Subgroups — D₄×C₁₃×M₃₂ #15719776

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2169	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2168	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2112	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₁₃×M₃₂	—	2	8	no	—
12	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
14	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×M₃₂	C₂²	1	4	yes	complemented
16	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	complemented
17	C₈×D₄×C₁₃	C₄	1	2	yes	—
18	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
19	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
20	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	2	yes	—
22	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
27	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
28	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
30	C₁₃×#346	C₂²	1	2	yes	complemented
31	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
32	C₂²×D₄×C₁₃	C₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₃	—	2	4	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₈	1	2	yes	—
44	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
45	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
46	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₁₃×M₃₂	—	2	4	no	—
53	C₁₃×M₃₂	—	2	2	no	—
54	C₁₃×M₃₂	—	2	8	no	—
55	C₁₃×M₃₂	D₄	1	4	yes	direct product factor
56	C₂×C₁₃×C₁₆	—	2	8	no	—
57	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
59	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
60	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	D₄×M₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	C₂×C₈	1	2	yes	—
73	C₂×D₄×C₁₃	—	2	4	no	—
74	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
76	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₃	—	2	4	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	4	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₃	#41	1	2	yes	—
102	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
104	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
106	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
107	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
108	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
110	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₁₃×C₁₆	—	2	4	no	—
115	C₁₃×C₁₆	—	2	2	no	—
116	C₁₃×C₁₆	C₂×D₄	1	4	yes	complemented
117	C₂²×M₃₂	C₂×C₁₃	1	2	yes	complemented
118	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
119	#2169	C₂×C₁₃	1	2	yes	complemented
120	#2168	C₂×C₁₃	1	4	yes	complemented
121	D₄×C₁₆	C₂×C₁₃	1	2	yes	complemented
122	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
123	#2112	C₂×C₁₃	1	2	yes	complemented
124	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
129	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
130	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
131	D₄×C₁₃	—	2	4	no	—
132	D₄×C₁₃	—	2	2	no	—
133	D₄×C₁₃	M₃₂	1	4	yes	direct product factor
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	4	1	no	—
143	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#131	1	2	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	C₈×C₁₃	—	2	2	no	—
154	C₈×C₁₃	—	2	2	no	—
155	C₈×C₁₃	—	2	1	no	—
156	C₈×C₁₃	—	2	1	no	—
157	C₈×C₁₃	C₄×D₄	1	2	yes	—
158	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
161	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
162	C₂×M₃₂	—	2	8	no	—
163	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
164	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
165	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×M₃₂	C₂²×C₁₃	1	4	yes	complemented
167	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	complemented
168	C₈×D₄	C₄×C₁₃	1	2	yes	—
169	C₈×D₄	C₄×C₁₃	1	1	yes	characteristic
170	C₈×D₄	C₄×C₁₃	1	1	yes	characteristic
171	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
172	C₈×D₄	C₂²×C₁₃	1	2	yes	—
173	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
175	C₂×C₂²⋊C₈	C₄×C₁₃	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
177	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
178	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
179	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
180	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
181	#346	C₂²×C₁₃	1	2	yes	complemented
182	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	2	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	4	8	no	—
191	C₂²×C₁₃	C₈×D₄	1	2	yes	—
192	C₂²×C₁₃	C₂×M₃₂	1	4	yes	complemented
193	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
194	C₄×C₁₃	—	2	1	no	—
195	C₄×C₁₃	—	2	1	no	—
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	2	no	—
199	C₄×C₁₃	C₈×D₄	1	2	yes	—
200	C₄×C₁₃	C₂×M₃₂	1	2	yes	complemented
201	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
203	C₂²×D₄	C₈×C₁₃	1	1	yes	characteristic
204	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
209	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
214	C₄×D₄	C₈×C₁₃	1	2	yes	—
215	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
216	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
217	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
218	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
219	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₈×C₁₃	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₈×C₁₃	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
223	M₃₂	—	2	4	no	—
224	M₃₂	—	2	2	no	—
225	M₃₂	—	2	8	no	—
226	M₃₂	D₄×C₁₃	1	4	yes	direct product factor
227	C₂×C₁₆	—	2	8	no	—
228	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
229	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
230	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
231	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
233	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
235	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
236	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
237	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
238	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
240	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×C₁₃	—	2	2	no	—
243	C₂×C₁₃	—	2	4	no	—
244	C₂×C₁₃	—	4	2	no	—
245	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
246	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
247	C₂×C₁₃	#3407	1	1	yes	characteristic
248	C₂⁴	C₂×C₈×C₁₃	1	2	yes	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
251	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
252	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
257	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
259	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
272	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
273	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
275	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
276	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
277	C₂×C₈	C₁₃×#41	1	2	yes	—
278	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
279	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
280	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
281	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
282	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
283	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
284	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
285	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
286	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
287	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
288	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
290	C₁₆	—	2	4	no	—
291	C₁₆	—	2	2	no	—
292	C₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
293	C₁₃	D₄×M₃₂	1	1	yes	characteristic, direct product factor, Sylow
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
298	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
299	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
300	D₄	—	2	4	no	—
301	D₄	—	2	2	no	—
302	D₄	C₁₃×M₃₂	1	4	yes	direct product factor
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
313	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
316	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
317	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
318	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
319	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
320	C₂×C₄	C₁₃×#131	1	2	yes	—
321	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	1	no	—
326	C₈	C₄×D₄×C₁₃	1	2	yes	—
327	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
328	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	C₈×D₄×C₁₃	1	2	yes	—
338	C₂²	C₂×C₁₃×M₃₂	1	4	yes	complemented
339	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	C₈×D₄×C₁₃	1	2	yes	—
346	C₄	C₂×C₁₃×M₃₂	1	2	yes	complemented
347	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
348	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×C₈×D₄×C₁₃	1	1	yes	characteristic
353	C₂	C₂²×C₁₃×M₃₂	1	1	yes	characteristic
354	C₂	C₁₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂²×D₄×C₁₃	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×M₃₂	C₂	semidirect
3. C₁₃×#2169	C₂	semidirect
4. C₁₃×#2168	C₂	semidirect
5. D₄×C₁₃×C₁₆	C₂	semidirect
6. C₁₃×#2150	C₂	semidirect
7. C₁₃×#2112	C₂	semidirect
8. C₄×C₁₃×M₃₂	C₂	semidirect
15. C₂×C₁₃×M₃₂	C₂²	semidirect
16. C₂²×C₁₃×C₁₆	C₂²	semidirect
26. C₁₃×C₄⋊C₁₆	C₂²	semidirect
27. C₁₃×C₄⋊C₁₆	C₂²	semidirect
28. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
29. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
30. C₁₃×#346	C₂²	semidirect
31. C₄×C₁₃×C₁₆	C₂²	semidirect
55. C₁₃×M₃₂	D₄	direct (N × H)
71. D₄×M₃₂	C₁₃	direct (N × H)
116. C₁₃×C₁₆	C₂×D₄	semidirect
117. C₂²×M₃₂	C₂×C₁₃	semidirect
119. #2169	C₂×C₁₃	semidirect
120. #2168	C₂×C₁₃	semidirect
121. D₄×C₁₆	C₂×C₁₃	semidirect
122. #2150	C₂×C₁₃	semidirect
123. #2112	C₂×C₁₃	semidirect
124. C₄×M₃₂	C₂×C₁₃	semidirect
133. D₄×C₁₃	M₃₂	direct (N × H)
166. C₂×M₃₂	C₂²×C₁₃	semidirect
167. C₂²×C₁₆	C₂²×C₁₃	semidirect
177. C₄⋊C₁₆	C₂²×C₁₃	semidirect
178. C₄⋊C₁₆	C₂²×C₁₃	semidirect
179. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
180. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
181. #346	C₂²×C₁₃	semidirect
182. C₄×C₁₆	C₂²×C₁₃	semidirect
192. C₂²×C₁₃	C₂×M₃₂	semidirect
200. C₄×C₁₃	C₂×M₃₂	semidirect
226. M₃₂	D₄×C₁₃	direct (N × H)
292. C₁₆	C₂×D₄×C₁₃	semidirect
293. C₁₃	D₄×M₃₂	direct (N × H)
302. D₄	C₁₃×M₃₂	direct (N × H)
338. C₂²	C₂×C₁₃×M₃₂	semidirect
346. C₄	C₂×C₁₃×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×M₃₂	2
C₂×C₈×D₄×C₁₃	2
C₁₃×#2169	2
C₁₃×#2168	2
D₄×C₁₃×C₁₆	2
C₁₃×#2150	2
C₁₃×#2112	2
C₄×C₁₃×M₃₂	2
D₄×M₃₂	13

Subgroups — D4×C13×M32 #15719776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×M₃₂ #15719776