Subgroups — C₁₃×#34227 #15720566

Order 3328.

2186 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2374	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2373	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2347	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2324	C₂	1	2	yes	maximal
9	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#529	C₄	1	16	yes	complemented
19	C₂×C₁₃×#126	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	4	yes	—
36	C₁₃×#389	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#388	C₂²	1	4	yes	—
42	C₁₃×#388	C₂²	1	4	yes	—
43	C₁₃×#388	C₂²	1	4	yes	—
44	C₁₃×#388	C₂²	1	4	yes	—
45	C₁₃×#387	C₂²	1	4	yes	—
46	C₁₃×#387	C₂²	1	4	yes	—
47	C₁₃×#387	C₂²	1	4	yes	—
48	C₁₃×#387	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	4	yes	—
51	C₁₃×#383	C₂²	1	2	yes	—
52	C₁₃×#383	C₂²	1	2	yes	—
53	C₁₃×#382	C₂²	1	2	yes	—
54	C₁₃×#382	C₂²	1	2	yes	—
55	C₁₃×#381	C₂²	1	2	yes	—
56	C₁₃×#381	C₂²	1	2	yes	—
57	C₁₃×#380	C₂²	1	2	yes	—
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₁₃×#376	C₂²	1	1	yes	characteristic
79	C₁₃×#376	C₂²	1	1	yes	characteristic
80	C₁₃×#376	C₂²	1	2	yes	—
81	C₁₃×#376	C₂²	1	2	yes	—
82	C₂×C₁₃×#95	C₂²	1	2	yes	—
83	C₄³×C₁₃	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₁₃×#126	C₂×C₄	1	16	yes	complemented
93	C₁₃×#125	C₂×C₄	1	8	yes	complemented
94	C₁₃×#124	C₂×C₄	1	8	yes	—
95	C₁₃×#123	C₂×C₄	1	16	yes	complemented
96	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₁₃×#121	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₁₃	—	2	8	no	—
99	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
103	C₁₃×#117	—	2	8	no	—
104	C₁₃×#117	C₂×C₄	1	16	yes	complemented
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
130	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₁₃×#95	C₂³	1	1	yes	characteristic
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	1	yes	characteristic
150	C₁₃×#95	C₂³	1	1	yes	characteristic
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	2	yes	—
155	C₁₃×#95	C₂³	1	1	yes	characteristic
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	#34227	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
168	C₂×D₄×C₁₃	—	2	4	no	—
169	C₂×D₄×C₁₃	—	4	2	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	8	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	—	4	1	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	4	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	—	4	4	no	—
181	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	8	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	4	4	no	—
206	C₁₃×C₄⋊C₄	—	4	4	no	—
207	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
208	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
209	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
210	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
211	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
212	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	—	2	8	no	—
216	C₁₃×C₂²⋊C₄	—	4	4	no	—
217	C₁₃×C₂²⋊C₄	—	4	4	no	—
218	C₁₃×C₂²⋊C₄	—	4	4	no	—
219	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
220	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
221	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
222	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
223	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
224	C₄²×C₁₃	—	2	4	no	—
225	C₄²×C₁₃	—	2	8	no	—
226	C₄²×C₁₃	—	4	2	no	—
227	C₄²×C₁₃	—	4	2	no	—
228	C₄²×C₁₃	—	4	4	no	—
229	C₄²×C₁₃	—	4	4	no	—
230	C₄²×C₁₃	—	4	2	no	—
231	C₄²×C₁₃	—	4	2	no	—
232	C₄²×C₁₃	—	4	2	no	—
233	C₄²×C₁₃	—	4	2	no	—
234	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
235	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
236	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
237	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
238	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
239	C₄²×C₁₃	#41	1	8	yes	—
240	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
241	#2374	C₂×C₁₃	1	4	yes	complemented
242	#2373	C₂×C₁₃	1	4	yes	complemented
243	#2357	C₂×C₁₃	1	2	yes	complemented
244	#2353	C₂×C₁₃	1	2	yes	complemented
245	#2347	C₂×C₁₃	1	2	yes	complemented
246	#2343	C₂×C₁₃	1	2	yes	complemented
247	#2324	C₂×C₁₃	1	2	yes	—
248	#2323	C₂×C₁₃	1	2	yes	complemented
249	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2319	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₄×#125	C₂×C₁₃	1	2	yes	complemented
252	C₄×#124	C₂×C₁₃	1	2	yes	complemented
253	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2276	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	4	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	4	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
266	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
267	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
268	Q₈×C₁₃	—	2	8	no	—
269	D₄×C₁₃	—	2	8	no	—
270	D₄×C₁₃	—	4	8	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	8	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	4	4	no	—
300	C₂×C₄×C₁₃	—	4	8	no	—
301	C₂×C₄×C₁₃	—	4	4	no	—
302	C₂×C₄×C₁₃	—	8	8	no	—
303	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
308	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
313	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
314	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
315	#529	C₄×C₁₃	1	16	yes	complemented
316	C₂×#126	C₂²×C₁₃	1	2	yes	—
317	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#123	C₂²×C₁₃	1	2	yes	—
320	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
327	C₂×#117	C₂²×C₁₃	1	2	yes	—
328	C₂×#117	C₂²×C₁₃	1	2	yes	—
329	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
330	#391	C₂²×C₁₃	1	2	yes	—
331	#390	C₂²×C₁₃	1	2	yes	—
332	#390	C₂²×C₁₃	1	4	yes	—
333	#389	C₂²×C₁₃	1	2	yes	—
334	#389	C₂²×C₁₃	1	2	yes	—
335	#389	C₂²×C₁₃	1	4	yes	—
336	#388	C₂²×C₁₃	1	4	yes	—
337	#388	C₂²×C₁₃	1	4	yes	—
338	#388	C₂²×C₁₃	1	4	yes	—
339	#388	C₂²×C₁₃	1	4	yes	—
340	#388	C₂²×C₁₃	1	4	yes	—
341	#388	C₂²×C₁₃	1	4	yes	—
342	#387	C₂²×C₁₃	1	4	yes	—
343	#387	C₂²×C₁₃	1	4	yes	—
344	#387	C₂²×C₁₃	1	4	yes	—
345	#387	C₂²×C₁₃	1	4	yes	—
346	#386	C₂²×C₁₃	1	4	yes	—
347	#385	C₂²×C₁₃	1	4	yes	—
348	#383	C₂²×C₁₃	1	2	yes	—
349	#383	C₂²×C₁₃	1	2	yes	—
350	#382	C₂²×C₁₃	1	2	yes	—
351	#382	C₂²×C₁₃	1	2	yes	—
352	#381	C₂²×C₁₃	1	2	yes	—
353	#381	C₂²×C₁₃	1	2	yes	—
354	#380	C₂²×C₁₃	1	2	yes	—
355	#380	C₂²×C₁₃	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
357	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
359	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
360	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
365	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
368	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
369	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
375	#376	C₂²×C₁₃	1	1	yes	characteristic
376	#376	C₂²×C₁₃	1	2	yes	—
377	#376	C₂²×C₁₃	1	2	yes	—
378	#376	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#95	C₂²×C₁₃	1	2	yes	—
380	C₄³	C₂²×C₁₃	1	2	yes	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	4	no	—
387	C₂²×C₁₃	—	4	4	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	4	no	—
391	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
392	C₂²×C₁₃	C₂²×#41	1	2	yes	—
393	C₂²×C₁₃	#585	1	1	yes	characteristic
394	C₂²×C₁₃	#585	1	2	yes	—
395	C₂²×C₁₃	#585	1	1	yes	characteristic
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	2	4	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	4	no	—
403	C₄×C₁₃	—	2	4	no	—
404	C₄×C₁₃	—	2	4	no	—
405	C₄×C₁₃	—	2	4	no	—
406	C₄×C₁₃	—	4	2	no	—
407	C₄×C₁₃	—	4	4	no	—
408	C₄×C₁₃	—	4	2	no	—
409	C₄×C₁₃	—	4	4	no	—
410	C₄×C₁₃	C₄×#41	1	4	yes	—
411	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
414	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
416	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
417	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
419	#126	C₂×C₄×C₁₃	1	16	yes	complemented
420	#125	C₂×C₄×C₁₃	1	8	yes	complemented
421	#124	C₂×C₄×C₁₃	1	8	yes	—
422	#123	C₂×C₄×C₁₃	1	16	yes	complemented
423	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
424	#121	C₂×C₄×C₁₃	1	8	yes	—
425	C₄×Q₈	—	2	8	no	—
426	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
427	C₄×D₄	—	2	8	no	—
428	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
429	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
430	#117	—	2	8	no	—
431	#117	C₂×C₄×C₁₃	1	16	yes	complemented
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
457	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
473	#95	C₂³×C₁₃	1	1	yes	characteristic
474	#95	C₂³×C₁₃	1	2	yes	—
475	#95	C₂³×C₁₃	1	4	yes	—
476	#95	C₂³×C₁₃	1	1	yes	characteristic
477	#95	C₂³×C₁₃	1	2	yes	—
478	#95	C₂³×C₁₃	1	1	yes	characteristic
479	#95	C₂³×C₁₃	1	1	yes	characteristic
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	2	yes	—
482	#95	C₂³×C₁₃	1	2	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	#95	C₂³×C₁₃	1	4	yes	—
487	#95	C₂³×C₁₃	1	4	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	4	4	no	—
492	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
493	C₂×C₁₃	#3428	1	1	yes	characteristic
494	C₂×C₁₃	#3428	1	1	yes	characteristic
495	C₂×C₁₃	#3510	1	2	yes	—
496	C₂×C₁₃	#3512	1	2	yes	—
497	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
505	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	4	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
515	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
516	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
517	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
518	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	4	4	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
541	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
542	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
543	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
544	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
545	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	4	4	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
553	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
556	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	8	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	4	4	no	—
562	C₄²	—	4	4	no	—
563	C₄²	—	4	2	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
568	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
569	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
570	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
571	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
572	C₄²	C₁₃×#41	1	8	yes	—
573	C₁₃	#34227	1	1	yes	characteristic, direct product factor, Sylow
574	C₂³	—	2	2	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
583	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
584	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
585	Q₈	—	2	8	no	—
586	D₄	—	2	8	no	—
587	D₄	—	4	8	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	8	8	no	—
620	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
621	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
626	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
629	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
630	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
631	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
643	C₂²	C₂²×C₁₃×#41	1	2	yes	—
644	C₂²	C₁₃×#585	1	1	yes	characteristic
645	C₂²	C₁₃×#585	1	2	yes	—
646	C₂²	C₁₃×#585	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	C₄×C₁₃×#41	1	4	yes	—
662	C₂	—	4	2	no	—
663	C₂	—	4	4	no	—
664	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
665	C₂	C₁₃×#3428	1	1	yes	characteristic
666	C₂	C₁₃×#3428	1	1	yes	characteristic
667	C₂	C₁₃×#3510	1	2	yes	—
668	C₂	C₁₃×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2374	C₂	semidirect
3. C₁₃×#2373	C₂	semidirect
4. C₁₃×#2357	C₂	semidirect
5. C₁₃×#2353	C₂	semidirect
6. C₁₃×#2347	C₂	semidirect
7. C₁₃×#2343	C₂	semidirect
9. C₁₃×#2323	C₂	semidirect
10. C₁₃×#2320	C₂	semidirect
11. C₁₃×#2319	C₂	semidirect
12. C₄×C₁₃×#125	C₂	semidirect
13. C₄×C₁₃×#124	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
15. C₁₃×#2276	C₂	semidirect
16. C₁₃×#2275	C₂	semidirect
17. C₄×C₁₃×#117	C₂	semidirect
18. C₁₃×#529	C₄	semidirect
92. C₁₃×#126	C₂×C₄	semidirect
93. C₁₃×#125	C₂×C₄	semidirect
95. C₁₃×#123	C₂×C₄	semidirect
96. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×Q₈×C₁₃	C₂×C₄	semidirect
102. C₄×D₄×C₁₃	C₂×C₄	semidirect
104. C₁₃×#117	C₂×C₄	semidirect
129. C₂×C₄²×C₁₃	C₂×C₄	semidirect
163. #34227	C₁₃	direct (N × H)
241. #2374	C₂×C₁₃	semidirect
242. #2373	C₂×C₁₃	semidirect
243. #2357	C₂×C₁₃	semidirect
244. #2353	C₂×C₁₃	semidirect
245. #2347	C₂×C₁₃	semidirect
246. #2343	C₂×C₁₃	semidirect
248. #2323	C₂×C₁₃	semidirect
249. #2320	C₂×C₁₃	semidirect
250. #2319	C₂×C₁₃	semidirect
251. C₄×#125	C₂×C₁₃	semidirect
252. C₄×#124	C₂×C₁₃	semidirect
253. #2283	C₂×C₁₃	semidirect
254. #2276	C₂×C₁₃	semidirect
255. #2275	C₂×C₁₃	semidirect
256. C₄×#117	C₂×C₁₃	semidirect
315. #529	C₄×C₁₃	semidirect
419. #126	C₂×C₄×C₁₃	semidirect
420. #125	C₂×C₄×C₁₃	semidirect
422. #123	C₂×C₄×C₁₃	semidirect
423. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
426. C₄×Q₈	C₂×C₄×C₁₃	semidirect
429. C₄×D₄	C₂×C₄×C₁₃	semidirect
431. #117	C₂×C₄×C₁₃	semidirect
456. C₂×C₄²	C₂×C₄×C₁₃	semidirect
573. C₁₃	#34227	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#529	2
C₁₃×#2374	2
C₁₃×#2373	2
C₁₃×#2357	2
C₁₃×#2353	2
C₁₃×#2347	2
C₁₃×#2343	2
C₁₃×#2324	2
C₁₃×#2323	2
C₁₃×#2320	2
C₁₃×#2319	2
C₄×C₁₃×#125	2
C₄×C₁₃×#124	2
C₁₃×#2283	2
C₁₃×#2276	2
C₁₃×#2275	2
C₄×C₁₃×#117	2
#34227	13

Subgroups — C13×#34227 #15720566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34227 #15720566