Subgroups — C₁₀₃×#18662 #39923937

Order 26368.

1260 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#1647	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1639	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1625	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1619	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₁₀₃	—	2	1	no	—
13	C₂×AGL(1,ℤ/8)×C₁₀₃	—	2	1	no	—
14	#547×C₁₀₃	—	2	1	no	—
15	#547×C₁₀₃	C₂²	1	2	yes	—
16	#546×C₁₀₃	—	2	2	no	—
17	#546×C₁₀₃	—	2	2	no	—
18	D₄²×C₁₀₃	—	2	1	no	—
19	D₄²×C₁₀₃	C₂²	1	2	yes	—
20	#537×C₁₀₃	—	2	1	no	—
21	#534×C₁₀₃	—	2	2	no	—
22	#532×C₁₀₃	C₂²	1	1	yes	characteristic
23	#532×C₁₀₃	C₂²	1	1	yes	characteristic
24	#532×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#121×C₁₀₃	—	2	2	no	—
26	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
27	#500×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
28	#493×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
29	#486×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
30	#486×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
31	#474×C₁₀₃	—	2	1	no	—
32	#474×C₁₀₃	C₂²	1	2	yes	complemented
33	#466×C₁₀₃	—	2	2	no	—
34	#466×C₁₀₃	—	2	2	no	—
35	#463×C₁₀₃	—	2	2	no	—
36	#461×C₁₀₃	C₂²	1	2	yes	complemented
37	#459×C₁₀₃	—	2	1	no	—
38	#459×C₁₀₃	C₂²	1	2	yes	complemented
39	#459×C₁₀₃	C₂²	1	2	yes	complemented
40	C₄×D₈×C₁₀₃	—	2	2	no	—
41	#423×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
43	#417×C₁₀₃	—	2	1	no	—
44	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
45	#332×C₁₀₃	C₂²	1	2	yes	complemented
46	#331×C₁₀₃	C₂²	1	2	yes	complemented
47	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
48	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
49	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
50	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
51	H(5,𝔽₂)×C₁₀₃	—	4	4	no	—
52	H(5,𝔽₂)×C₁₀₃	—	4	4	no	—
53	C₂×#41×C₁₀₃	—	2	2	no	—
54	C₂×#41×C₁₀₃	—	2	2	no	—
55	C₂×#41×C₁₀₃	—	2	1	no	—
56	C₂×#41×C₁₀₃	—	2	1	no	—
57	C₂×#41×C₁₀₃	—	2	1	no	—
58	C₂²×D₄×C₁₀₃	—	2	4	no	—
59	C₂²×D₄×C₁₀₃	—	2	2	no	—
60	C₂²×D₄×C₁₀₃	—	2	2	no	—
61	C₂²×D₄×C₁₀₃	—	2	2	no	—
62	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₀₃	—	2	1	no	—
64	AGL(1,ℤ/8)×C₁₀₃	—	4	4	no	—
65	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
66	C₂×D₈×C₁₀₃	—	2	2	no	—
67	C₂×D₈×C₁₀₃	—	2	2	no	—
68	C₂×D₈×C₁₀₃	—	2	2	no	—
69	C₂×M₁₆×C₁₀₃	—	2	1	no	—
70	C₂²×C₈×C₁₀₃	—	2	1	no	—
71	C₂²×C₈×C₁₀₃	—	2	1	no	—
72	C₄⋊Q₈×C₁₀₃	D₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
75	#127×C₁₀₃	D₄	1	1	yes	characteristic
76	#127×C₁₀₃	C₂³	1	1	yes	characteristic
77	#127×C₁₀₃	C₂³	1	1	yes	characteristic
78	#124×C₁₀₃	—	2	1	no	—
79	#124×C₁₀₃	—	2	1	no	—
80	#124×C₁₀₃	—	2	1	no	—
81	#123×C₁₀₃	—	2	4	no	—
82	#123×C₁₀₃	—	2	4	no	—
83	C₂²⋊Q₈×C₁₀₃	—	2	2	no	—
84	C₂²⋊Q₈×C₁₀₃	—	2	2	no	—
85	#121×C₁₀₃	—	2	4	no	—
86	#121×C₁₀₃	—	2	4	no	—
87	#121×C₁₀₃	—	2	2	no	—
88	#121×C₁₀₃	—	2	2	no	—
89	#121×C₁₀₃	—	2	1	no	—
90	#121×C₁₀₃	—	2	1	no	—
91	#121×C₁₀₃	—	2	2	no	—
92	#121×C₁₀₃	—	2	2	no	—
93	#121×C₁₀₃	—	2	1	no	—
94	#121×C₁₀₃	—	2	1	no	—
95	#121×C₁₀₃	D₄	1	2	yes	—
96	#121×C₁₀₃	D₄	1	2	yes	—
97	#120×C₁₀₃	—	2	4	no	—
98	#120×C₁₀₃	—	2	4	no	—
99	C₄×D₄×C₁₀₃	—	2	1	no	—
100	C₄×D₄×C₁₀₃	—	2	1	no	—
101	C₄×D₄×C₁₀₃	—	2	1	no	—
102	C₄×D₄×C₁₀₃	—	2	1	no	—
103	C₄×D₄×C₁₀₃	—	2	1	no	—
104	C₄×D₄×C₁₀₃	—	2	1	no	—
105	C₄×D₄×C₁₀₃	D₄	1	2	yes	—
106	C₄×D₄×C₁₀₃	D₄	1	2	yes	—
107	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
108	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₀₃	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
113	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
114	#107×C₁₀₃	—	2	2	no	—
115	#107×C₁₀₃	—	2	2	no	—
116	C₄⋊C₈×C₁₀₃	—	2	1	no	—
117	C₄⋊C₈×C₁₀₃	—	2	1	no	—
118	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
119	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
120	#103×C₁₀₃	—	2	2	no	—
121	#102×C₁₀₃	—	2	2	no	—
122	#102×C₁₀₃	—	2	2	no	—
123	#102×C₁₀₃	—	2	2	no	—
124	#102×C₁₀₃	—	2	2	no	—
125	#102×C₁₀₃	—	2	2	no	—
126	C₄×C₈×C₁₀₃	—	2	1	no	—
127	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
129	C₂⁴×C₁₀₃	—	2	1	no	—
130	C₂⁴×C₁₀₃	—	2	4	no	—
131	#41×C₁₀₃	—	4	4	no	—
132	#41×C₁₀₃	—	4	8	no	—
133	#41×C₁₀₃	—	4	4	no	—
134	#41×C₁₀₃	—	4	2	no	—
135	#41×C₁₀₃	—	4	2	no	—
136	#41×C₁₀₃	—	4	2	no	—
137	#41×C₁₀₃	—	4	2	no	—
138	#41×C₁₀₃	—	4	2	no	—
139	#41×C₁₀₃	—	4	2	no	—
140	C₂×Q₈×C₁₀₃	—	2	1	no	—
141	C₂×Q₈×C₁₀₃	—	2	1	no	—
142	C₂×Q₈×C₁₀₃	—	2	1	no	—
143	C₂×D₄×C₁₀₃	—	2	4	no	—
144	C₂×D₄×C₁₀₃	—	2	4	no	—
145	C₂×D₄×C₁₀₃	—	2	2	no	—
146	C₂×D₄×C₁₀₃	—	2	2	no	—
147	C₂×D₄×C₁₀₃	—	2	4	no	—
148	C₂×D₄×C₁₀₃	—	2	1	no	—
149	C₂×D₄×C₁₀₃	—	2	1	no	—
150	C₂×D₄×C₁₀₃	—	2	1	no	—
151	C₂×D₄×C₁₀₃	—	2	2	no	—
152	C₂×D₄×C₁₀₃	—	2	1	no	—
153	C₂×D₄×C₁₀₃	—	2	1	no	—
154	C₂×D₄×C₁₀₃	—	2	1	no	—
155	C₂×D₄×C₁₀₃	—	2	1	no	—
156	C₂×D₄×C₁₀₃	—	2	1	no	—
157	C₂×D₄×C₁₀₃	—	4	4	no	—
158	C₂×D₄×C₁₀₃	—	4	8	no	—
159	C₂×D₄×C₁₀₃	—	4	16	no	—
160	C₂×D₄×C₁₀₃	—	4	4	no	—
161	C₂×D₄×C₁₀₃	—	4	1	no	—
162	C₂×D₄×C₁₀₃	—	8	2	no	—
163	C₂×D₄×C₁₀₃	—	8	2	no	—
164	C₂×D₄×C₁₀₃	D₈	1	4	yes	complemented
165	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₀₃	—	2	4	no	—
169	C₂²×C₄×C₁₀₃	—	2	1	no	—
170	C₂²×C₄×C₁₀₃	—	2	2	no	—
171	C₂²×C₄×C₁₀₃	—	2	2	no	—
172	C₂²×C₄×C₁₀₃	—	2	2	no	—
173	C₂²×C₄×C₁₀₃	—	2	2	no	—
174	C₂²×C₄×C₁₀₃	—	4	1	no	—
175	C₂²×C₄×C₁₀₃	—	8	1	no	—
176	C₂²×C₄×C₁₀₃	—	8	1	no	—
177	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
180	SD₁₆×C₁₀₃	—	4	4	no	—
181	D₈×C₁₀₃	—	4	4	no	—
182	D₈×C₁₀₃	—	4	4	no	—
183	D₈×C₁₀₃	—	8	2	no	—
184	M₁₆×C₁₀₃	—	4	2	no	—
185	C₂×C₈×C₁₀₃	—	2	1	no	—
186	C₂×C₈×C₁₀₃	—	2	1	no	—
187	C₂×C₈×C₁₀₃	—	2	2	no	—
188	C₂×C₈×C₁₀₃	—	2	2	no	—
189	C₂×C₈×C₁₀₃	—	4	2	no	—
190	C₂×C₈×C₁₀₃	—	8	1	no	—
191	C₄⋊C₄×C₁₀₃	—	2	4	no	—
192	C₄⋊C₄×C₁₀₃	—	2	1	no	—
193	C₄⋊C₄×C₁₀₃	—	2	1	no	—
194	C₄⋊C₄×C₁₀₃	—	2	1	no	—
195	C₄⋊C₄×C₁₀₃	—	2	1	no	—
196	C₄⋊C₄×C₁₀₃	—	2	1	no	—
197	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
201	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
202	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
203	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
204	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
205	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
206	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
207	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
208	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
209	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
210	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
214	C₂³×C₁₀₃	—	2	2	no	—
215	C₂³×C₁₀₃	—	2	4	no	—
216	C₂³×C₁₀₃	—	2	2	no	—
217	C₂³×C₁₀₃	—	2	2	no	—
218	C₂³×C₁₀₃	—	4	8	no	—
219	C₂³×C₁₀₃	—	4	1	no	—
220	C₂³×C₁₀₃	—	8	1	no	—
221	C₂³×C₁₀₃	—	8	1	no	—
222	C₂³×C₁₀₃	—	8	4	no	—
223	C₂³×C₁₀₃	—	8	4	no	—
224	C₂³×C₁₀₃	#120	1	1	yes	characteristic
225	Q₈×C₁₀₃	—	4	1	no	—
226	Q₈×C₁₀₃	—	4	1	no	—
227	Q₈×C₁₀₃	—	4	2	no	—
228	Q₈×C₁₀₃	—	4	1	no	—
229	Q₈×C₁₀₃	—	4	1	no	—
230	D₄×C₁₀₃	—	2	2	no	—
231	D₄×C₁₀₃	—	2	2	no	—
232	D₄×C₁₀₃	—	2	2	no	—
233	D₄×C₁₀₃	—	2	4	no	—
234	D₄×C₁₀₃	—	4	2	no	—
235	D₄×C₁₀₃	—	4	2	no	—
236	D₄×C₁₀₃	—	4	8	no	—
237	D₄×C₁₀₃	—	4	8	no	—
238	D₄×C₁₀₃	—	4	4	no	—
239	D₄×C₁₀₃	—	4	4	no	—
240	D₄×C₁₀₃	—	4	1	no	—
241	D₄×C₁₀₃	—	4	1	no	—
242	D₄×C₁₀₃	—	4	1	no	—
243	D₄×C₁₀₃	—	4	1	no	—
244	D₄×C₁₀₃	—	4	1	no	—
245	D₄×C₁₀₃	—	4	1	no	—
246	D₄×C₁₀₃	—	4	1	no	—
247	D₄×C₁₀₃	—	4	1	no	—
248	D₄×C₁₀₃	—	4	2	no	—
249	D₄×C₁₀₃	—	8	1	no	—
250	D₄×C₁₀₃	—	8	4	no	—
251	D₄×C₁₀₃	—	8	2	no	—
252	D₄×C₁₀₃	C₂×D₈	1	4	yes	—
253	C₂×C₄×C₁₀₃	—	2	1	no	—
254	C₂×C₄×C₁₀₃	—	2	1	no	—
255	C₂×C₄×C₁₀₃	—	2	2	no	—
256	C₂×C₄×C₁₀₃	—	2	2	no	—
257	C₂×C₄×C₁₀₃	—	2	2	no	—
258	C₂×C₄×C₁₀₃	—	4	1	no	—
259	C₂×C₄×C₁₀₃	—	4	8	no	—
260	C₂×C₄×C₁₀₃	—	4	2	no	—
261	C₂×C₄×C₁₀₃	—	4	2	no	—
262	C₂×C₄×C₁₀₃	—	4	2	no	—
263	C₂×C₄×C₁₀₃	—	4	2	no	—
264	C₂×C₄×C₁₀₃	—	4	4	no	—
265	C₂×C₄×C₁₀₃	—	4	1	no	—
266	C₂×C₄×C₁₀₃	—	8	2	no	—
267	C₂×C₄×C₁₀₃	—	8	1	no	—
268	C₂×C₄×C₁₀₃	—	8	2	no	—
269	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₀₃	C₂×D₈	1	2	yes	—
273	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
274	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
277	C₈×C₁₀₃	—	2	2	no	—
278	C₈×C₁₀₃	—	4	1	no	—
279	C₈×C₁₀₃	—	4	2	no	—
280	C₈×C₁₀₃	—	4	2	no	—
281	C₂²×C₁₀₃	—	2	1	no	—
282	C₂²×C₁₀₃	—	2	1	no	—
283	C₂²×C₁₀₃	—	2	4	no	—
284	C₂²×C₁₀₃	—	4	2	no	—
285	C₂²×C₁₀₃	—	4	2	no	—
286	C₂²×C₁₀₃	—	4	2	no	—
287	C₂²×C₁₀₃	—	4	2	no	—
288	C₂²×C₁₀₃	—	4	2	no	—
289	C₂²×C₁₀₃	—	4	2	no	—
290	C₂²×C₁₀₃	—	4	2	no	—
291	C₂²×C₁₀₃	—	4	2	no	—
292	C₂²×C₁₀₃	—	8	4	no	—
293	C₂²×C₁₀₃	—	8	1	no	—
294	C₂²×C₁₀₃	—	8	1	no	—
295	C₂²×C₁₀₃	—	8	1	no	—
296	C₂²×C₁₀₃	—	16	8	no	—
297	C₂²×C₁₀₃	#447	1	2	yes	—
298	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
299	C₄×C₁₀₃	—	2	1	no	—
300	C₄×C₁₀₃	—	2	1	no	—
301	C₄×C₁₀₃	—	2	1	no	—
302	C₄×C₁₀₃	—	4	2	no	—
303	C₄×C₁₀₃	—	4	2	no	—
304	C₄×C₁₀₃	—	4	2	no	—
305	C₄×C₁₀₃	—	8	1	no	—
306	C₄×C₁₀₃	#447	1	2	yes	—
307	C₄×C₁₀₃	C₂²×D₈	1	1	yes	characteristic
308	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
309	C₄×C₁₀₃	#576	1	1	yes	characteristic
310	C₄×C₁₀₃	#577	1	1	yes	characteristic
311	#18662	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂×C₁₀₃	—	2	2	no	—
313	C₂×C₁₀₃	—	4	4	no	—
314	C₂×C₁₀₃	—	8	2	no	—
315	C₂×C₁₀₃	—	8	2	no	—
316	C₂×C₁₀₃	—	16	1	no	—
317	C₂×C₁₀₃	C₂×#447	1	1	yes	characteristic
318	C₂×C₁₀₃	#3012	1	1	yes	characteristic
319	C₂×C₁₀₃	#3018	1	1	yes	characteristic
320	#3496	C₂×C₁₀₃	1	1	yes	characteristic, complemented
321	#3245	C₂×C₁₀₃	1	1	yes	characteristic, complemented
322	#3169	C₂×C₁₀₃	1	1	yes	characteristic, complemented
323	#3036	C₂×C₁₀₃	1	1	yes	characteristic, complemented
324	#1647	C₂×C₁₀₃	1	2	yes	complemented
325	#1639	C₂×C₁₀₃	1	2	yes	complemented
326	#1625	C₂×C₁₀₃	1	2	yes	complemented
327	#1619	C₂×C₁₀₃	1	2	yes	complemented
328	#1547	C₂×C₁₀₃	1	1	yes	characteristic, complemented
329	#1492	C₂×C₁₀₃	1	1	yes	characteristic, complemented
330	C₂×D₄⋊C₈	C₂×C₁₀₃	1	1	yes	characteristic, complemented
331	C₁₀₃	#18662	1	1	yes	characteristic, direct product factor, Sylow
332	C₂×H(5,𝔽₂)	—	2	1	no	—
333	C₂×AGL(1,ℤ/8)	—	2	1	no	—
334	#547	—	2	1	no	—
335	#547	C₂²×C₁₀₃	1	2	yes	—
336	#546	—	2	2	no	—
337	#546	—	2	2	no	—
338	D₄²	—	2	1	no	—
339	D₄²	C₂²×C₁₀₃	1	2	yes	—
340	#537	—	2	1	no	—
341	#534	—	2	2	no	—
342	#532	C₂²×C₁₀₃	1	1	yes	characteristic
343	#532	C₂²×C₁₀₃	1	1	yes	characteristic
344	#532	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
345	C₂×#121	—	2	2	no	—
346	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
347	#500	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
348	#493	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
349	#486	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
350	#486	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
351	#474	—	2	1	no	—
352	#474	C₂²×C₁₀₃	1	2	yes	complemented
353	#466	—	2	2	no	—
354	#466	—	2	2	no	—
355	#463	—	2	2	no	—
356	#461	C₂²×C₁₀₃	1	2	yes	complemented
357	#459	—	2	1	no	—
358	#459	C₂²×C₁₀₃	1	2	yes	complemented
359	#459	C₂²×C₁₀₃	1	2	yes	complemented
360	C₄×D₈	—	2	2	no	—
361	#423	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
362	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
363	#417	—	2	1	no	—
364	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
365	#332	C₂²×C₁₀₃	1	2	yes	complemented
366	#331	C₂²×C₁₀₃	1	2	yes	complemented
367	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
368	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
369	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
370	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
371	H(5,𝔽₂)	—	4	4	no	—
372	H(5,𝔽₂)	—	4	4	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	2	2	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	2	no	—
381	C₂²×D₄	—	2	2	no	—
382	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	AGL(1,ℤ/8)	—	4	4	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×D₈	—	2	2	no	—
388	C₂×D₈	—	2	2	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₄⋊Q₈	D₄×C₁₀₃	1	1	yes	characteristic
393	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
395	#127	D₄×C₁₀₃	1	1	yes	characteristic
396	#127	C₂³×C₁₀₃	1	1	yes	characteristic
397	#127	C₂³×C₁₀₃	1	1	yes	characteristic
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#123	—	2	4	no	—
402	#123	—	2	4	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	#121	—	2	4	no	—
406	#121	—	2	4	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	1	no	—
410	#121	—	2	1	no	—
411	#121	—	2	2	no	—
412	#121	—	2	2	no	—
413	#121	—	2	1	no	—
414	#121	—	2	1	no	—
415	#121	D₄×C₁₀₃	1	2	yes	—
416	#121	D₄×C₁₀₃	1	2	yes	—
417	#120	—	2	4	no	—
418	#120	—	2	4	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	D₄×C₁₀₃	1	2	yes	—
426	C₄×D₄	D₄×C₁₀₃	1	2	yes	—
427	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
428	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	4	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
434	#107	—	2	2	no	—
435	#107	—	2	2	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
439	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
440	#103	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	C₄×C₈	—	2	1	no	—
447	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
448	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	4	no	—
451	#41	—	4	8	no	—
452	#41	—	4	4	no	—
453	#41	—	4	4	no	—
454	#41	—	4	2	no	—
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	#41	—	4	2	no	—
458	#41	—	4	2	no	—
459	#41	—	4	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	4	8	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	—	4	16	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	—	8	2	no	—
484	C₂×D₄	D₈×C₁₀₃	1	4	yes	complemented
485	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
486	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
487	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
500	SD₁₆	—	4	4	no	—
501	D₈	—	4	4	no	—
502	D₈	—	4	4	no	—
503	D₈	—	8	2	no	—
504	M₁₆	—	4	2	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	2	no	—
510	C₂×C₈	—	8	1	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
519	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
533	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	4	8	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	8	1	no	—
541	C₂³	—	8	1	no	—
542	C₂³	—	8	4	no	—
543	C₂³	—	8	4	no	—
544	C₂³	#120×C₁₀₃	1	1	yes	characteristic
545	Q₈	—	4	2	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	8	no	—
558	D₄	—	4	4	no	—
559	D₄	—	4	4	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	8	1	no	—
570	D₄	—	8	4	no	—
571	D₄	—	8	2	no	—
572	D₄	C₂×D₈×C₁₀₃	1	4	yes	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
590	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
591	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
592	C₂×C₄	C₂×D₈×C₁₀₃	1	2	yes	—
593	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	4	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	16	8	no	—
617	C₂²	#447×C₁₀₃	1	2	yes	—
618	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	8	1	no	—
626	C₄	#447×C₁₀₃	1	2	yes	—
627	C₄	C₂²×D₈×C₁₀₃	1	1	yes	characteristic
628	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
629	C₄	#576×C₁₀₃	1	1	yes	characteristic
630	C₄	#577×C₁₀₃	1	1	yes	characteristic
631	C₂	—	2	2	no	—
632	C₂	—	4	4	no	—
633	C₂	—	8	2	no	—
634	C₂	—	8	2	no	—
635	C₂	—	16	1	no	—
636	C₂	C₂×#447×C₁₀₃	1	1	yes	characteristic
637	C₂	C₁₀₃×#3012	1	1	yes	characteristic
638	C₂	C₁₀₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
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
1. C₁₀₃×#3496	C₂	semidirect
2. C₁₀₃×#3245	C₂	semidirect
3. C₁₀₃×#3169	C₂	semidirect
4. C₁₀₃×#3036	C₂	semidirect
5. C₁₀₃×#1647	C₂	semidirect
6. C₁₀₃×#1639	C₂	semidirect
7. C₁₀₃×#1625	C₂	semidirect
8. C₁₀₃×#1619	C₂	semidirect
9. C₁₀₃×#1547	C₂	semidirect
10. C₁₀₃×#1492	C₂	semidirect
11. C₂×D₄⋊C₈×C₁₀₃	C₂	semidirect
24. #532×C₁₀₃	C₂²	semidirect
27. #500×C₁₀₃	C₂²	semidirect
28. #493×C₁₀₃	C₂²	semidirect
29. #486×C₁₀₃	C₂²	semidirect
30. #486×C₁₀₃	C₂²	semidirect
32. #474×C₁₀₃	C₂²	semidirect
36. #461×C₁₀₃	C₂²	semidirect
38. #459×C₁₀₃	C₂²	semidirect
39. #459×C₁₀₃	C₂²	semidirect
41. #423×C₁₀₃	C₂²	semidirect
42. C₂×C₄⋊C₈×C₁₀₃	C₂²	semidirect
44. C₂×C₄×C₈×C₁₀₃	C₂²	semidirect
45. #332×C₁₀₃	C₂²	semidirect
46. #331×C₁₀₃	C₂²	semidirect
47. D₄⋊C₈×C₁₀₃	C₂²	semidirect
48. D₄⋊C₈×C₁₀₃	C₂²	semidirect
49. D₄⋊C₈×C₁₀₃	C₂²	semidirect
50. D₄⋊C₈×C₁₀₃	C₂²	semidirect
164. C₂×D₄×C₁₀₃	D₈	semidirect
311. #18662	C₁₀₃	direct (N × H)
320. #3496	C₂×C₁₀₃	semidirect
321. #3245	C₂×C₁₀₃	semidirect
322. #3169	C₂×C₁₀₃	semidirect
323. #3036	C₂×C₁₀₃	semidirect
324. #1647	C₂×C₁₀₃	semidirect
325. #1639	C₂×C₁₀₃	semidirect
326. #1625	C₂×C₁₀₃	semidirect
327. #1619	C₂×C₁₀₃	semidirect
328. #1547	C₂×C₁₀₃	semidirect
329. #1492	C₂×C₁₀₃	semidirect
330. C₂×D₄⋊C₈	C₂×C₁₀₃	semidirect
331. C₁₀₃	#18662	direct (N × H)
344. #532	C₂²×C₁₀₃	semidirect
347. #500	C₂²×C₁₀₃	semidirect
348. #493	C₂²×C₁₀₃	semidirect
349. #486	C₂²×C₁₀₃	semidirect
350. #486	C₂²×C₁₀₃	semidirect
352. #474	C₂²×C₁₀₃	semidirect
356. #461	C₂²×C₁₀₃	semidirect
358. #459	C₂²×C₁₀₃	semidirect
359. #459	C₂²×C₁₀₃	semidirect
361. #423	C₂²×C₁₀₃	semidirect
362. C₂×C₄⋊C₈	C₂²×C₁₀₃	semidirect
364. C₂×C₄×C₈	C₂²×C₁₀₃	semidirect
365. #332	C₂²×C₁₀₃	semidirect
366. #331	C₂²×C₁₀₃	semidirect
367. D₄⋊C₈	C₂²×C₁₀₃	semidirect
368. D₄⋊C₈	C₂²×C₁₀₃	semidirect
369. D₄⋊C₈	C₂²×C₁₀₃	semidirect
370. D₄⋊C₈	C₂²×C₁₀₃	semidirect
484. C₂×D₄	D₈×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×#3496	2
C₁₀₃×#3245	2
C₁₀₃×#3169	2
C₁₀₃×#3036	2
C₁₀₃×#1647	2
C₁₀₃×#1639	2
C₁₀₃×#1625	2
C₁₀₃×#1619	2
C₁₀₃×#1547	2
C₁₀₃×#1492	2
C₂×D₄⋊C₈×C₁₀₃	2
#18662	103

Subgroups — C103×#18662 #39923937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#18662 #39923937