Subgroups — C₁₀₃×#7574 #39912849

Order 26368.

520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#2293	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#1271	C₂	1	2	yes	maximal, complemented
5	C₁₀₃×#1270	C₂	1	2	yes	maximal
6	C₂×C₄×D₄×C₁₀₃	C₄	1	1	yes	characteristic
7	C₂×#117×C₁₀₃	—	2	1	no	—
8	C₂×C₄⋊C₈×C₁₀₃	—	2	1	no	—
9	C₂×C₄⋊C₈×C₁₀₃	—	2	1	no	—
10	C₂×C₄×C₈×C₁₀₃	—	2	1	no	—
11	#390×C₁₀₃	C₄	1	1	yes	characteristic
12	#390×C₁₀₃	C₂²	1	1	yes	characteristic
13	#389×C₁₀₃	C₄	1	1	yes	characteristic
14	#389×C₁₀₃	C₂²	1	1	yes	characteristic
15	#388×C₁₀₃	—	2	1	no	—
16	#388×C₁₀₃	—	2	1	no	—
17	C₄×C₄⋊C₄×C₁₀₃	C₄	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
19	C₄³×C₁₀₃	C₂²	1	1	yes	characteristic
20	#336×C₁₀₃	—	2	1	no	—
21	#336×C₁₀₃	C₂²	1	2	yes	—
22	#336×C₁₀₃	C₂²	1	2	yes	—
23	C₂²×D₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₃	—	2	1	no	—
25	C₂²×C₈×C₁₀₃	—	2	2	no	—
26	C₂²×C₈×C₁₀₃	—	2	2	no	—
27	C₄×D₄×C₁₀₃	—	2	2	no	—
28	C₄×D₄×C₁₀₃	C₈	1	4	yes	complemented
29	#117×C₁₀₃	—	4	2	no	—
30	#117×C₁₀₃	—	4	2	no	—
31	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
41	C₂×C₄²×C₁₀₃	—	2	1	no	—
42	C₂×C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₀₃	—	2	4	no	—
50	C₄⋊C₈×C₁₀₃	—	4	2	no	—
51	C₄×C₈×C₁₀₃	—	4	2	no	—
52	#95×C₁₀₃	—	2	1	no	—
53	#95×C₁₀₃	—	2	1	no	—
54	#95×C₁₀₃	—	2	1	no	—
55	C₂⁴×C₁₀₃	—	2	1	no	—
56	C₂×D₄×C₁₀₃	—	2	1	no	—
57	C₂×D₄×C₁₀₃	—	4	1	no	—
58	C₂×D₄×C₁₀₃	—	4	1	no	—
59	C₂×D₄×C₁₀₃	C₂×C₈	1	2	yes	—
60	C₂²×C₄×C₁₀₃	—	2	1	no	—
61	C₂²×C₄×C₁₀₃	—	2	4	no	—
62	C₂²×C₄×C₁₀₃	—	2	1	no	—
63	C₂²×C₄×C₁₀₃	—	2	1	no	—
64	C₂²×C₄×C₁₀₃	—	4	2	no	—
65	C₂²×C₄×C₁₀₃	—	4	2	no	—
66	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₀₃	—	2	4	no	—
74	C₂×C₈×C₁₀₃	—	4	2	no	—
75	C₂×C₈×C₁₀₃	—	4	2	no	—
76	C₂×C₈×C₁₀₃	—	4	2	no	—
77	C₂×C₈×C₁₀₃	—	4	2	no	—
78	C₂×C₈×C₁₀₃	—	4	2	no	—
79	C₄⋊C₄×C₁₀₃	—	2	1	no	—
80	C₄⋊C₄×C₁₀₃	—	4	1	no	—
81	C₄⋊C₄×C₁₀₃	—	4	1	no	—
82	C₄⋊C₄×C₁₀₃	—	4	2	no	—
83	C₄⋊C₄×C₁₀₃	—	4	1	no	—
84	C₄⋊C₄×C₁₀₃	—	4	1	no	—
85	C₄⋊C₄×C₁₀₃	C₂×C₈	1	2	yes	—
86	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
87	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
88	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
89	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
90	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
91	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
92	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
93	C₄²×C₁₀₃	—	2	2	no	—
94	C₄²×C₁₀₃	—	2	1	no	—
95	C₄²×C₁₀₃	—	2	1	no	—
96	C₄²×C₁₀₃	—	4	1	no	—
97	C₄²×C₁₀₃	—	4	1	no	—
98	C₄²×C₁₀₃	—	4	1	no	—
99	C₄²×C₁₀₃	—	4	2	no	—
100	C₄²×C₁₀₃	C₂×C₈	1	2	yes	—
101	C₄²×C₁₀₃	M₁₆	1	2	yes	—
102	C₄²×C₁₀₃	D₈	1	2	yes	—
103	C₄²×C₁₀₃	SD₁₆	1	2	yes	—
104	C₂³×C₁₀₃	—	2	2	no	—
105	C₂³×C₁₀₃	—	4	1	no	—
106	C₂³×C₁₀₃	—	4	1	no	—
107	C₂³×C₁₀₃	—	4	1	no	—
108	C₂³×C₁₀₃	—	4	1	no	—
109	C₂³×C₁₀₃	—	4	1	no	—
110	C₂³×C₁₀₃	—	4	1	no	—
111	C₂³×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	D₄×C₁₀₃	—	4	2	no	—
113	D₄×C₁₀₃	—	4	2	no	—
114	C₂×C₄×C₁₀₃	—	2	1	no	—
115	C₂×C₄×C₁₀₃	—	2	1	no	—
116	C₂×C₄×C₁₀₃	—	2	1	no	—
117	C₂×C₄×C₁₀₃	—	2	1	no	—
118	C₂×C₄×C₁₀₃	—	2	1	no	—
119	C₂×C₄×C₁₀₃	—	2	1	no	—
120	C₂×C₄×C₁₀₃	—	2	1	no	—
121	C₂×C₄×C₁₀₃	—	2	1	no	—
122	C₂×C₄×C₁₀₃	—	2	1	no	—
123	C₂×C₄×C₁₀₃	—	2	1	no	—
124	C₂×C₄×C₁₀₃	—	2	2	no	—
125	C₂×C₄×C₁₀₃	—	2	1	no	—
126	C₂×C₄×C₁₀₃	—	2	1	no	—
127	C₂×C₄×C₁₀₃	—	2	1	no	—
128	C₂×C₄×C₁₀₃	—	4	1	no	—
129	C₂×C₄×C₁₀₃	—	4	1	no	—
130	C₂×C₄×C₁₀₃	—	4	8	no	—
131	C₂×C₄×C₁₀₃	—	4	1	no	—
132	C₂×C₄×C₁₀₃	—	4	1	no	—
133	C₂×C₄×C₁₀₃	—	4	1	no	—
134	C₂×C₄×C₁₀₃	—	4	1	no	—
135	C₂×C₄×C₁₀₃	—	4	1	no	—
136	C₂×C₄×C₁₀₃	—	4	1	no	—
137	C₂×C₄×C₁₀₃	C₂²⋊C₈	1	2	yes	—
138	C₂×C₄×C₁₀₃	C₂²⋊C₈	1	2	yes	—
139	C₂×C₄×C₁₀₃	#102	1	2	yes	—
140	C₂×C₄×C₁₀₃	#102	1	2	yes	—
141	C₂×C₄×C₁₀₃	#104	1	2	yes	—
142	C₂×C₄×C₁₀₃	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₀₃	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₁₀₃	#137	1	1	yes	characteristic
148	C₈×C₁₀₃	—	4	4	no	—
149	C₈×C₁₀₃	—	8	2	no	—
150	C₂²×C₁₀₃	—	4	2	no	—
151	C₂²×C₁₀₃	—	4	2	no	—
152	C₂²×C₁₀₃	—	4	2	no	—
153	C₂²×C₁₀₃	—	8	1	no	—
154	C₂²×C₁₀₃	—	8	1	no	—
155	C₂²×C₁₀₃	—	8	1	no	—
156	C₂²×C₁₀₃	—	8	1	no	—
157	C₂²×C₁₀₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
158	C₂²×C₁₀₃	#410	1	1	yes	characteristic
159	C₂²×C₁₀₃	#413	1	1	yes	characteristic
160	C₂²×C₁₀₃	C₂×#102	1	1	yes	characteristic
161	C₂²×C₁₀₃	#417	1	1	yes	characteristic
162	C₂²×C₁₀₃	C₂×#104	1	1	yes	characteristic
163	C₂²×C₁₀₃	#421	1	1	yes	characteristic
164	C₄×C₁₀₃	—	2	2	no	—
165	C₄×C₁₀₃	—	2	1	no	—
166	C₄×C₁₀₃	—	2	1	no	—
167	C₄×C₁₀₃	—	2	2	no	—
168	C₄×C₁₀₃	—	2	1	no	—
169	C₄×C₁₀₃	—	2	1	no	—
170	C₄×C₁₀₃	—	2	1	no	—
171	C₄×C₁₀₃	—	2	1	no	—
172	C₄×C₁₀₃	—	4	2	no	—
173	C₄×C₁₀₃	—	4	1	no	—
174	C₄×C₁₀₃	—	8	1	no	—
175	C₄×C₁₀₃	—	8	1	no	—
176	C₄×C₁₀₃	D₄⋊C₈	1	4	yes	—
177	#7574	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₃	—	8	2	no	—
179	C₂×C₁₀₃	#1458	1	1	yes	characteristic
180	C₂×C₁₀₃	C₂×D₄⋊C₈	1	1	yes	characteristic
181	C₂×C₁₀₃	#1477	1	1	yes	characteristic
182	C₂×C₁₀₃	#1509	1	1	yes	characteristic
183	C₂×C₁₀₃	#1517	1	1	yes	characteristic
184	C₂×C₁₀₃	#1529	1	1	yes	characteristic
185	C₂×C₁₀₃	#1547	1	1	yes	characteristic
186	#2293	C₂×C₁₀₃	1	1	yes	characteristic
187	#1831	C₂×C₁₀₃	1	1	yes	characteristic, complemented
188	C₄×C₄⋊C₈	C₂×C₁₀₃	1	1	yes	characteristic, complemented
189	#1271	C₂×C₁₀₃	1	2	yes	complemented
190	#1270	C₂×C₁₀₃	1	2	yes	—
191	C₁₀₃	#7574	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×C₄×D₄	C₄×C₁₀₃	1	1	yes	characteristic
193	C₂×#117	—	2	1	no	—
194	C₂×C₄⋊C₈	—	2	1	no	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₄×C₈	—	2	1	no	—
197	#390	C₄×C₁₀₃	1	1	yes	characteristic
198	#390	C₂²×C₁₀₃	1	1	yes	characteristic
199	#389	C₄×C₁₀₃	1	1	yes	characteristic
200	#389	C₂²×C₁₀₃	1	1	yes	characteristic
201	#388	—	2	1	no	—
202	#388	—	2	1	no	—
203	C₄×C₄⋊C₄	C₄×C₁₀₃	1	1	yes	characteristic
204	C₄×C₂²⋊C₄	—	2	1	no	—
205	C₄³	C₂²×C₁₀₃	1	1	yes	characteristic
206	#336	—	2	1	no	—
207	#336	C₂²×C₁₀₃	1	2	yes	—
208	#336	C₂²×C₁₀₃	1	2	yes	—
209	C₂²×D₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
210	C₂³×C₄	—	2	1	no	—
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	C₈×C₁₀₃	1	4	yes	complemented
215	#117	—	4	2	no	—
216	#117	—	4	2	no	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	—	2	1	no	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₂²⋊C₄	—	2	1	no	—
226	C₂×C₂²⋊C₄	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	C₂×C₄×C₁₀₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₁₀₃	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
235	C₄⋊C₈	—	2	4	no	—
236	C₄⋊C₈	—	4	2	no	—
237	C₄×C₈	—	4	2	no	—
238	#95	—	2	1	no	—
239	#95	—	2	1	no	—
240	#95	—	2	1	no	—
241	C₂⁴	—	2	1	no	—
242	C₂×D₄	—	2	1	no	—
243	C₂×D₄	—	4	1	no	—
244	C₂×D₄	—	4	1	no	—
245	C₂×D₄	C₂×C₈×C₁₀₃	1	2	yes	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
253	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
254	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	2	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	4	1	no	—
267	C₄⋊C₄	—	4	1	no	—
268	C₄⋊C₄	—	4	2	no	—
269	C₄⋊C₄	—	4	1	no	—
270	C₄⋊C₄	—	4	1	no	—
271	C₄⋊C₄	C₂×C₈×C₁₀₃	1	2	yes	—
272	C₂²⋊C₄	—	2	4	no	—
273	C₂²⋊C₄	—	4	2	no	—
274	C₂²⋊C₄	—	4	2	no	—
275	C₂²⋊C₄	—	4	1	no	—
276	C₂²⋊C₄	—	4	1	no	—
277	C₂²⋊C₄	—	4	1	no	—
278	C₂²⋊C₄	—	4	1	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	1	no	—
281	C₄²	—	2	1	no	—
282	C₄²	—	4	1	no	—
283	C₄²	—	4	1	no	—
284	C₄²	—	4	1	no	—
285	C₄²	—	4	2	no	—
286	C₄²	C₂×C₈×C₁₀₃	1	2	yes	—
287	C₄²	M₁₆×C₁₀₃	1	2	yes	—
288	C₄²	D₈×C₁₀₃	1	2	yes	—
289	C₄²	SD₁₆×C₁₀₃	1	2	yes	—
290	C₂³	—	2	2	no	—
291	C₂³	—	4	1	no	—
292	C₂³	—	4	1	no	—
293	C₂³	—	4	1	no	—
294	C₂³	—	4	1	no	—
295	C₂³	—	4	1	no	—
296	C₂³	—	4	1	no	—
297	C₂³	C₂×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
298	D₄	—	4	2	no	—
299	D₄	—	4	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	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	C₂²⋊C₈×C₁₀₃	1	2	yes	—
324	C₂×C₄	C₂²⋊C₈×C₁₀₃	1	2	yes	—
325	C₂×C₄	#102×C₁₀₃	1	2	yes	—
326	C₂×C₄	#102×C₁₀₃	1	2	yes	—
327	C₂×C₄	#104×C₁₀₃	1	2	yes	—
328	C₂×C₄	C₂²×C₈×C₁₀₃	1	1	yes	characteristic
329	C₂×C₄	C₂×M₁₆×C₁₀₃	1	1	yes	characteristic
330	C₂×C₄	C₂×D₈×C₁₀₃	1	1	yes	characteristic
331	C₂×C₄	C₂×SD₁₆×C₁₀₃	1	1	yes	characteristic
332	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
333	C₂×C₄	#137×C₁₀₃	1	1	yes	characteristic
334	C₈	—	4	4	no	—
335	C₈	—	8	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	8	1	no	—
340	C₂²	—	8	1	no	—
341	C₂²	—	8	1	no	—
342	C₂²	—	8	1	no	—
343	C₂²	C₂×C₂²⋊C₈×C₁₀₃	1	1	yes	characteristic
344	C₂²	#410×C₁₀₃	1	1	yes	characteristic
345	C₂²	#413×C₁₀₃	1	1	yes	characteristic
346	C₂²	C₂×#102×C₁₀₃	1	1	yes	characteristic
347	C₂²	#417×C₁₀₃	1	1	yes	characteristic
348	C₂²	C₂×#104×C₁₀₃	1	1	yes	characteristic
349	C₂²	#421×C₁₀₃	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	1	no	—
360	C₄	—	8	1	no	—
361	C₄	—	8	1	no	—
362	C₄	D₄⋊C₈×C₁₀₃	1	4	yes	—
363	C₂	—	8	2	no	—
364	C₂	C₁₀₃×#1458	1	1	yes	characteristic
365	C₂	C₂×D₄⋊C₈×C₁₀₃	1	1	yes	characteristic
366	C₂	C₁₀₃×#1477	1	1	yes	characteristic
367	C₂	C₁₀₃×#1509	1	1	yes	characteristic
368	C₂	C₁₀₃×#1517	1	1	yes	characteristic
369	C₂	C₁₀₃×#1529	1	1	yes	characteristic
370	C₂	C₁₀₃×#1547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₀₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₃
prime radical	C₂²×D₄×C₁₀₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₄³×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₃×#1831	C₂	semidirect
3. C₄×C₄⋊C₈×C₁₀₃	C₂	semidirect
4. C₁₀₃×#1271	C₂	semidirect
28. C₄×D₄×C₁₀₃	C₈	semidirect
177. #7574	C₁₀₃	direct (N × H)
187. #1831	C₂×C₁₀₃	semidirect
188. C₄×C₄⋊C₈	C₂×C₁₀₃	semidirect
189. #1271	C₂×C₁₀₃	semidirect
191. C₁₀₃	#7574	direct (N × H)
214. C₄×D₄	C₈×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×#2293	2
C₁₀₃×#1831	2
C₄×C₄⋊C₈×C₁₀₃	2
C₁₀₃×#1271	2
C₁₀₃×#1270	2
#7574	103

Subgroups — C103×#7574 #39912849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#7574 #39912849