Subgroups — C₁₀₃×#26230 #39931505

Order 26368.

1070 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#480×C₁₀₃	C₂	1	2	yes	maximal, complemented
2	C₁₀₃×#2541	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#2033	C₂	1	2	yes	maximal, complemented
5	C₁₀₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₄×#107×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₀₃	—	2	1	no	—
13	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₁₀₃	C₂²	1	2	yes	—
15	C₂×#121×C₁₀₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₀₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
19	#480×C₁₀₃	—	2	8	no	—
20	C₂×#107×C₁₀₃	C₂²	1	2	yes	—
21	C₂×#107×C₁₀₃	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
25	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
26	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
27	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
31	#392×C₁₀₃	—	2	2	no	—
32	#390×C₁₀₃	—	2	1	no	—
33	#389×C₁₀₃	—	2	1	no	—
34	#385×C₁₀₃	—	2	2	no	—
35	#384×C₁₀₃	C₂²	1	1	yes	characteristic
36	#380×C₁₀₃	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
39	#340×C₁₀₃	C₂²	1	2	yes	—
40	#340×C₁₀₃	C₂²	1	1	yes	characteristic
41	#340×C₁₀₃	C₂²	1	1	yes	characteristic
42	C₂²×D₄×C₁₀₃	—	2	2	no	—
43	C₂²×D₄×C₁₀₃	—	2	2	no	—
44	C₂²×D₄×C₁₀₃	—	2	1	no	—
45	C₂²×D₄×C₁₀₃	—	2	1	no	—
46	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₀₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₀₃	—	2	2	no	—
49	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
53	#127×C₁₀₃	—	2	2	no	—
54	#127×C₁₀₃	—	2	2	no	—
55	#127×C₁₀₃	—	4	4	no	—
56	#121×C₁₀₃	—	2	4	no	—
57	#121×C₁₀₃	—	2	4	no	—
58	#121×C₁₀₃	—	4	2	no	—
59	#121×C₁₀₃	—	4	2	no	—
60	C₄×D₄×C₁₀₃	—	2	2	no	—
61	C₄×D₄×C₁₀₃	—	2	2	no	—
62	C₄×D₄×C₁₀₃	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₃	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₀₃	D₄	1	2	yes	—
78	C₂×C₄²×C₁₀₃	—	2	1	no	—
79	C₂×C₄²×C₁₀₃	—	2	1	no	—
80	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
81	#107×C₁₀₃	—	2	4	no	—
82	#107×C₁₀₃	—	2	2	no	—
83	#107×C₁₀₃	D₄	1	4	yes	complemented
84	C₄⋊C₈×C₁₀₃	—	2	2	no	—
85	#102×C₁₀₃	—	2	4	no	—
86	#102×C₁₀₃	—	2	4	no	—
87	#102×C₁₀₃	—	4	2	no	—
88	#102×C₁₀₃	—	4	2	no	—
89	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
90	C₂²⋊C₈×C₁₀₃	—	4	2	no	—
91	C₄×C₈×C₁₀₃	—	2	2	no	—
92	#95×C₁₀₃	—	2	1	no	—
93	#95×C₁₀₃	—	2	1	no	—
94	#95×C₁₀₃	—	2	2	no	—
95	C₂⁴×C₁₀₃	—	2	2	no	—
96	C₂⁴×C₁₀₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₀₃	—	2	2	no	—
98	C₂×D₄×C₁₀₃	—	2	2	no	—
99	C₂×D₄×C₁₀₃	—	2	2	no	—
100	C₂×D₄×C₁₀₃	—	2	2	no	—
101	C₂×D₄×C₁₀₃	—	2	2	no	—
102	C₂×D₄×C₁₀₃	—	2	2	no	—
103	C₂×D₄×C₁₀₃	—	2	2	no	—
104	C₂×D₄×C₁₀₃	—	2	2	no	—
105	C₂×D₄×C₁₀₃	—	4	4	no	—
106	C₂×D₄×C₁₀₃	—	4	4	no	—
107	C₂×D₄×C₁₀₃	—	4	4	no	—
108	C₂×D₄×C₁₀₃	—	4	4	no	—
109	C₂×D₄×C₁₀₃	—	4	2	no	—
110	C₂×D₄×C₁₀₃	—	4	2	no	—
111	C₂×D₄×C₁₀₃	—	4	2	no	—
112	C₂×D₄×C₁₀₃	—	4	2	no	—
113	C₂×D₄×C₁₀₃	—	8	1	no	—
114	C₂×D₄×C₁₀₃	—	8	1	no	—
115	C₂×D₄×C₁₀₃	—	8	2	no	—
116	C₂×D₄×C₁₀₃	—	8	2	no	—
117	C₂×D₄×C₁₀₃	D₈	1	4	yes	—
118	C₂²×C₄×C₁₀₃	—	2	1	no	—
119	C₂²×C₄×C₁₀₃	—	2	1	no	—
120	C₂²×C₄×C₁₀₃	—	2	1	no	—
121	C₂²×C₄×C₁₀₃	—	2	2	no	—
122	C₂²×C₄×C₁₀₃	—	2	2	no	—
123	C₂²×C₄×C₁₀₃	—	2	2	no	—
124	C₂²×C₄×C₁₀₃	—	2	2	no	—
125	C₂²×C₄×C₁₀₃	—	2	2	no	—
126	C₂²×C₄×C₁₀₃	—	2	2	no	—
127	C₂²×C₄×C₁₀₃	—	2	1	no	—
128	C₂²×C₄×C₁₀₃	—	2	2	no	—
129	C₂²×C₄×C₁₀₃	—	4	4	no	—
130	C₂²×C₄×C₁₀₃	—	4	4	no	—
131	C₂²×C₄×C₁₀₃	—	8	2	no	—
132	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₀₃	—	2	1	no	—
137	C₂×C₈×C₁₀₃	—	2	1	no	—
138	C₂×C₈×C₁₀₃	—	2	2	no	—
139	C₂×C₈×C₁₀₃	—	2	1	no	—
140	C₂×C₈×C₁₀₃	—	2	2	no	—
141	C₂×C₈×C₁₀₃	—	2	1	no	—
142	C₂×C₈×C₁₀₃	—	2	2	no	—
143	C₂×C₈×C₁₀₃	—	2	1	no	—
144	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₁₀₃	—	2	2	no	—
146	C₄⋊C₄×C₁₀₃	—	2	1	no	—
147	C₄⋊C₄×C₁₀₃	—	2	1	no	—
148	C₄⋊C₄×C₁₀₃	—	2	1	no	—
149	C₄⋊C₄×C₁₀₃	—	2	2	no	—
150	C₄⋊C₄×C₁₀₃	—	2	1	no	—
151	C₄⋊C₄×C₁₀₃	—	2	1	no	—
152	C₄⋊C₄×C₁₀₃	—	2	2	no	—
153	C₄⋊C₄×C₁₀₃	—	4	4	no	—
154	C₄⋊C₄×C₁₀₃	—	4	2	no	—
155	C₄⋊C₄×C₁₀₃	—	8	1	no	—
156	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₀₃	#41	1	2	yes	—
159	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
160	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
161	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
162	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
163	C₄²×C₁₀₃	—	4	2	no	—
164	C₄²×C₁₀₃	—	4	2	no	—
165	C₄²×C₁₀₃	#41	1	2	yes	—
166	C₄²×C₁₀₃	#41	1	2	yes	—
167	C₂³×C₁₀₃	—	2	2	no	—
168	C₂³×C₁₀₃	—	2	2	no	—
169	C₂³×C₁₀₃	—	2	2	no	—
170	C₂³×C₁₀₃	—	2	2	no	—
171	C₂³×C₁₀₃	—	2	2	no	—
172	C₂³×C₁₀₃	—	2	2	no	—
173	C₂³×C₁₀₃	—	4	2	no	—
174	C₂³×C₁₀₃	—	4	2	no	—
175	C₂³×C₁₀₃	—	4	2	no	—
176	C₂³×C₁₀₃	—	4	2	no	—
177	C₂³×C₁₀₃	—	4	2	no	—
178	C₂³×C₁₀₃	—	4	2	no	—
179	C₂³×C₁₀₃	—	4	2	no	—
180	C₂³×C₁₀₃	C₂×D₈	1	4	yes	—
181	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
182	D₄×C₁₀₃	—	2	8	no	—
183	D₄×C₁₀₃	—	4	2	no	—
184	D₄×C₁₀₃	—	4	2	no	—
185	D₄×C₁₀₃	—	4	2	no	—
186	D₄×C₁₀₃	—	4	2	no	—
187	D₄×C₁₀₃	—	8	4	no	—
188	D₄×C₁₀₃	—	8	8	no	—
189	D₄×C₁₀₃	—	8	8	no	—
190	D₄×C₁₀₃	—	8	4	no	—
191	C₂×C₄×C₁₀₃	—	2	1	no	—
192	C₂×C₄×C₁₀₃	—	2	1	no	—
193	C₂×C₄×C₁₀₃	—	2	2	no	—
194	C₂×C₄×C₁₀₃	—	2	2	no	—
195	C₂×C₄×C₁₀₃	—	2	2	no	—
196	C₂×C₄×C₁₀₃	—	2	2	no	—
197	C₂×C₄×C₁₀₃	—	2	2	no	—
198	C₂×C₄×C₁₀₃	—	2	2	no	—
199	C₂×C₄×C₁₀₃	—	4	1	no	—
200	C₂×C₄×C₁₀₃	—	4	1	no	—
201	C₂×C₄×C₁₀₃	—	4	1	no	—
202	C₂×C₄×C₁₀₃	—	4	1	no	—
203	C₂×C₄×C₁₀₃	—	4	1	no	—
204	C₂×C₄×C₁₀₃	—	4	1	no	—
205	C₂×C₄×C₁₀₃	—	4	2	no	—
206	C₂×C₄×C₁₀₃	—	4	2	no	—
207	C₂×C₄×C₁₀₃	—	4	2	no	—
208	C₂×C₄×C₁₀₃	—	4	2	no	—
209	C₂×C₄×C₁₀₃	—	4	2	no	—
210	C₂×C₄×C₁₀₃	—	4	1	no	—
211	C₂×C₄×C₁₀₃	—	4	1	no	—
212	C₂×C₄×C₁₀₃	—	4	2	no	—
213	C₂×C₄×C₁₀₃	—	4	2	no	—
214	C₂×C₄×C₁₀₃	—	4	1	no	—
215	C₂×C₄×C₁₀₃	—	8	8	no	—
216	C₂×C₄×C₁₀₃	#123	1	2	yes	—
217	C₂×C₄×C₁₀₃	#123	1	2	yes	—
218	C₂×C₄×C₁₀₃	C₂×D₈	1	2	yes	—
219	C₂×C₄×C₁₀₃	#137	1	2	yes	—
220	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₈×C₁₀₃	—	2	2	no	—
227	C₈×C₁₀₃	—	4	1	no	—
228	C₈×C₁₀₃	—	4	2	no	—
229	C₂²×C₁₀₃	—	2	4	no	—
230	C₂²×C₁₀₃	—	2	4	no	—
231	C₂²×C₁₀₃	—	2	4	no	—
232	C₂²×C₁₀₃	—	4	2	no	—
233	C₂²×C₁₀₃	—	4	2	no	—
234	C₂²×C₁₀₃	—	4	2	no	—
235	C₂²×C₁₀₃	—	4	2	no	—
236	C₂²×C₁₀₃	—	8	2	no	—
237	C₂²×C₁₀₃	—	8	2	no	—
238	C₂²×C₁₀₃	—	8	2	no	—
239	C₂²×C₁₀₃	—	8	2	no	—
240	C₂²×C₁₀₃	—	8	2	no	—
241	C₂²×C₁₀₃	—	8	2	no	—
242	C₂²×C₁₀₃	—	8	2	no	—
243	C₂²×C₁₀₃	C₂×#123	1	1	yes	characteristic
244	C₂²×C₁₀₃	D₄²	1	1	yes	characteristic
245	C₂²×C₁₀₃	#546	1	1	yes	characteristic
246	C₂²×C₁₀₃	C₂²×D₈	1	1	yes	characteristic
247	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
248	C₂²×C₁₀₃	#576	1	1	yes	characteristic
249	C₂²×C₁₀₃	#577	1	1	yes	characteristic
250	C₄×C₁₀₃	—	2	2	no	—
251	C₄×C₁₀₃	—	4	2	no	—
252	C₄×C₁₀₃	—	4	2	no	—
253	C₄×C₁₀₃	—	4	2	no	—
254	C₄×C₁₀₃	—	4	2	no	—
255	C₄×C₁₀₃	—	8	2	no	—
256	C₄×C₁₀₃	—	8	1	no	—
257	C₄×C₁₀₃	#480	1	4	yes	complemented
258	C₄×C₁₀₃	#532	1	1	yes	characteristic
259	C₄×C₁₀₃	#540	1	1	yes	characteristic
260	C₄×C₁₀₃	#550	1	1	yes	characteristic
261	C₄×C₁₀₃	#559	1	1	yes	characteristic
262	#26230	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂×C₁₀₃	—	4	4	no	—
264	C₂×C₁₀₃	—	16	2	no	—
265	C₂×C₁₀₃	#2445	1	1	yes	characteristic
266	C₂×C₁₀₃	C₂×#480	1	1	yes	characteristic
267	C₂×C₁₀₃	#3096	1	1	yes	characteristic
268	C₂×C₁₀₃	#3278	1	1	yes	characteristic
269	C₂×C₁₀₃	D₄×D₈	1	1	yes	characteristic
270	C₂×C₁₀₃	#3294	1	1	yes	characteristic
271	C₂×C₁₀₃	#3333	1	1	yes	characteristic
272	C₂×#480	C₂×C₁₀₃	1	2	yes	complemented
273	#2541	C₂×C₁₀₃	1	1	yes	characteristic
274	D₄×C₄⋊C₄	C₂×C₁₀₃	1	1	yes	characteristic, complemented
275	#2033	C₂×C₁₀₃	1	2	yes	complemented
276	#2033	C₂×C₁₀₃	1	2	yes	complemented
277	#1982	C₂×C₁₀₃	1	1	yes	characteristic, complemented
278	#1957	C₂×C₁₀₃	1	1	yes	characteristic, complemented
279	#1954	C₂×C₁₀₃	1	1	yes	characteristic, complemented
280	#1947	C₂×C₁₀₃	1	1	yes	characteristic, complemented
281	#1874	C₂×C₁₀₃	1	2	yes	complemented
282	C₄×#107	C₂×C₁₀₃	1	1	yes	characteristic, complemented
283	C₁₀₃	#26230	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×#127	—	2	1	no	—
285	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
286	C₂×#121	C₂²×C₁₀₃	1	2	yes	—
287	C₂×#121	C₂²×C₁₀₃	1	2	yes	—
288	C₂×C₄×D₄	—	2	1	no	—
289	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
291	#480	—	2	8	no	—
292	C₂×#107	C₂²×C₁₀₃	1	2	yes	—
293	C₂×#107	C₂²×C₁₀₃	1	1	yes	characteristic
294	C₂×#107	C₂²×C₁₀₃	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
296	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
297	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
298	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
299	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
300	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
302	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
303	#392	—	2	2	no	—
304	#390	—	2	1	no	—
305	#389	—	2	1	no	—
306	#385	—	2	2	no	—
307	#384	C₂²×C₁₀₃	1	1	yes	characteristic
308	#380	C₂²×C₁₀₃	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
311	#340	C₂²×C₁₀₃	1	1	yes	characteristic
312	#340	C₂²×C₁₀₃	1	2	yes	—
313	#340	C₂²×C₁₀₃	1	1	yes	characteristic
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₀₃	1	2	yes	—
320	C₂³×C₄	—	2	2	no	—
321	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
322	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
324	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
325	#127	—	2	2	no	—
326	#127	—	2	2	no	—
327	#127	—	4	4	no	—
328	#121	—	2	4	no	—
329	#121	—	2	4	no	—
330	#121	—	4	2	no	—
331	#121	—	4	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	4	4	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	4	2	no	—
340	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	D₄×C₁₀₃	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
353	#107	—	2	4	no	—
354	#107	—	2	2	no	—
355	#107	D₄×C₁₀₃	1	4	yes	complemented
356	C₄⋊C₈	—	2	2	no	—
357	#102	—	2	4	no	—
358	#102	—	2	4	no	—
359	#102	—	4	2	no	—
360	#102	—	4	2	no	—
361	C₂²⋊C₈	—	2	4	no	—
362	C₂²⋊C₈	—	4	2	no	—
363	C₄×C₈	—	2	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	2	no	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	C₂×D₄×C₁₀₃	1	2	yes	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	8	1	no	—
386	C₂×D₄	—	8	1	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂×D₄	D₈×C₁₀₃	1	4	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	8	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	8	1	no	—
428	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
430	C₄⋊C₄	#41×C₁₀₃	1	2	yes	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₄²	—	4	2	no	—
436	C₄²	—	4	2	no	—
437	C₄²	#41×C₁₀₃	1	2	yes	—
438	C₄²	#41×C₁₀₃	1	2	yes	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂×D₈×C₁₀₃	1	4	yes	—
453	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	8	no	—
461	D₄	—	8	8	no	—
462	D₄	—	8	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	#123×C₁₀₃	1	2	yes	—
489	C₂×C₄	#123×C₁₀₃	1	2	yes	—
490	C₂×C₄	C₂×D₈×C₁₀₃	1	2	yes	—
491	C₂×C₄	#137×C₁₀₃	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
496	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
497	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₂×#123×C₁₀₃	1	1	yes	characteristic
516	C₂²	D₄²×C₁₀₃	1	1	yes	characteristic
517	C₂²	#546×C₁₀₃	1	1	yes	characteristic
518	C₂²	C₂²×D₈×C₁₀₃	1	1	yes	characteristic
519	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
520	C₂²	#576×C₁₀₃	1	1	yes	characteristic
521	C₂²	#577×C₁₀₃	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	1	no	—
529	C₄	#480×C₁₀₃	1	4	yes	complemented
530	C₄	#532×C₁₀₃	1	1	yes	characteristic
531	C₄	#540×C₁₀₃	1	1	yes	characteristic
532	C₄	#550×C₁₀₃	1	1	yes	characteristic
533	C₄	#559×C₁₀₃	1	1	yes	characteristic
534	C₂	—	4	4	no	—
535	C₂	—	16	2	no	—
536	C₂	C₁₀₃×#2445	1	1	yes	characteristic
537	C₂	C₂×#480×C₁₀₃	1	1	yes	characteristic
538	C₂	C₁₀₃×#3096	1	1	yes	characteristic
539	C₂	C₁₀₃×#3278	1	1	yes	characteristic
540	C₂	D₄×D₈×C₁₀₃	1	1	yes	characteristic
541	C₂	C₁₀₃×#3294	1	1	yes	characteristic
542	C₂	C₁₀₃×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₁₀₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄×D₄×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#480×C₁₀₃	C₂	semidirect
3. D₄×C₄⋊C₄×C₁₀₃	C₂	semidirect
4. C₁₀₃×#2033	C₂	semidirect
5. C₁₀₃×#2033	C₂	semidirect
6. C₁₀₃×#1982	C₂	semidirect
7. C₁₀₃×#1957	C₂	semidirect
8. C₁₀₃×#1954	C₂	semidirect
9. C₁₀₃×#1947	C₂	semidirect
10. C₁₀₃×#1874	C₂	semidirect
11. C₄×#107×C₁₀₃	C₂	semidirect
83. #107×C₁₀₃	D₄	semidirect
257. C₄×C₁₀₃	#480	semidirect
262. #26230	C₁₀₃	direct (N × H)
272. C₂×#480	C₂×C₁₀₃	semidirect
274. D₄×C₄⋊C₄	C₂×C₁₀₃	semidirect
275. #2033	C₂×C₁₀₃	semidirect
276. #2033	C₂×C₁₀₃	semidirect
277. #1982	C₂×C₁₀₃	semidirect
278. #1957	C₂×C₁₀₃	semidirect
279. #1954	C₂×C₁₀₃	semidirect
280. #1947	C₂×C₁₀₃	semidirect
281. #1874	C₂×C₁₀₃	semidirect
282. C₄×#107	C₂×C₁₀₃	semidirect
283. C₁₀₃	#26230	direct (N × H)
355. #107	D₄×C₁₀₃	semidirect
529. C₄	#480×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#480×C₁₀₃	2
C₁₀₃×#2541	2
D₄×C₄⋊C₄×C₁₀₃	2
C₁₀₃×#2033	2
C₁₀₃×#1982	2
C₁₀₃×#1957	2
C₁₀₃×#1954	2
C₁₀₃×#1947	2
C₁₀₃×#1874	2
C₄×#107×C₁₀₃	2
#26230	103

Subgroups — C103×#26230 #39931505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#26230 #39931505