Subgroups — C₁₃×D₈×#41 #15747764

Order 3328.

2406 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3334	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3294	C₂	1	6	yes	maximal, complemented
7	D₄×C₁₃×D₈	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3169	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3100	C₂	1	6	yes	maximal, complemented
10	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	3	yes	maximal, complemented
12	C₂²×C₁₃×#41	—	2	2	no	—
13	C₂²×C₁₃×D₈	C₂²	1	3	yes	—
14	C₁₃×#550	C₂²	1	2	yes	complemented
15	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
16	C₁₃×#548	—	2	2	no	—
17	C₁₃×#547	C₂²	1	6	yes	complemented
18	C₁₃×#546	—	2	6	no	—
19	D₄²×C₁₃	C₂²	1	6	yes	complemented
20	C₁₃×#532	C₂²	1	6	yes	complemented
21	C₁₃×#525	—	2	6	no	—
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
24	C₁₃×#500	C₂²	1	3	yes	complemented
25	C₁₃×#493	C₂²	1	3	yes	complemented
26	C₁₃×#486	C₂²	1	6	yes	complemented
27	C₁₃×#480	C₂²	1	12	yes	complemented
28	C₁₃×#474	C₂²	1	6	yes	complemented
29	C₁₃×#474	C₂²	1	6	yes	complemented
30	C₁₃×#466	C₂²	1	6	yes	complemented
31	C₁₃×#466	C₂²	1	6	yes	complemented
32	C₁₃×#459	C₂²	1	6	yes	complemented
33	C₁₃×#459	C₂²	1	6	yes	complemented
34	C₁₃×#447	C₂²	1	12	yes	complemented
35	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₁₃×D₈	C₂²	1	3	yes	—
38	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
40	C₄×C₁₃×D₈	C₂²	1	3	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
42	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
43	C₄×C₁₃×D₈	C₂²	1	3	yes	complemented
44	C₈×D₄×C₁₃	C₂²	1	3	yes	complemented
45	C₈×D₄×C₁₃	C₂²	1	3	yes	complemented
46	C₁₃×#431	C₂²	1	3	yes	complemented
47	C₂×C₁₃×#107	C₂²	1	3	yes	complemented
48	C₂×C₁₃×#102	C₂²	1	6	yes	complemented
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	2	6	no	—
52	C₂×C₁₃×#41	—	2	6	no	—
53	C₂×C₁₃×#41	—	4	16	no	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	6	no	—
57	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
58	C₂³×C₄×C₁₃	—	2	6	no	—
59	C₂×C₁₃×D₈	—	2	12	no	—
60	C₂×C₁₃×D₈	C₂³	1	6	yes	—
61	C₂×C₁₃×D₈	C₂³	1	3	yes	—
62	C₂×C₁₃×D₈	C₂³	1	6	yes	—
63	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
67	C₁₃×#127	C₂³	1	6	yes	—
68	C₁₃×#124	—	2	6	no	—
69	C₁₃×#123	—	2	12	no	—
70	C₁₃×C₂²⋊Q₈	—	2	6	no	—
71	C₁₃×C₂²⋊Q₈	—	2	6	no	—
72	C₁₃×#121	—	2	6	no	—
73	C₁₃×#121	—	2	6	no	—
74	C₁₃×#121	—	2	6	no	—
75	C₁₃×#121	C₂³	1	12	yes	—
76	C₁₃×#120	—	2	12	no	—
77	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₁₃	—	2	6	no	—
80	C₄×D₄×C₁₃	—	2	6	no	—
81	C₄×D₄×C₁₃	—	2	6	no	—
82	C₄×D₄×C₁₃	D₄	1	3	yes	—
83	C₄×D₄×C₁₃	C₂³	1	2	yes	—
84	C₄×D₄×C₁₃	C₂³	1	6	yes	—
85	C₄×D₄×C₁₃	C₂³	1	6	yes	—
86	C₄×D₄×C₁₃	C₂³	1	6	yes	—
87	C₄×D₄×C₁₃	C₂³	1	3	yes	—
88	C₁₃×#117	D₄	1	3	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
91	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
92	C₁₃×#107	C₂³	1	1	yes	characteristic
93	C₁₃×#107	C₂³	1	3	yes	—
94	C₁₃×#107	C₂³	1	6	yes	—
95	C₁₃×#107	C₂³	1	6	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
98	C₁₃×#102	C₂³	1	2	yes	—
99	C₁₃×#102	C₂³	1	6	yes	—
100	C₁₃×#102	C₂³	1	6	yes	—
101	C₁₃×#102	C₂³	1	6	yes	—
102	C₁₃×#102	C₂³	1	12	yes	—
103	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
104	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₁₃	C₂³	1	3	yes	—
106	C₄×C₈×C₁₃	C₂³	1	3	yes	—
107	C₄×C₈×C₁₃	C₂³	1	3	yes	—
108	D₈×#41	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	6	no	—
110	C₁₃×#41	—	4	8	no	—
111	C₁₃×#41	—	4	24	no	—
112	C₁₃×#41	—	4	24	no	—
113	C₁₃×#41	D₈	1	8	yes	direct product factor
114	C₂×Q₈×C₁₃	—	2	6	no	—
115	C₂×Q₈×C₁₃	—	4	8	no	—
116	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₁₃	—	2	12	no	—
118	C₂×D₄×C₁₃	—	2	12	no	—
119	C₂×D₄×C₁₃	—	2	6	no	—
120	C₂×D₄×C₁₃	—	2	6	no	—
121	C₂×D₄×C₁₃	—	2	6	no	—
122	C₂×D₄×C₁₃	—	4	6	no	—
123	C₂×D₄×C₁₃	—	4	24	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
125	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
126	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	6	no	—
128	C₂²×C₄×C₁₃	—	2	6	no	—
129	C₂²×C₄×C₁₃	—	2	6	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	6	no	—
132	C₂²×C₄×C₁₃	—	4	24	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
136	C₁₃×D₈	—	2	12	no	—
137	C₁₃×D₈	—	2	6	no	—
138	C₁₃×D₈	—	4	6	no	—
139	C₁₃×D₈	#41	1	4	yes	direct product factor
140	C₂×C₈×C₁₃	—	2	6	no	—
141	C₂×C₈×C₁₃	—	4	3	no	—
142	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	—	2	6	no	—
147	C₁₃×C₄⋊C₄	—	2	6	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
151	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	2	6	no	—
154	C₁₃×C₂²⋊C₄	—	2	6	no	—
155	C₁₃×C₂²⋊C₄	—	2	6	no	—
156	C₁₃×C₂²⋊C₄	—	2	12	no	—
157	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
158	C₄²×C₁₃	C₂×D₄	1	3	yes	—
159	C₄²×C₁₃	C₂×D₄	1	3	yes	—
160	C₄²×C₁₃	C₂⁴	1	3	yes	—
161	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
162	D₄×#41	C₂×C₁₃	1	2	yes	complemented
163	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
164	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#3358	C₂×C₁₃	1	2	yes	complemented
166	#3334	C₂×C₁₃	1	3	yes	complemented
167	#3294	C₂×C₁₃	1	6	yes	complemented
168	D₄×D₈	C₂×C₁₃	1	3	yes	complemented
169	#3169	C₂×C₁₃	1	3	yes	complemented
170	#3100	C₂×C₁₃	1	6	yes	complemented
171	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×C₄×D₈	C₂×C₁₃	1	3	yes	complemented
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	6	no	—
175	C₂³×C₁₃	—	4	12	no	—
176	C₂³×C₁₃	—	4	12	no	—
177	C₂³×C₁₃	—	8	6	no	—
178	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
179	Q₈×C₁₃	—	4	12	no	—
180	Q₈×C₁₃	C₂×D₈	1	4	yes	complemented
181	D₄×C₁₃	—	2	6	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	6	no	—
184	D₄×C₁₃	—	4	12	no	—
185	D₄×C₁₃	—	4	24	no	—
186	D₄×C₁₃	—	4	12	no	—
187	D₄×C₁₃	—	8	6	no	—
188	D₄×C₁₃	C₂×D₈	1	12	yes	complemented
189	D₄×C₁₃	C₂×#41	1	4	yes	complemented
190	C₂×C₄×C₁₃	—	2	3	no	—
191	C₂×C₄×C₁₃	—	2	3	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	6	no	—
194	C₂×C₄×C₁₃	—	4	3	no	—
195	C₂×C₄×C₁₃	—	4	12	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	12	no	—
198	C₂×C₄×C₁₃	—	4	12	no	—
199	C₂×C₄×C₁₃	—	4	12	no	—
200	C₂×C₄×C₁₃	C₂×D₈	1	12	yes	complemented
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
207	C₈×C₁₃	—	2	3	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	2	3	no	—
210	C₈×C₁₃	C₂×#41	1	2	yes	complemented
211	C₂²×#41	—	2	2	no	—
212	C₂²×D₈	C₂²×C₁₃	1	3	yes	—
213	#550	C₂²×C₁₃	1	2	yes	complemented
214	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
215	#548	—	2	2	no	—
216	#547	C₂²×C₁₃	1	6	yes	complemented
217	#546	—	2	6	no	—
218	D₄²	C₂²×C₁₃	1	6	yes	complemented
219	#532	C₂²×C₁₃	1	6	yes	complemented
220	#525	—	2	6	no	—
221	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
223	#500	C₂²×C₁₃	1	3	yes	complemented
224	#493	C₂²×C₁₃	1	3	yes	complemented
225	#486	C₂²×C₁₃	1	6	yes	complemented
226	#480	C₂²×C₁₃	1	12	yes	complemented
227	#474	C₂²×C₁₃	1	6	yes	complemented
228	#474	C₂²×C₁₃	1	6	yes	complemented
229	#466	C₂²×C₁₃	1	6	yes	complemented
230	#466	C₂²×C₁₃	1	6	yes	complemented
231	#459	C₂²×C₁₃	1	6	yes	complemented
232	#459	C₂²×C₁₃	1	6	yes	complemented
233	#447	C₂²×C₁₃	1	12	yes	complemented
234	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
235	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	C₄×D₈	C₂²×C₁₃	1	3	yes	—
237	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₄×D₈	C₂²×C₁₃	1	3	yes	complemented
239	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
240	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
241	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
242	C₄×D₈	C₂²×C₁₃	1	3	yes	complemented
243	C₈×D₄	C₂²×C₁₃	1	3	yes	complemented
244	C₈×D₄	C₂²×C₁₃	1	3	yes	complemented
245	#431	C₂²×C₁₃	1	3	yes	complemented
246	C₂×#107	C₂²×C₁₃	1	3	yes	complemented
247	C₂×#102	C₂²×C₁₃	1	6	yes	complemented
248	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
249	C₂²×C₁₃	—	2	3	no	—
250	C₂²×C₁₃	—	2	3	no	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	6	no	—
255	C₂²×C₁₃	—	4	6	no	—
256	C₂²×C₁₃	—	4	6	no	—
257	C₂²×C₁₃	—	8	24	no	—
258	C₂²×C₁₃	C₂²×D₈	1	6	yes	—
259	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	3	no	—
262	C₄×C₁₃	—	2	3	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	6	no	—
265	C₄×C₁₃	C₂²×D₈	1	2	yes	—
266	C₄×C₁₃	C₂²×D₈	1	6	yes	—
267	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
268	C₄×C₁₃	#585	1	1	yes	characteristic
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	6	no	—
271	C₂×#41	—	2	6	no	—
272	C₂×#41	—	4	16	no	—
273	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×D₄	—	2	6	no	—
276	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
277	C₂³×C₄	—	2	6	no	—
278	C₂×D₈	—	2	12	no	—
279	C₂×D₈	C₂³×C₁₃	1	6	yes	—
280	C₂×D₈	C₂³×C₁₃	1	3	yes	—
281	C₂×D₈	C₂³×C₁₃	1	6	yes	—
282	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
284	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
285	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
286	#127	C₂³×C₁₃	1	6	yes	—
287	#124	—	2	6	no	—
288	#123	—	2	12	no	—
289	C₂²⋊Q₈	—	2	6	no	—
290	C₂²⋊Q₈	—	2	6	no	—
291	#121	—	2	6	no	—
292	#121	—	2	6	no	—
293	#121	—	2	6	no	—
294	#121	C₂³×C₁₃	1	12	yes	—
295	#120	—	2	12	no	—
296	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	6	no	—
299	C₄×D₄	—	2	6	no	—
300	C₄×D₄	—	2	6	no	—
301	C₄×D₄	D₄×C₁₃	1	3	yes	—
302	C₄×D₄	C₂³×C₁₃	1	2	yes	—
303	C₄×D₄	C₂³×C₁₃	1	6	yes	—
304	C₄×D₄	C₂³×C₁₃	1	6	yes	—
305	C₄×D₄	C₂³×C₁₃	1	6	yes	—
306	C₄×D₄	C₂³×C₁₃	1	3	yes	—
307	#117	D₄×C₁₃	1	3	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
309	C₂×C₂²⋊C₄	—	2	6	no	—
310	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
311	#107	C₂³×C₁₃	1	1	yes	characteristic
312	#107	C₂³×C₁₃	1	3	yes	—
313	#107	C₂³×C₁₃	1	6	yes	—
314	#107	C₂³×C₁₃	1	6	yes	—
315	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
316	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
317	#102	C₂³×C₁₃	1	2	yes	—
318	#102	C₂³×C₁₃	1	6	yes	—
319	#102	C₂³×C₁₃	1	6	yes	—
320	#102	C₂³×C₁₃	1	6	yes	—
321	#102	C₂³×C₁₃	1	12	yes	—
322	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
323	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₁₃	1	3	yes	—
325	C₄×C₈	C₂³×C₁₃	1	3	yes	—
326	C₄×C₈	C₂³×C₁₃	1	3	yes	—
327	C₂×C₁₃	—	2	6	no	—
328	C₂×C₁₃	—	4	4	no	—
329	C₂×C₁₃	—	8	6	no	—
330	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
331	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
332	C₂×C₁₃	#3584	1	1	yes	characteristic
333	C₂⁴	—	2	6	no	—
334	#41	—	4	8	no	—
335	#41	—	4	24	no	—
336	#41	—	4	24	no	—
337	#41	C₁₃×D₈	1	8	yes	direct product factor
338	C₂×Q₈	—	2	6	no	—
339	C₂×Q₈	—	4	8	no	—
340	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	—	2	6	no	—
344	C₂×D₄	—	2	6	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	4	6	no	—
347	C₂×D₄	—	4	24	no	—
348	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
349	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
350	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	—	2	6	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	6	no	—
354	C₂²×C₄	—	2	6	no	—
355	C₂²×C₄	—	2	6	no	—
356	C₂²×C₄	—	4	24	no	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
360	D₈	—	2	12	no	—
361	D₈	—	2	6	no	—
362	D₈	—	4	6	no	—
363	D₈	C₁₃×#41	1	4	yes	direct product factor
364	C₂×C₈	—	2	6	no	—
365	C₂×C₈	—	4	3	no	—
366	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
368	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
369	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	6	no	—
371	C₄⋊C₄	—	2	6	no	—
372	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
373	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
374	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
375	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	6	no	—
378	C₂²⋊C₄	—	2	6	no	—
379	C₂²⋊C₄	—	2	6	no	—
380	C₂²⋊C₄	—	2	12	no	—
381	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
382	C₄²	C₂×D₄×C₁₃	1	3	yes	—
383	C₄²	C₂×D₄×C₁₃	1	3	yes	—
384	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₄²	C₂⁴×C₁₃	1	3	yes	—
386	C₁₃	D₈×#41	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	6	no	—
389	C₂³	—	4	12	no	—
390	C₂³	—	4	12	no	—
391	C₂³	—	8	6	no	—
392	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
393	Q₈	—	4	12	no	—
394	Q₈	C₂×C₁₃×D₈	1	4	yes	complemented
395	D₄	—	2	6	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	6	no	—
398	D₄	—	4	12	no	—
399	D₄	—	4	24	no	—
400	D₄	—	4	12	no	—
401	D₄	—	8	6	no	—
402	D₄	C₂×C₁₃×D₈	1	12	yes	complemented
403	D₄	C₂×C₁₃×#41	1	4	yes	complemented
404	C₂×C₄	—	2	3	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	6	no	—
408	C₂×C₄	—	4	3	no	—
409	C₂×C₄	—	4	12	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	12	no	—
412	C₂×C₄	—	4	12	no	—
413	C₂×C₄	—	4	12	no	—
414	C₂×C₄	C₂×C₁₃×D₈	1	12	yes	complemented
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
420	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
421	C₈	—	2	3	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	3	no	—
424	C₈	C₂×C₁₃×#41	1	2	yes	complemented
425	C₂²	—	2	3	no	—
426	C₂²	—	2	3	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	6	no	—
431	C₂²	—	4	6	no	—
432	C₂²	—	4	6	no	—
433	C₂²	—	8	24	no	—
434	C₂²	C₂²×C₁₃×D₈	1	6	yes	—
435	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	3	no	—
438	C₄	—	2	3	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	6	no	—
441	C₄	C₂²×C₁₃×D₈	1	2	yes	—
442	C₄	C₂²×C₁₃×D₈	1	6	yes	—
443	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
444	C₄	C₁₃×#585	1	1	yes	characteristic
445	C₂	—	2	6	no	—
446	C₂	—	4	4	no	—
447	C₂	—	8	6	no	—
448	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
449	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
450	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
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. D₄×C₁₃×#41	C₂	semidirect
2. C₁₃×#3391	C₂	semidirect
3. Q₈×C₁₃×D₈	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3334	C₂	semidirect
6. C₁₃×#3294	C₂	semidirect
7. D₄×C₁₃×D₈	C₂	semidirect
8. C₁₃×#3169	C₂	semidirect
9. C₁₃×#3100	C₂	semidirect
10. C₈×C₁₃×#41	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
14. C₁₃×#550	C₂²	semidirect
15. D₄×Q₈×C₁₃	C₂²	semidirect
17. C₁₃×#547	C₂²	semidirect
19. D₄²×C₁₃	C₂²	semidirect
20. C₁₃×#532	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
24. C₁₃×#500	C₂²	semidirect
25. C₁₃×#493	C₂²	semidirect
26. C₁₃×#486	C₂²	semidirect
27. C₁₃×#480	C₂²	semidirect
28. C₁₃×#474	C₂²	semidirect
29. C₁₃×#474	C₂²	semidirect
30. C₁₃×#466	C₂²	semidirect
31. C₁₃×#466	C₂²	semidirect
32. C₁₃×#459	C₂²	semidirect
33. C₁₃×#459	C₂²	semidirect
34. C₁₃×#447	C₂²	semidirect
35. C₈×Q₈×C₁₃	C₂²	semidirect
36. C₈×Q₈×C₁₃	C₂²	semidirect
39. C₄×C₁₃×D₈	C₂²	semidirect
40. C₄×C₁₃×D₈	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₄×C₁₃×D₈	C₂²	semidirect
43. C₄×C₁₃×D₈	C₂²	semidirect
44. C₈×D₄×C₁₃	C₂²	semidirect
45. C₈×D₄×C₁₃	C₂²	semidirect
46. C₁₃×#431	C₂²	semidirect
47. C₂×C₁₃×#107	C₂²	semidirect
48. C₂×C₁₃×#102	C₂²	semidirect
49. C₂×C₄×C₈×C₁₃	C₂²	semidirect
108. D₈×#41	C₁₃	direct (N × H)
113. C₁₃×#41	D₈	direct (N × H)
139. C₁₃×D₈	#41	direct (N × H)
162. D₄×#41	C₂×C₁₃	semidirect
163. #3391	C₂×C₁₃	semidirect
164. Q₈×D₈	C₂×C₁₃	semidirect
165. #3358	C₂×C₁₃	semidirect
166. #3334	C₂×C₁₃	semidirect
167. #3294	C₂×C₁₃	semidirect
168. D₄×D₈	C₂×C₁₃	semidirect
169. #3169	C₂×C₁₃	semidirect
170. #3100	C₂×C₁₃	semidirect
171. C₈×#41	C₂×C₁₃	semidirect
172. C₂×C₄×D₈	C₂×C₁₃	semidirect
180. Q₈×C₁₃	C₂×D₈	semidirect
188. D₄×C₁₃	C₂×D₈	semidirect
189. D₄×C₁₃	C₂×#41	semidirect
200. C₂×C₄×C₁₃	C₂×D₈	semidirect
210. C₈×C₁₃	C₂×#41	semidirect
213. #550	C₂²×C₁₃	semidirect
214. D₄×Q₈	C₂²×C₁₃	semidirect
216. #547	C₂²×C₁₃	semidirect
218. D₄²	C₂²×C₁₃	semidirect
219. #532	C₂²×C₁₃	semidirect
222. C₂×C₄×D₄	C₂²×C₁₃	semidirect
223. #500	C₂²×C₁₃	semidirect
224. #493	C₂²×C₁₃	semidirect
225. #486	C₂²×C₁₃	semidirect
226. #480	C₂²×C₁₃	semidirect
227. #474	C₂²×C₁₃	semidirect
228. #474	C₂²×C₁₃	semidirect
229. #466	C₂²×C₁₃	semidirect
230. #466	C₂²×C₁₃	semidirect
231. #459	C₂²×C₁₃	semidirect
232. #459	C₂²×C₁₃	semidirect
233. #447	C₂²×C₁₃	semidirect
234. C₈×Q₈	C₂²×C₁₃	semidirect
235. C₈×Q₈	C₂²×C₁₃	semidirect
238. C₄×D₈	C₂²×C₁₃	semidirect
239. C₄×D₈	C₂²×C₁₃	semidirect
240. C₄×D₈	C₂²×C₁₃	semidirect
241. C₄×D₈	C₂²×C₁₃	semidirect
242. C₄×D₈	C₂²×C₁₃	semidirect
243. C₈×D₄	C₂²×C₁₃	semidirect
244. C₈×D₄	C₂²×C₁₃	semidirect
245. #431	C₂²×C₁₃	semidirect
246. C₂×#107	C₂²×C₁₃	semidirect
247. C₂×#102	C₂²×C₁₃	semidirect
248. C₂×C₄×C₈	C₂²×C₁₃	semidirect
337. #41	C₁₃×D₈	direct (N × H)
363. D₈	C₁₃×#41	direct (N × H)
386. C₁₃	D₈×#41	direct (N × H)
394. Q₈	C₂×C₁₃×D₈	semidirect
402. D₄	C₂×C₁₃×D₈	semidirect
403. D₄	C₂×C₁₃×#41	semidirect
414. C₂×C₄	C₂×C₁₃×D₈	semidirect
424. 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
D₄×C₁₃×#41	2
C₁₃×#3391	2
Q₈×C₁₃×D₈	2
C₁₃×#3358	2
C₁₃×#3334	2
C₁₃×#3294	2
D₄×C₁₃×D₈	2
C₁₃×#3169	2
C₁₃×#3100	2
C₈×C₁₃×#41	2
C₂×C₄×C₁₃×D₈	2
D₈×#41	13

Subgroups — C13×D8×#41 #15747764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₈×#41 #15747764