Subgroups — C₁₃×#61844 #15748183

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3385	C₂	1	6	yes	maximal, complemented
4	Q₈×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3375	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3238	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3226	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3112	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3108	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	C₂²	1	3	yes	—
13	Q₈²×C₁₃	—	2	1	no	—
14	Q₈²×C₁₃	—	2	3	no	—
15	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
16	Q₈²×C₁₃	C₂²	1	2	yes	—
17	Q₈²×C₁₃	C₂²	1	6	yes	—
18	C₁₃×#554	C₂²	1	3	yes	—
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#547	—	2	3	no	—
22	C₁₃×#542	—	2	3	no	—
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	—	2	3	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₃×#529	C₂²	1	3	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#501	C₂²	1	6	yes	—
32	C₁₃×#500	C₂²	1	6	yes	—
33	C₁₃×#489	C₂²	1	6	yes	—
34	C₁₃×#486	C₂²	1	6	yes	—
35	C₁₃×#483	C₂²	1	3	yes	—
36	C₁₃×#480	C₂²	1	3	yes	—
37	C₁₃×#480	C₂²	1	6	yes	—
38	C₁₃×#479	C₂²	1	6	yes	—
39	C₁₃×#477	C₂²	1	6	yes	—
40	C₁₃×#477	C₂²	1	6	yes	—
41	C₁₃×#476	C₂²	1	6	yes	—
42	C₁₃×#474	C₂²	1	12	yes	—
43	C₁₃×#464	C₂²	1	6	yes	—
44	C₁₃×#460	C₂²	1	6	yes	—
45	C₁₃×#451	C₂²	1	1	yes	characteristic
46	C₁₃×#448	C₂²	1	3	yes	—
47	C₁₃×#446	C₂²	1	6	yes	—
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
49	C₁₃×#440	C₂²	1	12	yes	—
50	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
51	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
52	C₁₃×#432	C₂²	1	3	yes	—
53	C₁₃×#431	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	3	no	—
56	C₂²×Q₈×C₁₃	—	2	3	no	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
61	C₁₃×C₄⋊Q₈	—	2	6	no	—
62	C₁₃×C₄⋊Q₈	—	2	6	no	—
63	C₁₃×C₄⋊Q₈	—	2	12	no	—
64	C₁₃×C₄⋊Q₈	—	2	3	no	—
65	C₁₃×C₄⋊Q₈	—	2	3	no	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₃×#127	C₂³	1	3	yes	—
71	C₁₃×#126	—	2	3	no	—
72	C₁₃×#125	C₂³	1	3	yes	—
73	C₁₃×#124	—	2	3	no	—
74	C₁₃×#124	—	2	3	no	—
75	C₁₃×#124	C₂³	1	3	yes	—
76	C₁₃×#123	—	2	3	no	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×#121	—	2	3	no	—
82	C₁₃×#121	—	2	3	no	—
83	C₁₃×#121	C₂³	1	3	yes	—
84	C₄×Q₈×C₁₃	—	2	6	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	3	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	D₄	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	6	yes	—
101	C₁₃×#117	—	2	3	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
105	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
107	C₂×C₄²×C₁₃	—	2	3	no	—
108	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
109	C₁₃×#107	C₂³	1	6	yes	—
110	C₁₃×#107	C₂³	1	12	yes	—
111	C₁₃×#106	C₂³	1	6	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₃×#103	C₂³	1	2	yes	—
115	C₁₃×#103	C₂³	1	6	yes	—
116	C₁₃×#103	C₂³	1	6	yes	—
117	C₁₃×#102	C₂³	1	6	yes	—
118	C₁₃×#102	C₂³	1	12	yes	—
119	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
121	C₁₃×#97	C₂³	1	6	yes	—
122	C₄×C₈×C₁₃	C₂³	1	6	yes	—
123	#61844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₁₃×#41	—	4	4	no	—
125	C₁₃×#41	—	8	6	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	3	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	2	6	no	—
132	C₂×Q₈×C₁₃	—	8	6	no	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	3	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	3	no	—
143	C₂²×C₄×C₁₃	—	2	3	no	—
144	C₂²×C₄×C₁₃	—	2	6	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×Q₁₆	—	2	4	no	—
149	C₁₃×SD₁₆	—	2	12	no	—
150	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
152	C₁₃×C₄⋊C₄	—	2	3	no	—
153	C₁₃×C₄⋊C₄	—	2	3	no	—
154	C₁₃×C₄⋊C₄	—	2	6	no	—
155	C₁₃×C₄⋊C₄	—	2	6	no	—
156	C₁₃×C₄⋊C₄	—	2	6	no	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	3	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
168	C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₁₃×C₂²⋊C₄	—	2	3	no	—
170	C₁₃×C₂²⋊C₄	—	2	3	no	—
171	C₁₃×C₂²⋊C₄	—	2	3	no	—
172	C₁₃×C₂²⋊C₄	—	2	3	no	—
173	C₁₃×C₂²⋊C₄	—	2	6	no	—
174	C₄²×C₁₃	—	2	6	no	—
175	C₄²×C₁₃	—	2	6	no	—
176	C₄²×C₁₃	—	2	3	no	—
177	C₄²×C₁₃	C₂×D₄	1	3	yes	—
178	C₄²×C₁₃	C₂×D₄	1	3	yes	—
179	C₄²×C₁₃	C₂⁴	1	3	yes	—
180	C₄²×C₁₃	C₂⁴	1	3	yes	—
181	#3522	C₂×C₁₃	1	1	yes	characteristic
182	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3385	C₂×C₁₃	1	6	yes	complemented
184	Q₈×Q₁₆	C₂×C₁₃	1	2	yes	complemented
185	#3375	C₂×C₁₃	1	6	yes	complemented
186	#3362	C₂×C₁₃	1	2	yes	complemented
187	#3238	C₂×C₁₃	1	3	yes	complemented
188	#3226	C₂×C₁₃	1	3	yes	complemented
189	#3112	C₂×C₁₃	1	3	yes	complemented
190	#3108	C₂×C₁₃	1	3	yes	complemented
191	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	3	no	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	—	2	6	no	—
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	8	6	no	—
199	Q₈×C₁₃	—	8	6	no	—
200	Q₈×C₁₃	—	8	3	no	—
201	Q₈×C₁₃	#137	1	4	yes	—
202	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
203	D₄×C₁₃	—	2	6	no	—
204	D₄×C₁₃	—	4	6	no	—
205	D₄×C₁₃	—	4	6	no	—
206	D₄×C₁₃	—	8	3	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	6	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	6	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	6	no	—
214	C₂×C₄×C₁₃	—	2	3	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	4	6	no	—
217	C₂×C₄×C₁₃	—	4	6	no	—
218	C₂×C₄×C₁₃	—	8	6	no	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₁₃	—	2	6	no	—
226	C₈×C₁₃	—	2	2	no	—
227	#559	C₂²×C₁₃	1	3	yes	—
228	Q₈²	—	2	1	no	—
229	Q₈²	—	2	3	no	—
230	Q₈²	C₂²×C₁₃	1	2	yes	—
231	Q₈²	C₂²×C₁₃	1	6	yes	—
232	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
233	#554	C₂²×C₁₃	1	3	yes	—
234	#550	C₂²×C₁₃	1	1	yes	characteristic
235	#548	—	2	1	no	—
236	#547	—	2	3	no	—
237	#542	—	2	3	no	—
238	#532	C₂²×C₁₃	1	3	yes	—
239	C₂×C₄⋊Q₈	—	2	3	no	—
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
241	#529	C₂²×C₁₃	1	3	yes	—
242	#520	—	2	1	no	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
245	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
246	#501	C₂²×C₁₃	1	6	yes	—
247	#500	C₂²×C₁₃	1	6	yes	—
248	#489	C₂²×C₁₃	1	6	yes	—
249	#486	C₂²×C₁₃	1	6	yes	—
250	#483	C₂²×C₁₃	1	3	yes	—
251	#480	C₂²×C₁₃	1	3	yes	—
252	#480	C₂²×C₁₃	1	6	yes	—
253	#479	C₂²×C₁₃	1	6	yes	—
254	#477	C₂²×C₁₃	1	6	yes	—
255	#477	C₂²×C₁₃	1	6	yes	—
256	#476	C₂²×C₁₃	1	6	yes	—
257	#474	C₂²×C₁₃	1	12	yes	—
258	#464	C₂²×C₁₃	1	6	yes	—
259	#460	C₂²×C₁₃	1	6	yes	—
260	#451	C₂²×C₁₃	1	1	yes	characteristic
261	#448	C₂²×C₁₃	1	3	yes	—
262	#446	C₂²×C₁₃	1	6	yes	—
263	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
264	#440	C₂²×C₁₃	1	12	yes	—
265	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
266	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
267	#432	C₂²×C₁₃	1	3	yes	—
268	#431	C₂²×C₁₃	1	3	yes	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	4	3	no	—
272	C₂²×C₁₃	—	4	3	no	—
273	C₂²×C₁₃	—	4	3	no	—
274	C₂²×C₁₃	#576	1	2	yes	—
275	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	3	no	—
279	C₄×C₁₃	—	2	3	no	—
280	C₄×C₁₃	—	2	3	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	1	no	—
283	C₄×C₁₃	—	4	6	no	—
284	C₄×C₁₃	—	4	3	no	—
285	C₄×C₁₃	C₂×#137	1	6	yes	—
286	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
287	C₂×#41	—	2	1	no	—
288	C₂×#41	—	2	3	no	—
289	C₂²×Q₈	—	2	3	no	—
290	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
293	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
294	C₄⋊Q₈	—	2	6	no	—
295	C₄⋊Q₈	—	2	6	no	—
296	C₄⋊Q₈	—	2	12	no	—
297	C₄⋊Q₈	—	2	3	no	—
298	C₄⋊Q₈	—	2	3	no	—
299	C₄⋊Q₈	—	2	3	no	—
300	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
301	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
302	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
303	#127	C₂³×C₁₃	1	3	yes	—
304	#126	—	2	3	no	—
305	#125	C₂³×C₁₃	1	3	yes	—
306	#124	—	2	3	no	—
307	#124	—	2	3	no	—
308	#124	C₂³×C₁₃	1	3	yes	—
309	#123	—	2	3	no	—
310	#123	—	2	6	no	—
311	C₂²⋊Q₈	—	2	3	no	—
312	C₂²⋊Q₈	—	2	6	no	—
313	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
314	#121	—	2	3	no	—
315	#121	—	2	3	no	—
316	#121	C₂³×C₁₃	1	3	yes	—
317	C₄×Q₈	—	2	6	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	3	no	—
321	C₄×Q₈	—	2	3	no	—
322	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
323	C₄×Q₈	D₄×C₁₃	1	3	yes	—
324	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
325	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
326	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
327	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
329	C₄×D₄	—	2	3	no	—
330	C₄×D₄	—	2	3	no	—
331	C₄×D₄	—	2	3	no	—
332	C₄×D₄	C₂³×C₁₃	1	3	yes	—
333	C₄×D₄	C₂³×C₁₃	1	6	yes	—
334	#117	—	2	3	no	—
335	C₂×C₄⋊C₄	—	2	3	no	—
336	C₂×C₄⋊C₄	—	2	3	no	—
337	C₂×C₄⋊C₄	—	2	3	no	—
338	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
340	C₂×C₄²	—	2	3	no	—
341	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
342	#107	C₂³×C₁₃	1	6	yes	—
343	#107	C₂³×C₁₃	1	12	yes	—
344	#106	C₂³×C₁₃	1	6	yes	—
345	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
346	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
347	#103	C₂³×C₁₃	1	2	yes	—
348	#103	C₂³×C₁₃	1	6	yes	—
349	#103	C₂³×C₁₃	1	6	yes	—
350	#102	C₂³×C₁₃	1	6	yes	—
351	#102	C₂³×C₁₃	1	12	yes	—
352	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
354	#97	C₂³×C₁₃	1	6	yes	—
355	C₄×C₈	C₂³×C₁₃	1	6	yes	—
356	C₂×C₁₃	—	2	2	no	—
357	C₂×C₁₃	—	8	3	no	—
358	C₂×C₁₃	#3486	1	1	yes	characteristic
359	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
361	#41	—	4	4	no	—
362	#41	—	8	6	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	3	no	—
367	C₂×Q₈	—	2	6	no	—
368	C₂×Q₈	—	2	6	no	—
369	C₂×Q₈	—	8	6	no	—
370	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
371	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
374	C₂×D₄	—	2	3	no	—
375	C₂×D₄	—	2	3	no	—
376	C₂×D₄	—	2	3	no	—
377	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	3	no	—
380	C₂²×C₄	—	2	3	no	—
381	C₂²×C₄	—	2	6	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
383	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	Q₁₆	—	2	4	no	—
386	SD₁₆	—	2	12	no	—
387	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
388	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
389	C₄⋊C₄	—	2	3	no	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	6	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	6	no	—
395	C₄⋊C₄	—	2	3	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
402	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
403	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	3	no	—
407	C₂²⋊C₄	—	2	3	no	—
408	C₂²⋊C₄	—	2	3	no	—
409	C₂²⋊C₄	—	2	3	no	—
410	C₂²⋊C₄	—	2	6	no	—
411	C₄²	—	2	6	no	—
412	C₄²	—	2	6	no	—
413	C₄²	—	2	3	no	—
414	C₄²	C₂×D₄×C₁₃	1	3	yes	—
415	C₄²	C₂×D₄×C₁₃	1	3	yes	—
416	C₄²	C₂⁴×C₁₃	1	3	yes	—
417	C₄²	C₂⁴×C₁₃	1	3	yes	—
418	C₁₃	#61844	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	—	2	3	no	—
420	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
421	Q₈	—	2	4	no	—
422	Q₈	—	2	6	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	8	6	no	—
426	Q₈	—	8	6	no	—
427	Q₈	—	8	3	no	—
428	Q₈	C₁₃×#137	1	4	yes	—
429	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
430	D₄	—	2	6	no	—
431	D₄	—	4	6	no	—
432	D₄	—	4	6	no	—
433	D₄	—	8	3	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	6	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	6	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	6	no	—
441	C₂×C₄	—	2	3	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	6	no	—
444	C₂×C₄	—	4	6	no	—
445	C₂×C₄	—	8	6	no	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
451	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
452	C₈	—	2	6	no	—
453	C₈	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	4	3	no	—
457	C₂²	—	4	3	no	—
458	C₂²	—	4	3	no	—
459	C₂²	C₁₃×#576	1	2	yes	—
460	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
461	C₄	—	2	3	no	—
462	C₄	—	2	3	no	—
463	C₄	—	2	3	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	6	no	—
468	C₄	—	4	3	no	—
469	C₄	—	4	1	no	—
470	C₄	C₂×C₁₃×#137	1	6	yes	—
471	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	8	3	no	—
474	C₂	C₁₃×#3486	1	1	yes	characteristic
475	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
476	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈²×C₁₃	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. Q₈×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#3375	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3238	C₂	semidirect
8. C₁₃×#3226	C₂	semidirect
9. C₁₃×#3112	C₂	semidirect
10. C₁₃×#3108	C₂	semidirect
11. C₁₃×#2984	C₂	semidirect
123. #61844	C₁₃	direct (N × H)
182. C₂×Q₈²	C₂×C₁₃	semidirect
183. #3385	C₂×C₁₃	semidirect
184. Q₈×Q₁₆	C₂×C₁₃	semidirect
185. #3375	C₂×C₁₃	semidirect
186. #3362	C₂×C₁₃	semidirect
187. #3238	C₂×C₁₃	semidirect
188. #3226	C₂×C₁₃	semidirect
189. #3112	C₂×C₁₃	semidirect
190. #3108	C₂×C₁₃	semidirect
191. #2984	C₂×C₁₃	semidirect
418. C₁₃	#61844	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×#3522	2
C₂×Q₈²×C₁₃	2
C₁₃×#3385	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3375	2
C₁₃×#3362	2
C₁₃×#3238	2
C₁₃×#3226	2
C₁₃×#3112	2
C₁₃×#3108	2
C₁₃×#2984	2
#61844	13

Subgroups — C13×#61844 #15748183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61844 #15748183