Subgroups — C₁₀₃×#20679 #39925954

Order 26368.

1330 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#430×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#428×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×#417×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃×#1816	C₂	1	4	yes	maximal, complemented
7	C₁₀₃×#1815	C₂	1	4	yes	maximal, complemented
8	C₁₀₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#343×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₀₃	C₂²	1	1	yes	characteristic
11	#568×C₁₀₃	—	2	4	no	—
12	#568×C₁₀₃	C₄	1	8	yes	complemented
13	C₂×#131×C₁₀₃	—	2	2	no	—
14	C₂×#131×C₁₀₃	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₁₀₃	—	2	2	no	—
16	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
22	#430×C₁₀₃	—	2	4	no	—
23	C₂×#108×C₁₀₃	C₂²	1	4	yes	complemented
24	#428×C₁₀₃	—	2	2	no	—
25	#428×C₁₀₃	—	2	2	no	—
26	C₂×#107×C₁₀₃	C₂²	1	2	yes	complemented
27	C₂×#106×C₁₀₃	C₂²	1	2	yes	complemented
28	#419×C₁₀₃	—	2	1	no	—
29	#418×C₁₀₃	—	2	1	no	—
30	#417×C₁₀₃	—	2	2	no	—
31	#417×C₁₀₃	C₂²	1	2	yes	—
32	#417×C₁₀₃	C₂²	1	4	yes	—
33	#417×C₁₀₃	C₂²	1	2	yes	—
34	#416×C₁₀₃	—	2	2	no	—
35	C₂×#103×C₁₀₃	—	2	1	no	—
36	C₂×#102×C₁₀₃	—	2	1	no	—
37	#343×C₁₀₃	C₂²	1	4	yes	complemented
38	#343×C₁₀₃	C₂²	1	2	yes	complemented
39	#343×C₁₀₃	C₂²	1	2	yes	complemented
40	C₂×#41×C₁₀₃	—	2	1	no	—
41	C₂×#41×C₁₀₃	—	2	2	no	—
42	C₂×#41×C₁₀₃	—	2	1	no	—
43	C₂×#41×C₁₀₃	—	2	2	no	—
44	C₂×#41×C₁₀₃	C₂×C₄	1	4	yes	—
45	C₂×#41×C₁₀₃	D₄	1	2	yes	—
46	C₂×#41×C₁₀₃	Q₈	1	4	yes	—
47	C₂×#41×C₁₀₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₀₃	—	2	1	no	—
50	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₃	—	2	1	no	—
52	C₂³×C₄×C₁₀₃	—	2	1	no	—
53	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
54	#131×C₁₀₃	—	2	16	no	—
55	#131×C₁₀₃	—	2	8	no	—
56	#131×C₁₀₃	C₂×C₄	1	16	yes	complemented
57	C₂×M₁₆×C₁₀₃	—	2	1	no	—
58	C₂×M₁₆×C₁₀₃	—	2	2	no	—
59	C₂×M₁₆×C₁₀₃	—	2	16	no	—
60	C₂×M₁₆×C₁₀₃	—	2	1	no	—
61	C₂×M₁₆×C₁₀₃	—	2	1	no	—
62	C₂×M₁₆×C₁₀₃	—	2	4	no	—
63	C₂×M₁₆×C₁₀₃	—	2	2	no	—
64	C₂×M₁₆×C₁₀₃	—	2	2	no	—
65	C₂×M₁₆×C₁₀₃	—	2	2	no	—
66	C₂×M₁₆×C₁₀₃	—	2	2	no	—
67	C₂×M₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
68	C₂×M₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
69	C₂×M₁₆×C₁₀₃	D₄	1	2	yes	—
70	C₂×M₁₆×C₁₀₃	D₄	1	2	yes	—
71	C₂×M₁₆×C₁₀₃	D₄	1	4	yes	—
72	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
73	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
74	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₀₃	—	2	1	no	—
76	C₂²×C₈×C₁₀₃	—	2	4	no	—
77	C₂²×C₈×C₁₀₃	—	2	1	no	—
78	C₂²×C₈×C₁₀₃	—	2	1	no	—
79	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
80	#117×C₁₀₃	—	2	1	no	—
81	#117×C₁₀₃	—	2	1	no	—
82	#117×C₁₀₃	—	2	1	no	—
83	#117×C₁₀₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
93	C₂×C₄²×C₁₀₃	—	2	1	no	—
94	#108×C₁₀₃	—	2	8	no	—
95	#107×C₁₀₃	—	2	4	no	—
96	#106×C₁₀₃	—	2	4	no	—
97	#103×C₁₀₃	—	2	4	no	—
98	#103×C₁₀₃	—	2	2	no	—
99	#103×C₁₀₃	—	2	2	no	—
100	#102×C₁₀₃	—	2	4	no	—
101	#102×C₁₀₃	—	2	2	no	—
102	#102×C₁₀₃	—	2	2	no	—
103	C₂⁴×C₁₀₃	—	2	1	no	—
104	C₂⁴×C₁₀₃	#41	1	1	yes	characteristic
105	#41×C₁₀₃	—	2	4	no	—
106	#41×C₁₀₃	—	2	4	no	—
107	#41×C₁₀₃	—	2	4	no	—
108	#41×C₁₀₃	—	2	4	no	—
109	#41×C₁₀₃	—	2	4	no	—
110	#41×C₁₀₃	—	2	2	no	—
111	#41×C₁₀₃	—	2	2	no	—
112	#41×C₁₀₃	C₄⋊C₄	1	8	yes	—
113	#41×C₁₀₃	C₂²×C₄	1	4	yes	—
114	#41×C₁₀₃	C₂×Q₈	1	4	yes	—
115	C₂×Q₈×C₁₀₃	—	2	1	no	—
116	C₂×Q₈×C₁₀₃	—	2	2	no	—
117	C₂×Q₈×C₁₀₃	C₄⋊C₄	1	4	yes	—
118	C₂×Q₈×C₁₀₃	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₀₃	—	2	4	no	—
120	C₂×D₄×C₁₀₃	—	2	2	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	—	2	1	no	—
125	C₂×D₄×C₁₀₃	C₄⋊C₄	1	4	yes	—
126	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₀₃	—	2	1	no	—
128	C₂²×C₄×C₁₀₃	—	2	4	no	—
129	C₂²×C₄×C₁₀₃	—	2	2	no	—
130	C₂²×C₄×C₁₀₃	—	2	4	no	—
131	C₂²×C₄×C₁₀₃	—	2	2	no	—
132	C₂²×C₄×C₁₀₃	—	2	1	no	—
133	C₂²×C₄×C₁₀₃	—	2	1	no	—
134	C₂²×C₄×C₁₀₃	—	2	2	no	—
135	C₂²×C₄×C₁₀₃	—	4	1	no	—
136	C₂²×C₄×C₁₀₃	—	4	1	no	—
137	C₂²×C₄×C₁₀₃	—	8	2	no	—
138	C₂²×C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₀₃	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₃	#41	1	2	yes	—
147	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₁₀₃	—	2	4	no	—
149	M₁₆×C₁₀₃	—	2	2	no	—
150	M₁₆×C₁₀₃	—	2	16	no	—
151	M₁₆×C₁₀₃	—	2	2	no	—
152	M₁₆×C₁₀₃	—	2	2	no	—
153	M₁₆×C₁₀₃	—	2	2	no	—
154	M₁₆×C₁₀₃	—	2	2	no	—
155	M₁₆×C₁₀₃	—	4	2	no	—
156	M₁₆×C₁₀₃	—	4	2	no	—
157	M₁₆×C₁₀₃	C₂²⋊C₄	1	8	yes	—
158	M₁₆×C₁₀₃	C₂²⋊C₄	1	8	yes	—
159	M₁₆×C₁₀₃	C₂²×C₄	1	4	yes	—
160	C₂×C₈×C₁₀₃	—	2	4	no	—
161	C₂×C₈×C₁₀₃	—	2	2	no	—
162	C₂×C₈×C₁₀₃	—	2	16	no	—
163	C₂×C₈×C₁₀₃	—	2	2	no	—
164	C₂×C₈×C₁₀₃	—	2	2	no	—
165	C₂×C₈×C₁₀₃	—	4	2	no	—
166	C₂×C₈×C₁₀₃	—	4	2	no	—
167	C₂×C₈×C₁₀₃	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
169	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₁₀₃	—	2	2	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	2	no	—
175	C₄⋊C₄×C₁₀₃	—	2	1	no	—
176	C₄⋊C₄×C₁₀₃	—	4	1	no	—
177	C₄⋊C₄×C₁₀₃	—	4	1	no	—
178	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
179	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
180	C₄²×C₁₀₃	—	4	1	no	—
181	C₄²×C₁₀₃	—	4	1	no	—
182	C₂³×C₁₀₃	—	2	2	no	—
183	C₂³×C₁₀₃	—	2	4	no	—
184	C₂³×C₁₀₃	—	4	1	no	—
185	C₂³×C₁₀₃	—	4	1	no	—
186	C₂³×C₁₀₃	—	8	1	no	—
187	C₂³×C₁₀₃	—	8	1	no	—
188	C₂³×C₁₀₃	#117	1	2	yes	—
189	C₂³×C₁₀₃	#121	1	1	yes	characteristic
190	C₂³×C₁₀₃	#121	1	1	yes	characteristic
191	C₂³×C₁₀₃	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₁₀₃	C₂×#41	1	1	yes	characteristic
193	Q₈×C₁₀₃	—	2	2	no	—
194	Q₈×C₁₀₃	—	2	4	no	—
195	Q₈×C₁₀₃	C₂×C₄⋊C₄	1	4	yes	—
196	D₄×C₁₀₃	—	2	4	no	—
197	D₄×C₁₀₃	—	2	4	no	—
198	D₄×C₁₀₃	—	2	8	no	—
199	D₄×C₁₀₃	—	2	2	no	—
200	D₄×C₁₀₃	—	2	4	no	—
201	D₄×C₁₀₃	C₂×C₄⋊C₄	1	4	yes	—
202	C₂×C₄×C₁₀₃	—	2	2	no	—
203	C₂×C₄×C₁₀₃	—	2	4	no	—
204	C₂×C₄×C₁₀₃	—	2	4	no	—
205	C₂×C₄×C₁₀₃	—	2	4	no	—
206	C₂×C₄×C₁₀₃	—	2	8	no	—
207	C₂×C₄×C₁₀₃	—	4	1	no	—
208	C₂×C₄×C₁₀₃	—	4	1	no	—
209	C₂×C₄×C₁₀₃	—	4	2	no	—
210	C₂×C₄×C₁₀₃	—	8	2	no	—
211	C₂×C₄×C₁₀₃	—	8	2	no	—
212	C₂×C₄×C₁₀₃	—	8	1	no	—
213	C₂×C₄×C₁₀₃	—	8	1	no	—
214	C₂×C₄×C₁₀₃	—	8	2	no	—
215	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₀₃	#117	1	2	yes	—
220	C₂×C₄×C₁₀₃	#121	1	2	yes	—
221	C₂×C₄×C₁₀₃	#121	1	2	yes	—
222	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	2	yes	—
225	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	2	yes	—
226	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
233	C₈×C₁₀₃	—	2	4	no	—
234	C₈×C₁₀₃	—	4	2	no	—
235	C₈×C₁₀₃	—	4	2	no	—
236	C₈×C₁₀₃	C₂×C₂²⋊C₄	1	8	yes	—
237	C₂²×C₁₀₃	—	2	1	no	—
238	C₂²×C₁₀₃	—	2	1	no	—
239	C₂²×C₁₀₃	—	2	1	no	—
240	C₂²×C₁₀₃	—	2	1	no	—
241	C₂²×C₁₀₃	—	2	1	no	—
242	C₂²×C₁₀₃	—	2	1	no	—
243	C₂²×C₁₀₃	—	2	4	no	—
244	C₂²×C₁₀₃	—	4	2	no	—
245	C₂²×C₁₀₃	—	4	2	no	—
246	C₂²×C₁₀₃	—	4	2	no	—
247	C₂²×C₁₀₃	—	4	2	no	—
248	C₂²×C₁₀₃	—	8	4	no	—
249	C₂²×C₁₀₃	#380	1	2	yes	—
250	C₂²×C₁₀₃	#380	1	2	yes	—
251	C₂²×C₁₀₃	C₂×#117	1	1	yes	characteristic
252	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
253	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
254	C₄×C₁₀₃	—	2	4	no	—
255	C₄×C₁₀₃	—	8	1	no	—
256	C₄×C₁₀₃	—	8	2	no	—
257	C₄×C₁₀₃	—	8	1	no	—
258	C₄×C₁₀₃	#380	1	2	yes	—
259	C₄×C₁₀₃	#380	1	2	yes	—
260	C₄×C₁₀₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
261	C₄×C₁₀₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
262	C₄×C₁₀₃	C₂×#121	1	1	yes	characteristic
263	C₄×C₁₀₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	#20679	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂×C₁₀₃	—	2	2	no	—
266	C₂×C₁₀₃	—	2	1	no	—
267	C₂×C₁₀₃	—	2	1	no	—
268	C₂×C₁₀₃	—	2	2	no	—
269	C₂×C₁₀₃	—	4	4	no	—
270	C₂×C₁₀₃	C₂×#380	1	1	yes	characteristic
271	C₂×C₁₀₃	#3068	1	1	yes	characteristic
272	C₂×C₁₀₃	#3069	1	1	yes	characteristic
273	C₂×#568	C₂×C₁₀₃	1	1	yes	characteristic
274	C₂×#430	C₂×C₁₀₃	1	1	yes	characteristic, complemented
275	C₂×#428	C₂×C₁₀₃	1	1	yes	characteristic, complemented
276	#2896	C₂×C₁₀₃	1	1	yes	characteristic
277	C₂×#417	C₂×C₁₀₃	1	1	yes	characteristic
278	#1816	C₂×C₁₀₃	1	4	yes	complemented
279	#1815	C₂×C₁₀₃	1	4	yes	complemented
280	#1742	C₂×C₁₀₃	1	1	yes	characteristic, complemented
281	C₂×#343	C₂×C₁₀₃	1	1	yes	characteristic, complemented
282	C₁₀₃	#20679	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×#41	C₂²×C₁₀₃	1	1	yes	characteristic
284	#568	—	2	4	no	—
285	#568	C₄×C₁₀₃	1	8	yes	complemented
286	C₂×#131	—	2	2	no	—
287	C₂×#131	C₂²×C₁₀₃	1	4	yes	—
288	C₂²×M₁₆	—	2	2	no	—
289	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
290	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₀₃	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
295	#430	—	2	4	no	—
296	C₂×#108	C₂²×C₁₀₃	1	4	yes	complemented
297	#428	—	2	2	no	—
298	#428	—	2	2	no	—
299	C₂×#107	C₂²×C₁₀₃	1	2	yes	complemented
300	C₂×#106	C₂²×C₁₀₃	1	2	yes	complemented
301	#419	—	2	1	no	—
302	#418	—	2	1	no	—
303	#417	—	2	2	no	—
304	#417	C₂²×C₁₀₃	1	2	yes	—
305	#417	C₂²×C₁₀₃	1	4	yes	—
306	#417	C₂²×C₁₀₃	1	2	yes	—
307	#416	—	2	2	no	—
308	C₂×#103	—	2	1	no	—
309	C₂×#102	—	2	1	no	—
310	#343	C₂²×C₁₀₃	1	2	yes	complemented
311	#343	C₂²×C₁₀₃	1	4	yes	complemented
312	#343	C₂²×C₁₀₃	1	2	yes	complemented
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	C₂×C₄×C₁₀₃	1	4	yes	—
318	C₂×#41	D₄×C₁₀₃	1	2	yes	—
319	C₂×#41	Q₈×C₁₀₃	1	4	yes	—
320	C₂×#41	C₂³×C₁₀₃	1	2	yes	—
321	C₂²×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
327	#131	—	2	16	no	—
328	#131	—	2	8	no	—
329	#131	C₂×C₄×C₁₀₃	1	16	yes	complemented
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	16	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	4	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
341	C₂×M₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
342	C₂×M₁₆	D₄×C₁₀₃	1	2	yes	—
343	C₂×M₁₆	D₄×C₁₀₃	1	2	yes	—
344	C₂×M₁₆	D₄×C₁₀₃	1	4	yes	—
345	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
347	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	4	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	#108	—	2	8	no	—
368	#107	—	2	4	no	—
369	#106	—	2	4	no	—
370	#103	—	2	4	no	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#102	—	2	4	no	—
374	#102	—	2	2	no	—
375	#102	—	2	2	no	—
376	C₂⁴	—	2	1	no	—
377	C₂⁴	#41×C₁₀₃	1	1	yes	characteristic
378	#41	—	2	4	no	—
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₄⋊C₄×C₁₀₃	1	8	yes	—
386	#41	C₂²×C₄×C₁₀₃	1	4	yes	—
387	#41	C₂×Q₈×C₁₀₃	1	4	yes	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₄⋊C₄×C₁₀₃	1	4	yes	—
391	C₂×Q₈	C₂×D₄×C₁₀₃	1	2	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₄⋊C₄×C₁₀₃	1	4	yes	—
399	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×Q₈×C₁₀₃	1	2	yes	—
418	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
419	C₂²×C₄	#41×C₁₀₃	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
421	M₁₆	—	2	4	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	16	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	4	2	no	—
429	M₁₆	—	4	2	no	—
430	M₁₆	C₂²⋊C₄×C₁₀₃	1	8	yes	—
431	M₁₆	C₂²⋊C₄×C₁₀₃	1	8	yes	—
432	M₁₆	C₂²×C₄×C₁₀₃	1	4	yes	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	16	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	C₂²×C₄×C₁₀₃	1	4	yes	—
441	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
442	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	4	1	no	—
454	C₄²	—	4	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	—	8	1	no	—
461	C₂³	#117×C₁₀₃	1	2	yes	—
462	C₂³	#121×C₁₀₃	1	1	yes	characteristic
463	C₂³	#121×C₁₀₃	1	1	yes	characteristic
464	C₂³	C₂²⋊Q₈×C₁₀₃	1	2	yes	—
465	C₂³	C₂×#41×C₁₀₃	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	2	no	—
468	Q₈	C₂×C₄⋊C₄×C₁₀₃	1	4	yes	—
469	D₄	—	2	8	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	C₂×C₄⋊C₄×C₁₀₃	1	4	yes	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	1	no	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
490	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
491	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
492	C₂×C₄	#117×C₁₀₃	1	2	yes	—
493	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
494	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
495	C₂×C₄	#121×C₁₀₃	1	2	yes	—
496	C₂×C₄	#121×C₁₀₃	1	2	yes	—
497	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	2	yes	—
498	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	2	yes	—
499	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	2	yes	—
500	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
504	C₂×C₄	C₂²×Q₈×C₁₀₃	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₈	C₂×C₂²⋊C₄×C₁₀₃	1	8	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	4	no	—
522	C₂²	#380×C₁₀₃	1	2	yes	—
523	C₂²	#380×C₁₀₃	1	2	yes	—
524	C₂²	C₂×#117×C₁₀₃	1	1	yes	characteristic
525	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
526	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	1	yes	characteristic
527	C₄	—	2	4	no	—
528	C₄	—	8	2	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	#380×C₁₀₃	1	2	yes	—
532	C₄	#380×C₁₀₃	1	2	yes	—
533	C₄	C₂²×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
534	C₄	C₂²×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
535	C₄	C₂×#121×C₁₀₃	1	1	yes	characteristic
536	C₄	C₂×C₂²⋊Q₈×C₁₀₃	1	1	yes	characteristic
537	C₂	—	2	2	no	—
538	C₂	—	2	2	no	—
539	C₂	—	2	1	no	—
540	C₂	—	2	1	no	—
541	C₂	—	4	4	no	—
542	C₂	C₂×#380×C₁₀₃	1	1	yes	characteristic
543	C₂	C₁₀₃×#3068	1	1	yes	characteristic
544	C₂	C₁₀₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×#121
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 ◁ C₂²×C₁₀₃ ◁ C₂³×C₄×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#430×C₁₀₃	C₂	semidirect
3. C₂×#428×C₁₀₃	C₂	semidirect
6. C₁₀₃×#1816	C₂	semidirect
7. C₁₀₃×#1815	C₂	semidirect
8. C₁₀₃×#1742	C₂	semidirect
9. C₂×#343×C₁₀₃	C₂	semidirect
12. #568×C₁₀₃	C₄	semidirect
23. C₂×#108×C₁₀₃	C₂²	semidirect
26. C₂×#107×C₁₀₃	C₂²	semidirect
27. C₂×#106×C₁₀₃	C₂²	semidirect
37. #343×C₁₀₃	C₂²	semidirect
38. #343×C₁₀₃	C₂²	semidirect
39. #343×C₁₀₃	C₂²	semidirect
56. #131×C₁₀₃	C₂×C₄	semidirect
264. #20679	C₁₀₃	direct (N × H)
274. C₂×#430	C₂×C₁₀₃	semidirect
275. C₂×#428	C₂×C₁₀₃	semidirect
278. #1816	C₂×C₁₀₃	semidirect
279. #1815	C₂×C₁₀₃	semidirect
280. #1742	C₂×C₁₀₃	semidirect
281. C₂×#343	C₂×C₁₀₃	semidirect
282. C₁₀₃	#20679	direct (N × H)
285. #568	C₄×C₁₀₃	semidirect
296. C₂×#108	C₂²×C₁₀₃	semidirect
299. C₂×#107	C₂²×C₁₀₃	semidirect
300. C₂×#106	C₂²×C₁₀₃	semidirect
310. #343	C₂²×C₁₀₃	semidirect
311. #343	C₂²×C₁₀₃	semidirect
312. #343	C₂²×C₁₀₃	semidirect
329. #131	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×#568×C₁₀₃	2
C₂×#430×C₁₀₃	2
C₂×#428×C₁₀₃	2
C₁₀₃×#2896	2
C₂×#417×C₁₀₃	2
C₁₀₃×#1816	2
C₁₀₃×#1815	2
C₁₀₃×#1742	2
C₂×#343×C₁₀₃	2
#20679	103

Subgroups — C103×#20679 #39925954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#20679 #39925954