Subgroups — C₁₀₃×#20849 #39926124

Order 26368.

1462 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#428×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#427×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#408×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₁₀₃×#2311	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃×#1854	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1853	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1852	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#340×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	#520×C₁₀₃	—	2	4	no	—
16	#520×C₁₀₃	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₀₃	—	2	1	no	—
18	C₂×C₄×D₄×C₁₀₃	—	2	2	no	—
19	C₂×C₄×D₄×C₁₀₃	—	2	1	no	—
20	C₂×#117×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₀₃	C₂²	1	2	yes	—
22	C₂×#117×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
26	#428×C₁₀₃	—	2	4	no	—
27	#427×C₁₀₃	—	2	4	no	—
28	C₂×#107×C₁₀₃	C₂²	1	1	yes	characteristic
29	C₂×#107×C₁₀₃	C₂²	1	2	yes	—
30	C₂×#107×C₁₀₃	C₂²	1	1	yes	characteristic
31	C₂×#106×C₁₀₃	C₂²	1	1	yes	characteristic
32	C₂×#106×C₁₀₃	C₂²	1	2	yes	—
33	C₂×#106×C₁₀₃	C₂²	1	1	yes	characteristic
34	#408×C₁₀₃	C₄	1	8	yes	complemented
35	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
37	#391×C₁₀₃	—	2	1	no	—
38	#390×C₁₀₃	—	2	1	no	—
39	#386×C₁₀₃	—	2	2	no	—
40	#380×C₁₀₃	C₂²	1	2	yes	—
41	#380×C₁₀₃	C₂²	1	2	yes	—
42	#340×C₁₀₃	C₂²	1	2	yes	—
43	#340×C₁₀₃	C₂²	1	2	yes	—
44	#340×C₁₀₃	C₂²	1	2	yes	—
45	#340×C₁₀₃	C₂²	1	2	yes	—
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	—	2	2	no	—
50	C₂×#41×C₁₀₃	C₂×C₄	1	4	yes	—
51	C₂×#41×C₁₀₃	Q₈	1	4	yes	—
52	C₂²×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₁₀₃	D₄	1	2	yes	—
54	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₃	—	2	2	no	—
56	C₂³×C₄×C₁₀₃	—	2	1	no	—
57	C₂³×C₄×C₁₀₃	—	2	1	no	—
58	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₁₀₃	—	2	2	no	—
61	C₂×M₁₆×C₁₀₃	—	2	2	no	—
62	C₂×M₁₆×C₁₀₃	C₂×C₄	1	4	yes	complemented
63	C₂²×C₈×C₁₀₃	—	2	2	no	—
64	C₂²×C₈×C₁₀₃	—	2	2	no	—
65	C₂²×C₈×C₁₀₃	C₂×C₄	1	4	yes	complemented
66	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₁₀₃	—	2	8	no	—
70	C₄×D₄×C₁₀₃	—	2	16	no	—
71	C₄×D₄×C₁₀₃	—	2	8	no	—
72	#117×C₁₀₃	—	2	2	no	—
73	#117×C₁₀₃	—	2	4	no	—
74	#117×C₁₀₃	—	2	4	no	—
75	#117×C₁₀₃	—	2	2	no	—
76	#117×C₁₀₃	—	2	2	no	—
77	#117×C₁₀₃	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₃	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
98	C₂×C₄²×C₁₀₃	—	2	2	no	—
99	C₂×C₄²×C₁₀₃	—	2	1	no	—
100	C₂×C₄²×C₁₀₃	—	2	1	no	—
101	#107×C₁₀₃	—	2	2	no	—
102	#107×C₁₀₃	—	2	2	no	—
103	#107×C₁₀₃	—	2	4	no	—
104	#106×C₁₀₃	—	2	2	no	—
105	#106×C₁₀₃	—	2	2	no	—
106	#106×C₁₀₃	—	2	4	no	—
107	C₂²⋊C₈×C₁₀₃	C₂×C₄	1	8	yes	complemented
108	C₂²⋊C₈×C₁₀₃	C₂×C₄	1	8	yes	complemented
109	#95×C₁₀₃	—	2	2	no	—
110	#95×C₁₀₃	—	2	2	no	—
111	C₂⁴×C₁₀₃	C₂×D₄	1	2	yes	—
112	C₂⁴×C₁₀₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₁₀₃	—	2	8	no	—
114	#41×C₁₀₃	—	2	8	no	—
115	#41×C₁₀₃	—	2	8	no	—
116	#41×C₁₀₃	—	2	8	no	—
117	C₂×Q₈×C₁₀₃	—	2	2	no	—
118	C₂×Q₈×C₁₀₃	—	2	2	no	—
119	C₂×Q₈×C₁₀₃	C₄⋊C₄	1	4	yes	—
120	C₂×D₄×C₁₀₃	—	2	4	no	—
121	C₂×D₄×C₁₀₃	—	2	4	no	—
122	C₂×D₄×C₁₀₃	—	2	2	no	—
123	C₂×D₄×C₁₀₃	—	2	2	no	—
124	C₂×D₄×C₁₀₃	C₄⋊C₄	1	8	yes	—
125	C₂×D₄×C₁₀₃	C₄⋊C₄	1	4	yes	—
126	C₂²×C₄×C₁₀₃	—	2	2	no	—
127	C₂²×C₄×C₁₀₃	—	2	2	no	—
128	C₂²×C₄×C₁₀₃	—	2	2	no	—
129	C₂²×C₄×C₁₀₃	—	2	2	no	—
130	C₂²×C₄×C₁₀₃	—	2	1	no	—
131	C₂²×C₄×C₁₀₃	—	2	2	no	—
132	C₂²×C₄×C₁₀₃	—	2	1	no	—
133	C₂²×C₄×C₁₀₃	—	2	8	no	—
134	C₂²×C₄×C₁₀₃	—	2	4	no	—
135	C₂²×C₄×C₁₀₃	—	2	1	no	—
136	C₂²×C₄×C₁₀₃	—	2	1	no	—
137	C₂²×C₄×C₁₀₃	—	2	2	no	—
138	C₂²×C₄×C₁₀₃	—	4	2	no	—
139	C₂²×C₄×C₁₀₃	—	8	1	no	—
140	C₂²×C₄×C₁₀₃	—	8	2	no	—
141	C₂²×C₄×C₁₀₃	—	8	1	no	—
142	C₂²×C₄×C₁₀₃	—	8	2	no	—
143	C₂²×C₄×C₁₀₃	—	8	1	no	—
144	C₂²×C₄×C₁₀₃	—	8	1	no	—
145	C₂²×C₄×C₁₀₃	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₀₃	C₂×Q₈	1	4	yes	—
152	C₂²×C₄×C₁₀₃	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₁₀₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₀₃	#41	1	2	yes	—
155	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₁₀₃	—	2	8	no	—
157	C₂×C₈×C₁₀₃	—	2	8	no	—
158	C₂×C₈×C₁₀₃	—	2	1	no	—
159	C₂×C₈×C₁₀₃	—	2	2	no	—
160	C₂×C₈×C₁₀₃	—	2	1	no	—
161	C₂×C₈×C₁₀₃	—	2	1	no	—
162	C₂×C₈×C₁₀₃	—	2	1	no	—
163	C₂×C₈×C₁₀₃	—	2	2	no	—
164	C₂×C₈×C₁₀₃	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₁₀₃	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₁₀₃	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₁₀₃	—	2	8	no	—
168	C₄⋊C₄×C₁₀₃	—	2	4	no	—
169	C₄⋊C₄×C₁₀₃	—	2	2	no	—
170	C₄⋊C₄×C₁₀₃	—	2	1	no	—
171	C₄⋊C₄×C₁₀₃	—	2	1	no	—
172	C₄⋊C₄×C₁₀₃	—	2	1	no	—
173	C₄⋊C₄×C₁₀₃	—	2	1	no	—
174	C₄⋊C₄×C₁₀₃	—	2	1	no	—
175	C₄⋊C₄×C₁₀₃	—	2	1	no	—
176	C₄⋊C₄×C₁₀₃	—	2	2	no	—
177	C₄⋊C₄×C₁₀₃	—	2	2	no	—
178	C₄⋊C₄×C₁₀₃	—	4	2	no	—
179	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₁₀₃	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
183	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
184	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
185	C₂²⋊C₄×C₁₀₃	—	8	2	no	—
186	C₂²⋊C₄×C₁₀₃	—	8	2	no	—
187	C₄²×C₁₀₃	—	2	8	no	—
188	C₄²×C₁₀₃	—	2	4	no	—
189	C₄²×C₁₀₃	—	4	2	no	—
190	C₂³×C₁₀₃	—	2	1	no	—
191	C₂³×C₁₀₃	—	2	1	no	—
192	C₂³×C₁₀₃	—	2	1	no	—
193	C₂³×C₁₀₃	—	2	1	no	—
194	C₂³×C₁₀₃	—	2	2	no	—
195	C₂³×C₁₀₃	—	2	2	no	—
196	C₂³×C₁₀₃	—	2	2	no	—
197	C₂³×C₁₀₃	—	2	2	no	—
198	C₂³×C₁₀₃	—	2	2	no	—
199	C₂³×C₁₀₃	—	2	2	no	—
200	C₂³×C₁₀₃	C₂×C₄⋊C₄	1	4	yes	—
201	C₂³×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
202	C₂³×C₁₀₃	#120	1	2	yes	—
203	C₂³×C₁₀₃	#123	1	2	yes	—
204	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₀₃	—	2	8	no	—
206	D₄×C₁₀₃	—	2	16	no	—
207	D₄×C₁₀₃	—	2	8	no	—
208	C₂×C₄×C₁₀₃	—	2	2	no	—
209	C₂×C₄×C₁₀₃	—	2	2	no	—
210	C₂×C₄×C₁₀₃	—	2	4	no	—
211	C₂×C₄×C₁₀₃	—	2	4	no	—
212	C₂×C₄×C₁₀₃	—	2	4	no	—
213	C₂×C₄×C₁₀₃	—	2	4	no	—
214	C₂×C₄×C₁₀₃	—	2	2	no	—
215	C₂×C₄×C₁₀₃	—	2	4	no	—
216	C₂×C₄×C₁₀₃	—	2	2	no	—
217	C₂×C₄×C₁₀₃	—	4	2	no	—
218	C₂×C₄×C₁₀₃	—	4	1	no	—
219	C₂×C₄×C₁₀₃	—	4	1	no	—
220	C₂×C₄×C₁₀₃	—	4	2	no	—
221	C₂×C₄×C₁₀₃	—	4	1	no	—
222	C₂×C₄×C₁₀₃	—	4	1	no	—
223	C₂×C₄×C₁₀₃	—	4	1	no	—
224	C₂×C₄×C₁₀₃	—	4	1	no	—
225	C₂×C₄×C₁₀₃	—	4	2	no	—
226	C₂×C₄×C₁₀₃	—	4	1	no	—
227	C₂×C₄×C₁₀₃	—	4	2	no	—
228	C₂×C₄×C₁₀₃	—	4	1	no	—
229	C₂×C₄×C₁₀₃	—	4	2	no	—
230	C₂×C₄×C₁₀₃	—	4	1	no	—
231	C₂×C₄×C₁₀₃	—	4	1	no	—
232	C₂×C₄×C₁₀₃	—	8	4	no	—
233	C₂×C₄×C₁₀₃	—	8	8	no	—
234	C₂×C₄×C₁₀₃	—	8	4	no	—
235	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
237	C₂×C₄×C₁₀₃	C₄×D₄	1	4	yes	—
238	C₂×C₄×C₁₀₃	C₄×D₄	1	4	yes	—
239	C₂×C₄×C₁₀₃	#120	1	2	yes	—
240	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	4	yes	—
241	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	4	yes	—
242	C₂×C₄×C₁₀₃	#123	1	2	yes	—
243	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₀₃	C₂²×Q₈	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	C₈×C₁₀₃	—	2	2	no	—
250	C₈×C₁₀₃	—	2	2	no	—
251	C₈×C₁₀₃	—	2	4	no	—
252	C₂²×C₁₀₃	—	2	2	no	—
253	C₂²×C₁₀₃	—	2	2	no	—
254	C₂²×C₁₀₃	—	2	2	no	—
255	C₂²×C₁₀₃	—	2	2	no	—
256	C₂²×C₁₀₃	—	2	2	no	—
257	C₂²×C₁₀₃	—	2	2	no	—
258	C₂²×C₁₀₃	—	2	4	no	—
259	C₂²×C₁₀₃	—	2	4	no	—
260	C₂²×C₁₀₃	—	2	4	no	—
261	C₂²×C₁₀₃	—	4	2	no	—
262	C₂²×C₁₀₃	—	4	2	no	—
263	C₂²×C₁₀₃	—	4	2	no	—
264	C₂²×C₁₀₃	—	4	2	no	—
265	C₂²×C₁₀₃	#385	1	4	yes	—
266	C₂²×C₁₀₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
267	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
268	C₂²×C₁₀₃	C₂×#123	1	1	yes	characteristic
269	C₂²×C₁₀₃	#576	1	1	yes	characteristic
270	C₂²×C₁₀₃	#577	1	1	yes	characteristic
271	C₂²×C₁₀₃	#577	1	1	yes	characteristic
272	C₂²×C₁₀₃	#578	1	1	yes	characteristic
273	C₄×C₁₀₃	—	2	4	no	—
274	C₄×C₁₀₃	—	4	4	no	—
275	C₄×C₁₀₃	—	4	2	no	—
276	C₄×C₁₀₃	—	4	2	no	—
277	C₄×C₁₀₃	—	8	2	no	—
278	C₄×C₁₀₃	—	8	1	no	—
279	C₄×C₁₀₃	—	8	1	no	—
280	C₄×C₁₀₃	#385	1	4	yes	—
281	C₄×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₁₀₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
284	C₄×C₁₀₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
285	#20849	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₁₀₃	—	2	4	no	—
287	C₂×C₁₀₃	—	4	4	no	—
288	C₂×C₁₀₃	C₂×#385	1	1	yes	characteristic
289	C₂×C₁₀₃	#2912	1	1	yes	characteristic
290	C₂×C₁₀₃	#2913	1	1	yes	characteristic
291	C₂×C₁₀₃	#3012	1	1	yes	characteristic
292	C₂×C₁₀₃	#3013	1	1	yes	characteristic
293	C₂×C₁₀₃	#3096	1	1	yes	characteristic
294	C₂×C₁₀₃	#3097	1	1	yes	characteristic
295	C₂×#520	C₂×C₁₀₃	1	1	yes	characteristic
296	C₂×#428	C₂×C₁₀₃	1	1	yes	characteristic, complemented
297	C₂×#427	C₂×C₁₀₃	1	1	yes	characteristic, complemented
298	C₂×#408	C₂×C₁₀₃	1	1	yes	characteristic
299	#2311	C₂×C₁₀₃	1	1	yes	characteristic
300	#1854	C₂×C₁₀₃	1	2	yes	complemented
301	#1854	C₂×C₁₀₃	1	2	yes	complemented
302	#1853	C₂×C₁₀₃	1	2	yes	complemented
303	#1852	C₂×C₁₀₃	1	2	yes	complemented
304	#1736	C₂×C₁₀₃	1	1	yes	characteristic, complemented
305	C₂×#340	C₂×C₁₀₃	1	1	yes	characteristic, complemented
306	C₁₀₃	#20849	1	1	yes	characteristic, direct product factor, Sylow
307	C₂²×#41	C₂²×C₁₀₃	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
309	C₂³×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
310	#520	—	2	4	no	—
311	#520	—	2	4	no	—
312	C₂×C₄×Q₈	—	2	1	no	—
313	C₂×C₄×D₄	—	2	2	no	—
314	C₂×C₄×D₄	—	2	1	no	—
315	C₂×#117	C₂²×C₁₀₃	1	1	yes	characteristic
316	C₂×#117	C₂²×C₁₀₃	1	2	yes	—
317	C₂×#117	C₂²×C₁₀₃	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
321	#428	—	2	4	no	—
322	#427	—	2	4	no	—
323	C₂×#107	C₂²×C₁₀₃	1	1	yes	characteristic
324	C₂×#107	C₂²×C₁₀₃	1	2	yes	—
325	C₂×#107	C₂²×C₁₀₃	1	1	yes	characteristic
326	C₂×#106	C₂²×C₁₀₃	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₀₃	1	2	yes	—
328	C₂×#106	C₂²×C₁₀₃	1	1	yes	characteristic
329	#408	C₄×C₁₀₃	1	8	yes	complemented
330	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
331	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
332	#391	—	2	1	no	—
333	#390	—	2	1	no	—
334	#386	—	2	2	no	—
335	#380	C₂²×C₁₀₃	1	2	yes	—
336	#380	C₂²×C₁₀₃	1	2	yes	—
337	#340	C₂²×C₁₀₃	1	2	yes	—
338	#340	C₂²×C₁₀₃	1	2	yes	—
339	#340	C₂²×C₁₀₃	1	2	yes	—
340	#340	C₂²×C₁₀₃	1	2	yes	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	C₂×C₄×C₁₀₃	1	4	yes	—
346	C₂×#41	Q₈×C₁₀₃	1	4	yes	—
347	C₂²×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
348	C₂²×D₄	D₄×C₁₀₃	1	2	yes	—
349	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	C₂×C₄×C₁₀₃	1	4	yes	complemented
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	C₂×C₄×C₁₀₃	1	4	yes	complemented
361	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
364	C₄×Q₈	—	2	8	no	—
365	C₄×D₄	—	2	16	no	—
366	C₄×D₄	—	2	8	no	—
367	#117	—	2	2	no	—
368	#117	—	2	4	no	—
369	#117	—	2	4	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	D₄×C₁₀₃	1	4	yes	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	4	no	—
377	C₂×C₄⋊C₄	—	2	4	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	D₄×C₁₀₃	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	#107	—	2	2	no	—
397	#107	—	2	2	no	—
398	#107	—	2	4	no	—
399	#106	—	2	2	no	—
400	#106	—	2	2	no	—
401	#106	—	2	4	no	—
402	C₂²⋊C₈	C₂×C₄×C₁₀₃	1	8	yes	complemented
403	C₂²⋊C₈	C₂×C₄×C₁₀₃	1	8	yes	complemented
404	#95	—	2	2	no	—
405	#95	—	2	2	no	—
406	C₂⁴	C₂×D₄×C₁₀₃	1	2	yes	—
407	C₂⁴	C₂×D₄×C₁₀₃	1	1	yes	characteristic
408	#41	—	2	8	no	—
409	#41	—	2	8	no	—
410	#41	—	2	8	no	—
411	#41	—	2	8	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	C₄⋊C₄×C₁₀₃	1	4	yes	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	C₄⋊C₄×C₁₀₃	1	8	yes	—
420	C₂×D₄	C₄⋊C₄×C₁₀₃	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	8	1	no	—
435	C₂²×C₄	—	8	2	no	—
436	C₂²×C₄	—	8	1	no	—
437	C₂²×C₄	—	8	2	no	—
438	C₂²×C₄	—	8	1	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	C₂²×C₄×C₁₀₃	1	4	yes	—
441	C₂²×C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
446	C₂²×C₄	C₂×Q₈×C₁₀₃	1	4	yes	—
447	C₂²×C₄	C₂×Q₈×C₁₀₃	1	2	yes	—
448	C₂²×C₄	#41×C₁₀₃	1	2	yes	—
449	C₂²×C₄	#41×C₁₀₃	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
451	M₁₆	—	2	8	no	—
452	C₂×C₈	—	2	8	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	C₂²×C₄×C₁₀₃	1	2	yes	—
460	C₂×C₈	C₂²×C₄×C₁₀₃	1	2	yes	—
461	C₂×C₈	C₂²×C₄×C₁₀₃	1	4	yes	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
475	C₄⋊C₄	C₂×D₄×C₁₀₃	1	4	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	8	2	no	—
481	C₂²⋊C₄	—	8	2	no	—
482	C₄²	—	2	8	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	4	2	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	C₂×C₄⋊C₄×C₁₀₃	1	4	yes	—
496	C₂³	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
497	C₂³	#120×C₁₀₃	1	2	yes	—
498	C₂³	#123×C₁₀₃	1	2	yes	—
499	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
500	Q₈	—	2	8	no	—
501	D₄	—	2	16	no	—
502	D₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	8	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	4	yes	—
531	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
532	C₂×C₄	C₄×D₄×C₁₀₃	1	4	yes	—
533	C₂×C₄	C₄×D₄×C₁₀₃	1	4	yes	—
534	C₂×C₄	#120×C₁₀₃	1	2	yes	—
535	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	4	yes	—
536	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	4	yes	—
537	C₂×C₄	#123×C₁₀₃	1	2	yes	—
538	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×Q₈×C₁₀₃	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	4	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	#385×C₁₀₃	1	4	yes	—
561	C₂²	C₂²×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
562	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
563	C₂²	C₂×#123×C₁₀₃	1	1	yes	characteristic
564	C₂²	#576×C₁₀₃	1	1	yes	characteristic
565	C₂²	#577×C₁₀₃	1	1	yes	characteristic
566	C₂²	#577×C₁₀₃	1	1	yes	characteristic
567	C₂²	#578×C₁₀₃	1	1	yes	characteristic
568	C₄	—	2	4	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	2	no	—
575	C₄	#385×C₁₀₃	1	4	yes	—
576	C₄	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
577	C₄	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
578	C₄	C₂×C₂²⋊Q₈×C₁₀₃	1	1	yes	characteristic
579	C₄	C₂×C₂²⋊Q₈×C₁₀₃	1	1	yes	characteristic
580	C₂	—	2	4	no	—
581	C₂	—	4	4	no	—
582	C₂	C₂×#385×C₁₀₃	1	1	yes	characteristic
583	C₂	C₁₀₃×#2912	1	1	yes	characteristic
584	C₂	C₁₀₃×#2913	1	1	yes	characteristic
585	C₂	C₁₀₃×#3012	1	1	yes	characteristic
586	C₂	C₁₀₃×#3013	1	1	yes	characteristic
587	C₂	C₁₀₃×#3096	1	1	yes	characteristic
588	C₂	C₁₀₃×#3097	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₂²×#41×C₁₀₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂²×#41×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#428×C₁₀₃	C₂	semidirect
3. C₂×#427×C₁₀₃	C₂	semidirect
6. C₁₀₃×#1854	C₂	semidirect
7. C₁₀₃×#1854	C₂	semidirect
8. C₁₀₃×#1853	C₂	semidirect
9. C₁₀₃×#1852	C₂	semidirect
10. C₁₀₃×#1736	C₂	semidirect
11. C₂×#340×C₁₀₃	C₂	semidirect
34. #408×C₁₀₃	C₄	semidirect
62. C₂×M₁₆×C₁₀₃	C₂×C₄	semidirect
65. C₂²×C₈×C₁₀₃	C₂×C₄	semidirect
107. C₂²⋊C₈×C₁₀₃	C₂×C₄	semidirect
108. C₂²⋊C₈×C₁₀₃	C₂×C₄	semidirect
285. #20849	C₁₀₃	direct (N × H)
296. C₂×#428	C₂×C₁₀₃	semidirect
297. C₂×#427	C₂×C₁₀₃	semidirect
300. #1854	C₂×C₁₀₃	semidirect
301. #1854	C₂×C₁₀₃	semidirect
302. #1853	C₂×C₁₀₃	semidirect
303. #1852	C₂×C₁₀₃	semidirect
304. #1736	C₂×C₁₀₃	semidirect
305. C₂×#340	C₂×C₁₀₃	semidirect
306. C₁₀₃	#20849	direct (N × H)
329. #408	C₄×C₁₀₃	semidirect
357. C₂×M₁₆	C₂×C₄×C₁₀₃	semidirect
360. C₂²×C₈	C₂×C₄×C₁₀₃	semidirect
402. C₂²⋊C₈	C₂×C₄×C₁₀₃	semidirect
403. C₂²⋊C₈	C₂×C₄×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#520×C₁₀₃	2
C₂×#428×C₁₀₃	2
C₂×#427×C₁₀₃	2
C₂×#408×C₁₀₃	2
C₁₀₃×#2311	2
C₁₀₃×#1854	2
C₁₀₃×#1853	2
C₁₀₃×#1852	2
C₁₀₃×#1736	2
C₂×#340×C₁₀₃	2
#20849	103

Subgroups — C103×#20849 #39926124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#20849 #39926124