Subgroups — C₁₀₃×#18747 #39924022

Order 26368.

1634 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#1639	C₂	1	4	yes	maximal, complemented
6	C₁₀₃×#1629	C₂	1	4	yes	maximal, complemented
7	C₁₀₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₀₃	—	2	1	no	—
11	C₂³×D₄×C₁₀₃	—	2	1	no	—
12	D₄²×C₁₀₃	—	2	2	no	—
13	D₄²×C₁₀₃	—	2	2	no	—
14	D₄²×C₁₀₃	—	2	2	no	—
15	D₄²×C₁₀₃	C₂²	1	4	yes	—
16	#533×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂×#121×C₁₀₃	—	2	1	no	—
19	C₂×#121×C₁₀₃	—	2	1	no	—
20	C₂×#120×C₁₀₃	—	2	2	no	—
21	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
23	#492×C₁₀₃	C₂²	1	2	yes	complemented
24	#486×C₁₀₃	C₂²	1	2	yes	complemented
25	#483×C₁₀₃	—	2	1	no	—
26	#478×C₁₀₃	—	2	2	no	—
27	#476×C₁₀₃	C₂²	1	2	yes	complemented
28	#476×C₁₀₃	C₂²	1	2	yes	complemented
29	#474×C₁₀₃	C₂²	1	2	yes	complemented
30	#461×C₁₀₃	C₂²	1	2	yes	complemented
31	#460×C₁₀₃	—	2	2	no	—
32	#450×C₁₀₃	—	2	1	no	—
33	#450×C₁₀₃	—	2	2	no	—
34	C₄×SD₁₆×C₁₀₃	—	2	2	no	—
35	#431×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
36	#431×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
37	#428×C₁₀₃	—	2	1	no	—
38	#423×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
39	#418×C₁₀₃	—	2	1	no	—
40	#331×C₁₀₃	C₂²	1	4	yes	complemented
41	D₄⋊C₈×C₁₀₃	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₀₃	C₂²	1	4	yes	complemented
43	C₂⁵×C₁₀₃	—	2	2	no	—
44	C₂²×D₄×C₁₀₃	—	2	2	no	—
45	C₂²×D₄×C₁₀₃	—	2	2	no	—
46	C₂²×D₄×C₁₀₃	—	2	4	no	—
47	C₂²×D₄×C₁₀₃	—	2	4	no	—
48	C₂²×D₄×C₁₀₃	—	2	4	no	—
49	C₂²×D₄×C₁₀₃	—	2	4	no	—
50	C₂²×D₄×C₁₀₃	—	2	1	no	—
51	C₂²×D₄×C₁₀₃	—	2	1	no	—
52	C₂²×D₄×C₁₀₃	—	4	8	no	—
53	C₂²×D₄×C₁₀₃	—	4	4	no	—
54	C₂²×D₄×C₁₀₃	—	4	4	no	—
55	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₀₃	D₄	1	2	yes	—
58	C₂³×C₄×C₁₀₃	—	2	1	no	—
59	C₂³×C₄×C₁₀₃	—	2	1	no	—
60	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
61	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
62	C₂×M₁₆×C₁₀₃	—	2	1	no	—
63	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic, complemented
64	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic, complemented
65	#127×C₁₀₃	—	2	1	no	—
66	#127×C₁₀₃	—	2	1	no	—
67	#127×C₁₀₃	D₄	1	2	yes	—
68	#127×C₁₀₃	C₂³	1	2	yes	—
69	#125×C₁₀₃	—	2	1	no	—
70	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
71	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
72	#121×C₁₀₃	—	2	4	no	—
73	#121×C₁₀₃	—	2	4	no	—
74	#121×C₁₀₃	—	2	4	no	—
75	#121×C₁₀₃	—	2	4	no	—
76	#120×C₁₀₃	—	2	8	no	—
77	#120×C₁₀₃	—	2	8	no	—
78	C₄×Q₈×C₁₀₃	—	2	1	no	—
79	C₄×Q₈×C₁₀₃	—	2	1	no	—
80	C₄×D₄×C₁₀₃	—	2	1	no	—
81	C₄×D₄×C₁₀₃	—	2	1	no	—
82	C₄×D₄×C₁₀₃	—	2	1	no	—
83	C₄×D₄×C₁₀₃	—	2	1	no	—
84	C₄×D₄×C₁₀₃	D₄	1	2	yes	—
85	C₄×D₄×C₁₀₃	D₄	1	2	yes	—
86	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
87	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
88	#117×C₁₀₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
94	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
95	#107×C₁₀₃	—	2	2	no	—
96	#106×C₁₀₃	—	2	2	no	—
97	#106×C₁₀₃	—	2	2	no	—
98	C₄⋊C₈×C₁₀₃	—	2	1	no	—
99	C₄⋊C₈×C₁₀₃	—	2	1	no	—
100	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	complemented
101	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	complemented
102	#103×C₁₀₃	—	2	2	no	—
103	#102×C₁₀₃	—	2	2	no	—
104	#102×C₁₀₃	—	2	2	no	—
105	#102×C₁₀₃	—	2	2	no	—
106	#102×C₁₀₃	—	2	4	no	—
107	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
108	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
109	C₄×C₈×C₁₀₃	—	2	1	no	—
110	C₄×C₈×C₁₀₃	C₂³	1	2	yes	complemented
111	C₂⁴×C₁₀₃	—	2	1	no	—
112	C₂⁴×C₁₀₃	—	2	1	no	—
113	C₂⁴×C₁₀₃	—	2	8	no	—
114	C₂⁴×C₁₀₃	—	2	2	no	—
115	C₂⁴×C₁₀₃	—	4	8	no	—
116	C₂⁴×C₁₀₃	—	4	8	no	—
117	C₂⁴×C₁₀₃	—	8	4	no	—
118	C₂×Q₈×C₁₀₃	—	2	1	no	—
119	C₂×Q₈×C₁₀₃	—	2	1	no	—
120	C₂×D₄×C₁₀₃	—	2	4	no	—
121	C₂×D₄×C₁₀₃	—	2	8	no	—
122	C₂×D₄×C₁₀₃	—	2	8	no	—
123	C₂×D₄×C₁₀₃	—	2	1	no	—
124	C₂×D₄×C₁₀₃	—	2	1	no	—
125	C₂×D₄×C₁₀₃	—	2	2	no	—
126	C₂×D₄×C₁₀₃	—	2	2	no	—
127	C₂×D₄×C₁₀₃	—	2	2	no	—
128	C₂×D₄×C₁₀₃	—	2	2	no	—
129	C₂×D₄×C₁₀₃	—	2	2	no	—
130	C₂×D₄×C₁₀₃	—	2	2	no	—
131	C₂×D₄×C₁₀₃	—	4	4	no	—
132	C₂×D₄×C₁₀₃	—	4	16	no	—
133	C₂×D₄×C₁₀₃	—	4	8	no	—
134	C₂×D₄×C₁₀₃	—	4	8	no	—
135	C₂×D₄×C₁₀₃	—	4	16	no	—
136	C₂×D₄×C₁₀₃	—	4	8	no	—
137	C₂×D₄×C₁₀₃	—	4	8	no	—
138	C₂×D₄×C₁₀₃	—	4	8	no	—
139	C₂×D₄×C₁₀₃	—	4	8	no	—
140	C₂×D₄×C₁₀₃	—	4	2	no	—
141	C₂×D₄×C₁₀₃	—	4	2	no	—
142	C₂×D₄×C₁₀₃	—	8	2	no	—
143	C₂×D₄×C₁₀₃	SD₁₆	1	4	yes	complemented
144	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₀₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₀₃	—	2	1	no	—
148	C₂²×C₄×C₁₀₃	—	2	1	no	—
149	C₂²×C₄×C₁₀₃	—	2	2	no	—
150	C₂²×C₄×C₁₀₃	—	2	2	no	—
151	C₂²×C₄×C₁₀₃	—	2	2	no	—
152	C₂²×C₄×C₁₀₃	—	2	2	no	—
153	C₂²×C₄×C₁₀₃	—	4	4	no	—
154	C₂²×C₄×C₁₀₃	—	4	2	no	—
155	C₂²×C₄×C₁₀₃	—	4	2	no	—
156	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
159	SD₁₆×C₁₀₃	—	4	4	no	—
160	SD₁₆×C₁₀₃	—	8	4	no	—
161	M₁₆×C₁₀₃	—	4	2	no	—
162	C₂×C₈×C₁₀₃	—	2	2	no	—
163	C₂×C₈×C₁₀₃	—	2	2	no	—
164	C₂×C₈×C₁₀₃	—	2	2	no	—
165	C₄⋊C₄×C₁₀₃	—	2	1	no	—
166	C₄⋊C₄×C₁₀₃	—	2	1	no	—
167	C₄⋊C₄×C₁₀₃	—	2	1	no	—
168	C₄⋊C₄×C₁₀₃	—	2	1	no	—
169	C₄⋊C₄×C₁₀₃	—	2	1	no	—
170	C₄⋊C₄×C₁₀₃	—	2	1	no	—
171	C₄⋊C₄×C₁₀₃	—	4	1	no	—
172	C₄⋊C₄×C₁₀₃	—	4	1	no	—
173	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
176	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
177	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
178	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
179	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
180	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
181	C₄²×C₁₀₃	—	4	1	no	—
182	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
186	C₂³×C₁₀₃	—	2	4	no	—
187	C₂³×C₁₀₃	—	2	2	no	—
188	C₂³×C₁₀₃	—	2	2	no	—
189	C₂³×C₁₀₃	—	2	4	no	—
190	C₂³×C₁₀₃	—	2	4	no	—
191	C₂³×C₁₀₃	—	4	2	no	—
192	C₂³×C₁₀₃	—	4	2	no	—
193	C₂³×C₁₀₃	—	4	2	no	—
194	C₂³×C₁₀₃	—	4	4	no	—
195	C₂³×C₁₀₃	—	4	16	no	—
196	C₂³×C₁₀₃	—	4	16	no	—
197	C₂³×C₁₀₃	—	4	4	no	—
198	C₂³×C₁₀₃	—	4	2	no	—
199	C₂³×C₁₀₃	—	4	4	no	—
200	C₂³×C₁₀₃	—	8	8	no	—
201	C₂³×C₁₀₃	—	8	32	no	—
202	C₂³×C₁₀₃	#120	1	1	yes	characteristic
203	Q₈×C₁₀₃	—	4	2	no	—
204	Q₈×C₁₀₃	—	4	2	no	—
205	D₄×C₁₀₃	—	2	4	no	—
206	D₄×C₁₀₃	—	2	2	no	—
207	D₄×C₁₀₃	—	2	2	no	—
208	D₄×C₁₀₃	—	2	4	no	—
209	D₄×C₁₀₃	—	4	4	no	—
210	D₄×C₁₀₃	—	4	4	no	—
211	D₄×C₁₀₃	—	4	16	no	—
212	D₄×C₁₀₃	—	4	16	no	—
213	D₄×C₁₀₃	—	4	2	no	—
214	D₄×C₁₀₃	—	4	2	no	—
215	D₄×C₁₀₃	—	4	4	no	—
216	D₄×C₁₀₃	—	4	4	no	—
217	D₄×C₁₀₃	—	8	2	no	—
218	D₄×C₁₀₃	C₂×SD₁₆	1	4	yes	—
219	D₄×C₁₀₃	AGL(1,ℤ/8)	1	4	yes	—
220	C₂×C₄×C₁₀₃	—	2	2	no	—
221	C₂×C₄×C₁₀₃	—	2	2	no	—
222	C₂×C₄×C₁₀₃	—	2	2	no	—
223	C₂×C₄×C₁₀₃	—	4	1	no	—
224	C₂×C₄×C₁₀₃	—	4	4	no	—
225	C₂×C₄×C₁₀₃	—	4	2	no	—
226	C₂×C₄×C₁₀₃	—	4	2	no	—
227	C₂×C₄×C₁₀₃	—	4	2	no	—
228	C₂×C₄×C₁₀₃	—	4	2	no	—
229	C₂×C₄×C₁₀₃	—	4	4	no	—
230	C₂×C₄×C₁₀₃	—	4	4	no	—
231	C₂×C₄×C₁₀₃	—	4	1	no	—
232	C₂×C₄×C₁₀₃	—	4	1	no	—
233	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₀₃	C₂×SD₁₆	1	2	yes	—
237	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
238	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
241	C₈×C₁₀₃	—	4	2	no	—
242	C₈×C₁₀₃	—	4	2	no	—
243	C₈×C₁₀₃	—	4	2	no	—
244	C₂²×C₁₀₃	—	2	1	no	—
245	C₂²×C₁₀₃	—	2	1	no	—
246	C₂²×C₁₀₃	—	2	4	no	—
247	C₂²×C₁₀₃	—	2	4	no	—
248	C₂²×C₁₀₃	—	4	8	no	—
249	C₂²×C₁₀₃	—	4	8	no	—
250	C₂²×C₁₀₃	—	4	2	no	—
251	C₂²×C₁₀₃	—	4	2	no	—
252	C₂²×C₁₀₃	—	4	2	no	—
253	C₂²×C₁₀₃	—	4	2	no	—
254	C₂²×C₁₀₃	—	4	4	no	—
255	C₂²×C₁₀₃	—	4	4	no	—
256	C₂²×C₁₀₃	—	4	4	no	—
257	C₂²×C₁₀₃	—	8	8	no	—
258	C₂²×C₁₀₃	—	8	32	no	—
259	C₂²×C₁₀₃	#450	1	2	yes	—
260	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
261	C₄×C₁₀₃	—	2	1	no	—
262	C₄×C₁₀₃	—	2	1	no	—
263	C₄×C₁₀₃	—	2	1	no	—
264	C₄×C₁₀₃	—	4	2	no	—
265	C₄×C₁₀₃	—	4	2	no	—
266	C₄×C₁₀₃	—	8	1	no	—
267	C₄×C₁₀₃	—	8	1	no	—
268	C₄×C₁₀₃	#450	1	2	yes	—
269	C₄×C₁₀₃	C₂²×SD₁₆	1	1	yes	characteristic
270	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
272	#18747	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₁₀₃	—	2	2	no	—
274	C₂×C₁₀₃	—	4	4	no	—
275	C₂×C₁₀₃	—	4	4	no	—
276	C₂×C₁₀₃	—	8	4	no	—
277	C₂×C₁₀₃	C₂×#450	1	1	yes	characteristic
278	C₂×C₁₀₃	#3003	1	1	yes	characteristic
279	C₂×C₁₀₃	#3019	1	1	yes	characteristic
280	C₂×D₄²	C₂×C₁₀₃	1	1	yes	characteristic
281	#3208	C₂×C₁₀₃	1	1	yes	characteristic, complemented
282	#3101	C₂×C₁₀₃	1	1	yes	characteristic, complemented
283	#3077	C₂×C₁₀₃	1	1	yes	characteristic, complemented
284	#1639	C₂×C₁₀₃	1	4	yes	complemented
285	#1629	C₂×C₁₀₃	1	4	yes	complemented
286	#1545	C₂×C₁₀₃	1	1	yes	characteristic, complemented
287	#1486	C₂×C₁₀₃	1	1	yes	characteristic, complemented
288	#1478	C₂×C₁₀₃	1	1	yes	characteristic, complemented
289	C₁₀₃	#18747	1	1	yes	characteristic, direct product factor, Sylow
290	C₂³×D₄	—	2	1	no	—
291	C₂³×D₄	—	2	1	no	—
292	D₄²	—	2	2	no	—
293	D₄²	—	2	2	no	—
294	D₄²	—	2	2	no	—
295	D₄²	C₂²×C₁₀₃	1	4	yes	—
296	#533	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
297	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
298	C₂×#121	—	2	1	no	—
299	C₂×#121	—	2	1	no	—
300	C₂×#120	—	2	2	no	—
301	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
303	#492	C₂²×C₁₀₃	1	2	yes	complemented
304	#486	C₂²×C₁₀₃	1	2	yes	complemented
305	#483	—	2	1	no	—
306	#478	—	2	2	no	—
307	#476	C₂²×C₁₀₃	1	2	yes	complemented
308	#476	C₂²×C₁₀₃	1	2	yes	complemented
309	#474	C₂²×C₁₀₃	1	2	yes	complemented
310	#461	C₂²×C₁₀₃	1	2	yes	complemented
311	#460	—	2	2	no	—
312	#450	—	2	1	no	—
313	#450	—	2	2	no	—
314	C₄×SD₁₆	—	2	2	no	—
315	#431	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
316	#431	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
317	#428	—	2	1	no	—
318	#423	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
319	#418	—	2	1	no	—
320	#331	C₂²×C₁₀₃	1	4	yes	complemented
321	D₄⋊C₈	C₂²×C₁₀₃	1	4	yes	complemented
322	D₄⋊C₈	C₂²×C₁₀₃	1	4	yes	complemented
323	C₂⁵	—	2	2	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	—	2	4	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	4	8	no	—
333	C₂²×D₄	—	4	4	no	—
334	C₂²×D₄	—	4	4	no	—
335	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
336	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
337	C₂²×D₄	D₄×C₁₀₃	1	2	yes	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic, complemented
344	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic, complemented
345	#127	—	2	1	no	—
346	#127	—	2	1	no	—
347	#127	D₄×C₁₀₃	1	2	yes	—
348	#127	C₂³×C₁₀₃	1	2	yes	—
349	#125	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	4	no	—
355	#121	—	2	4	no	—
356	#120	—	2	8	no	—
357	#120	—	2	8	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	D₄×C₁₀₃	1	2	yes	—
365	C₄×D₄	D₄×C₁₀₃	1	2	yes	—
366	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
367	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
368	#117	—	2	1	no	—
369	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
375	#107	—	2	2	no	—
376	#106	—	2	2	no	—
377	#106	—	2	2	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	complemented
381	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	complemented
382	#103	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	4	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	C₂³×C₁₀₃	1	2	yes	complemented
391	C₂⁴	—	2	1	no	—
392	C₂⁴	—	2	1	no	—
393	C₂⁴	—	2	8	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	8	no	—
396	C₂⁴	—	4	8	no	—
397	C₂⁴	—	8	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	—	4	16	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	—	4	8	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	8	2	no	—
423	C₂×D₄	SD₁₆×C₁₀₃	1	4	yes	complemented
424	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₀₃	1	4	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	8	4	no	—
441	M₁₆	—	4	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₄²	—	4	1	no	—
462	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
465	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	16	no	—
476	C₂³	—	4	16	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	8	8	no	—
481	C₂³	—	8	32	no	—
482	C₂³	#120×C₁₀₃	1	1	yes	characteristic
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	16	no	—
492	D₄	—	4	16	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	8	2	no	—
498	D₄	C₂×SD₁₆×C₁₀₃	1	4	yes	—
499	D₄	AGL(1,ℤ/8)×C₁₀₃	1	4	yes	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
514	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
515	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
516	C₂×C₄	C₂×SD₁₆×C₁₀₃	1	2	yes	—
517	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	8	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	8	8	no	—
538	C₂²	—	8	32	no	—
539	C₂²	#450×C₁₀₃	1	2	yes	—
540	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	#450×C₁₀₃	1	2	yes	—
549	C₄	C₂²×SD₁₆×C₁₀₃	1	1	yes	characteristic
550	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
551	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	4	4	no	—
554	C₂	—	4	4	no	—
555	C₂	—	8	4	no	—
556	C₂	C₂×#450×C₁₀₃	1	1	yes	characteristic
557	C₂	C₁₀₃×#3003	1	1	yes	characteristic
558	C₂	C₁₀₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
prime radical	C₂×D₄²×C₁₀₃	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₃×#3208	C₂	semidirect
3. C₁₀₃×#3101	C₂	semidirect
4. C₁₀₃×#3077	C₂	semidirect
5. C₁₀₃×#1639	C₂	semidirect
6. C₁₀₃×#1629	C₂	semidirect
7. C₁₀₃×#1545	C₂	semidirect
8. C₁₀₃×#1486	C₂	semidirect
9. C₁₀₃×#1478	C₂	semidirect
16. #533×C₁₀₃	C₂²	semidirect
23. #492×C₁₀₃	C₂²	semidirect
24. #486×C₁₀₃	C₂²	semidirect
27. #476×C₁₀₃	C₂²	semidirect
28. #476×C₁₀₃	C₂²	semidirect
29. #474×C₁₀₃	C₂²	semidirect
30. #461×C₁₀₃	C₂²	semidirect
35. #431×C₁₀₃	C₂²	semidirect
36. #431×C₁₀₃	C₂²	semidirect
38. #423×C₁₀₃	C₂²	semidirect
40. #331×C₁₀₃	C₂²	semidirect
41. D₄⋊C₈×C₁₀₃	C₂²	semidirect
42. D₄⋊C₈×C₁₀₃	C₂²	semidirect
63. C₄⋊Q₈×C₁₀₃	C₂³	semidirect
64. C₄⋊Q₈×C₁₀₃	C₂³	semidirect
100. C₄⋊C₈×C₁₀₃	C₂³	semidirect
101. C₄⋊C₈×C₁₀₃	C₂³	semidirect
110. C₄×C₈×C₁₀₃	C₂³	semidirect
143. C₂×D₄×C₁₀₃	SD₁₆	semidirect
272. #18747	C₁₀₃	direct (N × H)
281. #3208	C₂×C₁₀₃	semidirect
282. #3101	C₂×C₁₀₃	semidirect
283. #3077	C₂×C₁₀₃	semidirect
284. #1639	C₂×C₁₀₃	semidirect
285. #1629	C₂×C₁₀₃	semidirect
286. #1545	C₂×C₁₀₃	semidirect
287. #1486	C₂×C₁₀₃	semidirect
288. #1478	C₂×C₁₀₃	semidirect
289. C₁₀₃	#18747	direct (N × H)
296. #533	C₂²×C₁₀₃	semidirect
303. #492	C₂²×C₁₀₃	semidirect
304. #486	C₂²×C₁₀₃	semidirect
307. #476	C₂²×C₁₀₃	semidirect
308. #476	C₂²×C₁₀₃	semidirect
309. #474	C₂²×C₁₀₃	semidirect
310. #461	C₂²×C₁₀₃	semidirect
315. #431	C₂²×C₁₀₃	semidirect
316. #431	C₂²×C₁₀₃	semidirect
318. #423	C₂²×C₁₀₃	semidirect
320. #331	C₂²×C₁₀₃	semidirect
321. D₄⋊C₈	C₂²×C₁₀₃	semidirect
322. D₄⋊C₈	C₂²×C₁₀₃	semidirect
343. C₄⋊Q₈	C₂³×C₁₀₃	semidirect
344. C₄⋊Q₈	C₂³×C₁₀₃	semidirect
380. C₄⋊C₈	C₂³×C₁₀₃	semidirect
381. C₄⋊C₈	C₂³×C₁₀₃	semidirect
390. C₄×C₈	C₂³×C₁₀₃	semidirect
423. C₂×D₄	SD₁₆×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₀₃	2
C₁₀₃×#3208	2
C₁₀₃×#3101	2
C₁₀₃×#3077	2
C₁₀₃×#1639	2
C₁₀₃×#1629	2
C₁₀₃×#1545	2
C₁₀₃×#1486	2
C₁₀₃×#1478	2
#18747	103

Subgroups — C103×#18747 #39924022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#18747 #39924022