Subgroups — D₄×C₁₃×#108 #15709006

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#108	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1950	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1855	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1810	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×M₁₆	C₂²	1	4	yes	—
10	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#436	—	2	2	no	—
13	C₁₃×#435	—	2	4	no	—
14	C₈×D₄×C₁₃	—	2	2	no	—
15	C₈×D₄×C₁₃	C₄	1	4	yes	—
16	C₈×D₄×C₁₃	C₄	1	2	yes	—
17	C₈×D₄×C₁₃	C₄	1	2	yes	—
18	C₂×C₁₃×#108	—	2	8	no	—
19	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#108	C₂²	1	2	yes	—
21	C₂×C₁₃×#108	C₂²	1	4	yes	—
22	C₂×C₁₃×#108	C₂²	1	2	yes	—
23	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
24	C₁₃×#423	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₃×#407	C₂²	1	4	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#341	C₂²	1	2	yes	—
31	C₁₃×#341	C₂²	1	4	yes	—
32	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
34	C₂×C₁₃×M₁₆	—	2	4	no	—
35	C₂×C₁₃×M₁₆	—	2	8	no	—
36	C₂×C₁₃×M₁₆	—	4	4	no	—
37	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
38	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
39	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	—	2	4	no	—
41	C₂²×C₈×C₁₃	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	D₄	1	2	yes	—
53	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#108	—	2	8	no	—
58	C₁₃×#108	—	2	4	no	—
59	C₁₃×#108	—	2	2	no	—
60	C₁₃×#108	—	4	2	no	—
61	C₁₃×#108	D₄	1	4	yes	direct product factor
62	C₁₃×C₄⋊C₈	—	2	2	no	—
63	C₁₃×C₄⋊C₈	—	2	2	no	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
66	C₁₃×C₂²⋊C₈	—	2	4	no	—
67	C₁₃×C₂²⋊C₈	—	2	4	no	—
68	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
69	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₁₃×#97	—	2	2	no	—
71	C₄×C₈×C₁₃	—	2	2	no	—
72	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
74	D₄×#108	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
76	C₂×D₄×C₁₃	—	2	4	no	—
77	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
78	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₁₃×M₁₆	—	2	2	no	—
93	C₁₃×M₁₆	—	2	4	no	—
94	C₁₃×M₁₆	—	2	2	no	—
95	C₁₃×M₁₆	—	2	4	no	—
96	C₁₃×M₁₆	—	2	2	no	—
97	C₁₃×M₁₆	—	4	8	no	—
98	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	8	no	—
105	C₂×C₈×C₁₃	—	2	8	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₂×C₈×C₁₃	—	4	8	no	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃	#41	1	2	yes	—
114	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
117	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
125	D₄×M₁₆	C₂×C₁₃	1	2	yes	—
126	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
127	C₂²×#108	C₂×C₁₃	1	2	yes	complemented
128	#1950	C₂×C₁₃	1	2	yes	complemented
129	#1855	C₂×C₁₃	1	4	yes	complemented
130	#1848	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#1810	C₂×C₁₃	1	2	yes	complemented
132	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	—	2	2	no	—
135	C₂³×C₁₃	—	2	4	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
140	D₄×C₁₃	—	2	4	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	#108	1	4	yes	direct product factor
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₈×C₁₃	—	2	4	no	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	2	4	no	—
170	C₈×C₁₃	—	4	4	no	—
171	C₈×C₁₃	—	4	2	no	—
172	C₈×C₁₃	C₄×D₄	1	4	yes	—
173	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	—
174	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
175	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
176	#436	—	2	2	no	—
177	#435	—	2	4	no	—
178	C₈×D₄	—	2	2	no	—
179	C₈×D₄	C₄×C₁₃	1	4	yes	—
180	C₈×D₄	C₄×C₁₃	1	2	yes	—
181	C₈×D₄	C₄×C₁₃	1	2	yes	—
182	C₂×#108	—	2	8	no	—
183	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#108	C₂²×C₁₃	1	2	yes	—
185	C₂×#108	C₂²×C₁₃	1	4	yes	—
186	C₂×#108	C₂²×C₁₃	1	2	yes	—
187	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
188	#423	C₂²×C₁₃	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
190	#407	C₂²×C₁₃	1	4	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
192	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	#341	C₂²×C₁₃	1	4	yes	—
195	#341	C₂²×C₁₃	1	2	yes	—
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	4	4	no	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	C₂×#108	1	4	yes	complemented
206	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
208	C₂²×C₁₃	#554	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	C₂×#108	1	2	yes	complemented
215	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₁₃	#520	1	1	yes	characteristic
217	C₄×C₁₃	D₄²	1	1	yes	characteristic
218	C₄×C₁₃	#547	1	1	yes	characteristic
219	C₂²×D₄	Q₈×C₁₃	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	8	no	—
223	C₂×M₁₆	—	4	4	no	—
224	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
225	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
226	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
231	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
232	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
236	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
237	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
239	C₄×D₄	D₄×C₁₃	1	2	yes	—
240	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	Q₈×C₁₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	Q₈×C₁₃	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	#108	—	2	8	no	—
245	#108	—	2	4	no	—
246	#108	—	2	2	no	—
247	#108	—	4	2	no	—
248	#108	D₄×C₁₃	1	4	yes	direct product factor
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
252	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
256	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
257	#97	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
260	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
261	C₂×C₁₃	—	2	1	no	—
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	—	2	4	no	—
264	C₂×C₁₃	—	4	2	no	—
265	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
267	C₂×C₁₃	#2916	1	1	yes	characteristic
268	C₂⁴	C₂×Q₈×C₁₃	1	2	yes	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
271	C₂×D₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
272	C₂×D₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
283	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	4	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	4	8	no	—
291	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	—	2	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	8	no	—
302	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
304	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
306	C₂×C₈	C₁₃×#41	1	2	yes	—
307	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
308	C₄⋊C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
309	C₄⋊C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
310	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
311	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
312	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
313	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
314	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₁₃	D₄×#108	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	4	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
324	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
325	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	C₁₃×#108	1	4	yes	direct product factor
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
345	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
346	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
351	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	4	no	—
356	C₈	—	4	4	no	—
357	C₈	—	4	2	no	—
358	C₈	C₄×D₄×C₁₃	1	4	yes	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	C₂×C₁₃×#108	1	4	yes	complemented
369	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
370	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
371	C₂²	C₁₃×#554	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	C₂×C₁₃×#108	1	2	yes	complemented
378	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
379	C₄	C₁₃×#520	1	1	yes	characteristic
380	C₄	D₄²×C₁₃	1	1	yes	characteristic
381	C₄	C₁₃×#547	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	4	no	—
385	C₂	—	4	2	no	—
386	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
387	C₂	C₂²×C₁₃×#108	1	1	yes	characteristic
388	C₂	C₁₃×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₁₃×#108	C₂	semidirect
4. C₁₃×#1950	C₂	semidirect
5. C₁₃×#1855	C₂	semidirect
6. C₁₃×#1848	C₂	semidirect
7. C₁₃×#1810	C₂	semidirect
8. C₄×C₁₃×#108	C₂	semidirect
61. C₁₃×#108	D₄	direct (N × H)
74. D₄×#108	C₁₃	direct (N × H)
127. C₂²×#108	C₂×C₁₃	semidirect
128. #1950	C₂×C₁₃	semidirect
129. #1855	C₂×C₁₃	semidirect
130. #1848	C₂×C₁₃	semidirect
131. #1810	C₂×C₁₃	semidirect
132. C₄×#108	C₂×C₁₃	semidirect
142. D₄×C₁₃	#108	direct (N × H)
205. C₂²×C₁₃	C₂×#108	semidirect
214. C₄×C₁₃	C₂×#108	semidirect
248. #108	D₄×C₁₃	direct (N × H)
318. C₁₃	D₄×#108	direct (N × H)
328. D₄	C₁₃×#108	direct (N × H)
368. C₂²	C₂×C₁₃×#108	semidirect
377. C₄	C₂×C₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×M₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#108	2
C₁₃×#1950	2
C₁₃×#1855	2
C₁₃×#1848	2
C₁₃×#1810	2
C₄×C₁₃×#108	2
D₄×#108	13

Subgroups — D4×C13×#108 #15709006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×#108 #15709006