Subgroups — C₁₃×SD₁₆×#41 #15747765

Order 3328.

2116 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3335	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3298	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3295	C₂	1	3	yes	maximal, complemented
10	D₄×C₁₃×SD₁₆	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3167	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3103	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3101	C₂	1	3	yes	maximal, complemented
14	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×SD₁₆	C₂	1	3	yes	maximal, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	3	yes	—
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#554	—	2	3	no	—
22	C₁₃×#554	C₂²	1	3	yes	complemented
23	C₁₃×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₁₃	C₂²	1	3	yes	complemented
26	C₁₃×#548	—	2	1	no	—
27	C₁₃×#547	C₂²	1	3	yes	—
28	C₁₃×#546	—	2	3	no	—
29	D₄²×C₁₃	C₂²	1	3	yes	—
30	C₁₃×#533	—	2	3	no	—
31	C₁₃×#533	C₂²	1	3	yes	complemented
32	C₁₃×#532	C₂²	1	3	yes	—
33	C₁₃×#525	—	2	3	no	—
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#498	C₂²	1	3	yes	complemented
39	C₁₃×#492	C₂²	1	3	yes	complemented
40	C₁₃×#487	C₂²	1	3	yes	complemented
41	C₁₃×#486	C₂²	1	3	yes	complemented
42	C₁₃×#483	C₂²	1	6	yes	complemented
43	C₁₃×#481	C₂²	1	6	yes	complemented
44	C₁₃×#476	C₂²	1	3	yes	—
45	C₁₃×#476	C₂²	1	3	yes	complemented
46	C₁₃×#475	C₂²	1	3	yes	complemented
47	C₁₃×#475	C₂²	1	3	yes	complemented
48	C₁₃×#465	C₂²	1	6	yes	complemented
49	C₁₃×#465	C₂²	1	6	yes	complemented
50	C₁₃×#461	C₂²	1	3	yes	—
51	C₁₃×#461	C₂²	1	3	yes	complemented
52	C₁₃×#460	C₂²	1	3	yes	complemented
53	C₁₃×#460	C₂²	1	3	yes	complemented
54	C₁₃×#450	C₂²	1	6	yes	—
55	C₁₃×#448	C₂²	1	6	yes	complemented
56	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
59	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
60	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
61	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
63	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
64	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
65	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
67	C₈×D₄×C₁₃	C₂²	1	3	yes	complemented
68	C₈×D₄×C₁₃	C₂²	1	3	yes	complemented
69	C₁₃×#431	C₂²	1	3	yes	complemented
70	C₂×C₁₃×#106	C₂²	1	3	yes	complemented
71	C₂×C₁₃×#103	C₂²	1	3	yes	complemented
72	C₂×C₁₃×#102	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	3	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	—	4	8	no	—
78	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	—	2	1	no	—
80	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
81	C₂²×D₄×C₁₃	—	2	3	no	—
82	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
83	C₂³×C₄×C₁₃	—	2	3	no	—
84	C₂×C₁₃×SD₁₆	—	2	12	no	—
85	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
91	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
92	C₁₃×C₄⋊Q₈	—	2	3	no	—
93	C₁₃×C₄⋊Q₈	—	2	3	no	—
94	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
97	C₁₃×#127	C₂³	1	3	yes	—
98	C₁₃×#125	—	2	3	no	—
99	C₁₃×#125	—	2	3	no	—
100	C₁₃×#125	—	2	3	no	—
101	C₁₃×#124	—	2	3	no	—
102	C₁₃×#123	—	2	6	no	—
103	C₁₃×C₂²⋊Q₈	—	2	3	no	—
104	C₁₃×C₂²⋊Q₈	—	2	3	no	—
105	C₁₃×C₂²⋊Q₈	—	2	3	no	—
106	C₁₃×C₂²⋊Q₈	—	2	6	no	—
107	C₁₃×C₂²⋊Q₈	—	2	6	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	3	no	—
112	C₁₃×#121	C₂³	1	6	yes	—
113	C₁₃×#120	—	2	6	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	—	2	3	no	—
117	C₄×Q₈×C₁₃	—	2	3	no	—
118	C₄×Q₈×C₁₃	—	2	3	no	—
119	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	—	2	3	no	—
130	C₄×D₄×C₁₃	D₄	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₄×D₄×C₁₃	C₂³	1	3	yes	—
135	C₄×D₄×C₁₃	C₂³	1	3	yes	—
136	C₁₃×#117	—	2	3	no	—
137	C₁₃×#117	D₄	1	3	yes	—
138	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
142	C₂×C₄²×C₁₃	—	2	3	no	—
143	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
144	C₁₃×#106	C₂³	1	1	yes	characteristic
145	C₁₃×#106	C₂³	1	3	yes	—
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×#106	C₂³	1	3	yes	—
148	C₁₃×#106	C₂³	1	6	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
151	C₁₃×#103	C₂³	1	1	yes	characteristic
152	C₁₃×#103	C₂³	1	3	yes	—
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#103	C₂³	1	6	yes	—
156	C₁₃×#102	C₂³	1	1	yes	characteristic
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	3	yes	—
160	C₁₃×#102	C₂³	1	6	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
162	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	C₄×C₈×C₁₃	C₂³	1	3	yes	—
166	SD₁₆×#41	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	3	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	12	no	—
170	C₁₃×#41	—	4	12	no	—
171	C₁₃×#41	SD₁₆	1	8	yes	direct product factor
172	C₂×Q₈×C₁₃	—	2	3	no	—
173	C₂×Q₈×C₁₃	—	2	3	no	—
174	C₂×Q₈×C₁₃	—	2	3	no	—
175	C₂×Q₈×C₁₃	—	2	6	no	—
176	C₂×Q₈×C₁₃	—	4	3	no	—
177	C₂×Q₈×C₁₃	—	4	4	no	—
178	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
180	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂×D₄×C₁₃	—	2	6	no	—
182	C₂×D₄×C₁₃	—	2	6	no	—
183	C₂×D₄×C₁₃	—	2	3	no	—
184	C₂×D₄×C₁₃	—	2	3	no	—
185	C₂×D₄×C₁₃	—	2	3	no	—
186	C₂×D₄×C₁₃	—	4	3	no	—
187	C₂×D₄×C₁₃	—	4	12	no	—
188	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
189	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
190	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	—	2	3	no	—
192	C₂²×C₄×C₁₃	—	2	3	no	—
193	C₂²×C₄×C₁₃	—	2	3	no	—
194	C₂²×C₄×C₁₃	—	2	3	no	—
195	C₂²×C₄×C₁₃	—	2	3	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	3	no	—
198	C₂²×C₄×C₁₃	—	4	12	no	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
202	C₁₃×SD₁₆	—	2	6	no	—
203	C₁₃×SD₁₆	—	2	6	no	—
204	C₁₃×SD₁₆	—	2	6	no	—
205	C₁₃×SD₁₆	—	4	6	no	—
206	C₁₃×SD₁₆	#41	1	4	yes	direct product factor
207	C₂×C₈×C₁₃	—	2	6	no	—
208	C₂×C₈×C₁₃	—	4	3	no	—
209	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
211	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
212	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	3	no	—
216	C₁₃×C₄⋊C₄	—	2	3	no	—
217	C₁₃×C₄⋊C₄	—	2	3	no	—
218	C₁₃×C₄⋊C₄	—	2	3	no	—
219	C₁₃×C₄⋊C₄	—	2	3	no	—
220	C₁₃×C₄⋊C₄	—	2	3	no	—
221	C₁₃×C₄⋊C₄	—	2	3	no	—
222	C₁₃×C₄⋊C₄	—	2	3	no	—
223	C₁₃×C₄⋊C₄	—	2	6	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
230	C₁₃×C₂²⋊C₄	—	2	6	no	—
231	C₁₃×C₂²⋊C₄	—	2	1	no	—
232	C₁₃×C₂²⋊C₄	—	2	3	no	—
233	C₁₃×C₂²⋊C₄	—	2	3	no	—
234	C₁₃×C₂²⋊C₄	—	2	3	no	—
235	C₁₃×C₂²⋊C₄	—	2	6	no	—
236	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
237	C₄²×C₁₃	—	2	3	no	—
238	C₄²×C₁₃	—	2	3	no	—
239	C₄²×C₁₃	—	2	1	no	—
240	C₄²×C₁₃	—	2	3	no	—
241	C₄²×C₁₃	C₂×D₄	1	3	yes	—
242	C₄²×C₁₃	C₂×D₄	1	3	yes	—
243	C₄²×C₁₃	C₂⁴	1	3	yes	—
244	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
245	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
246	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
247	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
248	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3335	C₂×C₁₃	1	3	yes	complemented
252	#3298	C₂×C₁₃	1	3	yes	complemented
253	#3295	C₂×C₁₃	1	3	yes	complemented
254	D₄×SD₁₆	C₂×C₁₃	1	3	yes	complemented
255	#3167	C₂×C₁₃	1	3	yes	complemented
256	#3103	C₂×C₁₃	1	3	yes	complemented
257	#3101	C₂×C₁₃	1	3	yes	complemented
258	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×C₄×SD₁₆	C₂×C₁₃	1	3	yes	complemented
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	3	no	—
262	C₂³×C₁₃	—	4	6	no	—
263	C₂³×C₁₃	—	4	6	no	—
264	C₂³×C₁₃	—	8	3	no	—
265	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
266	Q₈×C₁₃	—	2	1	no	—
267	Q₈×C₁₃	—	2	3	no	—
268	Q₈×C₁₃	—	2	3	no	—
269	Q₈×C₁₃	—	4	6	no	—
270	Q₈×C₁₃	—	4	6	no	—
271	Q₈×C₁₃	—	8	3	no	—
272	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	complemented
273	Q₈×C₁₃	C₂×#41	1	2	yes	complemented
274	D₄×C₁₃	—	2	3	no	—
275	D₄×C₁₃	—	2	1	no	—
276	D₄×C₁₃	—	2	3	no	—
277	D₄×C₁₃	—	4	6	no	—
278	D₄×C₁₃	—	4	12	no	—
279	D₄×C₁₃	—	4	6	no	—
280	D₄×C₁₃	—	8	3	no	—
281	D₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
282	D₄×C₁₃	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	3	no	—
285	C₂×C₄×C₁₃	—	2	3	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	3	no	—
288	C₂×C₄×C₁₃	—	2	3	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	3	no	—
291	C₂×C₄×C₁₃	—	4	3	no	—
292	C₂×C₄×C₁₃	—	4	6	no	—
293	C₂×C₄×C₁₃	—	4	6	no	—
294	C₂×C₄×C₁₃	—	4	2	no	—
295	C₂×C₄×C₁₃	—	4	6	no	—
296	C₂×C₄×C₁₃	—	4	6	no	—
297	C₂×C₄×C₁₃	—	4	6	no	—
298	C₂×C₄×C₁₃	—	8	3	no	—
299	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
300	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
306	C₈×C₁₃	—	2	3	no	—
307	C₈×C₁₃	—	2	1	no	—
308	C₈×C₁₃	—	2	3	no	—
309	C₈×C₁₃	C₂×#41	1	2	yes	complemented
310	C₂²×#41	—	2	1	no	—
311	C₂²×SD₁₆	C₂²×C₁₃	1	3	yes	—
312	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	#557	—	2	1	no	—
314	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	#554	—	2	3	no	—
316	#554	C₂²×C₁₃	1	3	yes	complemented
317	#550	C₂²×C₁₃	1	1	yes	characteristic
318	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	D₄×Q₈	C₂²×C₁₃	1	3	yes	complemented
320	#548	—	2	1	no	—
321	#547	C₂²×C₁₃	1	3	yes	—
322	#546	—	2	3	no	—
323	D₄²	C₂²×C₁₃	1	3	yes	—
324	#533	—	2	3	no	—
325	#533	C₂²×C₁₃	1	3	yes	complemented
326	#532	C₂²×C₁₃	1	3	yes	—
327	#525	—	2	3	no	—
328	C₄×#41	—	2	1	no	—
329	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	complemented
331	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
332	#498	C₂²×C₁₃	1	3	yes	complemented
333	#492	C₂²×C₁₃	1	3	yes	complemented
334	#487	C₂²×C₁₃	1	3	yes	complemented
335	#486	C₂²×C₁₃	1	3	yes	complemented
336	#483	C₂²×C₁₃	1	6	yes	complemented
337	#481	C₂²×C₁₃	1	6	yes	complemented
338	#476	C₂²×C₁₃	1	3	yes	—
339	#476	C₂²×C₁₃	1	3	yes	complemented
340	#475	C₂²×C₁₃	1	3	yes	complemented
341	#475	C₂²×C₁₃	1	3	yes	complemented
342	#465	C₂²×C₁₃	1	6	yes	complemented
343	#465	C₂²×C₁₃	1	6	yes	complemented
344	#461	C₂²×C₁₃	1	3	yes	—
345	#461	C₂²×C₁₃	1	3	yes	complemented
346	#460	C₂²×C₁₃	1	3	yes	complemented
347	#460	C₂²×C₁₃	1	3	yes	complemented
348	#450	C₂²×C₁₃	1	6	yes	—
349	#448	C₂²×C₁₃	1	6	yes	complemented
350	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
351	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
352	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
353	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
354	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
355	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
356	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
357	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
358	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
359	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
360	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
361	C₈×D₄	C₂²×C₁₃	1	3	yes	complemented
362	C₈×D₄	C₂²×C₁₃	1	3	yes	complemented
363	#431	C₂²×C₁₃	1	3	yes	complemented
364	C₂×#106	C₂²×C₁₃	1	3	yes	complemented
365	C₂×#103	C₂²×C₁₃	1	3	yes	complemented
366	C₂×#102	C₂²×C₁₃	1	3	yes	—
367	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
368	C₂²×C₁₃	—	2	3	no	—
369	C₂²×C₁₃	—	2	3	no	—
370	C₂²×C₁₃	—	2	2	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	1	no	—
373	C₂²×C₁₃	—	4	3	no	—
374	C₂²×C₁₃	—	4	3	no	—
375	C₂²×C₁₃	—	4	3	no	—
376	C₂²×C₁₃	—	8	12	no	—
377	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
378	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₁₃	—	2	1	no	—
380	C₄×C₁₃	—	2	3	no	—
381	C₄×C₁₃	—	2	3	no	—
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	3	no	—
385	C₄×C₁₃	—	4	3	no	—
386	C₄×C₁₃	—	4	1	no	—
387	C₄×C₁₃	—	4	3	no	—
388	C₄×C₁₃	C₂²×SD₁₆	1	2	yes	—
389	C₄×C₁₃	C₂²×SD₁₆	1	6	yes	—
390	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
391	C₄×C₁₃	#585	1	1	yes	characteristic
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	3	no	—
394	C₂×#41	—	2	3	no	—
395	C₂×#41	—	4	8	no	—
396	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
397	C₂²×Q₈	—	2	1	no	—
398	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
399	C₂²×D₄	—	2	3	no	—
400	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
401	C₂³×C₄	—	2	3	no	—
402	C₂×SD₁₆	—	2	12	no	—
403	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
404	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
405	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
406	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
407	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
409	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
410	C₄⋊Q₈	—	2	3	no	—
411	C₄⋊Q₈	—	2	3	no	—
412	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
413	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
414	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
415	#127	C₂³×C₁₃	1	3	yes	—
416	#125	—	2	3	no	—
417	#125	—	2	3	no	—
418	#125	—	2	3	no	—
419	#124	—	2	3	no	—
420	#123	—	2	6	no	—
421	C₂²⋊Q₈	—	2	3	no	—
422	C₂²⋊Q₈	—	2	3	no	—
423	C₂²⋊Q₈	—	2	3	no	—
424	C₂²⋊Q₈	—	2	6	no	—
425	C₂²⋊Q₈	—	2	6	no	—
426	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
427	#121	—	2	3	no	—
428	#121	—	2	3	no	—
429	#121	—	2	3	no	—
430	#121	C₂³×C₁₃	1	6	yes	—
431	#120	—	2	6	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	3	no	—
435	C₄×Q₈	—	2	3	no	—
436	C₄×Q₈	—	2	3	no	—
437	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
438	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
440	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
441	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
442	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₄×D₄	—	2	3	no	—
444	C₄×D₄	—	2	3	no	—
445	C₄×D₄	—	2	3	no	—
446	C₄×D₄	—	2	3	no	—
447	C₄×D₄	—	2	3	no	—
448	C₄×D₄	D₄×C₁₃	1	3	yes	—
449	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₄×D₄	C₂³×C₁₃	1	3	yes	—
451	C₄×D₄	C₂³×C₁₃	1	3	yes	—
452	C₄×D₄	C₂³×C₁₃	1	3	yes	—
453	C₄×D₄	C₂³×C₁₃	1	3	yes	—
454	#117	—	2	3	no	—
455	#117	D₄×C₁₃	1	3	yes	—
456	C₂×C₄⋊C₄	—	2	3	no	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
459	C₂×C₂²⋊C₄	—	2	3	no	—
460	C₂×C₄²	—	2	3	no	—
461	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
462	#106	C₂³×C₁₃	1	1	yes	characteristic
463	#106	C₂³×C₁₃	1	3	yes	—
464	#106	C₂³×C₁₃	1	3	yes	—
465	#106	C₂³×C₁₃	1	3	yes	—
466	#106	C₂³×C₁₃	1	6	yes	—
467	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
468	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
469	#103	C₂³×C₁₃	1	1	yes	characteristic
470	#103	C₂³×C₁₃	1	3	yes	—
471	#103	C₂³×C₁₃	1	3	yes	—
472	#103	C₂³×C₁₃	1	3	yes	—
473	#103	C₂³×C₁₃	1	6	yes	—
474	#102	C₂³×C₁₃	1	1	yes	characteristic
475	#102	C₂³×C₁₃	1	3	yes	—
476	#102	C₂³×C₁₃	1	3	yes	—
477	#102	C₂³×C₁₃	1	3	yes	—
478	#102	C₂³×C₁₃	1	6	yes	—
479	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
480	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₄×C₈	C₂³×C₁₃	1	3	yes	—
482	C₄×C₈	C₂³×C₁₃	1	3	yes	—
483	C₄×C₈	C₂³×C₁₃	1	3	yes	—
484	C₂×C₁₃	—	2	6	no	—
485	C₂×C₁₃	—	4	2	no	—
486	C₂×C₁₃	—	8	3	no	—
487	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
488	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
489	C₂×C₁₃	#3584	1	1	yes	characteristic
490	C₂⁴	—	2	3	no	—
491	#41	—	4	4	no	—
492	#41	—	4	12	no	—
493	#41	—	4	12	no	—
494	#41	C₁₃×SD₁₆	1	8	yes	direct product factor
495	C₂×Q₈	—	2	3	no	—
496	C₂×Q₈	—	2	3	no	—
497	C₂×Q₈	—	2	3	no	—
498	C₂×Q₈	—	2	6	no	—
499	C₂×Q₈	—	4	3	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
503	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₂×D₄	—	2	6	no	—
505	C₂×D₄	—	2	6	no	—
506	C₂×D₄	—	2	3	no	—
507	C₂×D₄	—	2	3	no	—
508	C₂×D₄	—	2	3	no	—
509	C₂×D₄	—	4	3	no	—
510	C₂×D₄	—	4	12	no	—
511	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
512	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
513	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₂²×C₄	—	2	3	no	—
515	C₂²×C₄	—	2	3	no	—
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	3	no	—
519	C₂²×C₄	—	2	3	no	—
520	C₂²×C₄	—	2	3	no	—
521	C₂²×C₄	—	4	12	no	—
522	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
525	SD₁₆	—	2	6	no	—
526	SD₁₆	—	2	6	no	—
527	SD₁₆	—	2	6	no	—
528	SD₁₆	—	4	6	no	—
529	SD₁₆	C₁₃×#41	1	4	yes	direct product factor
530	C₂×C₈	—	2	6	no	—
531	C₂×C₈	—	4	3	no	—
532	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
534	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
535	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	3	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	—	2	3	no	—
540	C₄⋊C₄	—	2	3	no	—
541	C₄⋊C₄	—	2	3	no	—
542	C₄⋊C₄	—	2	3	no	—
543	C₄⋊C₄	—	2	3	no	—
544	C₄⋊C₄	—	2	3	no	—
545	C₄⋊C₄	—	2	3	no	—
546	C₄⋊C₄	—	2	6	no	—
547	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
548	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
549	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
551	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
553	C₂²⋊C₄	—	2	6	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	2	3	no	—
556	C₂²⋊C₄	—	2	3	no	—
557	C₂²⋊C₄	—	2	3	no	—
558	C₂²⋊C₄	—	2	6	no	—
559	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	3	no	—
562	C₄²	—	2	3	no	—
563	C₄²	—	2	3	no	—
564	C₄²	C₂×D₄×C₁₃	1	3	yes	—
565	C₄²	C₂×D₄×C₁₃	1	3	yes	—
566	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
567	C₄²	C₂⁴×C₁₃	1	3	yes	—
568	C₁₃	SD₁₆×#41	1	1	yes	characteristic, direct product factor, Sylow
569	C₂³	—	2	1	no	—
570	C₂³	—	2	3	no	—
571	C₂³	—	4	6	no	—
572	C₂³	—	4	6	no	—
573	C₂³	—	8	3	no	—
574	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
575	Q₈	—	2	1	no	—
576	Q₈	—	2	3	no	—
577	Q₈	—	2	3	no	—
578	Q₈	—	4	6	no	—
579	Q₈	—	4	6	no	—
580	Q₈	—	8	3	no	—
581	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	complemented
582	Q₈	C₂×C₁₃×#41	1	2	yes	complemented
583	D₄	—	2	3	no	—
584	D₄	—	2	1	no	—
585	D₄	—	2	3	no	—
586	D₄	—	4	6	no	—
587	D₄	—	4	12	no	—
588	D₄	—	4	6	no	—
589	D₄	—	8	3	no	—
590	D₄	C₂×C₁₃×SD₁₆	1	12	yes	complemented
591	D₄	C₂×C₁₃×#41	1	2	yes	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	2	3	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	3	no	—
600	C₂×C₄	—	4	3	no	—
601	C₂×C₄	—	4	6	no	—
602	C₂×C₄	—	4	6	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	6	no	—
605	C₂×C₄	—	4	6	no	—
606	C₂×C₄	—	4	6	no	—
607	C₂×C₄	—	8	3	no	—
608	C₂×C₄	C₂×C₁₃×SD₁₆	1	12	yes	complemented
609	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
611	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
614	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
615	C₈	—	2	3	no	—
616	C₈	—	2	1	no	—
617	C₈	—	2	3	no	—
618	C₈	C₂×C₁₃×#41	1	2	yes	complemented
619	C₂²	—	2	3	no	—
620	C₂²	—	2	3	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	3	no	—
625	C₂²	—	4	3	no	—
626	C₂²	—	4	3	no	—
627	C₂²	—	8	12	no	—
628	C₂²	C₂²×C₁₃×SD₁₆	1	6	yes	—
629	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
630	C₄	—	2	1	no	—
631	C₄	—	2	3	no	—
632	C₄	—	2	3	no	—
633	C₄	—	2	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	3	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	3	no	—
638	C₄	—	4	3	no	—
639	C₄	C₂²×C₁₃×SD₁₆	1	2	yes	—
640	C₄	C₂²×C₁₃×SD₁₆	1	6	yes	—
641	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
642	C₄	C₁₃×#585	1	1	yes	characteristic
643	C₂	—	2	6	no	—
644	C₂	—	4	2	no	—
645	C₂	—	8	3	no	—
646	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
647	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
648	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	D₄×C₁₃×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. Q₈×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3362	C₂	semidirect
6. C₁₃×#3359	C₂	semidirect
7. C₁₃×#3335	C₂	semidirect
8. C₁₃×#3298	C₂	semidirect
9. C₁₃×#3295	C₂	semidirect
10. D₄×C₁₃×SD₁₆	C₂	semidirect
11. C₁₃×#3167	C₂	semidirect
12. C₁₃×#3103	C₂	semidirect
13. C₁₃×#3101	C₂	semidirect
14. C₈×C₁₃×#41	C₂	semidirect
15. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
18. Q₈²×C₁₃	C₂²	semidirect
20. C₁₃×#557	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
31. C₁₃×#533	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
39. C₁₃×#492	C₂²	semidirect
40. C₁₃×#487	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#483	C₂²	semidirect
43. C₁₃×#481	C₂²	semidirect
45. C₁₃×#476	C₂²	semidirect
46. C₁₃×#475	C₂²	semidirect
47. C₁₃×#475	C₂²	semidirect
48. C₁₃×#465	C₂²	semidirect
49. C₁₃×#465	C₂²	semidirect
51. C₁₃×#461	C₂²	semidirect
52. C₁₃×#460	C₂²	semidirect
53. C₁₃×#460	C₂²	semidirect
55. C₁₃×#448	C₂²	semidirect
56. C₈×Q₈×C₁₃	C₂²	semidirect
57. C₈×Q₈×C₁₃	C₂²	semidirect
62. C₄×C₁₃×SD₁₆	C₂²	semidirect
63. C₄×C₁₃×SD₁₆	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
65. C₄×C₁₃×SD₁₆	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₈×D₄×C₁₃	C₂²	semidirect
68. C₈×D₄×C₁₃	C₂²	semidirect
69. C₁₃×#431	C₂²	semidirect
70. C₂×C₁₃×#106	C₂²	semidirect
71. C₂×C₁₃×#103	C₂²	semidirect
73. C₂×C₄×C₈×C₁₃	C₂²	semidirect
166. SD₁₆×#41	C₁₃	direct (N × H)
171. C₁₃×#41	SD₁₆	direct (N × H)
206. C₁₃×SD₁₆	#41	direct (N × H)
245. Q₈×#41	C₂×C₁₃	semidirect
247. #3392	C₂×C₁₃	semidirect
248. Q₈×SD₁₆	C₂×C₁₃	semidirect
249. #3362	C₂×C₁₃	semidirect
250. #3359	C₂×C₁₃	semidirect
251. #3335	C₂×C₁₃	semidirect
252. #3298	C₂×C₁₃	semidirect
253. #3295	C₂×C₁₃	semidirect
254. D₄×SD₁₆	C₂×C₁₃	semidirect
255. #3167	C₂×C₁₃	semidirect
256. #3103	C₂×C₁₃	semidirect
257. #3101	C₂×C₁₃	semidirect
258. C₈×#41	C₂×C₁₃	semidirect
259. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
272. Q₈×C₁₃	C₂×SD₁₆	semidirect
273. Q₈×C₁₃	C₂×#41	semidirect
281. D₄×C₁₃	C₂×SD₁₆	semidirect
299. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
309. C₈×C₁₃	C₂×#41	semidirect
312. Q₈²	C₂²×C₁₃	semidirect
314. #557	C₂²×C₁₃	semidirect
316. #554	C₂²×C₁₃	semidirect
319. D₄×Q₈	C₂²×C₁₃	semidirect
325. #533	C₂²×C₁₃	semidirect
330. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
332. #498	C₂²×C₁₃	semidirect
333. #492	C₂²×C₁₃	semidirect
334. #487	C₂²×C₁₃	semidirect
335. #486	C₂²×C₁₃	semidirect
336. #483	C₂²×C₁₃	semidirect
337. #481	C₂²×C₁₃	semidirect
339. #476	C₂²×C₁₃	semidirect
340. #475	C₂²×C₁₃	semidirect
341. #475	C₂²×C₁₃	semidirect
342. #465	C₂²×C₁₃	semidirect
343. #465	C₂²×C₁₃	semidirect
345. #461	C₂²×C₁₃	semidirect
346. #460	C₂²×C₁₃	semidirect
347. #460	C₂²×C₁₃	semidirect
349. #448	C₂²×C₁₃	semidirect
350. C₈×Q₈	C₂²×C₁₃	semidirect
351. C₈×Q₈	C₂²×C₁₃	semidirect
356. C₄×SD₁₆	C₂²×C₁₃	semidirect
357. C₄×SD₁₆	C₂²×C₁₃	semidirect
358. C₄×SD₁₆	C₂²×C₁₃	semidirect
359. C₄×SD₁₆	C₂²×C₁₃	semidirect
360. C₄×SD₁₆	C₂²×C₁₃	semidirect
361. C₈×D₄	C₂²×C₁₃	semidirect
362. C₈×D₄	C₂²×C₁₃	semidirect
363. #431	C₂²×C₁₃	semidirect
364. C₂×#106	C₂²×C₁₃	semidirect
365. C₂×#103	C₂²×C₁₃	semidirect
367. C₂×C₄×C₈	C₂²×C₁₃	semidirect
494. #41	C₁₃×SD₁₆	direct (N × H)
529. SD₁₆	C₁₃×#41	direct (N × H)
568. C₁₃	SD₁₆×#41	direct (N × H)
581. Q₈	C₂×C₁₃×SD₁₆	semidirect
582. Q₈	C₂×C₁₃×#41	semidirect
590. D₄	C₂×C₁₃×SD₁₆	semidirect
608. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect
618. C₈	C₂×C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×#41	2
D₄×C₁₃×#41	2
C₁₃×#3392	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3362	2
C₁₃×#3359	2
C₁₃×#3335	2
C₁₃×#3298	2
C₁₃×#3295	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3167	2
C₁₃×#3103	2
C₁₃×#3101	2
C₈×C₁₃×#41	2
C₂×C₄×C₁₃×SD₁₆	2
SD₁₆×#41	13

Subgroups — C13×SD16×#41 #15747765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×SD₁₆×#41 #15747765