Subgroups — C₁₀₃×#24661 #39929936

Order 26368.

1016 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#460×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#432×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#2856	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂²⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1973	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1936	C₂	1	2	yes	maximal, complemented
11	C₁₀₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₀₃	C₂²	1	2	yes	—
13	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₁₀₃	—	2	1	no	—
16	C₂×#121×C₁₀₃	—	2	1	no	—
17	C₂×#121×C₁₀₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
20	#460×C₁₀₃	—	2	4	no	—
21	#432×C₁₀₃	—	2	4	no	—
22	C₂×#107×C₁₀₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
26	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
27	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
28	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
30	C₂×#97×C₁₀₃	C₂²	1	2	yes	—
31	#391×C₁₀₃	C₂²	1	1	yes	characteristic
32	#390×C₁₀₃	—	2	1	no	—
33	#390×C₁₀₃	—	2	1	no	—
34	#390×C₁₀₃	C₂²	1	2	yes	—
35	#389×C₁₀₃	C₂²	1	1	yes	characteristic
36	#387×C₁₀₃	—	2	1	no	—
37	#385×C₁₀₃	—	2	1	no	—
38	#384×C₁₀₃	C₂²	1	1	yes	characteristic
39	#380×C₁₀₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₀₃	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
43	#340×C₁₀₃	C₂²	1	2	yes	—
44	#340×C₁₀₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₀₃	—	2	2	no	—
47	C₂²×D₄×C₁₀₃	—	2	1	no	—
48	C₂²×D₄×C₁₀₃	—	2	1	no	—
49	C₂²×D₄×C₁₀₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
54	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
55	C₂×SD₁₆×C₁₀₃	—	4	2	no	—
56	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
58	#127×C₁₀₃	—	2	2	no	—
59	#127×C₁₀₃	—	2	2	no	—
60	C₂²⋊Q₈×C₁₀₃	—	2	2	no	—
61	C₂²⋊Q₈×C₁₀₃	—	2	2	no	—
62	#121×C₁₀₃	—	4	2	no	—
63	#121×C₁₀₃	—	4	2	no	—
64	#121×C₁₀₃	—	4	4	no	—
65	#121×C₁₀₃	—	4	4	no	—
66	C₄×Q₈×C₁₀₃	—	2	2	no	—
67	C₄×Q₈×C₁₀₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
82	C₂×C₄²×C₁₀₃	—	2	2	no	—
83	C₂×C₄²×C₁₀₃	—	2	2	no	—
84	C₂×C₄²×C₁₀₃	—	2	1	no	—
85	C₂×C₄²×C₁₀₃	—	2	1	no	—
86	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
90	#107×C₁₀₃	—	4	2	no	—
91	C₄⋊C₈×C₁₀₃	—	2	2	no	—
92	C₄⋊C₈×C₁₀₃	D₄	1	4	yes	complemented
93	#103×C₁₀₃	—	4	2	no	—
94	#102×C₁₀₃	—	2	4	no	—
95	#102×C₁₀₃	—	2	4	no	—
96	#102×C₁₀₃	—	4	2	no	—
97	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
98	#97×C₁₀₃	—	2	4	no	—
99	#95×C₁₀₃	—	2	1	no	—
100	#95×C₁₀₃	—	2	1	no	—
101	#95×C₁₀₃	—	2	1	no	—
102	#95×C₁₀₃	—	2	1	no	—
103	#95×C₁₀₃	—	2	1	no	—
104	C₂⁴×C₁₀₃	—	2	2	no	—
105	C₂⁴×C₁₀₃	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₀₃	—	2	1	no	—
107	C₂×Q₈×C₁₀₃	—	2	1	no	—
108	C₂×Q₈×C₁₀₃	—	2	1	no	—
109	C₂×Q₈×C₁₀₃	—	2	1	no	—
110	C₂×Q₈×C₁₀₃	—	2	1	no	—
111	C₂×Q₈×C₁₀₃	#41	1	2	yes	—
112	C₂×D₄×C₁₀₃	—	2	2	no	—
113	C₂×D₄×C₁₀₃	—	2	2	no	—
114	C₂×D₄×C₁₀₃	—	2	2	no	—
115	C₂×D₄×C₁₀₃	—	2	2	no	—
116	C₂×D₄×C₁₀₃	—	2	2	no	—
117	C₂×D₄×C₁₀₃	—	2	2	no	—
118	C₂×D₄×C₁₀₃	—	4	2	no	—
119	C₂×D₄×C₁₀₃	—	4	2	no	—
120	C₂×D₄×C₁₀₃	—	4	4	no	—
121	C₂×D₄×C₁₀₃	—	4	4	no	—
122	C₂×D₄×C₁₀₃	—	4	4	no	—
123	C₂×D₄×C₁₀₃	—	4	2	no	—
124	C₂×D₄×C₁₀₃	—	4	2	no	—
125	C₂×D₄×C₁₀₃	—	4	2	no	—
126	C₂×D₄×C₁₀₃	—	4	2	no	—
127	C₂²×C₄×C₁₀₃	—	2	2	no	—
128	C₂²×C₄×C₁₀₃	—	2	1	no	—
129	C₂²×C₄×C₁₀₃	—	2	1	no	—
130	C₂²×C₄×C₁₀₃	—	2	2	no	—
131	C₂²×C₄×C₁₀₃	—	2	2	no	—
132	C₂²×C₄×C₁₀₃	—	2	2	no	—
133	C₂²×C₄×C₁₀₃	—	2	2	no	—
134	C₂²×C₄×C₁₀₃	—	2	1	no	—
135	C₂²×C₄×C₁₀₃	—	2	1	no	—
136	C₂²×C₄×C₁₀₃	—	2	1	no	—
137	C₂²×C₄×C₁₀₃	—	2	1	no	—
138	C₂²×C₄×C₁₀₃	—	2	1	no	—
139	C₂²×C₄×C₁₀₃	—	2	1	no	—
140	C₂²×C₄×C₁₀₃	—	2	1	no	—
141	C₂²×C₄×C₁₀₃	—	2	1	no	—
142	C₂²×C₄×C₁₀₃	—	2	2	no	—
143	C₂²×C₄×C₁₀₃	—	4	1	no	—
144	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
150	SD₁₆×C₁₀₃	—	4	8	no	—
151	C₂×C₈×C₁₀₃	—	2	2	no	—
152	C₂×C₈×C₁₀₃	—	2	2	no	—
153	C₂×C₈×C₁₀₃	—	2	2	no	—
154	C₂×C₈×C₁₀₃	—	2	2	no	—
155	C₂×C₈×C₁₀₃	—	2	2	no	—
156	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₀₃	—	2	4	no	—
158	C₄⋊C₄×C₁₀₃	—	2	1	no	—
159	C₄⋊C₄×C₁₀₃	—	2	1	no	—
160	C₄⋊C₄×C₁₀₃	—	2	1	no	—
161	C₄⋊C₄×C₁₀₃	—	2	1	no	—
162	C₄⋊C₄×C₁₀₃	—	2	2	no	—
163	C₄⋊C₄×C₁₀₃	—	2	1	no	—
164	C₄⋊C₄×C₁₀₃	—	2	2	no	—
165	C₄⋊C₄×C₁₀₃	—	4	2	no	—
166	C₄⋊C₄×C₁₀₃	—	4	2	no	—
167	C₄⋊C₄×C₁₀₃	—	4	2	no	—
168	C₄⋊C₄×C₁₀₃	—	4	2	no	—
169	C₄⋊C₄×C₁₀₃	#41	1	2	yes	—
170	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
171	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
172	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
173	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
174	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
175	C₄²×C₁₀₃	—	2	2	no	—
176	C₄²×C₁₀₃	—	2	2	no	—
177	C₄²×C₁₀₃	—	2	1	no	—
178	C₄²×C₁₀₃	—	2	1	no	—
179	C₄²×C₁₀₃	—	4	2	no	—
180	C₄²×C₁₀₃	—	4	2	no	—
181	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
182	C₄²×C₁₀₃	#41	1	2	yes	—
183	C₂³×C₁₀₃	—	2	1	no	—
184	C₂³×C₁₀₃	—	2	1	no	—
185	C₂³×C₁₀₃	—	2	1	no	—
186	C₂³×C₁₀₃	—	2	1	no	—
187	C₂³×C₁₀₃	—	2	1	no	—
188	C₂³×C₁₀₃	—	2	1	no	—
189	C₂³×C₁₀₃	—	4	2	no	—
190	C₂³×C₁₀₃	—	4	2	no	—
191	C₂³×C₁₀₃	—	4	2	no	—
192	C₂³×C₁₀₃	—	4	2	no	—
193	C₂³×C₁₀₃	—	4	2	no	—
194	C₂³×C₁₀₃	—	4	2	no	—
195	C₂³×C₁₀₃	—	4	2	no	—
196	C₂³×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₀₃	—	2	2	no	—
199	Q₈×C₁₀₃	—	2	2	no	—
200	Q₈×C₁₀₃	—	4	1	no	—
201	Q₈×C₁₀₃	—	4	1	no	—
202	D₄×C₁₀₃	—	4	2	no	—
203	D₄×C₁₀₃	—	4	2	no	—
204	D₄×C₁₀₃	—	4	2	no	—
205	D₄×C₁₀₃	—	4	2	no	—
206	D₄×C₁₀₃	—	8	4	no	—
207	D₄×C₁₀₃	—	8	8	no	—
208	D₄×C₁₀₃	—	8	4	no	—
209	C₂×C₄×C₁₀₃	—	2	1	no	—
210	C₂×C₄×C₁₀₃	—	2	1	no	—
211	C₂×C₄×C₁₀₃	—	2	1	no	—
212	C₂×C₄×C₁₀₃	—	2	1	no	—
213	C₂×C₄×C₁₀₃	—	2	1	no	—
214	C₂×C₄×C₁₀₃	—	2	2	no	—
215	C₂×C₄×C₁₀₃	—	2	2	no	—
216	C₂×C₄×C₁₀₃	—	2	1	no	—
217	C₂×C₄×C₁₀₃	—	2	1	no	—
218	C₂×C₄×C₁₀₃	—	2	1	no	—
219	C₂×C₄×C₁₀₃	—	2	1	no	—
220	C₂×C₄×C₁₀₃	—	2	1	no	—
221	C₂×C₄×C₁₀₃	—	2	1	no	—
222	C₂×C₄×C₁₀₃	—	4	4	no	—
223	C₂×C₄×C₁₀₃	—	4	1	no	—
224	C₂×C₄×C₁₀₃	—	4	1	no	—
225	C₂×C₄×C₁₀₃	—	4	1	no	—
226	C₂×C₄×C₁₀₃	—	4	1	no	—
227	C₂×C₄×C₁₀₃	—	4	1	no	—
228	C₂×C₄×C₁₀₃	—	4	1	no	—
229	C₂×C₄×C₁₀₃	—	4	1	no	—
230	C₂×C₄×C₁₀₃	—	4	1	no	—
231	C₂×C₄×C₁₀₃	—	4	4	no	—
232	C₂×C₄×C₁₀₃	—	4	1	no	—
233	C₂×C₄×C₁₀₃	—	4	2	no	—
234	C₂×C₄×C₁₀₃	—	4	1	no	—
235	C₂×C₄×C₁₀₃	—	4	1	no	—
236	C₂×C₄×C₁₀₃	—	4	2	no	—
237	C₂×C₄×C₁₀₃	—	4	2	no	—
238	C₂×C₄×C₁₀₃	—	4	1	no	—
239	C₂×C₄×C₁₀₃	—	4	1	no	—
240	C₂×C₄×C₁₀₃	—	4	1	no	—
241	C₂×C₄×C₁₀₃	#121	1	2	yes	—
242	C₂×C₄×C₁₀₃	#121	1	2	yes	—
243	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
244	C₂×C₄×C₁₀₃	#137	1	2	yes	—
245	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
251	C₈×C₁₀₃	—	2	4	no	—
252	C₈×C₁₀₃	—	4	2	no	—
253	C₂²×C₁₀₃	—	2	2	no	—
254	C₂²×C₁₀₃	—	2	2	no	—
255	C₂²×C₁₀₃	—	2	2	no	—
256	C₂²×C₁₀₃	—	4	1	no	—
257	C₂²×C₁₀₃	—	4	1	no	—
258	C₂²×C₁₀₃	—	4	1	no	—
259	C₂²×C₁₀₃	—	4	1	no	—
260	C₂²×C₁₀₃	—	8	2	no	—
261	C₂²×C₁₀₃	—	8	2	no	—
262	C₂²×C₁₀₃	—	8	2	no	—
263	C₂²×C₁₀₃	—	8	2	no	—
264	C₂²×C₁₀₃	—	8	2	no	—
265	C₂²×C₁₀₃	—	8	2	no	—
266	C₂²×C₁₀₃	—	8	2	no	—
267	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
268	C₂²×C₁₀₃	#525	1	1	yes	characteristic
269	C₂²×C₁₀₃	#535	1	1	yes	characteristic
270	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
273	C₂²×C₁₀₃	#575	1	1	yes	characteristic
274	C₄×C₁₀₃	—	2	2	no	—
275	C₄×C₁₀₃	—	4	2	no	—
276	C₄×C₁₀₃	—	4	1	no	—
277	C₄×C₁₀₃	—	4	2	no	—
278	C₄×C₁₀₃	—	4	1	no	—
279	C₄×C₁₀₃	—	4	1	no	—
280	C₄×C₁₀₃	—	8	1	no	—
281	C₄×C₁₀₃	—	8	2	no	—
282	C₄×C₁₀₃	—	8	1	no	—
283	C₄×C₁₀₃	#468	1	4	yes	—
284	C₄×C₁₀₃	#546	1	1	yes	characteristic
285	C₄×C₁₀₃	#550	1	1	yes	characteristic
286	C₄×C₁₀₃	#553	1	1	yes	characteristic
287	C₄×C₁₀₃	#555	1	1	yes	characteristic
288	#24661	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂×C₁₀₃	—	4	2	no	—
290	C₂×C₁₀₃	—	16	2	no	—
291	C₂×C₁₀₃	#2414	1	1	yes	characteristic
292	C₂×C₁₀₃	C₂×#468	1	1	yes	characteristic
293	C₂×C₁₀₃	#3055	1	1	yes	characteristic
294	C₂×C₁₀₃	#3112	1	1	yes	characteristic
295	C₂×C₁₀₃	#3115	1	1	yes	characteristic
296	C₂×C₁₀₃	#3216	1	1	yes	characteristic
297	C₂×C₁₀₃	#3217	1	1	yes	characteristic
298	C₂×#460	C₂×C₁₀₃	1	1	yes	characteristic, complemented
299	C₂×#432	C₂×C₁₀₃	1	1	yes	characteristic, complemented
300	#2856	C₂×C₁₀₃	1	1	yes	characteristic
301	C₄×C₂²⋊Q₈	C₂×C₁₀₃	1	1	yes	characteristic, complemented
302	#2033	C₂×C₁₀₃	1	2	yes	complemented
303	#2000	C₂×C₁₀₃	1	2	yes	complemented
304	#1982	C₂×C₁₀₃	1	1	yes	characteristic, complemented
305	#1973	C₂×C₁₀₃	1	2	yes	complemented
306	#1947	C₂×C₁₀₃	1	1	yes	characteristic, complemented
307	#1936	C₂×C₁₀₃	1	2	yes	complemented
308	#1803	C₂×C₁₀₃	1	1	yes	characteristic, complemented
309	C₁₀₃	#24661	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²×SD₁₆	C₂²×C₁₀₃	1	2	yes	—
311	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
312	C₂×C₂²⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
313	C₂×#121	—	2	1	no	—
314	C₂×#121	—	2	1	no	—
315	C₂×#121	C₂²×C₁₀₃	1	2	yes	—
316	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
318	#460	—	2	4	no	—
319	#432	—	2	4	no	—
320	C₂×#107	C₂²×C₁₀₃	1	2	yes	—
321	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
324	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
325	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
326	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
327	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
328	C₂×#97	C₂²×C₁₀₃	1	2	yes	—
329	#391	C₂²×C₁₀₃	1	1	yes	characteristic
330	#390	—	2	1	no	—
331	#390	—	2	1	no	—
332	#390	C₂²×C₁₀₃	1	2	yes	—
333	#389	C₂²×C₁₀₃	1	1	yes	characteristic
334	#387	—	2	1	no	—
335	#385	—	2	1	no	—
336	#384	C₂²×C₁₀₃	1	1	yes	characteristic
337	#380	C₂²×C₁₀₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	—	2	1	no	—
339	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	—	2	1	no	—
341	#340	C₂²×C₁₀₃	1	2	yes	—
342	#340	C₂²×C₁₀₃	1	2	yes	—
343	C₂²×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	C₂³×C₁₀₃	1	2	yes	—
348	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
349	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
355	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
356	#127	—	2	2	no	—
357	#127	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	#121	—	4	2	no	—
361	#121	—	4	2	no	—
362	#121	—	4	4	no	—
363	#121	—	4	4	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
388	#107	—	4	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	D₄×C₁₀₃	1	4	yes	complemented
391	#103	—	4	2	no	—
392	#102	—	2	4	no	—
393	#102	—	2	4	no	—
394	#102	—	4	2	no	—
395	C₂²⋊C₈	—	2	4	no	—
396	#97	—	2	4	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	C₂×D₄×C₁₀₃	1	1	yes	characteristic
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	#41×C₁₀₃	1	2	yes	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
448	SD₁₆	—	4	8	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	#41×C₁₀₃	1	2	yes	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	4	2	no	—
478	C₄²	—	4	2	no	—
479	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
480	C₄²	#41×C₁₀₃	1	2	yes	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
495	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	8	no	—
506	D₄	—	8	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	#121×C₁₀₃	1	2	yes	—
540	C₂×C₄	#121×C₁₀₃	1	2	yes	—
541	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
542	C₂×C₄	#137×C₁₀₃	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
546	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
547	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
548	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
566	C₂²	#525×C₁₀₃	1	1	yes	characteristic
567	C₂²	#535×C₁₀₃	1	1	yes	characteristic
568	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
569	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
570	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
571	C₂²	#575×C₁₀₃	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	2	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	#468×C₁₀₃	1	4	yes	—
582	C₄	#546×C₁₀₃	1	1	yes	characteristic
583	C₄	#550×C₁₀₃	1	1	yes	characteristic
584	C₄	#553×C₁₀₃	1	1	yes	characteristic
585	C₄	#555×C₁₀₃	1	1	yes	characteristic
586	C₂	—	4	2	no	—
587	C₂	—	16	2	no	—
588	C₂	C₁₀₃×#2414	1	1	yes	characteristic
589	C₂	C₂×#468×C₁₀₃	1	1	yes	characteristic
590	C₂	C₁₀₃×#3055	1	1	yes	characteristic
591	C₂	C₁₀₃×#3112	1	1	yes	characteristic
592	C₂	C₁₀₃×#3115	1	1	yes	characteristic
593	C₂	C₁₀₃×#3216	1	1	yes	characteristic
594	C₂	C₁₀₃×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₁₀₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂²×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#460×C₁₀₃	C₂	semidirect
2. C₂×#432×C₁₀₃	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₁₀₃	C₂	semidirect
5. C₁₀₃×#2033	C₂	semidirect
6. C₁₀₃×#2000	C₂	semidirect
7. C₁₀₃×#1982	C₂	semidirect
8. C₁₀₃×#1973	C₂	semidirect
9. C₁₀₃×#1947	C₂	semidirect
10. C₁₀₃×#1936	C₂	semidirect
11. C₁₀₃×#1803	C₂	semidirect
92. C₄⋊C₈×C₁₀₃	D₄	semidirect
288. #24661	C₁₀₃	direct (N × H)
298. C₂×#460	C₂×C₁₀₃	semidirect
299. C₂×#432	C₂×C₁₀₃	semidirect
301. C₄×C₂²⋊Q₈	C₂×C₁₀₃	semidirect
302. #2033	C₂×C₁₀₃	semidirect
303. #2000	C₂×C₁₀₃	semidirect
304. #1982	C₂×C₁₀₃	semidirect
305. #1973	C₂×C₁₀₃	semidirect
306. #1947	C₂×C₁₀₃	semidirect
307. #1936	C₂×C₁₀₃	semidirect
308. #1803	C₂×C₁₀₃	semidirect
309. C₁₀₃	#24661	direct (N × H)
390. C₄⋊C₈	D₄×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#460×C₁₀₃	2
C₂×#432×C₁₀₃	2
C₁₀₃×#2856	2
C₄×C₂²⋊Q₈×C₁₀₃	2
C₁₀₃×#2033	2
C₁₀₃×#2000	2
C₁₀₃×#1982	2
C₁₀₃×#1973	2
C₁₀₃×#1947	2
C₁₀₃×#1936	2
C₁₀₃×#1803	2
#24661	103

Subgroups — C103×#24661 #39929936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#24661 #39929936