Subgroups — C₁₃×#61570 #15747909

Order 3328.

2234 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3314	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3266	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3189	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3110	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	4	yes	complemented
18	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
19	C₁₃×#546	—	2	4	no	—
20	C₁₃×#546	C₂²	1	8	yes	—
21	C₁₃×#544	—	2	1	no	—
22	C₁₃×#543	—	2	1	no	—
23	C₁₃×#543	—	2	1	no	—
24	C₁₃×#533	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#121	—	2	1	no	—
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#120	—	2	1	no	—
33	C₁₃×#518	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#497	C₂²	1	4	yes	complemented
38	C₁₃×#489	C₂²	1	4	yes	complemented
39	C₁₃×#484	C₂²	1	4	yes	complemented
40	C₁₃×#484	C₂²	1	4	yes	complemented
41	C₁₃×#480	C₂²	1	4	yes	complemented
42	C₁₃×#474	C₂²	1	4	yes	complemented
43	C₁₃×#468	C₂²	1	8	yes	complemented
44	C₁₃×#467	C₂²	1	8	yes	complemented
45	C₁₃×#464	C₂²	1	8	yes	complemented
46	C₁₃×#461	C₂²	1	4	yes	complemented
47	C₁₃×#452	C₂²	1	8	yes	complemented
48	C₁₃×#451	C₂²	1	4	yes	complemented
49	C₁₃×#451	C₂²	1	4	yes	complemented
50	C₁₃×#450	C₂²	1	4	yes	—
51	C₁₃×#450	C₂²	1	4	yes	—
52	C₁₃×#450	C₂²	1	8	yes	complemented
53	C₁₃×#448	C₂²	1	4	yes	complemented
54	C₁₃×#440	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#432	C₂²	1	2	yes	complemented
57	C₁₃×#417	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	complemented
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
61	C₂⁵×C₁₃	—	2	1	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	4	4	no	—
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	complemented
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	—	4	4	no	—
73	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	—	2	1	no	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#137	—	4	8	no	—
82	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
83	C₂×C₁₃×SD₁₆	—	4	8	no	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
86	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
87	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
88	C₁₃×C₄⋊Q₈	—	2	4	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
90	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
91	C₁₃×#125	—	2	4	no	—
92	C₁₃×#125	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×C₂²⋊Q₈	—	2	4	no	—
103	C₁₃×C₂²⋊Q₈	—	2	4	no	—
104	C₁₃×C₂²⋊Q₈	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	8	no	—
112	C₁₃×#121	C₂³	1	4	yes	—
113	C₁₃×#120	—	2	8	no	—
114	C₄×Q₈×C₁₃	—	2	2	no	—
115	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	D₄	1	4	yes	—
120	C₄×D₄×C₁₃	C₂³	1	4	yes	—
121	C₄×D₄×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#117	—	2	2	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
130	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×#107	C₂³	1	8	yes	complemented
142	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
143	C₁₃×#103	C₂³	1	8	yes	complemented
144	C₁₃×#103	C₂³	1	8	yes	complemented
145	C₁₃×#102	C₂³	1	8	yes	—
146	C₁₃×#102	C₂³	1	8	yes	—
147	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
150	C₁₃×#97	C₂³	1	4	yes	complemented
151	#61570	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	2	4	no	—
155	C₂⁴×C₁₃	—	4	4	no	—
156	C₂⁴×C₁₃	—	4	4	no	—
157	C₂⁴×C₁₃	—	8	2	no	—
158	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₁₃×#41	—	2	8	no	—
161	C₁₃×#41	—	4	4	no	—
162	C₁₃×#41	—	4	8	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	2	no	—
165	C₂×Q₈×C₁₃	—	2	2	no	—
166	C₂×Q₈×C₁₃	—	2	2	no	—
167	C₂×Q₈×C₁₃	—	4	2	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂×Q₈×C₁₃	—	4	4	no	—
170	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
171	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	4	4	no	—
181	C₂×D₄×C₁₃	—	4	2	no	—
182	C₂×D₄×C₁₃	—	4	8	no	—
183	C₂×D₄×C₁₃	—	4	4	no	—
184	C₂×D₄×C₁₃	—	4	4	no	—
185	C₂×D₄×C₁₃	—	8	2	no	—
186	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	4	2	no	—
198	C₂²×C₄×C₁₃	—	4	2	no	—
199	C₂²×C₄×C₁₃	—	4	4	no	—
200	C₂²×C₄×C₁₃	—	8	2	no	—
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₁₃×Q₁₆	—	4	8	no	—
211	C₁₃×SD₁₆	—	2	16	no	—
212	C₁₃×SD₁₆	—	4	8	no	—
213	C₁₃×M₁₆	—	4	4	no	—
214	C₂×C₈×C₁₃	—	4	4	no	—
215	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	4	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	4	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
239	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
240	C₄²×C₁₃	—	2	4	no	—
241	C₄²×C₁₃	C₂×D₄	1	2	yes	—
242	C₄²×C₁₃	C₂⁴	1	2	yes	—
243	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
245	#3314	C₂×C₁₃	1	8	yes	complemented
246	#3266	C₂×C₁₃	1	8	yes	complemented
247	#3215	C₂×C₁₃	1	2	yes	complemented
248	#3193	C₂×C₁₃	1	2	yes	complemented
249	#3189	C₂×C₁₃	1	2	yes	complemented
250	#3110	C₂×C₁₃	1	2	yes	complemented
251	#3007	C₂×C₁₃	1	2	yes	complemented
252	C₂×#450	C₂×C₁₃	1	2	yes	complemented
253	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	4	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	8	no	—
263	C₂³×C₁₃	—	4	2	no	—
264	C₂³×C₁₃	—	4	2	no	—
265	C₂³×C₁₃	—	4	2	no	—
266	C₂³×C₁₃	—	4	2	no	—
267	C₂³×C₁₃	—	4	8	no	—
268	C₂³×C₁₃	—	4	2	no	—
269	C₂³×C₁₃	—	8	4	no	—
270	C₂³×C₁₃	—	8	16	no	—
271	C₂³×C₁₃	#137	1	4	yes	complemented
272	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	Q₈×C₁₃	—	2	8	no	—
276	Q₈×C₁₃	—	2	4	no	—
277	Q₈×C₁₃	—	4	2	no	—
278	Q₈×C₁₃	—	8	2	no	—
279	Q₈×C₁₃	—	8	2	no	—
280	Q₈×C₁₃	—	8	2	no	—
281	D₄×C₁₃	—	2	4	no	—
282	D₄×C₁₃	—	2	8	no	—
283	D₄×C₁₃	—	2	2	no	—
284	D₄×C₁₃	—	2	4	no	—
285	D₄×C₁₃	—	4	8	no	—
286	D₄×C₁₃	—	4	2	no	—
287	D₄×C₁₃	—	4	8	no	—
288	D₄×C₁₃	—	8	4	no	—
289	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	2	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	2	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	8	no	—
304	C₂×C₄×C₁₃	—	4	2	no	—
305	C₂×C₄×C₁₃	—	4	2	no	—
306	C₂×C₄×C₁₃	—	8	4	no	—
307	C₂×C₄×C₁₃	—	8	2	no	—
308	C₂×C₄×C₁₃	—	8	2	no	—
309	C₂×C₄×C₁₃	—	8	2	no	—
310	C₂×C₄×C₁₃	—	8	2	no	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
317	C₈×C₁₃	—	2	8	no	—
318	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
319	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
321	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
322	#554	—	2	4	no	—
323	#554	C₂²×C₁₃	1	4	yes	complemented
324	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
325	#546	—	2	4	no	—
326	#546	C₂²×C₁₃	1	8	yes	—
327	#544	—	2	1	no	—
328	#543	—	2	1	no	—
329	#543	—	2	1	no	—
330	#533	C₂²×C₁₃	1	2	yes	complemented
331	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#123	—	2	1	no	—
333	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
335	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
336	C₂×#121	—	2	1	no	—
337	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#120	—	2	1	no	—
339	#518	—	2	1	no	—
340	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	—	2	1	no	—
343	#497	C₂²×C₁₃	1	4	yes	complemented
344	#489	C₂²×C₁₃	1	4	yes	complemented
345	#484	C₂²×C₁₃	1	4	yes	complemented
346	#484	C₂²×C₁₃	1	4	yes	complemented
347	#480	C₂²×C₁₃	1	4	yes	complemented
348	#474	C₂²×C₁₃	1	4	yes	complemented
349	#468	C₂²×C₁₃	1	8	yes	complemented
350	#467	C₂²×C₁₃	1	8	yes	complemented
351	#464	C₂²×C₁₃	1	8	yes	complemented
352	#461	C₂²×C₁₃	1	4	yes	complemented
353	#452	C₂²×C₁₃	1	8	yes	complemented
354	#451	C₂²×C₁₃	1	4	yes	complemented
355	#451	C₂²×C₁₃	1	4	yes	complemented
356	#450	C₂²×C₁₃	1	4	yes	—
357	#450	C₂²×C₁₃	1	4	yes	—
358	#450	C₂²×C₁₃	1	8	yes	complemented
359	#448	C₂²×C₁₃	1	4	yes	complemented
360	#440	C₂²×C₁₃	1	8	yes	complemented
361	#435	C₂²×C₁₃	1	8	yes	complemented
362	#432	C₂²×C₁₃	1	2	yes	complemented
363	#417	C₂²×C₁₃	1	4	yes	complemented
364	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
365	#407	C₂²×C₁₃	1	2	yes	complemented
366	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
367	C₂²×C₁₃	—	2	1	no	—
368	C₂²×C₁₃	—	2	2	no	—
369	C₂²×C₁₃	—	2	1	no	—
370	C₂²×C₁₃	—	2	2	no	—
371	C₂²×C₁₃	—	2	2	no	—
372	C₂²×C₁₃	—	2	2	no	—
373	C₂²×C₁₃	—	2	4	no	—
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	4	4	no	—
376	C₂²×C₁₃	—	4	8	no	—
377	C₂²×C₁₃	—	4	2	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	2	no	—
382	C₂²×C₁₃	—	8	2	no	—
383	C₂²×C₁₃	—	8	16	no	—
384	C₂²×C₁₃	—	8	4	no	—
385	C₂²×C₁₃	C₂×#137	1	2	yes	—
386	C₂²×C₁₃	C₂×#137	1	4	yes	—
387	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₁₃	—	2	2	no	—
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	2	1	no	—
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	2	2	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	—	4	4	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	4	no	—
397	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₂⁵	—	2	1	no	—
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	4	4	no	—
401	C₂×#41	C₂³×C₁₃	1	4	yes	—
402	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
404	C₂²×Q₈	C₂³×C₁₃	1	2	yes	complemented
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	2	no	—
409	C₂²×D₄	—	4	4	no	—
410	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
413	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
418	#137	—	4	8	no	—
419	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
420	C₂×SD₁₆	—	4	8	no	—
421	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
422	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
423	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
424	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
425	C₄⋊Q₈	—	2	4	no	—
426	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
427	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
428	#125	—	2	4	no	—
429	#125	—	2	2	no	—
430	#124	—	2	2	no	—
431	#124	C₂³×C₁₃	1	4	yes	—
432	#123	—	2	8	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	2	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	—	2	4	no	—
440	C₂²⋊Q₈	—	2	4	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
444	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
445	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
446	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
447	#121	—	2	2	no	—
448	#121	—	2	8	no	—
449	#121	C₂³×C₁₃	1	4	yes	—
450	#120	—	2	8	no	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	4	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	D₄×C₁₃	1	4	yes	—
457	C₄×D₄	C₂³×C₁₃	1	4	yes	—
458	C₄×D₄	C₂³×C₁₃	1	4	yes	—
459	#117	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	2	no	—
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	8	no	—
475	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	#107	C₂³×C₁₃	1	8	yes	complemented
479	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
480	#103	C₂³×C₁₃	1	8	yes	complemented
481	#103	C₂³×C₁₃	1	8	yes	complemented
482	#102	C₂³×C₁₃	1	8	yes	—
483	#102	C₂³×C₁₃	1	8	yes	—
484	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
487	#97	C₂³×C₁₃	1	4	yes	complemented
488	C₂×C₁₃	—	2	2	no	—
489	C₂×C₁₃	—	2	4	no	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	4	4	no	—
492	C₂×C₁₃	—	8	2	no	—
493	C₂×C₁₃	#3484	1	1	yes	characteristic
494	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
495	C₂×C₁₃	#3585	1	1	yes	characteristic
496	C₂⁴	—	2	1	no	—
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	4	4	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	—	8	2	no	—
502	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
504	#41	—	2	8	no	—
505	#41	—	4	4	no	—
506	#41	—	4	8	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×Q₈	—	4	4	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
515	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	4	8	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	8	2	no	—
530	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
531	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	8	2	no	—
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
554	Q₁₆	—	4	8	no	—
555	SD₁₆	—	2	16	no	—
556	SD₁₆	—	4	8	no	—
557	M₁₆	—	4	4	no	—
558	C₂×C₈	—	4	4	no	—
559	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
572	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
573	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
583	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	C₂×D₄×C₁₃	1	2	yes	—
586	C₄²	C₂⁴×C₁₃	1	2	yes	—
587	C₁₃	#61570	1	1	yes	characteristic, direct product factor, Sylow
588	C₂³	—	2	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	8	4	no	—
604	C₂³	—	8	16	no	—
605	C₂³	C₁₃×#137	1	4	yes	complemented
606	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
607	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
608	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
609	Q₈	—	2	8	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	4	2	no	—
612	Q₈	—	8	2	no	—
613	Q₈	—	8	2	no	—
614	Q₈	—	8	2	no	—
615	D₄	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	8	no	—
622	D₄	—	8	4	no	—
623	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
646	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
650	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
651	C₈	—	2	8	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	8	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	8	2	no	—
668	C₂²	—	8	16	no	—
669	C₂²	—	8	4	no	—
670	C₂²	C₂×C₁₃×#137	1	2	yes	—
671	C₂²	C₂×C₁₃×#137	1	4	yes	—
672	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	4	no	—
682	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	2	4	no	—
685	C₂	—	4	2	no	—
686	C₂	—	4	4	no	—
687	C₂	—	8	2	no	—
688	C₂	C₁₃×#3484	1	1	yes	characteristic
689	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
690	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3314	C₂	semidirect
4. C₁₃×#3266	C₂	semidirect
5. C₁₃×#3215	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3189	C₂	semidirect
8. C₁₃×#3110	C₂	semidirect
9. C₁₃×#3007	C₂	semidirect
10. C₂×C₁₃×#450	C₂	semidirect
11. C₁₃×#2973	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
17. C₁₃×#554	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
24. C₁₃×#533	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
39. C₁₃×#484	C₂²	semidirect
40. C₁₃×#484	C₂²	semidirect
41. C₁₃×#480	C₂²	semidirect
42. C₁₃×#474	C₂²	semidirect
43. C₁₃×#468	C₂²	semidirect
44. C₁₃×#467	C₂²	semidirect
45. C₁₃×#464	C₂²	semidirect
46. C₁₃×#461	C₂²	semidirect
47. C₁₃×#452	C₂²	semidirect
48. C₁₃×#451	C₂²	semidirect
49. C₁₃×#451	C₂²	semidirect
52. C₁₃×#450	C₂²	semidirect
53. C₁₃×#448	C₂²	semidirect
54. C₁₃×#440	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#432	C₂²	semidirect
57. C₁₃×#417	C₂²	semidirect
58. C₂×C₁₃×#102	C₂²	semidirect
59. C₁₃×#407	C₂²	semidirect
67. C₂²×Q₈×C₁₃	C₂³	semidirect
82. C₂×C₁₃×Q₁₆	C₂³	semidirect
86. C₂×C₁₃×M₁₆	C₂³	semidirect
89. C₁₃×C₄⋊Q₈	C₂³	semidirect
90. C₁₃×C₄⋊Q₈	C₂³	semidirect
109. C₁₃×C₂²⋊Q₈	C₂³	semidirect
115. C₄×Q₈×C₁₃	C₂³	semidirect
129. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
141. C₁₃×#107	C₂³	semidirect
142. C₁₃×C₄⋊C₈	C₂³	semidirect
143. C₁₃×#103	C₂³	semidirect
144. C₁₃×#103	C₂³	semidirect
149. C₁₃×C₂²⋊C₈	C₂³	semidirect
150. C₁₃×#97	C₂³	semidirect
151. #61570	C₁₃	direct (N × H)
243. #3501	C₂×C₁₃	semidirect
245. #3314	C₂×C₁₃	semidirect
246. #3266	C₂×C₁₃	semidirect
247. #3215	C₂×C₁₃	semidirect
248. #3193	C₂×C₁₃	semidirect
249. #3189	C₂×C₁₃	semidirect
250. #3110	C₂×C₁₃	semidirect
251. #3007	C₂×C₁₃	semidirect
252. C₂×#450	C₂×C₁₃	semidirect
253. #2973	C₂×C₁₃	semidirect
271. C₂³×C₁₃	#137	semidirect
320. C₂×#137	C₂²×C₁₃	semidirect
321. C₂²×SD₁₆	C₂²×C₁₃	semidirect
323. #554	C₂²×C₁₃	semidirect
324. D₄×Q₈	C₂²×C₁₃	semidirect
330. #533	C₂²×C₁₃	semidirect
335. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
343. #497	C₂²×C₁₃	semidirect
344. #489	C₂²×C₁₃	semidirect
345. #484	C₂²×C₁₃	semidirect
346. #484	C₂²×C₁₃	semidirect
347. #480	C₂²×C₁₃	semidirect
348. #474	C₂²×C₁₃	semidirect
349. #468	C₂²×C₁₃	semidirect
350. #467	C₂²×C₁₃	semidirect
351. #464	C₂²×C₁₃	semidirect
352. #461	C₂²×C₁₃	semidirect
353. #452	C₂²×C₁₃	semidirect
354. #451	C₂²×C₁₃	semidirect
355. #451	C₂²×C₁₃	semidirect
358. #450	C₂²×C₁₃	semidirect
359. #448	C₂²×C₁₃	semidirect
360. #440	C₂²×C₁₃	semidirect
361. #435	C₂²×C₁₃	semidirect
362. #432	C₂²×C₁₃	semidirect
363. #417	C₂²×C₁₃	semidirect
364. C₂×#102	C₂²×C₁₃	semidirect
365. #407	C₂²×C₁₃	semidirect
404. C₂²×Q₈	C₂³×C₁₃	semidirect
419. C₂×Q₁₆	C₂³×C₁₃	semidirect
423. C₂×M₁₆	C₂³×C₁₃	semidirect
426. C₄⋊Q₈	C₂³×C₁₃	semidirect
427. C₄⋊Q₈	C₂³×C₁₃	semidirect
446. C₂²⋊Q₈	C₂³×C₁₃	semidirect
452. C₄×Q₈	C₂³×C₁₃	semidirect
466. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
478. #107	C₂³×C₁₃	semidirect
479. C₄⋊C₈	C₂³×C₁₃	semidirect
480. #103	C₂³×C₁₃	semidirect
481. #103	C₂³×C₁₃	semidirect
486. C₂²⋊C₈	C₂³×C₁₃	semidirect
487. #97	C₂³×C₁₃	semidirect
587. C₁₃	#61570	direct (N × H)
605. C₂³	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×#3501	2
C₂×C₁₃×#546	2
C₁₃×#3314	2
C₁₃×#3266	2
C₁₃×#3215	2
C₁₃×#3193	2
C₁₃×#3189	2
C₁₃×#3110	2
C₁₃×#3007	2
C₂×C₁₃×#450	2
C₁₃×#2973	2
#61570	13

Subgroups — C13×#61570 #15747909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61570 #15747909