Subgroups — C₂×C₁₀₃×#1442 #39919115

Order 26368.

2942 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#95×C₁₀₃	C₂	1	2	yes	maximal
3	C₂²×#95×C₁₀₃	C₂	1	2	yes	maximal
4	C₂²×#95×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#95×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃×#1442	C₂	1	8	yes	maximal, direct product factor
7	C₂⁴×C₄×C₁₀₃	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₀₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₃	—	2	8	no	—
13	C₂²×C₄⋊C₄×C₁₀₃	—	2	4	no	—
14	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	4	yes	—
15	C₂×#95×C₁₀₃	—	2	8	no	—
16	C₂×#95×C₁₀₃	—	2	8	no	—
17	C₂×#95×C₁₀₃	—	2	4	no	—
18	C₂×#95×C₁₀₃	C₄	1	8	yes	complemented
19	C₂×#95×C₁₀₃	C₂²	1	8	yes	—
20	C₂×#95×C₁₀₃	C₂²	1	8	yes	—
21	C₂×#95×C₁₀₃	C₂²	1	4	yes	—
22	C₂×#95×C₁₀₃	C₂²	1	4	yes	—
23	C₂⁵×C₁₀₃	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₃	—	2	4	no	—
25	C₂³×C₄×C₁₀₃	—	2	4	no	—
26	C₂³×C₄×C₁₀₃	—	2	4	no	—
27	C₂³×C₄×C₁₀₃	—	2	4	no	—
28	C₂³×C₄×C₁₀₃	—	2	4	no	—
29	C₂³×C₄×C₁₀₃	—	2	2	no	—
30	C₂³×C₄×C₁₀₃	—	2	2	no	—
31	C₂³×C₄×C₁₀₃	—	2	4	no	—
32	C₂³×C₄×C₁₀₃	—	2	4	no	—
33	C₂³×C₄×C₁₀₃	—	2	4	no	—
34	C₂³×C₄×C₁₀₃	—	2	4	no	—
35	C₂³×C₄×C₁₀₃	—	2	4	no	—
36	C₂³×C₄×C₁₀₃	—	2	4	no	—
37	C₂³×C₄×C₁₀₃	—	2	4	no	—
38	C₂³×C₄×C₁₀₃	—	2	4	no	—
39	C₂³×C₄×C₁₀₃	—	2	2	no	—
40	C₂³×C₄×C₁₀₃	—	2	4	no	—
41	C₂³×C₄×C₁₀₃	—	2	2	no	—
42	C₂³×C₄×C₁₀₃	—	2	4	no	—
43	C₂³×C₄×C₁₀₃	—	2	4	no	—
44	C₂³×C₄×C₁₀₃	—	2	4	no	—
45	C₂³×C₄×C₁₀₃	—	2	4	no	—
46	C₂³×C₄×C₁₀₃	C₂×C₄	1	8	yes	—
47	C₂³×C₄×C₁₀₃	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₁₀₃	D₄	1	4	yes	—
49	C₂³×C₄×C₁₀₃	D₄	1	8	yes	—
50	C₂³×C₄×C₁₀₃	D₄	1	4	yes	—
51	C₂³×C₄×C₁₀₃	Q₈	1	4	yes	—
52	C₂³×C₄×C₁₀₃	Q₈	1	4	yes	—
53	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₃	—	2	32	no	—
59	C₂×C₄⋊C₄×C₁₀₃	—	2	16	no	—
60	C₂×C₄⋊C₄×C₁₀₃	—	2	8	no	—
61	#95×C₁₀₃	—	2	16	no	—
62	#95×C₁₀₃	—	2	16	no	—
63	#95×C₁₀₃	—	2	8	no	—
64	#95×C₁₀₃	C₂×C₄	1	16	yes	complemented
65	C₂⁴×C₁₀₃	C₂²×C₄	1	2	yes	—
66	C₂⁴×C₁₀₃	C₂×D₄	1	2	yes	—
67	C₂⁴×C₁₀₃	C₂×D₄	1	4	yes	—
68	C₂⁴×C₁₀₃	C₂×D₄	1	2	yes	—
69	C₂⁴×C₁₀₃	C₂×Q₈	1	2	yes	—
70	C₂⁴×C₁₀₃	C₂×Q₈	1	2	yes	—
71	C₂⁴×C₁₀₃	#41	1	4	yes	—
72	C₂⁴×C₁₀₃	#41	1	4	yes	—
73	C₂⁴×C₁₀₃	#41	1	4	yes	—
74	C₂⁴×C₁₀₃	#41	1	2	yes	—
75	C₂⁴×C₁₀₃	#41	1	2	yes	—
76	C₂⁴×C₁₀₃	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₃	—	2	16	no	—
78	C₂²×C₄×C₁₀₃	—	2	8	no	—
79	C₂²×C₄×C₁₀₃	—	2	16	no	—
80	C₂²×C₄×C₁₀₃	—	2	8	no	—
81	C₂²×C₄×C₁₀₃	—	2	4	no	—
82	C₂²×C₄×C₁₀₃	—	2	4	no	—
83	C₂²×C₄×C₁₀₃	—	2	16	no	—
84	C₂²×C₄×C₁₀₃	—	2	16	no	—
85	C₂²×C₄×C₁₀₃	—	2	16	no	—
86	C₂²×C₄×C₁₀₃	—	2	16	no	—
87	C₂²×C₄×C₁₀₃	—	2	16	no	—
88	C₂²×C₄×C₁₀₃	—	2	8	no	—
89	C₂²×C₄×C₁₀₃	—	2	16	no	—
90	C₂²×C₄×C₁₀₃	—	2	8	no	—
91	C₂²×C₄×C₁₀₃	—	2	16	no	—
92	C₂²×C₄×C₁₀₃	—	2	16	no	—
93	C₂²×C₄×C₁₀₃	—	2	4	no	—
94	C₂²×C₄×C₁₀₃	—	2	4	no	—
95	C₂²×C₄×C₁₀₃	—	2	4	no	—
96	C₂²×C₄×C₁₀₃	—	2	2	no	—
97	C₂²×C₄×C₁₀₃	—	2	2	no	—
98	C₂²×C₄×C₁₀₃	—	2	4	no	—
99	C₂²×C₄×C₁₀₃	—	2	4	no	—
100	C₂²×C₄×C₁₀₃	—	2	4	no	—
101	C₂²×C₄×C₁₀₃	—	2	4	no	—
102	C₂²×C₄×C₁₀₃	—	2	4	no	—
103	C₂²×C₄×C₁₀₃	—	2	4	no	—
104	C₂²×C₄×C₁₀₃	—	2	4	no	—
105	C₂²×C₄×C₁₀₃	—	2	4	no	—
106	C₂²×C₄×C₁₀₃	—	2	2	no	—
107	C₂²×C₄×C₁₀₃	—	2	4	no	—
108	C₂²×C₄×C₁₀₃	—	2	2	no	—
109	C₂²×C₄×C₁₀₃	—	2	4	no	—
110	C₂²×C₄×C₁₀₃	—	2	4	no	—
111	C₂²×C₄×C₁₀₃	—	2	4	no	—
112	C₂²×C₄×C₁₀₃	—	2	4	no	—
113	C₂²×C₄×C₁₀₃	—	4	4	no	—
114	C₂²×C₄×C₁₀₃	—	4	8	no	—
115	C₂²×C₄×C₁₀₃	—	4	8	no	—
116	C₂²×C₄×C₁₀₃	—	4	8	no	—
117	C₂²×C₄×C₁₀₃	—	4	8	no	—
118	C₂²×C₄×C₁₀₃	—	4	8	no	—
119	C₂²×C₄×C₁₀₃	—	4	4	no	—
120	C₂²×C₄×C₁₀₃	—	4	8	no	—
121	C₂²×C₄×C₁₀₃	—	4	4	no	—
122	C₂²×C₄×C₁₀₃	—	4	8	no	—
123	C₂²×C₄×C₁₀₃	—	4	8	no	—
124	C₂²×C₄×C₁₀₃	—	4	4	no	—
125	C₂²×C₄×C₁₀₃	—	4	8	no	—
126	C₂²×C₄×C₁₀₃	—	4	8	no	—
127	C₂²×C₄×C₁₀₃	C₄⋊C₄	1	16	yes	—
128	C₂²×C₄×C₁₀₃	C₂²×C₄	1	8	yes	—
129	C₂²×C₄×C₁₀₃	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₀₃	C₂×D₄	1	8	yes	—
132	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₀₃	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₁₀₃	C₂×Q₈	1	4	yes	—
135	C₄⋊C₄×C₁₀₃	—	2	32	no	—
136	C₂³×C₁₀₃	C₂×C₄⋊C₄	1	4	yes	—
137	C₂³×C₁₀₃	#117	1	8	yes	—
138	C₂³×C₁₀₃	C₄×D₄	1	8	yes	—
139	C₂³×C₁₀₃	C₄×D₄	1	4	yes	—
140	C₂³×C₁₀₃	C₄×Q₈	1	4	yes	—
141	C₂³×C₁₀₃	#120	1	4	yes	—
142	C₂³×C₁₀₃	#121	1	8	yes	—
143	C₂³×C₁₀₃	#121	1	4	yes	—
144	C₂³×C₁₀₃	C₂²⋊Q₈	1	8	yes	—
145	C₂³×C₁₀₃	C₂²⋊Q₈	1	8	yes	—
146	C₂³×C₁₀₃	C₂²⋊Q₈	1	4	yes	—
147	C₂³×C₁₀₃	#123	1	4	yes	—
148	C₂³×C₁₀₃	#123	1	8	yes	—
149	C₂³×C₁₀₃	#123	1	8	yes	—
150	C₂³×C₁₀₃	#124	1	4	yes	—
151	C₂³×C₁₀₃	#124	1	4	yes	—
152	C₂³×C₁₀₃	#124	1	8	yes	—
153	C₂³×C₁₀₃	#125	1	8	yes	—
154	C₂³×C₁₀₃	#125	1	8	yes	—
155	C₂³×C₁₀₃	#125	1	4	yes	—
156	C₂³×C₁₀₃	#126	1	8	yes	—
157	C₂³×C₁₀₃	#126	1	8	yes	—
158	C₂³×C₁₀₃	C₄⋊Q₈	1	4	yes	—
159	C₂³×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
160	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₀₃	C₂²×D₄	1	2	yes	—
162	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
163	C₂³×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂³×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
165	C₂³×C₁₀₃	C₂×#41	1	2	yes	—
166	C₂³×C₁₀₃	C₂×#41	1	2	yes	—
167	C₂³×C₁₀₃	C₂×#41	1	2	yes	—
168	C₂³×C₁₀₃	C₂×#41	1	1	yes	characteristic
169	C₂³×C₁₀₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₀₃	—	2	8	no	—
171	C₂×C₄×C₁₀₃	—	2	4	no	—
172	C₂×C₄×C₁₀₃	—	2	8	no	—
173	C₂×C₄×C₁₀₃	—	2	4	no	—
174	C₂×C₄×C₁₀₃	—	2	32	no	—
175	C₂×C₄×C₁₀₃	—	2	8	no	—
176	C₂×C₄×C₁₀₃	—	2	8	no	—
177	C₂×C₄×C₁₀₃	—	2	8	no	—
178	C₂×C₄×C₁₀₃	—	2	8	no	—
179	C₂×C₄×C₁₀₃	—	2	8	no	—
180	C₂×C₄×C₁₀₃	—	2	4	no	—
181	C₂×C₄×C₁₀₃	—	2	8	no	—
182	C₂×C₄×C₁₀₃	—	2	4	no	—
183	C₂×C₄×C₁₀₃	—	2	8	no	—
184	C₂×C₄×C₁₀₃	—	2	8	no	—
185	C₂×C₄×C₁₀₃	—	4	2	no	—
186	C₂×C₄×C₁₀₃	—	4	4	no	—
187	C₂×C₄×C₁₀₃	—	4	4	no	—
188	C₂×C₄×C₁₀₃	—	4	4	no	—
189	C₂×C₄×C₁₀₃	—	4	4	no	—
190	C₂×C₄×C₁₀₃	—	4	2	no	—
191	C₂×C₄×C₁₀₃	—	4	4	no	—
192	C₂×C₄×C₁₀₃	—	4	2	no	—
193	C₂×C₄×C₁₀₃	—	4	4	no	—
194	C₂×C₄×C₁₀₃	—	4	4	no	—
195	C₂×C₄×C₁₀₃	—	4	2	no	—
196	C₂×C₄×C₁₀₃	—	4	4	no	—
197	C₂×C₄×C₁₀₃	—	4	4	no	—
198	C₂×C₄×C₁₀₃	—	4	4	no	—
199	C₂×C₄×C₁₀₃	—	4	32	no	—
200	C₂×C₄×C₁₀₃	—	4	16	no	—
201	C₂×C₄×C₁₀₃	—	4	32	no	—
202	C₂×C₄×C₁₀₃	—	4	16	no	—
203	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	8	yes	—
204	C₂²×C₁₀₃	#382	1	8	yes	—
205	C₂²×C₁₀₃	#385	1	8	yes	—
206	C₂²×C₁₀₃	#387	1	16	yes	—
207	C₂²×C₁₀₃	#388	1	16	yes	—
208	C₂²×C₁₀₃	#389	1	8	yes	—
209	C₂²×C₁₀₃	#393	1	8	yes	—
210	C₂²×C₁₀₃	#394	1	8	yes	—
211	C₂²×C₁₀₃	#397	1	8	yes	—
212	C₂²×C₁₀₃	#398	1	16	yes	—
213	C₂²×C₁₀₃	#400	1	16	yes	—
214	C₂²×C₁₀₃	#400	1	8	yes	—
215	C₂²×C₁₀₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₀₃	C₂×#117	1	2	yes	—
217	C₂²×C₁₀₃	C₂×C₄×D₄	1	2	yes	—
218	C₂²×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₁₀₃	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
221	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
222	C₂²×C₁₀₃	C₂×#121	1	2	yes	—
223	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	2	yes	—
224	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	2	yes	—
226	C₂²×C₁₀₃	C₂×#123	1	2	yes	—
227	C₂²×C₁₀₃	C₂×#123	1	2	yes	—
228	C₂²×C₁₀₃	C₂×#123	1	1	yes	characteristic
229	C₂²×C₁₀₃	C₂×#124	1	1	yes	characteristic
230	C₂²×C₁₀₃	C₂×#124	1	2	yes	—
231	C₂²×C₁₀₃	C₂×#124	1	1	yes	characteristic
232	C₂²×C₁₀₃	C₂×#125	1	2	yes	—
233	C₂²×C₁₀₃	C₂×#125	1	2	yes	—
234	C₂²×C₁₀₃	C₂×#125	1	1	yes	characteristic
235	C₂²×C₁₀₃	C₂×#126	1	2	yes	—
236	C₂²×C₁₀₃	C₂×#126	1	2	yes	—
237	C₂²×C₁₀₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
238	C₄×C₁₀₃	—	2	8	no	—
239	C₄×C₁₀₃	—	4	4	no	—
240	C₄×C₁₀₃	—	4	8	no	—
241	C₄×C₁₀₃	—	4	4	no	—
242	C₄×C₁₀₃	—	4	8	no	—
243	C₂×#1442	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₁₀₃	#1442	1	16	yes	direct product factor
245	C₂×C₁₀₃	C₂×#382	1	1	yes	characteristic
246	C₂×C₁₀₃	C₂×#385	1	1	yes	characteristic
247	C₂×C₁₀₃	C₂×#387	1	2	yes	—
248	C₂×C₁₀₃	C₂×#388	1	2	yes	—
249	C₂×C₁₀₃	C₂×#389	1	1	yes	characteristic
250	C₂×C₁₀₃	C₂×#393	1	1	yes	characteristic
251	C₂×C₁₀₃	C₂×#394	1	1	yes	characteristic
252	C₂×C₁₀₃	C₂×#397	1	1	yes	characteristic
253	C₂×C₁₀₃	C₂×#398	1	2	yes	—
254	C₂×C₁₀₃	C₂×#400	1	1	yes	characteristic
255	C₂×C₁₀₃	C₂×#400	1	2	yes	—
256	C₂³×C₄⋊C₄	C₂×C₁₀₃	1	1	yes	characteristic
257	C₂²×#95	C₂×C₁₀₃	1	2	yes	—
258	C₂²×#95	C₂×C₁₀₃	1	2	yes	—
259	C₂²×#95	C₂×C₁₀₃	1	1	yes	characteristic
260	C₂²×#95	C₂×C₁₀₃	1	1	yes	characteristic
261	#1442	C₂×C₁₀₃	1	8	yes	direct product factor
262	C₁₀₃	C₂×#1442	1	1	yes	characteristic, direct product factor, Sylow
263	C₂⁴×C₄	C₂²×C₁₀₃	1	2	yes	—
264	C₂⁴×C₄	C₂²×C₁₀₃	1	2	yes	—
265	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
266	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	—	2	8	no	—
269	C₂²×C₄⋊C₄	—	2	4	no	—
270	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	4	yes	—
271	C₂×#95	—	2	8	no	—
272	C₂×#95	—	2	8	no	—
273	C₂×#95	—	2	4	no	—
274	C₂×#95	C₄×C₁₀₃	1	8	yes	complemented
275	C₂×#95	C₂²×C₁₀₃	1	8	yes	—
276	C₂×#95	C₂²×C₁₀₃	1	8	yes	—
277	C₂×#95	C₂²×C₁₀₃	1	4	yes	—
278	C₂×#95	C₂²×C₁₀₃	1	4	yes	—
279	C₂⁵	C₂³×C₁₀₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	4	no	—
285	C₂³×C₄	—	2	4	no	—
286	C₂³×C₄	—	2	4	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	4	no	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	—	2	4	no	—
292	C₂³×C₄	—	2	4	no	—
293	C₂³×C₄	—	2	4	no	—
294	C₂³×C₄	—	2	4	no	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	4	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	4	no	—
299	C₂³×C₄	—	2	4	no	—
300	C₂³×C₄	—	2	4	no	—
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	C₂×C₄×C₁₀₃	1	8	yes	—
303	C₂³×C₄	C₂×C₄×C₁₀₃	1	4	yes	—
304	C₂³×C₄	D₄×C₁₀₃	1	8	yes	—
305	C₂³×C₄	D₄×C₁₀₃	1	4	yes	—
306	C₂³×C₄	D₄×C₁₀₃	1	4	yes	—
307	C₂³×C₄	Q₈×C₁₀₃	1	4	yes	—
308	C₂³×C₄	Q₈×C₁₀₃	1	4	yes	—
309	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
310	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
311	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
314	C₂×C₄⋊C₄	—	2	32	no	—
315	C₂×C₄⋊C₄	—	2	16	no	—
316	C₂×C₄⋊C₄	—	2	8	no	—
317	#95	—	2	16	no	—
318	#95	—	2	16	no	—
319	#95	—	2	8	no	—
320	#95	C₂×C₄×C₁₀₃	1	16	yes	complemented
321	C₂⁴	C₂²×C₄×C₁₀₃	1	2	yes	—
322	C₂⁴	C₂×D₄×C₁₀₃	1	2	yes	—
323	C₂⁴	C₂×D₄×C₁₀₃	1	4	yes	—
324	C₂⁴	C₂×D₄×C₁₀₃	1	2	yes	—
325	C₂⁴	C₂×Q₈×C₁₀₃	1	2	yes	—
326	C₂⁴	C₂×Q₈×C₁₀₃	1	2	yes	—
327	C₂⁴	#41×C₁₀₃	1	4	yes	—
328	C₂⁴	#41×C₁₀₃	1	4	yes	—
329	C₂⁴	#41×C₁₀₃	1	4	yes	—
330	C₂⁴	#41×C₁₀₃	1	2	yes	—
331	C₂⁴	#41×C₁₀₃	1	2	yes	—
332	C₂⁴	C₂⁴×C₁₀₃	1	1	yes	characteristic
333	C₂²×C₄	—	2	16	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	16	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	16	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	2	16	no	—
343	C₂²×C₄	—	2	16	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	16	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	16	no	—
348	C₂²×C₄	—	2	16	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	8	no	—
371	C₂²×C₄	—	4	8	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	8	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	8	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	—	4	8	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	—	4	8	no	—
383	C₂²×C₄	C₄⋊C₄×C₁₀₃	1	16	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₀₃	1	8	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₀₃	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
387	C₂²×C₄	C₂×D₄×C₁₀₃	1	8	yes	—
388	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
389	C₂²×C₄	C₂×Q₈×C₁₀₃	1	4	yes	—
390	C₂²×C₄	C₂×Q₈×C₁₀₃	1	4	yes	—
391	C₄⋊C₄	—	2	32	no	—
392	C₂³	C₂×C₄⋊C₄×C₁₀₃	1	4	yes	—
393	C₂³	#117×C₁₀₃	1	8	yes	—
394	C₂³	C₄×D₄×C₁₀₃	1	8	yes	—
395	C₂³	C₄×D₄×C₁₀₃	1	4	yes	—
396	C₂³	C₄×Q₈×C₁₀₃	1	4	yes	—
397	C₂³	#120×C₁₀₃	1	4	yes	—
398	C₂³	#121×C₁₀₃	1	8	yes	—
399	C₂³	#121×C₁₀₃	1	4	yes	—
400	C₂³	C₂²⋊Q₈×C₁₀₃	1	8	yes	—
401	C₂³	C₂²⋊Q₈×C₁₀₃	1	8	yes	—
402	C₂³	C₂²⋊Q₈×C₁₀₃	1	4	yes	—
403	C₂³	#123×C₁₀₃	1	4	yes	—
404	C₂³	#123×C₁₀₃	1	8	yes	—
405	C₂³	#123×C₁₀₃	1	8	yes	—
406	C₂³	#124×C₁₀₃	1	4	yes	—
407	C₂³	#124×C₁₀₃	1	4	yes	—
408	C₂³	#124×C₁₀₃	1	8	yes	—
409	C₂³	#125×C₁₀₃	1	8	yes	—
410	C₂³	#125×C₁₀₃	1	8	yes	—
411	C₂³	#125×C₁₀₃	1	4	yes	—
412	C₂³	#126×C₁₀₃	1	8	yes	—
413	C₂³	#126×C₁₀₃	1	8	yes	—
414	C₂³	C₄⋊Q₈×C₁₀₃	1	4	yes	—
415	C₂³	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
416	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
417	C₂³	C₂²×D₄×C₁₀₃	1	2	yes	—
418	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
419	C₂³	C₂²×Q₈×C₁₀₃	1	1	yes	characteristic
420	C₂³	C₂²×Q₈×C₁₀₃	1	1	yes	characteristic
421	C₂³	C₂×#41×C₁₀₃	1	2	yes	—
422	C₂³	C₂×#41×C₁₀₃	1	2	yes	—
423	C₂³	C₂×#41×C₁₀₃	1	2	yes	—
424	C₂³	C₂×#41×C₁₀₃	1	1	yes	characteristic
425	C₂³	C₂×#41×C₁₀₃	1	1	yes	characteristic
426	C₂×C₄	—	2	32	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	4	32	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	—	4	32	no	—
444	C₂×C₄	—	4	16	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	8	yes	—
460	C₂²	#382×C₁₀₃	1	8	yes	—
461	C₂²	#385×C₁₀₃	1	8	yes	—
462	C₂²	#387×C₁₀₃	1	16	yes	—
463	C₂²	#388×C₁₀₃	1	16	yes	—
464	C₂²	#389×C₁₀₃	1	8	yes	—
465	C₂²	#393×C₁₀₃	1	8	yes	—
466	C₂²	#394×C₁₀₃	1	8	yes	—
467	C₂²	#397×C₁₀₃	1	8	yes	—
468	C₂²	#398×C₁₀₃	1	16	yes	—
469	C₂²	#400×C₁₀₃	1	16	yes	—
470	C₂²	#400×C₁₀₃	1	8	yes	—
471	C₂²	C₂²×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
472	C₂²	C₂×#117×C₁₀₃	1	2	yes	—
473	C₂²	C₂×C₄×D₄×C₁₀₃	1	2	yes	—
474	C₂²	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
475	C₂²	C₂×C₄×Q₈×C₁₀₃	1	1	yes	characteristic
476	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
477	C₂²	C₂×#121×C₁₀₃	1	2	yes	—
478	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
479	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	2	yes	—
480	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	2	yes	—
481	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	1	yes	characteristic
482	C₂²	C₂×#123×C₁₀₃	1	1	yes	characteristic
483	C₂²	C₂×#123×C₁₀₃	1	2	yes	—
484	C₂²	C₂×#123×C₁₀₃	1	2	yes	—
485	C₂²	C₂×#124×C₁₀₃	1	1	yes	characteristic
486	C₂²	C₂×#124×C₁₀₃	1	1	yes	characteristic
487	C₂²	C₂×#124×C₁₀₃	1	2	yes	—
488	C₂²	C₂×#125×C₁₀₃	1	2	yes	—
489	C₂²	C₂×#125×C₁₀₃	1	2	yes	—
490	C₂²	C₂×#125×C₁₀₃	1	1	yes	characteristic
491	C₂²	C₂×#126×C₁₀₃	1	2	yes	—
492	C₂²	C₂×#126×C₁₀₃	1	2	yes	—
493	C₂²	C₂×C₄⋊Q₈×C₁₀₃	1	1	yes	characteristic
494	C₄	—	2	8	no	—
495	C₄	—	4	8	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	8	no	—
498	C₄	—	4	4	no	—
499	C₂	C₁₀₃×#1442	1	16	yes	direct product factor
500	C₂	C₂×#382×C₁₀₃	1	1	yes	characteristic
501	C₂	C₂×#385×C₁₀₃	1	1	yes	characteristic
502	C₂	C₂×#387×C₁₀₃	1	2	yes	—
503	C₂	C₂×#388×C₁₀₃	1	2	yes	—
504	C₂	C₂×#389×C₁₀₃	1	1	yes	characteristic
505	C₂	C₂×#393×C₁₀₃	1	1	yes	characteristic
506	C₂	C₂×#394×C₁₀₃	1	1	yes	characteristic
507	C₂	C₂×#397×C₁₀₃	1	1	yes	characteristic
508	C₂	C₂×#398×C₁₀₃	1	2	yes	—
509	C₂	C₂×#400×C₁₀₃	1	2	yes	—
510	C₂	C₂×#400×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₁₀₃	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₀₃×#1442	C₂	direct (N × H)
18. C₂×#95×C₁₀₃	C₄	semidirect
64. #95×C₁₀₃	C₂×C₄	semidirect
243. C₂×#1442	C₁₀₃	direct (N × H)
244. C₂×C₁₀₃	#1442	direct (N × H)
261. #1442	C₂×C₁₀₃	direct (N × H)
262. C₁₀₃	C₂×#1442	direct (N × H)
274. C₂×#95	C₄×C₁₀₃	semidirect
320. #95	C₂×C₄×C₁₀₃	semidirect
499. C₂	C₁₀₃×#1442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₀₃	2
C₂²×#95×C₁₀₃	2
C₁₀₃×#1442	2
C₂×#1442	103

Subgroups — C2×C103×#1442 #39919115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₃×#1442 #39919115