Subgroups — C₄×C₁₃×#525 #15720370

Order 3328.

3902 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
5	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
6	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2290	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×D₄×C₁₃	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#525	C₄	1	16	yes	direct product factor
18	C₂×C₁₃×#123	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#120	C₂²	1	2	yes	—
22	C₄×C₁₃×#41	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₃	—	2	8	no	—
33	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
40	C₁₃×#391	C₂²	1	2	yes	complemented
41	C₁₃×#390	C₂²	1	2	yes	complemented
42	C₁₃×#389	C₂²	1	4	yes	complemented
43	C₁₃×#388	C₂²	1	8	yes	complemented
44	C₁₃×#387	C₂²	1	8	yes	complemented
45	C₁₃×#386	C₂²	1	8	yes	—
46	C₁₃×#386	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	8	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#381	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	4	yes	—
51	C₁₃×#379	C₂²	1	2	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
60	C₁₃×#376	C₂²	1	2	yes	complemented
61	C₄³×C₁₃	C₂²	1	2	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	4	no	—
64	C₂×C₁₃×#41	—	2	4	no	—
65	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	8	no	—
71	C₂³×C₄×C₁₃	—	2	4	no	—
72	C₂³×C₄×C₁₃	—	2	4	no	—
73	C₂³×C₄×C₁₃	—	2	16	no	—
74	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#123	C₂×C₄	1	16	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
87	C₁₃×#121	C₂×C₄	1	16	yes	complemented
88	C₁₃×#120	C₂×C₄	1	16	yes	complemented
89	C₄×Q₈×C₁₃	—	2	8	no	—
90	C₄×D₄×C₁₃	—	2	16	no	—
91	C₄×D₄×C₁₃	—	2	32	no	—
92	C₄×D₄×C₁₃	—	2	8	no	—
93	C₄×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
94	C₁₃×#117	—	2	4	no	—
95	C₁₃×#117	—	2	4	no	—
96	C₁₃×#117	—	2	8	no	—
97	C₁₃×#117	C₂×C₄	1	8	yes	complemented
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	—	2	8	no	—
113	C₂×C₄²×C₁₃	—	2	4	no	—
114	C₂×C₄²×C₁₃	—	2	8	no	—
115	C₂×C₄²×C₁₃	—	2	8	no	—
116	C₂×C₄²×C₁₃	—	2	16	no	—
117	C₂×C₄²×C₁₃	—	2	8	no	—
118	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₁₃×#95	C₂³	1	8	yes	—
132	C₁₃×#95	C₂³	1	8	yes	—
133	C₁₃×#95	C₂³	1	8	yes	—
134	C₁₃×#95	C₂³	1	8	yes	—
135	C₄×#525	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	—	2	8	no	—
138	C₂⁴×C₁₃	—	2	2	no	—
139	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
143	C₁₃×#41	—	2	32	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	complemented
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
153	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
154	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	complemented
155	C₂²×C₄×C₁₃	—	2	64	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	32	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	2	8	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	8	no	—
174	C₂²×C₄×C₁₃	—	2	16	no	—
175	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
176	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
177	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
180	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₁₃	#41	1	4	yes	—
183	C₂²×C₄×C₁₃	#41	1	16	yes	complemented
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
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	C₁₃×C₄⋊C₄	—	2	8	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	16	no	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	16	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	16	no	—
205	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
206	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
207	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
208	C₄²×C₁₃	—	2	8	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	—	2	8	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	8	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	—	2	16	no	—
216	C₄²×C₁₃	C₂²×C₄	1	8	yes	complemented
217	C₄²×C₁₃	C₂×D₄	1	4	yes	—
218	C₄²×C₁₃	C₂×D₄	1	4	yes	—
219	C₄²×C₁₃	C₂×D₄	1	8	yes	—
220	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
221	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
224	C₄×#123	C₂×C₁₃	1	4	yes	complemented
225	C₄×#121	C₂×C₁₃	1	4	yes	complemented
226	C₄×#120	C₂×C₁₃	1	4	yes	complemented
227	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2290	C₂×C₁₃	1	4	yes	complemented
230	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₄²×D₄	C₂×C₁₃	1	4	yes	complemented
232	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	16	no	—
234	C₂³×C₁₃	—	2	16	no	—
235	C₂³×C₁₃	—	2	8	no	—
236	C₂³×C₁₃	—	2	16	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	8	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
245	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
246	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
247	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂³×C₁₃	C₂×#41	1	2	yes	—
249	C₂³×C₁₃	C₂×#41	1	8	yes	—
250	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	8	no	—
252	D₄×C₁₃	—	2	16	no	—
253	D₄×C₁₃	—	2	32	no	—
254	D₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	2	32	no	—
256	C₂×C₄×C₁₃	—	2	16	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	8	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	16	no	—
267	C₂×C₄×C₁₃	—	2	16	no	—
268	C₂×C₄×C₁₃	—	2	16	no	—
269	C₂×C₄×C₁₃	—	2	16	no	—
270	C₂×C₄×C₁₃	—	2	32	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	8	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	8	no	—
275	C₂×C₄×C₁₃	—	4	16	no	—
276	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
277	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
278	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
279	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
280	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
287	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
290	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
291	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
292	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
293	#525	C₄×C₁₃	1	16	yes	direct product factor
294	C₂×#123	C₂²×C₁₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
296	C₂×#121	C₂²×C₁₃	1	2	yes	—
297	C₂×#120	C₂²×C₁₃	1	2	yes	—
298	C₄×#41	—	2	8	no	—
299	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
300	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
301	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
302	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
303	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
304	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
308	C₂²×C₄²	—	2	8	no	—
309	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
311	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
312	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
313	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
316	#391	C₂²×C₁₃	1	2	yes	complemented
317	#390	C₂²×C₁₃	1	2	yes	complemented
318	#389	C₂²×C₁₃	1	4	yes	complemented
319	#388	C₂²×C₁₃	1	8	yes	complemented
320	#387	C₂²×C₁₃	1	8	yes	complemented
321	#386	C₂²×C₁₃	1	8	yes	—
322	#386	C₂²×C₁₃	1	4	yes	—
323	#385	C₂²×C₁₃	1	8	yes	—
324	#385	C₂²×C₁₃	1	4	yes	—
325	#381	C₂²×C₁₃	1	2	yes	—
326	#380	C₂²×C₁₃	1	4	yes	—
327	#379	C₂²×C₁₃	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
329	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
330	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
332	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
335	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
336	#376	C₂²×C₁₃	1	2	yes	complemented
337	C₄³	C₂²×C₁₃	1	2	yes	complemented
338	C₂²×C₁₃	—	2	32	no	—
339	C₂²×C₁₃	—	2	4	no	—
340	C₂²×C₁₃	—	2	4	no	—
341	C₂²×C₁₃	—	2	4	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	2	8	no	—
344	C₂²×C₁₃	—	2	4	no	—
345	C₂²×C₁₃	—	2	8	no	—
346	C₂²×C₁₃	—	2	4	no	—
347	C₂²×C₁₃	—	2	8	no	—
348	C₂²×C₁₃	—	4	4	no	—
349	C₂²×C₁₃	—	4	4	no	—
350	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
351	C₂²×C₁₃	C₄×#41	1	8	yes	complemented
352	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
353	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₁₃	C₂²×#41	1	4	yes	—
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	2	8	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	—	2	8	no	—
361	C₄×C₁₃	—	4	4	no	—
362	C₄×C₁₃	—	4	4	no	—
363	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
364	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
365	C₄×C₁₃	#525	1	8	yes	direct product factor
366	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×#41	—	2	4	no	—
368	C₂×#41	—	2	4	no	—
369	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
370	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
373	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	—	2	8	no	—
375	C₂³×C₄	—	2	4	no	—
376	C₂³×C₄	—	2	4	no	—
377	C₂³×C₄	—	2	16	no	—
378	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
379	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
380	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
387	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	#123	C₂×C₄×C₁₃	1	16	yes	complemented
390	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
391	#121	C₂×C₄×C₁₃	1	16	yes	complemented
392	#120	C₂×C₄×C₁₃	1	16	yes	complemented
393	C₄×Q₈	—	2	8	no	—
394	C₄×D₄	—	2	16	no	—
395	C₄×D₄	—	2	32	no	—
396	C₄×D₄	—	2	8	no	—
397	C₄×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
398	#117	—	2	4	no	—
399	#117	—	2	4	no	—
400	#117	—	2	8	no	—
401	#117	C₂×C₄×C₁₃	1	8	yes	complemented
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₄²	—	2	8	no	—
417	C₂×C₄²	—	2	4	no	—
418	C₂×C₄²	—	2	8	no	—
419	C₂×C₄²	—	2	8	no	—
420	C₂×C₄²	—	2	8	no	—
421	C₂×C₄²	—	2	16	no	—
422	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
435	#95	C₂³×C₁₃	1	8	yes	—
436	#95	C₂³×C₁₃	1	8	yes	—
437	#95	C₂³×C₁₃	1	8	yes	—
438	#95	C₂³×C₁₃	1	8	yes	—
439	C₂×C₁₃	—	2	4	no	—
440	C₂×C₁₃	—	2	8	no	—
441	C₂×C₁₃	—	4	4	no	—
442	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
443	C₂×C₁₃	C₂×C₄×#41	1	2	yes	—
444	C₂×C₁₃	C₂×#525	1	2	yes	—
445	C₂×C₁₃	#3444	1	2	yes	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	8	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
450	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
451	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
453	#41	—	2	32	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	complemented
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
463	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
464	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	complemented
465	C₂²×C₄	—	2	64	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	32	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	2	16	no	—
485	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
486	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
488	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
489	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
490	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
492	C₂²×C₄	C₁₃×#41	1	4	yes	—
493	C₂²×C₄	C₁₃×#41	1	16	yes	complemented
494	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
504	C₄⋊C₄	—	2	8	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	16	no	—
508	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
509	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	16	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	16	no	—
515	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
516	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
518	C₄²	—	2	8	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	8	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	8	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	16	no	—
526	C₄²	C₂²×C₄×C₁₃	1	8	yes	complemented
527	C₄²	C₂×D₄×C₁₃	1	4	yes	—
528	C₄²	C₂×D₄×C₁₃	1	4	yes	—
529	C₄²	C₂×D₄×C₁₃	1	8	yes	—
530	C₁₃	C₄×#525	1	1	yes	characteristic, direct product factor, Sylow
531	C₂³	—	2	16	no	—
532	C₂³	—	2	16	no	—
533	C₂³	—	2	8	no	—
534	C₂³	—	2	16	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
543	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
544	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
545	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
546	C₂³	C₂×C₁₃×#41	1	2	yes	—
547	C₂³	C₂×C₁₃×#41	1	8	yes	—
548	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
549	Q₈	—	2	8	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	32	no	—
552	D₄	—	2	8	no	—
553	C₂×C₄	—	2	32	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	16	no	—
565	C₂×C₄	—	2	16	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	16	no	—
568	C₂×C₄	—	2	32	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	4	16	no	—
574	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
575	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
576	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
577	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
578	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
583	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
584	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
586	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
587	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
588	C₂²	—	2	32	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	8	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
601	C₂²	C₄×C₁₃×#41	1	8	yes	complemented
602	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
603	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
604	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
605	C₂²	C₂²×C₁₃×#41	1	4	yes	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	2	8	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	8	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	4	no	—
613	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
614	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
615	C₄	C₁₃×#525	1	8	yes	direct product factor
616	C₂	—	2	4	no	—
617	C₂	—	2	8	no	—
618	C₂	—	4	4	no	—
619	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
620	C₂	C₂×C₄×C₁₃×#41	1	2	yes	—
621	C₂	C₂×C₁₃×#525	1	2	yes	—
622	C₂	C₁₃×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₂³×C₄²×C₁₃	C₂	semidirect
4. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₄×C₁₃×#123	C₂	semidirect
6. C₄×C₁₃×#121	C₂	semidirect
7. C₄×C₁₃×#120	C₂	semidirect
8. C₁₃×#2297	C₂	semidirect
9. C₁₃×#2296	C₂	semidirect
10. C₁₃×#2290	C₂	semidirect
11. C₁₃×#2280	C₂	semidirect
12. C₄²×D₄×C₁₃	C₂	semidirect
13. C₄×C₁₃×#117	C₂	semidirect
17. C₁₃×#525	C₄	direct (N × H)
23. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#117	C₂²	semidirect
39. C₂²×C₄²×C₁₃	C₂²	semidirect
40. C₁₃×#391	C₂²	semidirect
41. C₁₃×#390	C₂²	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#388	C₂²	semidirect
44. C₁₃×#387	C₂²	semidirect
52. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
53. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
54. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
58. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
59. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
60. C₁₃×#376	C₂²	semidirect
61. C₄³×C₁₃	C₂²	semidirect
65. C₂×C₁₃×#41	C₂×C₄	semidirect
74. C₂³×C₄×C₁₃	C₂×C₄	semidirect
85. C₁₃×#123	C₂×C₄	semidirect
86. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
87. C₁₃×#121	C₂×C₄	semidirect
88. C₁₃×#120	C₂×C₄	semidirect
93. C₄×D₄×C₁₃	C₂×C₄	semidirect
97. C₁₃×#117	C₂×C₄	semidirect
118. C₂×C₄²×C₁₃	D₄	semidirect
135. C₄×#525	C₁₃	direct (N × H)
146. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
154. C₂×D₄×C₁₃	C₂²×C₄	semidirect
179. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
183. C₂²×C₄×C₁₃	#41	semidirect
198. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
199. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
207. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
216. C₄²×C₁₃	C₂²×C₄	semidirect
221. C₂×C₄×#41	C₂×C₁₃	semidirect
222. C₂³×C₄²	C₂×C₁₃	semidirect
223. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
224. C₄×#123	C₂×C₁₃	semidirect
225. C₄×#121	C₂×C₁₃	semidirect
226. C₄×#120	C₂×C₁₃	semidirect
227. #2297	C₂×C₁₃	semidirect
228. #2296	C₂×C₁₃	semidirect
229. #2290	C₂×C₁₃	semidirect
230. #2280	C₂×C₁₃	semidirect
231. C₄²×D₄	C₂×C₁₃	semidirect
232. C₄×#117	C₂×C₁₃	semidirect
276. C₂×C₄×C₁₃	C₄×D₄	semidirect
293. #525	C₄×C₁₃	direct (N × H)
299. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
303. C₂×C₄×D₄	C₂²×C₁₃	semidirect
307. C₂×#117	C₂²×C₁₃	semidirect
315. C₂²×C₄²	C₂²×C₁₃	semidirect
316. #391	C₂²×C₁₃	semidirect
317. #390	C₂²×C₁₃	semidirect
318. #389	C₂²×C₁₃	semidirect
319. #388	C₂²×C₁₃	semidirect
320. #387	C₂²×C₁₃	semidirect
328. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
329. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
330. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
334. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
335. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
336. #376	C₂²×C₁₃	semidirect
337. C₄³	C₂²×C₁₃	semidirect
351. C₂²×C₁₃	C₄×#41	semidirect
365. C₄×C₁₃	#525	direct (N × H)
369. C₂×#41	C₂×C₄×C₁₃	semidirect
378. C₂³×C₄	C₂×C₄×C₁₃	semidirect
389. #123	C₂×C₄×C₁₃	semidirect
390. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
391. #121	C₂×C₄×C₁₃	semidirect
392. #120	C₂×C₄×C₁₃	semidirect
397. C₄×D₄	C₂×C₄×C₁₃	semidirect
401. #117	C₂×C₄×C₁₃	semidirect
422. C₂×C₄²	D₄×C₁₃	semidirect
456. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
464. C₂×D₄	C₂²×C₄×C₁₃	semidirect
489. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
493. C₂²×C₄	C₁₃×#41	semidirect
508. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
509. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
517. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
526. C₄²	C₂²×C₄×C₁₃	semidirect
530. C₁₃	C₄×#525	direct (N × H)
574. C₂×C₄	C₄×D₄×C₁₃	semidirect
601. C₂²	C₄×C₁₃×#41	semidirect
615. C₄	C₁₃×#525	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×#525	2
C₂×C₄×C₁₃×#41	2
C₂³×C₄²×C₁₃	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₄×C₁₃×#120	2
C₁₃×#2297	2
C₁₃×#2296	2
C₁₃×#2290	2
C₁₃×#2280	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
C₄×#525	13

Subgroups — C4×C13×#525 #15720370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#525 #15720370