	C₂³	1	3	yes	—
130	C₄×D₄×C₁₃	C₂³	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₁₃×#117	—	2	3	no	—
133	C₁₃×#117	—	2	3	no	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	D₄	1	3	yes	—
137	C₁₃×#117	C₂³	1	3	yes	—
138	C₁₃×#117	C₂³	1	3	yes	—
139	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
140	C₂×C₄²×C₁₃	—	2	3	no	—
141	C₂×C₄²×C₁₃	—	2	3	no	—
142	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
143	C₁₃×#107	C₂³	1	3	yes	—
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#106	C₂³	1	1	yes	characteristic
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×#106	C₂³	1	6	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×#103	C₂³	1	1	yes	characteristic
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	3	yes	—
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#103	C₂³	1	6	yes	—
155	C₁₃×#102	C₂³	1	1	yes	characteristic
156	C₁₃×#102	C₂³	1	3	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	6	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₄×C₈×C₁₃	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#61434	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	2	6	no	—
168	C₁₃×#41	—	2	6	no	—
169	C₁₃×#41	—	4	3	no	—
170	C₁₃×#41	—	4	3	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	8	6	no	—
173	C₂×Q₈×C₁₃	—	2	3	no	—
174	C₂×Q₈×C₁₃	—	2	3	no	—
175	C₂×Q₈×C₁₃	—	4	4	no	—
176	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×D₄×C₁₃	—	2	3	no	—
180	C₂×D₄×C₁₃	—	2	3	no	—
181	C₂×D₄×C₁₃	—	2	6	no	—
182	C₂×D₄×C₁₃	—	2	3	no	—
183	C₂×D₄×C₁₃	—	2	3	no	—
184	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
186	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	—	2	3	no	—
188	C₂²×C₄×C₁₃	—	2	3	no	—
189	C₂²×C₄×C₁₃	—	2	3	no	—
190	C₂²×C₄×C₁₃	—	2	3	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	3	no	—
193	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
196	C₁₃×Q₁₆	—	2	6	no	—
197	C₁₃×SD₁₆	—	2	6	no	—
198	C₁₃×SD₁₆	—	4	6	no	—
199	C₁₃×SD₁₆	#41	1	4	yes	complemented
200	C₁₃×D₈	—	2	6	no	—
201	C₂×C₈×C₁₃	—	2	6	no	—
202	C₂×C₈×C₁₃	—	4	3	no	—
203	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
205	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
206	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	—	2	3	no	—
208	C₁₃×C₄⋊C₄	—	2	6	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	—	2	3	no	—
212	C₁₃×C₄⋊C₄	—	2	3	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	3	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₄	—	2	6	no	—
223	C₁₃×C₂²⋊C₄	—	2	3	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	2	6	no	—
227	C₁₃×C₂²⋊C₄	—	2	3	no	—
228	C₁₃×C₂²⋊C₄	—	2	3	no	—
229	C₁₃×C₂²⋊C₄	—	2	3	no	—
230	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
231	C₄²×C₁₃	—	2	3	no	—
232	C₄²×C₁₃	—	2	3	no	—
233	C₄²×C₁₃	—	2	3	no	—
234	C₄²×C₁₃	—	2	3	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	2	3	no	—
237	C₄²×C₁₃	C₂×D₄	1	3	yes	—
238	C₄²×C₁₃	C₂×D₄	1	3	yes	—
239	C₄²×C₁₃	C₂⁴	1	3	yes	—
240	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
241	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
244	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#3340	C₂×C₁₃	1	3	yes	complemented
248	#3304	C₂×C₁₃	1	3	yes	complemented
249	#3303	C₂×C₁₃	1	3	yes	complemented
250	#3284	C₂×C₁₃	1	3	yes	complemented
251	#3167	C₂×C₁₃	1	3	yes	complemented
252	#3107	C₂×C₁₃	1	3	yes	complemented
253	#3106	C₂×C₁₃	1	3	yes	complemented
254	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₄×#135	C₂×C₁₃	1	3	yes	complemented
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	3	no	—
258	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
259	Q₈×C₁₃	—	2	1	no	—
260	Q₈×C₁₃	—	2	3	no	—
261	Q₈×C₁₃	—	2	3	no	—
262	Q₈×C₁₃	—	4	6	no	—
263	Q₈×C₁₃	—	8	3	no	—
264	Q₈×C₁₃	#135	1	4	yes	complemented
265	Q₈×C₁₃	C₂×#41	1	2	yes	—
266	D₄×C₁₃	—	2	6	no	—
267	D₄×C₁₃	—	2	3	no	—
268	D₄×C₁₃	—	2	1	no	—
269	D₄×C₁₃	—	2	3	no	—
270	D₄×C₁₃	—	4	6	no	—
271	D₄×C₁₃	—	4	6	no	—
272	D₄×C₁₃	—	4	6	no	—
273	D₄×C₁₃	—	8	3	no	—
274	D₄×C₁₃	—	8	6	no	—
275	D₄×C₁₃	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	6	no	—
278	C₂×C₄×C₁₃	—	2	6	no	—
279	C₂×C₄×C₁₃	—	2	3	no	—
280	C₂×C₄×C₁₃	—	2	3	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	3	no	—
284	C₂×C₄×C₁₃	—	2	3	no	—
285	C₂×C₄×C₁₃	—	2	3	no	—
286	C₂×C₄×C₁₃	—	4	6	no	—
287	C₂×C₄×C₁₃	—	4	6	no	—
288	C₂×C₄×C₁₃	—	4	6	no	—
289	C₂×C₄×C₁₃	—	4	6	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	6	no	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
298	C₈×C₁₃	—	2	3	no	—
299	C₈×C₁₃	—	2	1	no	—
300	C₈×C₁₃	—	2	3	no	—
301	C₈×C₁₃	C₂×#41	1	2	yes	—
302	C₂×#135	C₂²×C₁₃	1	3	yes	—
303	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
304	#557	C₂²×C₁₃	1	1	yes	characteristic
305	#556	C₂²×C₁₃	1	3	yes	—
306	#555	—	2	3	no	—
307	#555	C₂²×C₁₃	1	3	yes	—
308	#552	—	2	3	no	—
309	#550	—	2	1	no	—
310	#550	C₂²×C₁₃	1	3	yes	—
311	#550	C₂²×C₁₃	1	1	yes	characteristic
312	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	#548	—	2	1	no	—
314	#547	C₂²×C₁₃	1	3	yes	—
315	#533	C₂²×C₁₃	1	3	yes	—
316	#532	—	2	3	no	—
317	#532	C₂²×C₁₃	1	3	yes	—
318	#529	—	2	3	no	—
319	C₄×#41	—	2	1	no	—
320	C₄×#41	C₂²×C₁₃	1	3	yes	—
321	C₄×#41	C₂²×C₁₃	1	3	yes	—
322	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄×Q₈	—	2	1	no	—
324	#498	C₂²×C₁₃	1	3	yes	—
325	#492	C₂²×C₁₃	1	3	yes	—
326	#487	C₂²×C₁₃	1	3	yes	—
327	#486	C₂²×C₁₃	1	3	yes	—
328	#485	C₂²×C₁₃	1	6	yes	—
329	#482	C₂²×C₁₃	1	6	yes	—
330	#477	C₂²×C₁₃	1	3	yes	—
331	#476	C₂²×C₁₃	1	3	yes	—
332	#475	C₂²×C₁₃	1	3	yes	—
333	#474	C₂²×C₁₃	1	3	yes	—
334	#465	C₂²×C₁₃	1	6	yes	—
335	#465	C₂²×C₁₃	1	6	yes	—
336	#462	C₂²×C₁₃	1	3	yes	—
337	#461	C₂²×C₁₃	1	3	yes	—
338	#460	C₂²×C₁₃	1	3	yes	—
339	#459	C₂²×C₁₃	1	3	yes	—
340	#452	C₂²×C₁₃	1	6	yes	—
341	#449	C₂²×C₁₃	1	6	yes	—
342	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
343	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
345	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
346	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
347	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
348	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
349	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
350	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
351	C₄×D₈	C₂²×C₁₃	1	3	yes	—
352	C₄×D₈	C₂²×C₁₃	1	3	yes	—
353	C₈×D₄	C₂²×C₁₃	1	3	yes	—
354	C₈×D₄	C₂²×C₁₃	1	3	yes	—
355	#431	C₂²×C₁₃	1	3	yes	—
356	#427	C₂²×C₁₃	1	3	yes	—
357	#416	C₂²×C₁₃	1	3	yes	—
358	#416	C₂²×C₁₃	1	3	yes	—
359	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
360	C₂²×C₁₃	—	2	3	no	—
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	2	3	no	—
363	C₂²×C₁₃	—	2	3	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	3	no	—
367	C₂²×C₁₃	—	4	3	no	—
368	C₂²×C₁₃	—	4	3	no	—
369	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₁₃	—	2	3	no	—
371	C₄×C₁₃	—	2	2	no	—
372	C₄×C₁₃	—	2	1	no	—
373	C₄×C₁₃	—	2	3	no	—
374	C₄×C₁₃	—	4	3	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	3	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	3	no	—
379	C₄×C₁₃	C₂×#135	1	6	yes	—
380	C₄×C₁₃	#577	1	2	yes	—
381	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
382	C₄×C₁₃	#585	1	1	yes	characteristic
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	3	no	—
385	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
386	C₂×#41	C₂³×C₁₃	1	3	yes	—
387	C₂×#41	C₂³×C₁₃	1	3	yes	—
388	C₂²×Q₈	—	2	1	no	—
389	#135	—	2	12	no	—
390	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
391	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
392	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
393	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×D₈	C₂³×C₁₃	1	3	yes	—
395	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
396	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
397	C₄⋊Q₈	—	2	3	no	—
398	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
399	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
400	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
401	#127	—	2	3	no	—
402	#127	C₂³×C₁₃	1	3	yes	—
403	#126	—	2	6	no	—
404	#125	—	2	3	no	—
405	#125	—	2	3	no	—
406	#124	—	2	3	no	—
407	#124	—	2	6	no	—
408	#124	—	2	3	no	—
409	#123	—	2	6	no	—
410	C₂²⋊Q₈	—	2	3	no	—
411	C₂²⋊Q₈	—	2	3	no	—
412	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
413	#121	—	2	3	no	—
414	#121	—	2	3	no	—
415	#121	—	2	3	no	—
416	#121	—	2	3	no	—
417	#121	—	2	6	no	—
418	#121	C₂³×C₁₃	1	6	yes	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	3	no	—
422	C₄×Q₈	—	2	3	no	—
423	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
424	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
428	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×D₄	—	2	3	no	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	D₄×C₁₃	1	3	yes	—
436	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₄×D₄	C₂³×C₁₃	1	3	yes	—
438	C₄×D₄	C₂³×C₁₃	1	3	yes	—
439	C₄×D₄	C₂³×C₁₃	1	3	yes	—
440	C₄×D₄	C₂³×C₁₃	1	3	yes	—
441	#117	—	2	3	no	—
442	#117	—	2	3	no	—
443	#117	—	2	3	no	—
444	#117	—	2	3	no	—
445	#117	D₄×C₁₃	1	3	yes	—
446	#117	C₂³×C₁₃	1	3	yes	—
447	#117	C₂³×C₁₃	1	3	yes	—
448	C₂×C₄⋊C₄	—	2	3	no	—
449	C₂×C₄²	—	2	3	no	—
450	C₂×C₄²	—	2	3	no	—
451	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
452	#107	C₂³×C₁₃	1	3	yes	—
453	#107	C₂³×C₁₃	1	3	yes	—
454	#106	C₂³×C₁₃	1	1	yes	characteristic
455	#106	C₂³×C₁₃	1	3	yes	—
456	#106	C₂³×C₁₃	1	6	yes	—
457	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
458	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
459	#103	C₂³×C₁₃	1	1	yes	characteristic
460	#103	C₂³×C₁₃	1	3	yes	—
461	#103	C₂³×C₁₃	1	3	yes	—
462	#103	C₂³×C₁₃	1	3	yes	—
463	#103	C₂³×C₁₃	1	6	yes	—
464	#102	C₂³×C₁₃	1	1	yes	characteristic
465	#102	C₂³×C₁₃	1	3	yes	—
466	#102	C₂³×C₁₃	1	3	yes	—
467	#102	C₂³×C₁₃	1	3	yes	—
468	#102	C₂³×C₁₃	1	6	yes	—
469	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
470	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₄×C₈	C₂³×C₁₃	1	3	yes	—
472	C₄×C₈	C₂³×C₁₃	1	3	yes	—
473	C₄×C₈	C₂³×C₁₃	1	3	yes	—
474	C₂×C₁₃	—	4	3	no	—
475	C₂×C₁₃	—	4	2	no	—
476	C₂×C₁₃	—	8	3	no	—
477	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
478	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
479	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
480	#41	—	2	4	no	—
481	#41	—	2	6	no	—
482	#41	—	2	6	no	—
483	#41	—	4	3	no	—
484	#41	—	4	3	no	—
485	#41	—	4	4	no	—
486	#41	—	8	6	no	—
487	C₂×Q₈	—	2	3	no	—
488	C₂×Q₈	—	2	3	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
492	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₂×D₄	—	2	3	no	—
494	C₂×D₄	—	2	3	no	—
495	C₂×D₄	—	2	6	no	—
496	C₂×D₄	—	2	3	no	—
497	C₂×D₄	—	2	3	no	—
498	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
499	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
500	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	3	no	—
503	C₂²×C₄	—	2	3	no	—
504	C₂²×C₄	—	2	3	no	—
505	C₂²×C₄	—	2	3	no	—
506	C₂²×C₄	—	2	3	no	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
509	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
510	Q₁₆	—	2	6	no	—
511	SD₁₆	—	2	6	no	—
512	SD₁₆	—	4	6	no	—
513	SD₁₆	C₁₃×#41	1	4	yes	complemented
514	D₈	—	2	6	no	—
515	C₂×C₈	—	2	6	no	—
516	C₂×C₈	—	4	3	no	—
517	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
519	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
520	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₄⋊C₄	—	2	3	no	—
522	C₄⋊C₄	—	2	6	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	3	no	—
525	C₄⋊C₄	—	2	3	no	—
526	C₄⋊C₄	—	2	3	no	—
527	C₄⋊C₄	—	2	3	no	—
528	C₄⋊C₄	—	2	3	no	—
529	C₄⋊C₄	—	2	3	no	—
530	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
531	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
532	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
533	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₂²⋊C₄	—	2	6	no	—
537	C₂²⋊C₄	—	2	3	no	—
538	C₂²⋊C₄	—	2	3	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	6	no	—
541	C₂²⋊C₄	—	2	3	no	—
542	C₂²⋊C₄	—	2	3	no	—
543	C₂²⋊C₄	—	2	3	no	—
544	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	3	no	—
547	C₄²	—	2	3	no	—
548	C₄²	—	2	3	no	—
549	C₄²	—	2	3	no	—
550	C₄²	—	2	3	no	—
551	C₄²	C₂×D₄×C₁₃	1	3	yes	—
552	C₄²	C₂×D₄×C₁₃	1	3	yes	—
553	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
554	C₄²	C₂⁴×C₁₃	1	3	yes	—
555	C₁₃	#61434	1	1	yes	characteristic, direct product factor, Sylow
556	C₂³	—	2	1	no	—
557	C₂³	—	2	3	no	—
558	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
559	Q₈	—	2	1	no	—
560	Q₈	—	2	3	no	—
561	Q₈	—	2	3	no	—
562	Q₈	—	4	6	no	—
563	Q₈	—	8	3	no	—
564	Q₈	C₁₃×#135	1	4	yes	complemented
565	Q₈	C₂×C₁₃×#41	1	2	yes	—
566	D₄	—	2	6	no	—
567	D₄	—	2	3	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	3	no	—
570	D₄	—	4	6	no	—
571	D₄	—	4	6	no	—
572	D₄	—	4	6	no	—
573	D₄	—	8	3	no	—
574	D₄	—	8	6	no	—
575	D₄	C₂×C₁₃×#41	1	2	yes	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	6	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	2	3	no	—
580	C₂×C₄	—	2	3	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	3	no	—
584	C₂×C₄	—	2	3	no	—
585	C₂×C₄	—	2	3	no	—
586	C₂×C₄	—	4	6	no	—
587	C₂×C₄	—	4	6	no	—
588	C₂×C₄	—	4	6	no	—
589	C₂×C₄	—	4	6	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	6	no	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
598	C₈	—	2	3	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	3	no	—
601	C₈	C₂×C₁₃×#41	1	2	yes	—
602	C₂²	—	2	3	no	—
603	C₂²	—	2	3	no	—
604	C₂²	—	2	3	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	3	no	—
609	C₂²	—	4	3	no	—
610	C₂²	—	4	3	no	—
611	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
612	C₄	—	2	1	no	—
613	C₄	—	2	3	no	—
614	C₄	—	2	3	no	—
615	C₄	—	2	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	3	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	3	no	—
620	C₄	—	4	3	no	—
621	C₄	C₂×C₁₃×#135	1	6	yes	—
622	C₄	C₁₃×#577	1	2	yes	—
623	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
624	C₄	C₁₃×#585	1	1	yes	characteristic
625	C₂	—	4	3	no	—
626	C₂	—	4	2	no	—
627	C₂	—	8	3	no	—
628	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
629	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
630	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3483	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. Q₈×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3340	C₂	semidirect
8. C₁₃×#3304	C₂	semidirect
9. C₁₃×#3303	C₂	semidirect
10. C₁₃×#3284	C₂	semidirect
11. C₁₃×#3167	C₂	semidirect
12. C₁₃×#3107	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₈×C₁₃×#41	C₂	semidirect
15. C₄×C₁₃×#135	C₂	semidirect
165. #61434	C₁₃	direct (N × H)
199. C₁₃×SD₁₆	#41	semidirect
241. #3483	C₂×C₁₃	semidirect
242. #3482	C₂×C₁₃	semidirect
243. #3392	C₂×C₁₃	semidirect
244. Q₈×SD₁₆	C₂×C₁₃	semidirect
245. #3363	C₂×C₁₃	semidirect
246. #3358	C₂×C₁₃	semidirect
247. #3340	C₂×C₁₃	semidirect
248. #3304	C₂×C₁₃	semidirect
249. #3303	C₂×C₁₃	semidirect
250. #3284	C₂×C₁₃	semidirect
251. #3167	C₂×C₁₃	semidirect
252. #3107	C₂×C₁₃	semidirect
253. #3106	C₂×C₁₃	semidirect
254. C₈×#41	C₂×C₁₃	semidirect
255. C₄×#135	C₂×C₁₃	semidirect
264. Q₈×C₁₃	#135	semidirect
513. SD₁₆	C₁₃×#41	semidirect
555. C₁₃	#61434	direct (N × H)
564. Q₈	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3483	2
C₁₃×#3482	2
C₁₃×#3392	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3363	2
C₁₃×#3358	2
C₁₃×#3340	2
C₁₃×#3304	2
C₁₃×#3303	2
C₁₃×#3284	2
C₁₃×#3167	2
C₁₃×#3107	2
C₁₃×#3106	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
#61434	13

Subgroups — C13×#61434 #15747773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61434 #15747773