Subgroups — D₄×C₁₃×SD₃₂ #15720186

Order 3328.

738 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	C₂²×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	D₄×Q₈×C₁₃	—	2	1	no	—
15	D₄²×C₁₃	—	2	1	no	—
16	C₂×C₁₃×SD₃₂	—	2	8	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
23	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#493	C₂²	1	1	yes	characteristic
25	C₁₃×#467	C₂²	1	2	yes	complemented
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#462	—	2	1	no	—
28	C₁₃×#459	—	2	1	no	—
29	C₁₃×#451	—	2	2	no	—
30	C₁₃×#447	—	2	2	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#367	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#358	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	1	yes	characteristic
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₂×C₁₃×Q₁₆	—	2	4	no	—
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	4	2	no	—
49	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×D₈	—	2	4	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	4	2	no	—
55	C₂×C₁₃×D₈	C₂³	1	2	yes	—
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	4	1	no	—
60	C₁₃×#127	—	2	1	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	4	2	no	—
63	C₁₃×#121	—	2	2	no	—
64	C₁₃×#121	—	4	1	no	—
65	C₁₃×#120	—	4	2	no	—
66	C₄×Q₈×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	—	4	1	no	—
69	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₁₃×SD₃₂	—	2	4	no	—
71	C₁₃×SD₃₂	—	2	4	no	—
72	C₁₃×SD₃₂	—	2	4	no	—
73	C₁₃×SD₃₂	—	4	2	no	—
74	C₁₃×SD₃₂	D₄	1	4	yes	direct product factor
75	C₂×C₁₃×C₁₆	—	2	4	no	—
76	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₃×#103	—	2	1	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	D₄×SD₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	4	2	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	4	2	no	—
94	C₂×Q₈×C₁₃	—	8	2	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	—	8	2	no	—
103	C₂×D₄×C₁₃	—	8	4	no	—
104	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	—	2	2	no	—
111	C₁₃×Q₁₆	—	4	4	no	—
112	C₁₃×Q₁₆	—	8	1	no	—
113	C₁₃×Q₁₆	C₂×D₄	1	2	yes	complemented
114	C₁₃×D₈	—	2	2	no	—
115	C₁₃×D₈	—	2	1	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	4	4	no	—
118	C₁₃×D₈	—	8	1	no	—
119	C₁₃×D₈	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	4	1	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
136	C₄²×C₁₃	—	4	1	no	—
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	1	no	—
140	C₁₃×C₁₆	C₂×D₄	1	2	yes	complemented
141	C₂²×SD₃₂	C₂×C₁₃	1	2	yes	complemented
142	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
143	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic
144	#2248	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2217	C₂×C₁₃	1	2	yes	complemented
146	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2187	C₂×C₁₃	1	2	yes	complemented
149	#2185	C₂×C₁₃	1	2	yes	complemented
150	C₄×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
151	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	8	4	no	—
155	C₂³×C₁₃	—	8	4	no	—
156	C₂³×C₁₃	—	16	2	no	—
157	C₂³×C₁₃	C₂×D₈	1	2	yes	—
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	8	4	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	8	4	no	—
168	D₄×C₁₃	—	8	4	no	—
169	D₄×C₁₃	—	8	2	no	—
170	D₄×C₁₃	—	16	1	no	—
171	D₄×C₁₃	SD₃₂	1	4	yes	direct product factor
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	4	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
189	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
190	D₄×Q₈	—	2	1	no	—
191	D₄²	—	2	1	no	—
192	C₂×SD₃₂	—	2	8	no	—
193	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
194	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
196	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
197	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
198	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
199	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
200	#493	C₂²×C₁₃	1	1	yes	characteristic
201	#467	C₂²×C₁₃	1	2	yes	complemented
202	#466	C₂²×C₁₃	1	2	yes	—
203	#462	—	2	1	no	—
204	#459	—	2	1	no	—
205	#451	—	2	2	no	—
206	#447	—	2	2	no	—
207	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
208	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
210	#367	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
212	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
213	#358	C₂²×C₁₃	1	2	yes	complemented
214	#357	C₂²×C₁₃	1	1	yes	characteristic
215	#357	C₂²×C₁₃	1	2	yes	complemented
216	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
217	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	4	2	no	—
221	C₂²×C₁₃	—	8	1	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	16	8	no	—
227	C₂²×C₁₃	C₂×SD₃₂	1	4	yes	complemented
228	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	C₂×SD₃₂	1	2	yes	complemented
236	C₄×C₁₃	D₄²	1	1	yes	characteristic
237	C₄×C₁₃	#576	1	1	yes	characteristic
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	4	1	no	—
241	C₂×Q₁₆	—	2	4	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	4	2	no	—
245	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
246	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
247	C₂×D₈	—	2	4	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	4	2	no	—
251	C₂×D₈	C₂³×C₁₃	1	2	yes	—
252	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	4	1	no	—
256	#127	—	2	1	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	#121	—	2	2	no	—
260	#121	—	4	1	no	—
261	#120	—	4	2	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	4	1	no	—
265	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
266	SD₃₂	—	2	4	no	—
267	SD₃₂	—	2	4	no	—
268	SD₃₂	—	2	4	no	—
269	SD₃₂	—	4	2	no	—
270	SD₃₂	D₄×C₁₃	1	4	yes	direct product factor
271	C₂×C₁₆	—	2	4	no	—
272	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
274	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
275	#107	C₂³×C₁₃	1	1	yes	characteristic
276	#107	C₂³×C₁₃	1	1	yes	characteristic
277	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
278	#103	—	2	1	no	—
279	#103	—	2	2	no	—
280	#102	—	2	1	no	—
281	#102	—	2	2	no	—
282	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
283	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₁₃	—	2	4	no	—
285	C₂×C₁₃	—	8	2	no	—
286	C₂×C₁₃	—	16	2	no	—
287	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
288	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
289	C₂×C₁₃	#3416	1	1	yes	characteristic
290	C₂⁴	—	4	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	8	2	no	—
304	C₂×D₄	—	8	4	no	—
305	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	2	1	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	4	no	—
313	Q₁₆	—	8	1	no	—
314	Q₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
315	D₈	—	2	2	no	—
316	D₈	—	2	1	no	—
317	D₈	—	2	2	no	—
318	D₈	—	4	4	no	—
319	D₈	—	8	1	no	—
320	D₈	C₂×D₄×C₁₃	1	2	yes	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
337	C₄²	—	4	1	no	—
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₁₆	—	2	2	no	—
340	C₁₆	—	2	1	no	—
341	C₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
342	C₁₃	D₄×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	16	2	no	—
348	C₂³	C₂×C₁₃×D₈	1	2	yes	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	1	no	—
362	D₄	C₁₃×SD₃₂	1	4	yes	direct product factor
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×C₁₃×SD₃₂	1	4	yes	complemented
389	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×C₁₃×SD₃₂	1	2	yes	complemented
397	C₄	D₄²×C₁₃	1	1	yes	characteristic
398	C₄	C₁₃×#576	1	1	yes	characteristic
399	C₂	—	2	4	no	—
400	C₂	—	8	2	no	—
401	C₂	—	16	2	no	—
402	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
403	C₂	C₂²×C₁₃×SD₃₂	1	1	yes	characteristic
404	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	D₄×C₁₃×D₈	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×SD₃₂	C₂	semidirect
2. D₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2248	C₂	semidirect
5. C₁₃×#2217	C₂	semidirect
6. C₁₃×#2208	C₂	semidirect
7. C₁₃×#2207	C₂	semidirect
8. C₁₃×#2187	C₂	semidirect
9. C₁₃×#2185	C₂	semidirect
10. C₄×C₁₃×SD₃₂	C₂	semidirect
11. D₄×C₁₃×C₁₆	C₂	semidirect
12. C₂²×C₁₃×Q₁₆	C₂²	semidirect
19. C₂×C₁₃×SD₃₂	C₂²	semidirect
20. C₂×C₁₃×SD₃₂	C₂²	semidirect
21. C₂×C₁₃×SD₃₂	C₂²	semidirect
22. C₂²×C₁₃×C₁₆	C₂²	semidirect
23. C₁₃×#494	C₂²	semidirect
25. C₁₃×#467	C₂²	semidirect
31. C₄×C₁₃×Q₁₆	C₂²	semidirect
34. C₁₃×#367	C₂²	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
37. C₁₃×#358	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
40. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₃×C₁₆	C₂²	semidirect
74. C₁₃×SD₃₂	D₄	direct (N × H)
88. D₄×SD₃₂	C₁₃	direct (N × H)
113. C₁₃×Q₁₆	C₂×D₄	semidirect
140. C₁₃×C₁₆	C₂×D₄	semidirect
141. C₂²×SD₃₂	C₂×C₁₃	semidirect
142. D₄×Q₁₆	C₂×C₁₃	semidirect
144. #2248	C₂×C₁₃	semidirect
145. #2217	C₂×C₁₃	semidirect
146. #2208	C₂×C₁₃	semidirect
147. #2207	C₂×C₁₃	semidirect
148. #2187	C₂×C₁₃	semidirect
149. #2185	C₂×C₁₃	semidirect
150. C₄×SD₃₂	C₂×C₁₃	semidirect
151. D₄×C₁₆	C₂×C₁₃	semidirect
171. D₄×C₁₃	SD₃₂	direct (N × H)
188. C₂²×Q₁₆	C₂²×C₁₃	semidirect
195. C₂×SD₃₂	C₂²×C₁₃	semidirect
196. C₂×SD₃₂	C₂²×C₁₃	semidirect
197. C₂×SD₃₂	C₂²×C₁₃	semidirect
198. C₂²×C₁₆	C₂²×C₁₃	semidirect
199. #494	C₂²×C₁₃	semidirect
201. #467	C₂²×C₁₃	semidirect
207. C₄×Q₁₆	C₂²×C₁₃	semidirect
210. #367	C₂²×C₁₃	semidirect
211. C₄⋊C₁₆	C₂²×C₁₃	semidirect
212. #358	C₂²×C₁₃	semidirect
213. #358	C₂²×C₁₃	semidirect
215. #357	C₂²×C₁₃	semidirect
216. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
217. C₄×C₁₆	C₂²×C₁₃	semidirect
227. C₂²×C₁₃	C₂×SD₃₂	semidirect
235. C₄×C₁₃	C₂×SD₃₂	semidirect
270. SD₃₂	D₄×C₁₃	direct (N × H)
314. Q₁₆	C₂×D₄×C₁₃	semidirect
341. C₁₆	C₂×D₄×C₁₃	semidirect
342. C₁₃	D₄×SD₃₂	direct (N × H)
362. D₄	C₁₃×SD₃₂	direct (N × H)
388. C₂²	C₂×C₁₃×SD₃₂	semidirect
396. C₄	C₂×C₁₃×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×SD₃₂	2
D₄×C₁₃×Q₁₆	2
D₄×C₁₃×D₈	2
C₁₃×#2248	2
C₁₃×#2217	2
C₁₃×#2208	2
C₁₃×#2207	2
C₁₃×#2187	2
C₁₃×#2185	2
C₄×C₁₃×SD₃₂	2
D₄×C₁₃×C₁₆	2
D₄×SD₃₂	13

Subgroups — D4×C13×SD32 #15720186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×SD₃₂ #15720186