Subgroups — C₁₃×#61374 #15747713

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3387	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3384	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3381	C₂	1	4	yes	maximal, complemented
5	Q₈×C₁₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3084	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2952	C₂	1	2	yes	maximal
12	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₃	C₂²	1	4	yes	—
15	C₁₃×#557	C₂²	1	4	yes	—
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	4	yes	—
18	D₄×Q₈×C₁₃	—	2	4	no	—
19	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
20	C₁₃×#544	—	2	4	no	—
21	C₁₃×#544	C₂²	1	4	yes	—
22	C₁₃×#533	—	2	2	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×#520	C₂²	1	4	yes	—
27	C₄×C₁₃×#41	C₂²	1	2	yes	—
28	C₁₃×#501	C₂²	1	8	yes	—
29	C₁₃×#499	C₂²	1	4	yes	—
30	C₁₃×#498	C₂²	1	4	yes	—
31	C₁₃×#498	C₂²	1	4	yes	—
32	C₁₃×#498	C₂²	1	4	yes	—
33	C₁₃×#479	C₂²	1	8	yes	—
34	C₁₃×#478	C₂²	1	8	yes	—
35	C₁₃×#477	C₂²	1	4	yes	—
36	C₁₃×#476	C₂²	1	4	yes	—
37	C₁₃×#476	C₂²	1	8	yes	—
38	C₁₃×#475	C₂²	1	4	yes	—
39	C₁₃×#475	C₂²	1	8	yes	—
40	C₁₃×#474	C₂²	1	4	yes	—
41	C₁₃×#446	C₂²	1	4	yes	—
42	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
43	C₁₃×#442	C₂²	1	4	yes	—
44	C₁₃×#441	C₂²	1	4	yes	—
45	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
46	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
47	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
49	C₄×C₁₃×D₈	C₂²	1	2	yes	—
50	C₁₃×#428	C₂²	1	4	yes	—
51	C₁₃×#427	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#106	C₂²	1	2	yes	—
53	C₂×C₁₃×#106	C₂²	1	2	yes	—
54	C₁₃×#424	C₂²	1	2	yes	—
55	C₁₃×#423	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	4	yes	—
57	C₁₃×#416	C₂²	1	2	yes	—
58	C₁₃×#405	C₂²	1	2	yes	—
59	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#41	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₃	—	2	4	no	—
62	C₂²×Q₈×C₁₃	—	2	2	no	—
63	C₁₃×#135	Q₈	1	8	yes	complemented
64	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
66	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	—	2	4	no	—
71	C₁₃×C₄⋊Q₈	—	2	4	no	—
72	C₁₃×C₄⋊Q₈	—	2	4	no	—
73	C₁₃×C₄⋊Q₈	—	2	8	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₁₃×#125	—	2	4	no	—
81	C₁₃×#125	—	2	8	no	—
82	C₁₃×#125	D₄	1	2	yes	—
83	C₁₃×#125	C₂³	1	8	yes	—
84	C₁₃×C₂²⋊Q₈	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	8	no	—
87	C₁₃×C₂²⋊Q₈	—	2	8	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	8	no	—
99	C₄×D₄×C₁₃	C₂³	1	2	yes	—
100	C₄×D₄×C₁₃	C₂³	1	2	yes	—
101	C₄×D₄×C₁₃	C₂³	1	8	yes	—
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	C₂³	1	2	yes	—
105	C₁₃×#117	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃	—	2	2	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	C₂³	1	2	yes	—
113	C₁₃×#107	C₂³	1	8	yes	—
114	C₁₃×#106	C₂³	1	4	yes	—
115	C₁₃×#106	C₂³	1	4	yes	—
116	C₁₃×#106	C₂³	1	8	yes	—
117	C₁₃×#106	C₂³	1	1	yes	characteristic
118	C₁₃×#106	C₂³	1	1	yes	characteristic
119	C₁₃×#106	C₂³	1	8	yes	—
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#103	C₂³	1	2	yes	—
123	C₁₃×#103	C₂³	1	2	yes	—
124	C₁₃×#103	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	2	yes	—
126	C₁₃×#102	C₂³	1	2	yes	—
127	C₁₃×#102	C₂³	1	8	yes	—
128	C₁₃×#97	C₂³	1	4	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	C₄×C₈×C₁₃	C₂³	1	4	yes	—
132	#61374	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₁₃×#41	—	2	4	no	—
134	C₁₃×#41	C₂×Q₈	1	8	yes	complemented
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	8	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	8	4	no	—
139	C₂×Q₈×C₁₃	—	8	8	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×Q₁₆	C₂×Q₈	1	4	yes	complemented
152	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
153	C₁₃×D₈	C₂×Q₈	1	4	yes	complemented
154	C₁₃×M₁₆	—	2	4	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
159	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
174	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	8	no	—
180	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	8	no	—
185	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂⁴	1	2	yes	—
188	C₄²×C₁₃	C₂⁴	1	4	yes	—
189	#3503	C₂×C₁₃	1	2	yes	complemented
190	#3387	C₂×C₁₃	1	4	yes	complemented
191	#3384	C₂×C₁₃	1	4	yes	complemented
192	#3381	C₂×C₁₃	1	4	yes	complemented
193	Q₈×SD₁₆	C₂×C₁₃	1	4	yes	complemented
194	#3163	C₂×C₁₃	1	2	yes	complemented
195	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#3084	C₂×C₁₃	1	4	yes	complemented
197	#3079	C₂×C₁₃	1	2	yes	complemented
198	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2952	C₂×C₁₃	1	2	yes	—
200	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	8	no	—
204	Q₈×C₁₃	—	2	2	no	—
205	Q₈×C₁₃	—	4	8	no	—
206	Q₈×C₁₃	—	8	4	no	—
207	Q₈×C₁₃	—	8	8	no	—
208	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
209	D₄×C₁₃	—	2	8	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	8	8	no	—
221	C₂×C₄×C₁₃	—	8	4	no	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
227	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
228	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	4	no	—
231	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
232	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
233	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
234	Q₈²	C₂²×C₁₃	1	4	yes	—
235	#557	C₂²×C₁₃	1	4	yes	—
236	#554	—	2	4	no	—
237	#554	C₂²×C₁₃	1	4	yes	—
238	D₄×Q₈	—	2	4	no	—
239	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
240	#544	—	2	4	no	—
241	#544	C₂²×C₁₃	1	4	yes	—
242	#533	—	2	2	no	—
243	#533	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	—	2	2	no	—
245	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
246	#520	C₂²×C₁₃	1	4	yes	—
247	C₄×#41	C₂²×C₁₃	1	2	yes	—
248	#501	C₂²×C₁₃	1	8	yes	—
249	#499	C₂²×C₁₃	1	4	yes	—
250	#498	C₂²×C₁₃	1	4	yes	—
251	#498	C₂²×C₁₃	1	4	yes	—
252	#498	C₂²×C₁₃	1	4	yes	—
253	#479	C₂²×C₁₃	1	8	yes	—
254	#478	C₂²×C₁₃	1	8	yes	—
255	#477	C₂²×C₁₃	1	4	yes	—
256	#476	C₂²×C₁₃	1	4	yes	—
257	#476	C₂²×C₁₃	1	8	yes	—
258	#475	C₂²×C₁₃	1	4	yes	—
259	#475	C₂²×C₁₃	1	8	yes	—
260	#474	C₂²×C₁₃	1	4	yes	—
261	#446	C₂²×C₁₃	1	4	yes	—
262	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
263	#442	C₂²×C₁₃	1	4	yes	—
264	#441	C₂²×C₁₃	1	4	yes	—
265	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
266	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
267	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
268	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
269	C₄×D₈	C₂²×C₁₃	1	2	yes	—
270	#428	C₂²×C₁₃	1	4	yes	—
271	#427	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#106	C₂²×C₁₃	1	2	yes	—
273	C₂×#106	C₂²×C₁₃	1	2	yes	—
274	#424	C₂²×C₁₃	1	2	yes	—
275	#423	C₂²×C₁₃	1	1	yes	characteristic
276	#417	C₂²×C₁₃	1	4	yes	—
277	#416	C₂²×C₁₃	1	2	yes	—
278	#405	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
285	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
286	C₄×C₁₃	—	2	4	no	—
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	8	no	—
289	C₄×C₁₃	—	4	2	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	8	no	—
292	C₄×C₁₃	D₄×Q₈	1	2	yes	—
293	C₄×C₁₃	#577	1	4	yes	—
294	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
295	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×#41	C₂³×C₁₃	1	2	yes	—
297	C₂²×Q₈	—	2	4	no	—
298	C₂²×Q₈	—	2	2	no	—
299	#135	Q₈×C₁₃	1	8	yes	complemented
300	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
302	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	C₄⋊Q₈	—	2	8	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
316	#125	—	2	4	no	—
317	#125	—	2	8	no	—
318	#125	D₄×C₁₃	1	2	yes	—
319	#125	C₂³×C₁₃	1	8	yes	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	8	no	—
324	C₂²⋊Q₈	—	2	8	no	—
325	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
326	C₄×Q₈	—	2	4	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
329	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
331	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	8	no	—
335	C₄×D₄	C₂³×C₁₃	1	2	yes	—
336	C₄×D₄	C₂³×C₁₃	1	2	yes	—
337	C₄×D₄	C₂³×C₁₃	1	8	yes	—
338	#117	—	2	4	no	—
339	#117	—	2	2	no	—
340	#117	C₂³×C₁₃	1	2	yes	—
341	#117	C₂³×C₁₃	1	2	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
348	#107	C₂³×C₁₃	1	2	yes	—
349	#107	C₂³×C₁₃	1	8	yes	—
350	#106	C₂³×C₁₃	1	4	yes	—
351	#106	C₂³×C₁₃	1	4	yes	—
352	#106	C₂³×C₁₃	1	8	yes	—
353	#106	C₂³×C₁₃	1	1	yes	characteristic
354	#106	C₂³×C₁₃	1	1	yes	characteristic
355	#106	C₂³×C₁₃	1	8	yes	—
356	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
357	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
358	#103	C₂³×C₁₃	1	2	yes	—
359	#103	C₂³×C₁₃	1	2	yes	—
360	#103	C₂³×C₁₃	1	8	yes	—
361	#102	C₂³×C₁₃	1	2	yes	—
362	#102	C₂³×C₁₃	1	2	yes	—
363	#102	C₂³×C₁₃	1	8	yes	—
364	#97	C₂³×C₁₃	1	4	yes	—
365	C₄×C₈	C₂³×C₁₃	1	2	yes	—
366	C₄×C₈	C₂³×C₁₃	1	2	yes	—
367	C₄×C₈	C₂³×C₁₃	1	4	yes	—
368	C₂×C₁₃	—	2	2	no	—
369	C₂×C₁₃	—	4	4	no	—
370	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#577	1	2	yes	—
372	#41	—	2	4	no	—
373	#41	C₂×Q₈×C₁₃	1	8	yes	complemented
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	8	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	8	4	no	—
378	C₂×Q₈	—	8	8	no	—
379	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
380	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
390	Q₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
391	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
392	D₈	C₂×Q₈×C₁₃	1	4	yes	complemented
393	M₁₆	—	2	4	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
396	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
397	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
398	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
412	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
413	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
414	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	8	no	—
424	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂⁴×C₁₃	1	2	yes	—
427	C₄²	C₂⁴×C₁₃	1	4	yes	—
428	C₁₃	#61374	1	1	yes	characteristic, direct product factor, Sylow
429	C₂³	—	2	2	no	—
430	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	Q₈	—	2	8	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	8	no	—
434	Q₈	—	8	4	no	—
435	Q₈	—	8	8	no	—
436	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
437	D₄	—	2	8	no	—
438	D₄	—	2	2	no	—
439	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	8	8	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
454	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
455	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
456	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	4	no	—
459	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
460	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
466	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	8	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	8	no	—
473	C₄	D₄×Q₈×C₁₃	1	2	yes	—
474	C₄	C₁₃×#577	1	4	yes	—
475	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
476	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
477	C₂	—	2	2	no	—
478	C₂	—	4	4	no	—
479	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
2. C₁₃×#3387	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. Q₈×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3163	C₂	semidirect
7. C₂×C₁₃×#498	C₂	semidirect
8. C₁₃×#3084	C₂	semidirect
9. C₁₃×#3079	C₂	semidirect
10. C₁₃×#2960	C₂	semidirect
63. C₁₃×#135	Q₈	semidirect
132. #61374	C₁₃	direct (N × H)
134. C₁₃×#41	C₂×Q₈	semidirect
151. C₁₃×Q₁₆	C₂×Q₈	semidirect
152. C₁₃×SD₁₆	C₂×Q₈	semidirect
153. C₁₃×D₈	C₂×Q₈	semidirect
156. C₂×C₈×C₁₃	C₂×Q₈	semidirect
189. #3503	C₂×C₁₃	semidirect
190. #3387	C₂×C₁₃	semidirect
191. #3384	C₂×C₁₃	semidirect
192. #3381	C₂×C₁₃	semidirect
193. Q₈×SD₁₆	C₂×C₁₃	semidirect
194. #3163	C₂×C₁₃	semidirect
195. C₂×#498	C₂×C₁₃	semidirect
196. #3084	C₂×C₁₃	semidirect
197. #3079	C₂×C₁₃	semidirect
198. #2960	C₂×C₁₃	semidirect
299. #135	Q₈×C₁₃	semidirect
373. #41	C₂×Q₈×C₁₃	semidirect
390. Q₁₆	C₂×Q₈×C₁₃	semidirect
391. SD₁₆	C₂×Q₈×C₁₃	semidirect
392. D₈	C₂×Q₈×C₁₃	semidirect
395. C₂×C₈	C₂×Q₈×C₁₃	semidirect
428. C₁₃	#61374	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×#3503	2
C₁₃×#3387	2
C₁₃×#3384	2
C₁₃×#3381	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3163	2
C₂×C₁₃×#498	2
C₁₃×#3084	2
C₁₃×#3079	2
C₁₃×#2960	2
C₁₃×#2952	2
C₄×C₁₃×#135	2
#61374	13

Subgroups — C13×#61374 #15747713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61374 #15747713