Subgroups — C₁₀₃×#20917 #39926192

Order 26368.

1698 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#421×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#408×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₃×#1876	C₂	1	8	yes	maximal, complemented
7	C₁₀₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₁₀₃	C₂²	1	1	yes	characteristic
11	#575×C₁₀₃	—	2	4	no	—
12	#575×C₁₀₃	—	2	4	no	—
13	C₂×#137×C₁₀₃	C₄	1	2	yes	complemented
14	C₂×#137×C₁₀₃	C₄	1	2	yes	complemented
15	C₂×AGL(1,ℤ/8)×C₁₀₃	C₄	1	2	yes	complemented
16	C₂×AGL(1,ℤ/8)×C₁₀₃	C₄	1	2	yes	complemented
17	C₂×#135×C₁₀₃	C₂²	1	4	yes	—
18	C₂×#131×C₁₀₃	—	2	4	no	—
19	C₂×#131×C₁₀₃	—	2	4	no	—
20	C₂×#131×C₁₀₃	—	2	2	no	—
21	C₂×#131×C₁₀₃	C₂²	1	4	yes	complemented
22	C₂²×M₁₆×C₁₀₃	—	2	1	no	—
23	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₀₃	—	2	1	no	—
27	C₂³×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₀₃	C₂²	1	1	yes	characteristic
29	#421×C₁₀₃	—	2	4	no	—
30	#421×C₁₀₃	—	2	4	no	—
31	C₂×#104×C₁₀₃	C₂²	1	4	yes	complemented
32	C₂×#104×C₁₀₃	C₂²	1	4	yes	complemented
33	#408×C₁₀₃	—	2	1	no	—
34	#408×C₁₀₃	—	2	1	no	—
35	#408×C₁₀₃	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊C₈×C₁₀₃	—	2	2	no	—
37	#341×C₁₀₃	C₂²	1	4	yes	complemented
38	#336×C₁₀₃	C₂²	1	4	yes	complemented
39	C₂×#41×C₁₀₃	—	2	2	no	—
40	C₂×#41×C₁₀₃	—	2	1	no	—
41	C₂×#41×C₁₀₃	—	2	1	no	—
42	C₂×#41×C₁₀₃	—	2	1	no	—
43	C₂×#41×C₁₀₃	—	2	2	no	—
44	C₂×#41×C₁₀₃	—	2	1	no	—
45	C₂×#41×C₁₀₃	—	2	2	no	—
46	C₂×#41×C₁₀₃	—	2	2	no	—
47	C₂×#41×C₁₀₃	—	2	2	no	—
48	C₂×#41×C₁₀₃	—	2	2	no	—
49	C₂×#41×C₁₀₃	C₂×C₄	1	2	yes	—
50	C₂×#41×C₁₀₃	C₂×C₄	1	2	yes	—
51	C₂×#41×C₁₀₃	D₄	1	4	yes	—
52	C₂×#41×C₁₀₃	D₄	1	4	yes	—
53	C₂×#41×C₁₀₃	C₂³	1	2	yes	—
54	C₂×#41×C₁₀₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₀₃	—	2	1	no	—
58	C₂²×D₄×C₁₀₃	—	2	1	no	—
59	C₂²×D₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₀₃	—	2	1	no	—
62	C₂³×C₄×C₁₀₃	—	2	1	no	—
63	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
64	#137×C₁₀₃	—	2	8	no	—
65	#137×C₁₀₃	—	2	8	no	—
66	AGL(1,ℤ/8)×C₁₀₃	—	2	8	no	—
67	AGL(1,ℤ/8)×C₁₀₃	—	2	8	no	—
68	#135×C₁₀₃	—	2	8	no	—
69	#135×C₁₀₃	—	2	8	no	—
70	C₂×Q₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
71	C₂×SD₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
72	C₂×SD₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
73	C₂×D₈×C₁₀₃	C₂×C₄	1	4	yes	—
74	#131×C₁₀₃	—	2	16	no	—
75	#131×C₁₀₃	—	2	8	no	—
76	#131×C₁₀₃	—	2	8	no	—
77	C₂×M₁₆×C₁₀₃	—	2	8	no	—
78	C₂×M₁₆×C₁₀₃	—	2	2	no	—
79	C₂×M₁₆×C₁₀₃	—	2	1	no	—
80	C₂×M₁₆×C₁₀₃	—	2	2	no	—
81	C₂×M₁₆×C₁₀₃	—	2	2	no	—
82	C₂×M₁₆×C₁₀₃	—	2	1	no	—
83	C₂×M₁₆×C₁₀₃	—	2	4	no	—
84	C₂×M₁₆×C₁₀₃	—	2	2	no	—
85	C₂×M₁₆×C₁₀₃	—	2	2	no	—
86	C₂×M₁₆×C₁₀₃	C₂×C₄	1	2	yes	—
87	C₂×M₁₆×C₁₀₃	C₂×C₄	1	2	yes	—
88	C₂×M₁₆×C₁₀₃	D₄	1	4	yes	—
89	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
90	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
91	C₂²×C₈×C₁₀₃	—	2	8	no	—
92	C₂²×C₈×C₁₀₃	—	2	1	no	—
93	C₂²×C₈×C₁₀₃	—	2	2	no	—
94	C₂²×C₈×C₁₀₃	—	2	2	no	—
95	C₂²×C₈×C₁₀₃	—	2	4	no	—
96	C₂²×C₈×C₁₀₃	—	2	1	no	—
97	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
98	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
102	#117×C₁₀₃	—	2	2	no	—
103	#117×C₁₀₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
106	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
107	#104×C₁₀₃	—	2	8	no	—
108	#104×C₁₀₃	—	2	8	no	—
109	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
110	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
111	C₂⁴×C₁₀₃	—	2	1	no	—
112	C₂⁴×C₁₀₃	—	2	1	no	—
113	C₂⁴×C₁₀₃	#41	1	1	yes	characteristic
114	#41×C₁₀₃	—	2	4	no	—
115	#41×C₁₀₃	—	2	4	no	—
116	#41×C₁₀₃	—	2	4	no	—
117	#41×C₁₀₃	—	2	4	no	—
118	#41×C₁₀₃	—	2	4	no	—
119	#41×C₁₀₃	—	2	2	no	—
120	#41×C₁₀₃	—	2	2	no	—
121	#41×C₁₀₃	—	2	4	no	—
122	#41×C₁₀₃	—	2	4	no	—
123	#41×C₁₀₃	—	2	2	no	—
124	#41×C₁₀₃	—	2	2	no	—
125	#41×C₁₀₃	—	2	2	no	—
126	#41×C₁₀₃	—	2	2	no	—
127	#41×C₁₀₃	—	4	2	no	—
128	#41×C₁₀₃	—	4	2	no	—
129	#41×C₁₀₃	—	4	2	no	—
130	#41×C₁₀₃	—	4	2	no	—
131	#41×C₁₀₃	C₂²⋊C₄	1	8	yes	—
132	#41×C₁₀₃	C₂×D₄	1	4	yes	—
133	#41×C₁₀₃	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₁₀₃	—	2	1	no	—
135	C₂×Q₈×C₁₀₃	—	2	2	no	—
136	C₂×Q₈×C₁₀₃	—	2	1	no	—
137	C₂×Q₈×C₁₀₃	—	2	2	no	—
138	C₂×Q₈×C₁₀₃	—	2	2	no	—
139	C₂×Q₈×C₁₀₃	C₂²⋊C₄	1	4	yes	—
140	C₂×Q₈×C₁₀₃	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₁₀₃	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₁₀₃	—	2	2	no	—
143	C₂×D₄×C₁₀₃	—	2	4	no	—
144	C₂×D₄×C₁₀₃	—	2	4	no	—
145	C₂×D₄×C₁₀₃	—	2	2	no	—
146	C₂×D₄×C₁₀₃	—	2	2	no	—
147	C₂×D₄×C₁₀₃	—	2	2	no	—
148	C₂×D₄×C₁₀₃	—	2	2	no	—
149	C₂×D₄×C₁₀₃	—	2	2	no	—
150	C₂×D₄×C₁₀₃	—	2	1	no	—
151	C₂×D₄×C₁₀₃	—	2	2	no	—
152	C₂×D₄×C₁₀₃	—	2	1	no	—
153	C₂×D₄×C₁₀₃	—	4	2	no	—
154	C₂×D₄×C₁₀₃	—	4	2	no	—
155	C₂×D₄×C₁₀₃	C₂²⋊C₄	1	4	yes	—
156	C₂×D₄×C₁₀₃	C₂²×C₄	1	2	yes	—
157	C₂×D₄×C₁₀₃	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₀₃	—	2	1	no	—
159	C₂²×C₄×C₁₀₃	—	2	2	no	—
160	C₂²×C₄×C₁₀₃	—	2	4	no	—
161	C₂²×C₄×C₁₀₃	—	2	4	no	—
162	C₂²×C₄×C₁₀₃	—	2	2	no	—
163	C₂²×C₄×C₁₀₃	—	2	1	no	—
164	C₂²×C₄×C₁₀₃	—	2	2	no	—
165	C₂²×C₄×C₁₀₃	—	2	2	no	—
166	C₂²×C₄×C₁₀₃	—	2	2	no	—
167	C₂²×C₄×C₁₀₃	—	4	2	no	—
168	C₂²×C₄×C₁₀₃	—	4	2	no	—
169	C₂²×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₀₃	#41	1	2	yes	—
178	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₁₀₃	—	2	8	no	—
180	SD₁₆×C₁₀₃	—	2	8	no	—
181	SD₁₆×C₁₀₃	—	2	8	no	—
182	D₈×C₁₀₃	—	2	8	no	—
183	M₁₆×C₁₀₃	—	2	16	no	—
184	M₁₆×C₁₀₃	—	2	4	no	—
185	M₁₆×C₁₀₃	—	2	4	no	—
186	M₁₆×C₁₀₃	—	2	4	no	—
187	M₁₆×C₁₀₃	—	2	2	no	—
188	M₁₆×C₁₀₃	—	2	2	no	—
189	M₁₆×C₁₀₃	—	2	2	no	—
190	M₁₆×C₁₀₃	—	4	2	no	—
191	M₁₆×C₁₀₃	C₂×D₄	1	4	yes	—
192	C₂×C₈×C₁₀₃	—	2	16	no	—
193	C₂×C₈×C₁₀₃	—	2	2	no	—
194	C₂×C₈×C₁₀₃	—	2	4	no	—
195	C₂×C₈×C₁₀₃	—	2	2	no	—
196	C₂×C₈×C₁₀₃	—	2	4	no	—
197	C₂×C₈×C₁₀₃	—	2	2	no	—
198	C₂×C₈×C₁₀₃	—	2	2	no	—
199	C₂×C₈×C₁₀₃	—	2	2	no	—
200	C₂×C₈×C₁₀₃	—	2	2	no	—
201	C₂×C₈×C₁₀₃	—	2	2	no	—
202	C₂×C₈×C₁₀₃	—	2	2	no	—
203	C₂×C₈×C₁₀₃	—	4	2	no	—
204	C₂×C₈×C₁₀₃	C₂²×C₄	1	4	yes	—
205	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₁₀₃	—	4	2	no	—
208	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
209	C₄²×C₁₀₃	—	2	2	no	—
210	C₄²×C₁₀₃	—	2	2	no	—
211	C₂³×C₁₀₃	—	2	2	no	—
212	C₂³×C₁₀₃	—	2	4	no	—
213	C₂³×C₁₀₃	—	2	2	no	—
214	C₂³×C₁₀₃	—	4	2	no	—
215	C₂³×C₁₀₃	—	4	4	no	—
216	C₂³×C₁₀₃	—	4	4	no	—
217	C₂³×C₁₀₃	—	4	2	no	—
218	C₂³×C₁₀₃	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₁₀₃	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₁₀₃	#121	1	2	yes	—
221	C₂³×C₁₀₃	#123	1	2	yes	—
222	C₂³×C₁₀₃	C₂×#41	1	1	yes	characteristic
223	Q₈×C₁₀₃	—	2	2	no	—
224	Q₈×C₁₀₃	—	2	4	no	—
225	Q₈×C₁₀₃	—	2	2	no	—
226	Q₈×C₁₀₃	—	2	2	no	—
227	Q₈×C₁₀₃	—	4	2	no	—
228	Q₈×C₁₀₃	C₂×C₂²⋊C₄	1	4	yes	—
229	D₄×C₁₀₃	—	2	4	no	—
230	D₄×C₁₀₃	—	2	4	no	—
231	D₄×C₁₀₃	—	2	8	no	—
232	D₄×C₁₀₃	—	2	2	no	—
233	D₄×C₁₀₃	—	2	2	no	—
234	D₄×C₁₀₃	—	2	2	no	—
235	D₄×C₁₀₃	—	2	4	no	—
236	D₄×C₁₀₃	—	4	2	no	—
237	D₄×C₁₀₃	—	4	2	no	—
238	D₄×C₁₀₃	—	4	4	no	—
239	D₄×C₁₀₃	—	4	2	no	—
240	D₄×C₁₀₃	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₁₀₃	—	2	2	no	—
242	C₂×C₄×C₁₀₃	—	2	4	no	—
243	C₂×C₄×C₁₀₃	—	2	4	no	—
244	C₂×C₄×C₁₀₃	—	2	4	no	—
245	C₂×C₄×C₁₀₃	—	2	8	no	—
246	C₂×C₄×C₁₀₃	—	2	2	no	—
247	C₂×C₄×C₁₀₃	—	4	2	no	—
248	C₂×C₄×C₁₀₃	—	4	2	no	—
249	C₂×C₄×C₁₀₃	—	4	2	no	—
250	C₂×C₄×C₁₀₃	—	4	4	no	—
251	C₂×C₄×C₁₀₃	—	4	4	no	—
252	C₂×C₄×C₁₀₃	—	4	2	no	—
253	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂×C₄×C₁₀₃	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₁₀₃	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₁₀₃	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₀₃	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₀₃	#120	1	2	yes	—
260	C₂×C₄×C₁₀₃	#120	1	2	yes	—
261	C₂×C₄×C₁₀₃	#121	1	2	yes	—
262	C₂×C₄×C₁₀₃	#121	1	2	yes	—
263	C₂×C₄×C₁₀₃	#121	1	2	yes	—
264	C₂×C₄×C₁₀₃	#123	1	2	yes	—
265	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
271	C₈×C₁₀₃	—	2	4	no	—
272	C₈×C₁₀₃	—	2	2	no	—
273	C₈×C₁₀₃	—	2	4	no	—
274	C₈×C₁₀₃	—	2	2	no	—
275	C₈×C₁₀₃	—	4	2	no	—
276	C₂²×C₁₀₃	—	2	2	no	—
277	C₂²×C₁₀₃	—	2	2	no	—
278	C₂²×C₁₀₃	—	2	2	no	—
279	C₂²×C₁₀₃	—	2	4	no	—
280	C₂²×C₁₀₃	—	4	2	no	—
281	C₂²×C₁₀₃	—	4	2	no	—
282	C₂²×C₁₀₃	—	4	8	no	—
283	C₂²×C₁₀₃	—	4	4	no	—
284	C₂²×C₁₀₃	—	4	4	no	—
285	C₂²×C₁₀₃	—	4	2	no	—
286	C₂²×C₁₀₃	—	8	4	no	—
287	C₂²×C₁₀₃	#386	1	2	yes	—
288	C₂²×C₁₀₃	#386	1	2	yes	—
289	C₂²×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
291	C₂²×C₁₀₃	C₂×#123	1	1	yes	characteristic
292	C₄×C₁₀₃	—	2	4	no	—
293	C₄×C₁₀₃	—	4	2	no	—
294	C₄×C₁₀₃	—	8	2	no	—
295	C₄×C₁₀₃	#386	1	2	yes	—
296	C₄×C₁₀₃	#386	1	2	yes	—
297	C₄×C₁₀₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
298	C₄×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
299	C₄×C₁₀₃	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₀₃	C₂×#121	1	1	yes	characteristic
301	#20917	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂×C₁₀₃	—	2	1	no	—
303	C₂×C₁₀₃	—	2	2	no	—
304	C₂×C₁₀₃	—	2	2	no	—
305	C₂×C₁₀₃	—	2	1	no	—
306	C₂×C₁₀₃	—	4	4	no	—
307	C₂×C₁₀₃	—	8	2	no	—
308	C₂×C₁₀₃	C₂×#386	1	1	yes	characteristic
309	C₂×C₁₀₃	#2955	1	2	yes	—
310	C₂×#575	C₂×C₁₀₃	1	1	yes	characteristic
311	C₂²×#131	C₂×C₁₀₃	1	1	yes	characteristic, complemented
312	C₂×#421	C₂×C₁₀₃	1	1	yes	characteristic, complemented
313	C₂×#421	C₂×C₁₀₃	1	1	yes	characteristic, complemented
314	C₂×#408	C₂×C₁₀₃	1	1	yes	characteristic, complemented
315	#1876	C₂×C₁₀₃	1	8	yes	complemented
316	#1738	C₂×C₁₀₃	1	1	yes	characteristic, complemented
317	#1729	C₂×C₁₀₃	1	1	yes	characteristic, complemented
318	C₁₀₃	#20917	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²×#41	C₂²×C₁₀₃	1	1	yes	characteristic
320	C₂²×#41	C₂²×C₁₀₃	1	1	yes	characteristic
321	#575	—	2	4	no	—
322	#575	—	2	4	no	—
323	C₂×#137	C₄×C₁₀₃	1	2	yes	complemented
324	C₂×#137	C₄×C₁₀₃	1	2	yes	complemented
325	C₂×AGL(1,ℤ/8)	C₄×C₁₀₃	1	2	yes	complemented
326	C₂×AGL(1,ℤ/8)	C₄×C₁₀₃	1	2	yes	complemented
327	C₂×#135	C₂²×C₁₀₃	1	4	yes	—
328	C₂×#131	—	2	4	no	—
329	C₂×#131	—	2	4	no	—
330	C₂×#131	—	2	2	no	—
331	C₂×#131	C₂²×C₁₀₃	1	4	yes	complemented
332	C₂²×M₁₆	—	2	1	no	—
333	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
334	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
335	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
336	C₂³×C₈	—	2	1	no	—
337	C₂³×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
338	C₂×#117	C₂²×C₁₀₃	1	1	yes	characteristic
339	#421	—	2	4	no	—
340	#421	—	2	4	no	—
341	C₂×#104	C₂²×C₁₀₃	1	4	yes	complemented
342	C₂×#104	C₂²×C₁₀₃	1	4	yes	complemented
343	#408	—	2	1	no	—
344	#408	—	2	1	no	—
345	#408	C₂²×C₁₀₃	1	4	yes	complemented
346	C₂×C₂²⋊C₈	—	2	2	no	—
347	#341	C₂²×C₁₀₃	1	4	yes	complemented
348	#336	C₂²×C₁₀₃	1	4	yes	complemented
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	C₂×C₄×C₁₀₃	1	2	yes	—
360	C₂×#41	C₂×C₄×C₁₀₃	1	2	yes	—
361	C₂×#41	D₄×C₁₀₃	1	4	yes	—
362	C₂×#41	D₄×C₁₀₃	1	4	yes	—
363	C₂×#41	C₂³×C₁₀₃	1	2	yes	—
364	C₂×#41	C₂³×C₁₀₃	1	2	yes	—
365	C₂²×Q₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
366	C₂²×Q₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
370	C₂²×D₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
374	#137	—	2	8	no	—
375	#137	—	2	8	no	—
376	AGL(1,ℤ/8)	—	2	8	no	—
377	AGL(1,ℤ/8)	—	2	8	no	—
378	#135	—	2	8	no	—
379	#135	—	2	8	no	—
380	C₂×Q₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
381	C₂×SD₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
382	C₂×SD₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
383	C₂×D₈	C₂×C₄×C₁₀₃	1	4	yes	—
384	#131	—	2	16	no	—
385	#131	—	2	8	no	—
386	#131	—	2	8	no	—
387	C₂×M₁₆	—	2	8	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	4	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	C₂×C₄×C₁₀₃	1	2	yes	—
397	C₂×M₁₆	C₂×C₄×C₁₀₃	1	2	yes	—
398	C₂×M₁₆	D₄×C₁₀₃	1	4	yes	—
399	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
400	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
401	C₂²×C₈	—	2	8	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	2	2	no	—
405	C₂²×C₈	—	2	4	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
408	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
409	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
410	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
411	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
417	#104	—	2	8	no	—
418	#104	—	2	8	no	—
419	C₂²⋊C₈	—	2	4	no	—
420	C₂²⋊C₈	—	2	4	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#41×C₁₀₃	1	1	yes	characteristic
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	C₂²⋊C₄×C₁₀₃	1	8	yes	—
442	#41	C₂×D₄×C₁₀₃	1	4	yes	—
443	#41	C₂×D₄×C₁₀₃	1	4	yes	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	C₂²⋊C₄×C₁₀₃	1	4	yes	—
450	C₂×Q₈	C₂²×C₄×C₁₀₃	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₁₀₃	1	2	yes	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	C₂²⋊C₄×C₁₀₃	1	4	yes	—
466	C₂×D₄	C₂²×C₄×C₁₀₃	1	2	yes	—
467	C₂×D₄	C₂²×C₄×C₁₀₃	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
483	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
486	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
487	C₂²×C₄	#41×C₁₀₃	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
489	Q₁₆	—	2	8	no	—
490	SD₁₆	—	2	8	no	—
491	SD₁₆	—	2	8	no	—
492	D₈	—	2	8	no	—
493	M₁₆	—	2	16	no	—
494	M₁₆	—	2	4	no	—
495	M₁₆	—	2	4	no	—
496	M₁₆	—	2	4	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	2	2	no	—
499	M₁₆	—	2	2	no	—
500	M₁₆	—	4	2	no	—
501	M₁₆	C₂×D₄×C₁₀₃	1	4	yes	—
502	C₂×C₈	—	2	16	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	4	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	4	2	no	—
514	C₂×C₈	C₂²×C₄×C₁₀₃	1	4	yes	—
515	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
517	C₄⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	2	no	—
528	C₂³	C₄×D₄×C₁₀₃	1	1	yes	characteristic
529	C₂³	C₄×D₄×C₁₀₃	1	1	yes	characteristic
530	C₂³	#121×C₁₀₃	1	2	yes	—
531	C₂³	#123×C₁₀₃	1	2	yes	—
532	C₂³	C₂×#41×C₁₀₃	1	1	yes	characteristic
533	Q₈	—	2	4	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	4	2	no	—
538	Q₈	C₂×C₂²⋊C₄×C₁₀₃	1	4	yes	—
539	D₄	—	2	8	no	—
540	D₄	—	2	4	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	C₂×C₂²⋊C₄×C₁₀₃	1	4	yes	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
565	C₂×C₄	C₄×D₄×C₁₀₃	1	1	yes	characteristic
566	C₂×C₄	C₄×D₄×C₁₀₃	1	1	yes	characteristic
567	C₂×C₄	C₄×D₄×C₁₀₃	1	2	yes	—
568	C₂×C₄	C₄×D₄×C₁₀₃	1	2	yes	—
569	C₂×C₄	#120×C₁₀₃	1	2	yes	—
570	C₂×C₄	#120×C₁₀₃	1	2	yes	—
571	C₂×C₄	#121×C₁₀₃	1	2	yes	—
572	C₂×C₄	#121×C₁₀₃	1	2	yes	—
573	C₂×C₄	#121×C₁₀₃	1	2	yes	—
574	C₂×C₄	#123×C₁₀₃	1	2	yes	—
575	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
580	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
581	C₈	—	2	4	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	4	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	8	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	8	4	no	—
597	C₂²	#386×C₁₀₃	1	2	yes	—
598	C₂²	#386×C₁₀₃	1	2	yes	—
599	C₂²	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
600	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
601	C₂²	C₂×#123×C₁₀₃	1	1	yes	characteristic
602	C₄	—	2	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	8	2	no	—
605	C₄	#386×C₁₀₃	1	2	yes	—
606	C₄	#386×C₁₀₃	1	2	yes	—
607	C₄	C₂²×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
608	C₄	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
609	C₄	C₂×#120×C₁₀₃	1	1	yes	characteristic
610	C₄	C₂×#121×C₁₀₃	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	2	no	—
613	C₂	—	2	2	no	—
614	C₂	—	2	1	no	—
615	C₂	—	4	4	no	—
616	C₂	—	8	2	no	—
617	C₂	C₂×#386×C₁₀₃	1	1	yes	characteristic
618	C₂	C₁₀₃×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₀₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
socle	C₂²×C₁₀₃	C₂×C₄×D₄
prime radical	C₂×#575×C₁₀₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₃ ◁ C₂³×C₈×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#131×C₁₀₃	C₂	semidirect
3. C₂×#421×C₁₀₃	C₂	semidirect
4. C₂×#421×C₁₀₃	C₂	semidirect
5. C₂×#408×C₁₀₃	C₂	semidirect
6. C₁₀₃×#1876	C₂	semidirect
7. C₁₀₃×#1738	C₂	semidirect
8. C₁₀₃×#1729	C₂	semidirect
13. C₂×#137×C₁₀₃	C₄	semidirect
14. C₂×#137×C₁₀₃	C₄	semidirect
15. C₂×AGL(1,ℤ/8)×C₁₀₃	C₄	semidirect
16. C₂×AGL(1,ℤ/8)×C₁₀₃	C₄	semidirect
21. C₂×#131×C₁₀₃	C₂²	semidirect
31. C₂×#104×C₁₀₃	C₂²	semidirect
32. C₂×#104×C₁₀₃	C₂²	semidirect
35. #408×C₁₀₃	C₂²	semidirect
37. #341×C₁₀₃	C₂²	semidirect
38. #336×C₁₀₃	C₂²	semidirect
301. #20917	C₁₀₃	direct (N × H)
311. C₂²×#131	C₂×C₁₀₃	semidirect
312. C₂×#421	C₂×C₁₀₃	semidirect
313. C₂×#421	C₂×C₁₀₃	semidirect
314. C₂×#408	C₂×C₁₀₃	semidirect
315. #1876	C₂×C₁₀₃	semidirect
316. #1738	C₂×C₁₀₃	semidirect
317. #1729	C₂×C₁₀₃	semidirect
318. C₁₀₃	#20917	direct (N × H)
323. C₂×#137	C₄×C₁₀₃	semidirect
324. C₂×#137	C₄×C₁₀₃	semidirect
325. C₂×AGL(1,ℤ/8)	C₄×C₁₀₃	semidirect
326. C₂×AGL(1,ℤ/8)	C₄×C₁₀₃	semidirect
331. C₂×#131	C₂²×C₁₀₃	semidirect
341. C₂×#104	C₂²×C₁₀₃	semidirect
342. C₂×#104	C₂²×C₁₀₃	semidirect
345. #408	C₂²×C₁₀₃	semidirect
347. #341	C₂²×C₁₀₃	semidirect
348. #336	C₂²×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₁₀₃	2
C₂²×#131×C₁₀₃	2
C₂×#421×C₁₀₃	2
C₂×#408×C₁₀₃	2
C₁₀₃×#1876	2
C₁₀₃×#1738	2
C₁₀₃×#1729	2
#20917	103

Subgroups — C103×#20917 #39926192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#20917 #39926192