Subgroups — #15832067

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	#13113612	C₂	1	4	yes	maximal, complemented
4	#13113610	C₂	1	4	yes	maximal, complemented
5	#13113594	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	—	2	1	no	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6099	—	2	1	no	—
10	C₁₃×#423	—	2	1	no	—
11	C₁₃×#423	—	2	1	no	—
12	C₁₃×#423	C₂²	1	2	yes	—
13	C₁₃×#423	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊#1055	C₄	1	2	yes	—
17	#11718586	C₄	1	2	yes	—
18	#11718586	C₄	1	2	yes	—
19	#11718586	C₂²	1	2	yes	—
20	#11718586	C₂²	1	2	yes	—
21	#11718585	—	2	1	no	—
22	#11718585	—	2	1	no	—
23	#11718585	C₂²	1	2	yes	—
24	#11718585	C₂²	1	2	yes	—
25	C₂×C₄⋊#1055	—	2	1	no	—
26	C₂×C₄⋊#1055	C₄	1	2	yes	—
27	C₂×C₄⋊#1055	C₂²	1	2	yes	—
28	C₂×C₄×#1055	C₂²	1	2	yes	—
29	#11718071	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
33	C₂×C₁₃×M₁₆	—	2	2	no	—
34	C₂×C₁₃×M₁₆	—	2	2	no	—
35	C₂×C₁₃×M₁₆	—	4	4	no	—
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6099	—	2	2	no	—
50	C₂×#6099	—	2	2	no	—
51	C₂×#6099	—	4	4	no	—
52	C₂²×#1055	—	2	2	no	—
53	C₂²×#1055	C₂×C₄	1	4	yes	—
54	C₁₃×C₄⋊C₈	—	2	2	no	—
55	C₁₃×C₄⋊C₈	—	2	2	no	—
56	C₁₃×C₄⋊C₈	—	2	2	no	—
57	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
58	C₂²⋊#1055	C₂×C₄	1	4	yes	—
59	C₂²⋊#1055	C₂×C₄	1	4	yes	—
60	C₄⋊#1055	—	2	2	no	—
61	C₄⋊#1055	—	2	2	no	—
62	C₄⋊#1055	—	2	2	no	—
63	C₄⋊#1055	C₂×C₄	1	4	yes	—
64	C₄⋊#1055	C₂×C₄	1	4	yes	—
65	C₄⋊#1055	C₂³	1	4	yes	—
66	C₄×#1055	C₂×C₄	1	4	yes	—
67	C₄×#1055	C₂³	1	4	yes	—
68	#17814	—	13	1	no	maximal, Sylow
69	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	D₈	1	4	yes	—
82	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₁₃×M₁₆	—	4	4	no	—
93	C₁₃×M₁₆	—	4	4	no	—
94	C₂×C₈×C₁₃	—	2	4	no	—
95	C₂×C₈×C₁₃	—	4	4	no	—
96	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
112	#6099	—	4	4	no	—
113	#6099	—	4	4	no	—
114	C₂×#1055	—	2	4	no	—
115	C₂×#1055	—	4	4	no	—
116	C₂×#1055	—	4	4	no	—
117	C₂×#1055	C₂²×C₄	1	8	yes	—
118	C₂×#431	—	13	1	no	—
119	C₂×#423	—	13	1	no	—
120	C₂×#423	D₁₃	1	1	yes	characteristic
121	#1571	—	13	4	no	—
122	#1571	—	13	4	no	—
123	#1567	—	13	4	no	—
124	C₂³×C₁₃	—	4	1	no	—
125	C₂³×C₁₃	—	4	1	no	—
126	C₂³×C₁₃	#107	1	4	yes	—
127	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	4	1	no	—
137	C₂×C₄×C₁₃	—	4	1	no	—
138	C₂×C₄×C₁₃	—	4	1	no	—
139	C₂×C₄×C₁₃	—	4	1	no	—
140	C₂×C₄×C₁₃	—	4	1	no	—
141	C₂×C₄×C₁₃	—	4	1	no	—
142	C₂×C₄×C₁₃	#107	1	4	yes	—
143	C₂×C₄×C₁₃	#107	1	4	yes	—
144	C₂×C₄×C₁₃	#107	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
163	C₈×C₁₃	—	4	4	no	—
164	#1055	—	2	8	no	—
165	#1055	—	4	4	no	—
166	C₂²×M₁₆	—	2	1	no	—
167	C₂²×M₁₆	—	26	1	no	—
168	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
169	#431	—	13	2	no	—
170	#431	—	13	2	no	—
171	#431	—	13	2	no	—
172	#431	—	13	2	no	—
173	#423	—	2	1	no	—
174	#423	—	2	1	no	—
175	#423	—	13	2	no	—
176	#423	—	13	2	no	—
177	#423	—	26	1	no	—
178	#423	—	26	1	no	—
179	#423	C₂×D₁₃	1	2	yes	—
180	#423	C₂×D₁₃	1	2	yes	—
181	C₂×C₄⋊C₈	—	2	1	no	—
182	C₂×C₄⋊C₈	—	13	2	no	—
183	C₂×C₄⋊C₈	—	13	2	no	—
184	C₂×C₄⋊C₈	—	26	1	no	—
185	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
186	C₂×C₂²⋊C₈	—	13	2	no	—
187	C₂×C₄×C₈	—	13	2	no	—
188	#335	—	13	16	no	—
189	C₂²×C₁₃	—	2	1	no	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	4	4	no	—
196	C₂²×C₁₃	C₂×#107	1	2	yes	—
197	C₂²×C₁₃	C₂×#107	1	2	yes	—
198	C₂²×C₁₃	C₂×#107	1	2	yes	—
199	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	C₂×#107	1	2	yes	—
207	C₄×C₁₃	C₂×#107	1	2	yes	—
208	C₄×C₁₃	C₂×#107	1	2	yes	—
209	C₄×C₁₃	#430	1	2	yes	—
210	C₄×C₁₃	#568	1	2	yes	—
211	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
212	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
213	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
214	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	4	4	no	—
219	C₂×M₁₆	—	26	2	no	—
220	C₂×M₁₆	—	26	2	no	—
221	C₂×M₁₆	—	52	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	13	4	no	—
224	C₂²×C₈	—	26	2	no	—
225	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
226	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
227	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	13	4	no	—
241	C₄⋊C₈	—	13	4	no	—
242	C₄⋊C₈	—	13	4	no	—
243	C₄⋊C₈	—	26	2	no	—
244	C₄⋊C₈	—	26	2	no	—
245	C₄⋊C₈	—	26	2	no	—
246	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
247	C₂²⋊C₈	—	13	4	no	—
248	C₂²⋊C₈	—	13	4	no	—
249	C₄×C₈	—	13	4	no	—
250	C₄×C₈	—	13	4	no	—
251	C₂×C₁₃	—	2	2	no	—
252	C₂×C₁₃	—	2	2	no	—
253	C₂×C₁₃	—	2	2	no	—
254	C₂×C₁₃	#2905	1	1	yes	characteristic
255	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
257	C₂⁴	#6101	1	1	yes	characteristic
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	#6101	1	1	yes	characteristic
261	C₂²×C₄	#6101	1	1	yes	characteristic
262	C₂²×C₄	#6101	1	1	yes	characteristic
263	C₂²×C₄	#6101	1	1	yes	characteristic
264	C₂²×C₄	#6101	1	1	yes	characteristic
265	C₂²×C₄	#6101	1	1	yes	characteristic
266	C₂²×C₄	#6101	1	1	yes	characteristic
267	C₂²×C₄	#6101	1	1	yes	characteristic
268	C₂²×C₄	#6101	1	1	yes	characteristic
269	C₂²×C₄	#6104	1	4	yes	—
270	C₂²×C₄	#6107	1	4	yes	—
271	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
280	M₁₆	—	4	4	no	—
281	M₁₆	—	4	4	no	—
282	M₁₆	—	52	4	no	—
283	M₁₆	—	52	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	—	13	8	no	—
287	C₂×C₈	—	26	4	no	—
288	C₂×C₈	—	52	4	no	—
289	C₂×C₈	—	52	4	no	—
290	C₄²	#6101	1	1	yes	characteristic
291	C₄²	#6101	1	1	yes	characteristic
292	C₄²	#6101	1	1	yes	characteristic
293	C₄²	#6101	1	1	yes	characteristic
294	C₄²	#6101	1	1	yes	characteristic
295	C₄²	#6101	1	1	yes	characteristic
296	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
297	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
298	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
305	C₄²	C₂³×D₁₃	1	1	yes	characteristic
306	C₁₃	#17814	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	#88047	1	4	yes	—
310	C₂³	C₂×#6101	1	1	yes	characteristic
311	C₂³	C₂×#6101	1	1	yes	characteristic
312	C₂³	C₂×#6101	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	#88047	1	4	yes	—
326	C₂×C₄	#88047	1	4	yes	—
327	C₂×C₄	#88047	1	4	yes	—
328	C₂×C₄	C₂×#6101	1	1	yes	characteristic
329	C₂×C₄	C₂×#6101	1	1	yes	characteristic
330	C₂×C₄	C₂×#6101	1	1	yes	characteristic
331	C₂×C₄	C₂×#6101	1	1	yes	characteristic
332	C₂×C₄	C₂×#6101	1	1	yes	characteristic
333	C₂×C₄	C₂×#6101	1	1	yes	characteristic
334	C₂×C₄	C₂×#6101	1	1	yes	characteristic
335	C₂×C₄	C₂×#6101	1	1	yes	characteristic
336	C₂×C₄	C₂×#6101	1	1	yes	characteristic
337	C₂×C₄	C₂×#6104	1	2	yes	—
338	C₂×C₄	C₂×#6104	1	2	yes	—
339	C₂×C₄	C₂×#6104	1	2	yes	—
340	C₂×C₄	C₂×#6107	1	2	yes	—
341	C₂×C₄	C₂×#6107	1	2	yes	—
342	C₂×C₄	C₂×#6107	1	2	yes	—
343	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	26	8	no	—
348	C₈	—	52	4	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#88047	1	2	yes	—
357	C₂²	C₂×#88047	1	2	yes	—
358	C₂²	C₂×#88047	1	2	yes	—
359	C₂²	C₂²×#6101	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	C₂×#88047	1	2	yes	—
367	C₄	C₂×#88047	1	2	yes	—
368	C₄	C₂×#88047	1	2	yes	—
369	C₄	#11718785	1	2	yes	—
370	C₄	#11719450	1	2	yes	—
371	C₄	C₂²×#6104	1	1	yes	characteristic
372	C₄	C₂²×#6107	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	#13123399	1	1	yes	characteristic
377	C₂	C₂²×#88047	1	1	yes	characteristic
378	C₂	C₂×#11718785	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#423	D₁₃
hypocenter	C₁₃	#17814
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #13113612	C₂	semidirect
4. #13113610	C₂	semidirect
5. #13113594	C₂	semidirect
29. #11718071	C₂²	semidirect
306. C₁₃	#17814	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
C₂×#11718585	2
#13113612	2
#13113610	2
#13113594	2
C₂×C₁₃×#423	2
#17814	13