Subgroups — C₁₃×Q₁₆×#41 #15747768

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 406 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	2	yes	maximal
2	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3338	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3299	C₂	1	6	yes	maximal, complemented
7	D₄×C₁₃×Q₁₆	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3170	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3104	C₂	1	6	yes	maximal, complemented
10	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	3	yes	maximal, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	3	yes	—
13	Q₈²×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#557	C₂²	1	2	yes	—
16	C₁₃×#554	—	2	6	no	—
17	C₁₃×#554	C₂²	1	6	yes	—
18	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
19	C₁₃×#533	—	2	6	no	—
20	C₁₃×#533	C₂²	1	6	yes	—
21	C₄×C₁₃×#41	—	2	2	no	—
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
24	C₁₃×#500	C₂²	1	3	yes	—
25	C₁₃×#494	C₂²	1	3	yes	—
26	C₁₃×#487	C₂²	1	6	yes	—
27	C₁₃×#484	C₂²	1	12	yes	—
28	C₁₃×#477	C₂²	1	6	yes	—
29	C₁₃×#477	C₂²	1	6	yes	—
30	C₁₃×#467	C₂²	1	6	yes	—
31	C₁₃×#467	C₂²	1	6	yes	—
32	C₁₃×#462	C₂²	1	6	yes	—
33	C₁₃×#462	C₂²	1	6	yes	—
34	C₁₃×#451	C₂²	1	12	yes	—
35	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
38	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
39	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
40	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
41	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
42	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
43	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₁₃	C₂²	1	3	yes	—
45	C₈×D₄×C₁₃	C₂²	1	3	yes	—
46	C₁₃×#431	C₂²	1	3	yes	—
47	C₂×C₁₃×#107	C₂²	1	3	yes	—
48	C₂×C₁₃×#103	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
50	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
52	C₂×C₁₃×Q₁₆	—	2	12	no	—
53	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
54	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
55	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
56	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
59	C₁₃×C₄⋊Q₈	—	2	6	no	—
60	C₁₃×C₄⋊Q₈	—	2	6	no	—
61	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₃×#125	—	2	6	no	—
64	C₁₃×#125	—	2	6	no	—
65	C₁₃×#125	—	2	6	no	—
66	C₁₃×C₂²⋊Q₈	—	2	6	no	—
67	C₁₃×C₂²⋊Q₈	—	2	12	no	—
68	C₁₃×C₂²⋊Q₈	—	2	12	no	—
69	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	6	no	—
73	C₄×Q₈×C₁₃	—	2	6	no	—
74	C₄×Q₈×C₁₃	—	2	6	no	—
75	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₁₃	—	2	6	no	—
82	C₄×D₄×C₁₃	—	2	6	no	—
83	C₄×D₄×C₁₃	D₄	1	3	yes	—
84	C₄×D₄×C₁₃	C₂³	1	3	yes	—
85	C₁₃×#117	—	2	6	no	—
86	C₁₃×#117	D₄	1	3	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₃	—	2	6	no	—
90	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
91	C₁₃×#107	C₂³	1	1	yes	characteristic
92	C₁₃×#107	C₂³	1	3	yes	—
93	C₁₃×#107	C₂³	1	6	yes	—
94	C₁₃×#107	C₂³	1	6	yes	—
95	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₃×#103	C₂³	1	2	yes	—
98	C₁₃×#103	C₂³	1	6	yes	—
99	C₁₃×#103	C₂³	1	6	yes	—
100	C₁₃×#103	C₂³	1	6	yes	—
101	C₁₃×#103	C₂³	1	12	yes	—
102	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×C₈×C₁₃	C₂³	1	3	yes	—
105	C₄×C₈×C₁₃	C₂³	1	3	yes	—
106	C₄×C₈×C₁₃	C₂³	1	3	yes	—
107	Q₁₆×#41	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₁₃×#41	Q₁₆	1	8	yes	direct product factor
109	C₂×Q₈×C₁₃	—	2	6	no	—
110	C₂×Q₈×C₁₃	—	2	6	no	—
111	C₂×Q₈×C₁₃	—	2	12	no	—
112	C₂×Q₈×C₁₃	—	4	6	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
115	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
116	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₁₃	—	2	6	no	—
118	C₂²×C₄×C₁₃	—	2	6	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
122	C₁₃×Q₁₆	—	2	12	no	—
123	C₁₃×Q₁₆	—	2	6	no	—
124	C₁₃×Q₁₆	—	4	6	no	—
125	C₁₃×Q₁₆	#41	1	4	yes	direct product factor
126	C₂×C₈×C₁₃	—	2	6	no	—
127	C₂×C₈×C₁₃	—	4	3	no	—
128	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
130	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
131	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	6	no	—
134	C₁₃×C₄⋊C₄	—	2	6	no	—
135	C₁₃×C₄⋊C₄	—	2	6	no	—
136	C₁₃×C₄⋊C₄	—	2	6	no	—
137	C₁₃×C₄⋊C₄	—	2	6	no	—
138	C₁₃×C₄⋊C₄	—	2	6	no	—
139	C₁₃×C₄⋊C₄	—	2	6	no	—
140	C₁₃×C₄⋊C₄	—	2	12	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
145	C₁₃×C₂²⋊C₄	—	2	12	no	—
146	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
147	C₄²×C₁₃	—	2	6	no	—
148	C₄²×C₁₃	—	2	6	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	6	no	—
151	C₄²×C₁₃	C₂×D₄	1	3	yes	—
152	C₄²×C₁₃	C₂×D₄	1	3	yes	—
153	C₄²×C₁₃	C₂⁴	1	3	yes	—
154	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
155	Q₈×#41	C₂×C₁₃	1	2	yes	—
156	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
157	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#3363	C₂×C₁₃	1	2	yes	complemented
159	#3338	C₂×C₁₃	1	3	yes	complemented
160	#3299	C₂×C₁₃	1	6	yes	complemented
161	D₄×Q₁₆	C₂×C₁₃	1	3	yes	complemented
162	#3170	C₂×C₁₃	1	3	yes	complemented
163	#3104	C₂×C₁₃	1	6	yes	complemented
164	C₈×#41	C₂×C₁₃	1	1	yes	characteristic
165	C₂×C₄×Q₁₆	C₂×C₁₃	1	3	yes	complemented
166	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	2	6	no	—
169	Q₈×C₁₃	—	2	6	no	—
170	Q₈×C₁₃	—	4	12	no	—
171	Q₈×C₁₃	—	8	6	no	—
172	Q₈×C₁₃	C₂×Q₁₆	1	4	yes	complemented
173	Q₈×C₁₃	C₂×#41	1	4	yes	—
174	D₄×C₁₃	C₂×Q₁₆	1	12	yes	complemented
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	3	no	—
177	C₂×C₄×C₁₃	—	2	3	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	6	no	—
180	C₂×C₄×C₁₃	—	2	6	no	—
181	C₂×C₄×C₁₃	—	4	3	no	—
182	C₂×C₄×C₁₃	—	4	12	no	—
183	C₂×C₄×C₁₃	—	8	6	no	—
184	C₂×C₄×C₁₃	C₂×Q₁₆	1	12	yes	complemented
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
191	C₈×C₁₃	—	2	3	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	—	2	3	no	—
194	C₈×C₁₃	C₂×#41	1	2	yes	—
195	C₂²×Q₁₆	C₂²×C₁₃	1	3	yes	—
196	Q₈²	C₂²×C₁₃	1	2	yes	—
197	#557	—	2	2	no	—
198	#557	C₂²×C₁₃	1	2	yes	—
199	#554	—	2	6	no	—
200	#554	C₂²×C₁₃	1	6	yes	—
201	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
202	#533	—	2	6	no	—
203	#533	C₂²×C₁₃	1	6	yes	—
204	C₄×#41	—	2	2	no	—
205	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
207	#500	C₂²×C₁₃	1	3	yes	—
208	#494	C₂²×C₁₃	1	3	yes	—
209	#487	C₂²×C₁₃	1	6	yes	—
210	#484	C₂²×C₁₃	1	12	yes	—
211	#477	C₂²×C₁₃	1	6	yes	—
212	#477	C₂²×C₁₃	1	6	yes	—
213	#467	C₂²×C₁₃	1	6	yes	—
214	#467	C₂²×C₁₃	1	6	yes	—
215	#462	C₂²×C₁₃	1	6	yes	—
216	#462	C₂²×C₁₃	1	6	yes	—
217	#451	C₂²×C₁₃	1	12	yes	—
218	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
221	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
222	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
223	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
224	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
225	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
226	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
227	C₈×D₄	C₂²×C₁₃	1	3	yes	—
228	C₈×D₄	C₂²×C₁₃	1	3	yes	—
229	#431	C₂²×C₁₃	1	3	yes	—
230	C₂×#107	C₂²×C₁₃	1	3	yes	—
231	C₂×#103	C₂²×C₁₃	1	6	yes	—
232	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
233	C₂²×C₁₃	—	2	3	no	—
234	C₂²×C₁₃	—	2	3	no	—
235	C₂²×C₁₃	C₂²×Q₁₆	1	6	yes	—
236	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	3	no	—
239	C₄×C₁₃	—	2	3	no	—
240	C₄×C₁₃	—	2	4	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	4	6	no	—
243	C₄×C₁₃	—	4	6	no	—
244	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
245	C₄×C₁₃	C₂²×Q₁₆	1	6	yes	—
246	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
247	C₄×C₁₃	#585	1	1	yes	characteristic
248	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
250	C₂×Q₁₆	—	2	12	no	—
251	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
252	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
253	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
254	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
257	C₄⋊Q₈	—	2	6	no	—
258	C₄⋊Q₈	—	2	6	no	—
259	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
260	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
261	#125	—	2	6	no	—
262	#125	—	2	6	no	—
263	#125	—	2	6	no	—
264	C₂²⋊Q₈	—	2	6	no	—
265	C₂²⋊Q₈	—	2	12	no	—
266	C₂²⋊Q₈	—	2	12	no	—
267	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	6	no	—
271	C₄×Q₈	—	2	6	no	—
272	C₄×Q₈	—	2	6	no	—
273	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
274	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
275	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
276	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
277	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
278	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄×D₄	—	2	6	no	—
280	C₄×D₄	—	2	6	no	—
281	C₄×D₄	D₄×C₁₃	1	3	yes	—
282	C₄×D₄	C₂³×C₁₃	1	3	yes	—
283	#117	—	2	6	no	—
284	#117	D₄×C₁₃	1	3	yes	—
285	C₂×C₄⋊C₄	—	2	6	no	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
287	C₂×C₄²	—	2	6	no	—
288	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
289	#107	C₂³×C₁₃	1	1	yes	characteristic
290	#107	C₂³×C₁₃	1	3	yes	—
291	#107	C₂³×C₁₃	1	6	yes	—
292	#107	C₂³×C₁₃	1	6	yes	—
293	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
294	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
295	#103	C₂³×C₁₃	1	2	yes	—
296	#103	C₂³×C₁₃	1	6	yes	—
297	#103	C₂³×C₁₃	1	6	yes	—
298	#103	C₂³×C₁₃	1	6	yes	—
299	#103	C₂³×C₁₃	1	12	yes	—
300	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
301	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₁₃	1	3	yes	—
303	C₄×C₈	C₂³×C₁₃	1	3	yes	—
304	C₄×C₈	C₂³×C₁₃	1	3	yes	—
305	C₂×C₁₃	—	2	6	no	—
306	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
307	C₂×C₁₃	C₂³×Q₁₆	1	1	yes	characteristic
308	C₂×C₁₃	#3584	1	1	yes	characteristic
309	#41	C₁₃×Q₁₆	1	8	yes	direct product factor
310	C₂×Q₈	—	2	6	no	—
311	C₂×Q₈	—	2	6	no	—
312	C₂×Q₈	—	2	12	no	—
313	C₂×Q₈	—	4	6	no	—
314	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
316	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
317	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
318	C₂²×C₄	—	2	6	no	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
322	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
323	Q₁₆	—	2	12	no	—
324	Q₁₆	—	2	6	no	—
325	Q₁₆	—	4	6	no	—
326	Q₁₆	C₁₃×#41	1	4	yes	direct product factor
327	C₂×C₈	—	2	6	no	—
328	C₂×C₈	—	4	3	no	—
329	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
330	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
331	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
332	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	6	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	12	no	—
342	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
343	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
344	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
345	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
346	C₂²⋊C₄	—	2	12	no	—
347	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	6	no	—
350	C₄²	—	2	6	no	—
351	C₄²	—	2	6	no	—
352	C₄²	C₂×D₄×C₁₃	1	3	yes	—
353	C₄²	C₂×D₄×C₁₃	1	3	yes	—
354	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
355	C₄²	C₂⁴×C₁₃	1	3	yes	—
356	C₁₃	Q₁₆×#41	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	6	no	—
360	Q₈	—	2	6	no	—
361	Q₈	—	4	12	no	—
362	Q₈	—	8	6	no	—
363	Q₈	C₂×C₁₃×Q₁₆	1	4	yes	complemented
364	Q₈	C₂×C₁₃×#41	1	4	yes	—
365	D₄	C₂×C₁₃×Q₁₆	1	12	yes	complemented
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	3	no	—
368	C₂×C₄	—	2	3	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	4	3	no	—
373	C₂×C₄	—	4	12	no	—
374	C₂×C₄	—	8	6	no	—
375	C₂×C₄	C₂×C₁₃×Q₁₆	1	12	yes	complemented
376	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
378	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
381	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
382	C₈	—	2	3	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	3	no	—
385	C₈	C₂×C₁₃×#41	1	2	yes	—
386	C₂²	—	2	3	no	—
387	C₂²	—	2	3	no	—
388	C₂²	C₂²×C₁₃×Q₁₆	1	6	yes	—
389	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	3	no	—
392	C₄	—	2	3	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	6	no	—
397	C₄	C₂²×C₁₃×Q₁₆	1	2	yes	—
398	C₄	C₂²×C₁₃×Q₁₆	1	6	yes	—
399	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
400	C₄	C₁₃×#585	1	1	yes	characteristic
401	C₂	—	2	6	no	—
402	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
403	C₂	C₂³×C₁₃×Q₁₆	1	1	yes	characteristic
404	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	C₂×C₁₃×#41	D₄
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
2. C₁₃×#3395	C₂	semidirect
3. Q₈×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#3363	C₂	semidirect
5. C₁₃×#3338	C₂	semidirect
6. C₁₃×#3299	C₂	semidirect
7. D₄×C₁₃×Q₁₆	C₂	semidirect
8. C₁₃×#3170	C₂	semidirect
9. C₁₃×#3104	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
107. Q₁₆×#41	C₁₃	direct (N × H)
108. C₁₃×#41	Q₁₆	direct (N × H)
125. C₁₃×Q₁₆	#41	direct (N × H)
156. #3395	C₂×C₁₃	semidirect
157. Q₈×Q₁₆	C₂×C₁₃	semidirect
158. #3363	C₂×C₁₃	semidirect
159. #3338	C₂×C₁₃	semidirect
160. #3299	C₂×C₁₃	semidirect
161. D₄×Q₁₆	C₂×C₁₃	semidirect
162. #3170	C₂×C₁₃	semidirect
163. #3104	C₂×C₁₃	semidirect
165. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
172. Q₈×C₁₃	C₂×Q₁₆	semidirect
174. D₄×C₁₃	C₂×Q₁₆	semidirect
184. C₂×C₄×C₁₃	C₂×Q₁₆	semidirect
309. #41	C₁₃×Q₁₆	direct (N × H)
326. Q₁₆	C₁₃×#41	direct (N × H)
356. C₁₃	Q₁₆×#41	direct (N × H)
363. Q₈	C₂×C₁₃×Q₁₆	semidirect
365. D₄	C₂×C₁₃×Q₁₆	semidirect
375. C₂×C₄	C₂×C₁₃×Q₁₆	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
C₁₃×#3395	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3363	2
C₁₃×#3338	2
C₁₃×#3299	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3170	2
C₁₃×#3104	2
C₈×C₁₃×#41	2
C₂×C₄×C₁₃×Q₁₆	2
Q₁₆×#41	13

Subgroups — C13×Q16×#41 #15747768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×Q₁₆×#41 #15747768