Subgroups — C₁₀₃×#23438 #39928713

Order 26368.

1922 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₀₃	C₂	1	2	yes	maximal, complemented
2	C₂²×#135×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#413×C₁₀₃	C₂	1	2	yes	maximal, complemented
4	C₂×#408×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#2020	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#2019	C₂	1	4	yes	maximal, complemented
7	C₁₀₃×#2018	C₂	1	2	yes	maximal, complemented
8	C₂×#341×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₁₀₃	C₂²	1	2	yes	—
11	#575×C₁₀₃	—	2	8	no	—
12	#575×C₁₀₃	—	2	8	no	—
13	C₂×#137×C₁₀₃	—	2	2	no	—
14	C₂×#137×C₁₀₃	C₂²	1	4	yes	—
15	C₂×AGL(1,ℤ/8)×C₁₀₃	—	2	2	no	—
16	C₂×AGL(1,ℤ/8)×C₁₀₃	C₂²	1	4	yes	—
17	C₂×#135×C₁₀₃	—	2	8	no	—
18	C₂×#135×C₁₀₃	—	2	4	no	—
19	C₂×#135×C₁₀₃	—	2	2	no	—
20	C₂×#135×C₁₀₃	—	2	2	no	—
21	C₂²×Q₁₆×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₁₀₃	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₀₃	C₂²	1	2	yes	—
26	C₂³×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
27	#413×C₁₀₃	—	2	8	no	—
28	C₂×#101×C₁₀₃	C₂²	1	4	yes	complemented
29	C₂×#100×C₁₀₃	C₂²	1	4	yes	complemented
30	#408×C₁₀₃	—	2	2	no	—
31	#408×C₁₀₃	C₂²	1	2	yes	—
32	#408×C₁₀₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₁₀₃	—	2	2	no	—
34	#341×C₁₀₃	C₂²	1	2	yes	complemented
35	#341×C₁₀₃	C₂²	1	2	yes	complemented
36	C₂×#41×C₁₀₃	—	2	1	no	—
37	C₂×#41×C₁₀₃	—	2	4	no	—
38	C₂×#41×C₁₀₃	—	2	1	no	—
39	C₂×#41×C₁₀₃	—	2	4	no	—
40	C₂×#41×C₁₀₃	—	2	2	no	—
41	C₂×#41×C₁₀₃	—	2	2	no	—
42	C₂×#41×C₁₀₃	—	2	2	no	—
43	C₂×#41×C₁₀₃	—	2	2	no	—
44	C₂×#41×C₁₀₃	—	2	4	no	—
45	C₂×#41×C₁₀₃	—	2	4	no	—
46	C₂×#41×C₁₀₃	—	2	4	no	—
47	C₂×#41×C₁₀₃	D₄	1	2	yes	—
48	C₂×#41×C₁₀₃	D₄	1	8	yes	—
49	C₂×#41×C₁₀₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₀₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₀₃	—	2	1	no	—
53	C₂²×D₄×C₁₀₃	—	2	2	no	—
54	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₀₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₀₃	—	2	1	no	—
57	C₂³×C₄×C₁₀₃	—	2	2	no	—
58	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
59	#137×C₁₀₃	—	2	16	no	—
60	#137×C₁₀₃	—	2	8	no	—
61	#137×C₁₀₃	—	2	8	no	—
62	AGL(1,ℤ/8)×C₁₀₃	—	2	16	no	—
63	AGL(1,ℤ/8)×C₁₀₃	—	2	8	no	—
64	AGL(1,ℤ/8)×C₁₀₃	—	2	8	no	—
65	#135×C₁₀₃	—	2	16	no	—
66	#135×C₁₀₃	—	2	16	no	—
67	#135×C₁₀₃	—	2	32	no	—
68	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
69	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
70	C₂×Q₁₆×C₁₀₃	—	2	2	no	—
71	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
72	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
73	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
74	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
75	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
76	C₂×D₈×C₁₀₃	—	2	4	no	—
77	C₂×D₈×C₁₀₃	—	2	4	no	—
78	C₂×D₈×C₁₀₃	—	2	2	no	—
79	C₂×M₁₆×C₁₀₃	—	2	2	no	—
80	C₂×M₁₆×C₁₀₃	—	2	4	no	—
81	C₂×M₁₆×C₁₀₃	—	2	1	no	—
82	C₂×M₁₆×C₁₀₃	—	2	4	no	—
83	C₂×M₁₆×C₁₀₃	D₄	1	8	yes	—
84	C₂×M₁₆×C₁₀₃	C₂³	1	2	yes	—
85	C₂×M₁₆×C₁₀₃	C₂³	1	4	yes	—
86	C₂²×C₈×C₁₀₃	—	2	4	no	—
87	C₂²×C₈×C₁₀₃	—	2	2	no	—
88	C₂²×C₈×C₁₀₃	—	2	1	no	—
89	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
90	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
91	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
93	#101×C₁₀₃	—	2	8	no	—
94	#100×C₁₀₃	—	2	8	no	—
95	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
96	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
97	C₂⁴×C₁₀₃	—	2	1	no	—
98	C₂⁴×C₁₀₃	—	2	2	no	—
99	C₂⁴×C₁₀₃	#41	1	1	yes	characteristic
100	#41×C₁₀₃	—	2	8	no	—
101	#41×C₁₀₃	—	2	8	no	—
102	#41×C₁₀₃	—	2	8	no	—
103	#41×C₁₀₃	—	2	8	no	—
104	#41×C₁₀₃	—	2	8	no	—
105	#41×C₁₀₃	—	2	4	no	—
106	#41×C₁₀₃	—	2	4	no	—
107	#41×C₁₀₃	—	4	2	no	—
108	#41×C₁₀₃	—	4	4	no	—
109	#41×C₁₀₃	—	4	4	no	—
110	#41×C₁₀₃	—	4	4	no	—
111	#41×C₁₀₃	—	4	2	no	—
112	#41×C₁₀₃	—	4	4	no	—
113	#41×C₁₀₃	—	4	4	no	—
114	C₂×Q₈×C₁₀₃	—	2	1	no	—
115	C₂×Q₈×C₁₀₃	—	2	2	no	—
116	C₂×Q₈×C₁₀₃	—	2	4	no	—
117	C₂×Q₈×C₁₀₃	—	2	2	no	—
118	C₂×Q₈×C₁₀₃	—	2	2	no	—
119	C₂×Q₈×C₁₀₃	—	2	2	no	—
120	C₂×Q₈×C₁₀₃	—	2	2	no	—
121	C₂×Q₈×C₁₀₃	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₁₀₃	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₁₀₃	—	2	2	no	—
124	C₂×D₄×C₁₀₃	—	2	8	no	—
125	C₂×D₄×C₁₀₃	—	2	2	no	—
126	C₂×D₄×C₁₀₃	—	2	4	no	—
127	C₂×D₄×C₁₀₃	—	2	1	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	—	2	2	no	—
132	C₂×D₄×C₁₀₃	—	2	2	no	—
133	C₂×D₄×C₁₀₃	—	4	2	no	—
134	C₂×D₄×C₁₀₃	—	4	2	no	—
135	C₂×D₄×C₁₀₃	—	4	4	no	—
136	C₂×D₄×C₁₀₃	—	4	4	no	—
137	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₀₃	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₀₃	—	2	1	no	—
140	C₂²×C₄×C₁₀₃	—	2	2	no	—
141	C₂²×C₄×C₁₀₃	—	2	8	no	—
142	C₂²×C₄×C₁₀₃	—	2	2	no	—
143	C₂²×C₄×C₁₀₃	—	2	2	no	—
144	C₂²×C₄×C₁₀₃	—	4	2	no	—
145	C₂²×C₄×C₁₀₃	—	4	4	no	—
146	C₂²×C₄×C₁₀₃	—	4	2	no	—
147	C₂²×C₄×C₁₀₃	—	4	2	no	—
148	C₂²×C₄×C₁₀₃	—	4	2	no	—
149	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
157	Q₁₆×C₁₀₃	—	2	8	no	—
158	Q₁₆×C₁₀₃	—	2	16	no	—
159	SD₁₆×C₁₀₃	—	2	16	no	—
160	SD₁₆×C₁₀₃	—	2	16	no	—
161	SD₁₆×C₁₀₃	—	2	16	no	—
162	D₈×C₁₀₃	—	2	8	no	—
163	D₈×C₁₀₃	—	2	16	no	—
164	M₁₆×C₁₀₃	—	2	8	no	—
165	M₁₆×C₁₀₃	—	2	4	no	—
166	M₁₆×C₁₀₃	—	2	4	no	—
167	M₁₆×C₁₀₃	—	4	2	no	—
168	M₁₆×C₁₀₃	C₂×D₄	1	8	yes	—
169	C₂×C₈×C₁₀₃	—	2	4	no	—
170	C₂×C₈×C₁₀₃	—	2	4	no	—
171	C₂×C₈×C₁₀₃	—	2	8	no	—
172	C₂×C₈×C₁₀₃	—	2	2	no	—
173	C₂×C₈×C₁₀₃	—	2	2	no	—
174	C₂×C₈×C₁₀₃	—	2	4	no	—
175	C₂×C₈×C₁₀₃	—	2	2	no	—
176	C₂×C₈×C₁₀₃	—	4	2	no	—
177	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
179	C₂³×C₁₀₃	—	2	2	no	—
180	C₂³×C₁₀₃	—	2	4	no	—
181	C₂³×C₁₀₃	—	4	2	no	—
182	C₂³×C₁₀₃	—	4	4	no	—
183	C₂³×C₁₀₃	—	4	2	no	—
184	C₂³×C₁₀₃	—	4	2	no	—
185	C₂³×C₁₀₃	—	4	2	no	—
186	C₂³×C₁₀₃	—	8	4	no	—
187	C₂³×C₁₀₃	#121	1	1	yes	characteristic
188	C₂³×C₁₀₃	#121	1	1	yes	characteristic
189	C₂³×C₁₀₃	#121	1	4	yes	—
190	C₂³×C₁₀₃	C₂×#41	1	1	yes	characteristic
191	Q₈×C₁₀₃	—	2	4	no	—
192	Q₈×C₁₀₃	—	2	4	no	—
193	Q₈×C₁₀₃	—	2	4	no	—
194	Q₈×C₁₀₃	—	4	2	no	—
195	Q₈×C₁₀₃	—	4	2	no	—
196	Q₈×C₁₀₃	—	4	2	no	—
197	D₄×C₁₀₃	—	2	4	no	—
198	D₄×C₁₀₃	—	2	4	no	—
199	D₄×C₁₀₃	—	2	4	no	—
200	D₄×C₁₀₃	—	4	4	no	—
201	D₄×C₁₀₃	—	4	8	no	—
202	D₄×C₁₀₃	—	4	8	no	—
203	D₄×C₁₀₃	—	4	4	no	—
204	D₄×C₁₀₃	—	4	2	no	—
205	D₄×C₁₀₃	—	4	2	no	—
206	D₄×C₁₀₃	—	4	2	no	—
207	C₂×C₄×C₁₀₃	—	2	4	no	—
208	C₂×C₄×C₁₀₃	—	2	2	no	—
209	C₂×C₄×C₁₀₃	—	4	2	no	—
210	C₂×C₄×C₁₀₃	—	4	2	no	—
211	C₂×C₄×C₁₀₃	—	4	2	no	—
212	C₂×C₄×C₁₀₃	—	4	2	no	—
213	C₂×C₄×C₁₀₃	—	4	2	no	—
214	C₂×C₄×C₁₀₃	—	4	8	no	—
215	C₂×C₄×C₁₀₃	—	4	4	no	—
216	C₂×C₄×C₁₀₃	—	4	8	no	—
217	C₂×C₄×C₁₀₃	#120	1	2	yes	—
218	C₂×C₄×C₁₀₃	#120	1	2	yes	—
219	C₂×C₄×C₁₀₃	#120	1	4	yes	—
220	C₂×C₄×C₁₀₃	#120	1	4	yes	—
221	C₂×C₄×C₁₀₃	#121	1	4	yes	—
222	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₀₃	#127	1	2	yes	—
225	C₂×C₄×C₁₀₃	#127	1	2	yes	—
226	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₀₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₀₃	C₂²×D₄	1	2	yes	—
230	C₈×C₁₀₃	—	2	2	no	—
231	C₈×C₁₀₃	—	2	2	no	—
232	C₈×C₁₀₃	—	2	8	no	—
233	C₈×C₁₀₃	—	4	2	no	—
234	C₂²×C₁₀₃	—	2	2	no	—
235	C₂²×C₁₀₃	—	2	2	no	—
236	C₂²×C₁₀₃	—	2	2	no	—
237	C₂²×C₁₀₃	—	4	4	no	—
238	C₂²×C₁₀₃	—	4	2	no	—
239	C₂²×C₁₀₃	—	4	4	no	—
240	C₂²×C₁₀₃	—	4	4	no	—
241	C₂²×C₁₀₃	—	8	4	no	—
242	C₂²×C₁₀₃	—	8	4	no	—
243	C₂²×C₁₀₃	—	8	4	no	—
244	C₂²×C₁₀₃	—	8	4	no	—
245	C₂²×C₁₀₃	#392	1	2	yes	—
246	C₂²×C₁₀₃	#392	1	2	yes	—
247	C₂²×C₁₀₃	C₂×#121	1	2	yes	—
248	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
249	C₄×C₁₀₃	—	4	4	no	—
250	C₄×C₁₀₃	—	4	2	no	—
251	C₄×C₁₀₃	#392	1	2	yes	—
252	C₄×C₁₀₃	#392	1	2	yes	—
253	C₄×C₁₀₃	C₂×#120	1	1	yes	characteristic
254	C₄×C₁₀₃	C₂×#120	1	2	yes	—
255	C₄×C₁₀₃	C₂×#127	1	1	yes	characteristic
256	#23438	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂×C₁₀₃	—	2	2	no	—
258	C₂×C₁₀₃	—	2	2	no	—
259	C₂×C₁₀₃	—	2	2	no	—
260	C₂×C₁₀₃	—	8	2	no	—
261	C₂×C₁₀₃	—	8	4	no	—
262	C₂×C₁₀₃	C₂×#392	1	1	yes	characteristic
263	C₂×C₁₀₃	#3067	1	2	yes	—
264	C₂×#575	C₂×C₁₀₃	1	2	yes	complemented
265	C₂²×#135	C₂×C₁₀₃	1	1	yes	characteristic, complemented
266	C₂×#413	C₂×C₁₀₃	1	2	yes	complemented
267	C₂×#408	C₂×C₁₀₃	1	1	yes	characteristic, complemented
268	#2020	C₂×C₁₀₃	1	2	yes	complemented
269	#2019	C₂×C₁₀₃	1	4	yes	complemented
270	#2018	C₂×C₁₀₃	1	2	yes	complemented
271	C₂×#341	C₂×C₁₀₃	1	1	yes	characteristic, complemented
272	C₁₀₃	#23438	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×#41	C₂²×C₁₀₃	1	1	yes	characteristic
274	C₂²×#41	C₂²×C₁₀₃	1	2	yes	—
275	#575	—	2	8	no	—
276	#575	—	2	8	no	—
277	C₂×#137	—	2	2	no	—
278	C₂×#137	C₂²×C₁₀₃	1	4	yes	—
279	C₂×AGL(1,ℤ/8)	—	2	2	no	—
280	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₃	1	4	yes	—
281	C₂×#135	—	2	8	no	—
282	C₂×#135	—	2	4	no	—
283	C₂×#135	—	2	2	no	—
284	C₂×#135	—	2	2	no	—
285	C₂²×Q₁₆	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
286	C₂²×SD₁₆	C₂²×C₁₀₃	1	2	yes	complemented
287	C₂²×D₈	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
288	C₂²×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
289	C₂²×M₁₆	C₂²×C₁₀₃	1	2	yes	—
290	C₂³×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
291	#413	—	2	8	no	—
292	C₂×#101	C₂²×C₁₀₃	1	4	yes	complemented
293	C₂×#100	C₂²×C₁₀₃	1	4	yes	complemented
294	#408	—	2	2	no	—
295	#408	C₂²×C₁₀₃	1	2	yes	—
296	#408	C₂²×C₁₀₃	1	2	yes	—
297	C₂×C₂²⋊C₈	—	2	2	no	—
298	#341	C₂²×C₁₀₃	1	2	yes	complemented
299	#341	C₂²×C₁₀₃	1	2	yes	complemented
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	4	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	4	no	—
311	C₂×#41	D₄×C₁₀₃	1	2	yes	—
312	C₂×#41	D₄×C₁₀₃	1	8	yes	—
313	C₂×#41	C₂³×C₁₀₃	1	2	yes	—
314	C₂²×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₀₃	1	2	yes	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₀₃	1	2	yes	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
323	#137	—	2	16	no	—
324	#137	—	2	8	no	—
325	#137	—	2	8	no	—
326	AGL(1,ℤ/8)	—	2	16	no	—
327	AGL(1,ℤ/8)	—	2	8	no	—
328	AGL(1,ℤ/8)	—	2	8	no	—
329	#135	—	2	16	no	—
330	#135	—	2	16	no	—
331	#135	—	2	32	no	—
332	C₂×Q₁₆	—	2	4	no	—
333	C₂×Q₁₆	—	2	4	no	—
334	C₂×Q₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	4	no	—
340	C₂×D₈	—	2	4	no	—
341	C₂×D₈	—	2	4	no	—
342	C₂×D₈	—	2	2	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	2	4	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	4	no	—
347	C₂×M₁₆	D₄×C₁₀₃	1	8	yes	—
348	C₂×M₁₆	C₂³×C₁₀₃	1	2	yes	—
349	C₂×M₁₆	C₂³×C₁₀₃	1	4	yes	—
350	C₂²×C₈	—	2	4	no	—
351	C₂²×C₈	—	2	2	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
354	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
355	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
357	#101	—	2	8	no	—
358	#100	—	2	8	no	—
359	C₂²⋊C₈	—	2	4	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	#41×C₁₀₃	1	1	yes	characteristic
364	#41	—	2	8	no	—
365	#41	—	2	8	no	—
366	#41	—	2	8	no	—
367	#41	—	2	8	no	—
368	#41	—	2	8	no	—
369	#41	—	2	4	no	—
370	#41	—	2	4	no	—
371	#41	—	4	4	no	—
372	#41	—	4	4	no	—
373	#41	—	4	2	no	—
374	#41	—	4	4	no	—
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	C₂×D₄×C₁₀₃	1	2	yes	—
386	C₂×Q₈	C₂×D₄×C₁₀₃	1	4	yes	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
402	C₂×D₄	C₂×D₄×C₁₀₃	1	4	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
419	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
421	Q₁₆	—	2	8	no	—
422	Q₁₆	—	2	16	no	—
423	SD₁₆	—	2	16	no	—
424	SD₁₆	—	2	16	no	—
425	SD₁₆	—	2	16	no	—
426	D₈	—	2	8	no	—
427	D₈	—	2	16	no	—
428	M₁₆	—	2	8	no	—
429	M₁₆	—	2	4	no	—
430	M₁₆	—	2	4	no	—
431	M₁₆	—	4	2	no	—
432	M₁₆	C₂×D₄×C₁₀₃	1	8	yes	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	2	8	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
442	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	8	4	no	—
451	C₂³	#121×C₁₀₃	1	1	yes	characteristic
452	C₂³	#121×C₁₀₃	1	1	yes	characteristic
453	C₂³	#121×C₁₀₃	1	4	yes	—
454	C₂³	C₂×#41×C₁₀₃	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	4	no	—
457	Q₈	—	2	4	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	8	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	#120×C₁₀₃	1	2	yes	—
482	C₂×C₄	#120×C₁₀₃	1	4	yes	—
483	C₂×C₄	#120×C₁₀₃	1	2	yes	—
484	C₂×C₄	#120×C₁₀₃	1	4	yes	—
485	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
486	C₂×C₄	#121×C₁₀₃	1	4	yes	—
487	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
488	C₂×C₄	#127×C₁₀₃	1	2	yes	—
489	C₂×C₄	#127×C₁₀₃	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₀₃	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₀₃	1	2	yes	—
494	C₈	—	2	2	no	—
495	C₈	—	2	2	no	—
496	C₈	—	2	8	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	4	no	—
508	C₂²	—	8	4	no	—
509	C₂²	#392×C₁₀₃	1	2	yes	—
510	C₂²	#392×C₁₀₃	1	2	yes	—
511	C₂²	C₂×#121×C₁₀₃	1	2	yes	—
512	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
513	C₄	—	4	2	no	—
514	C₄	—	4	4	no	—
515	C₄	#392×C₁₀₃	1	2	yes	—
516	C₄	#392×C₁₀₃	1	2	yes	—
517	C₄	C₂×#120×C₁₀₃	1	1	yes	characteristic
518	C₄	C₂×#120×C₁₀₃	1	2	yes	—
519	C₄	C₂×#127×C₁₀₃	1	1	yes	characteristic
520	C₂	—	2	2	no	—
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	8	2	no	—
524	C₂	—	8	4	no	—
525	C₂	C₂×#392×C₁₀₃	1	1	yes	characteristic
526	C₂	C₁₀₃×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₀₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
socle	C₂²×C₁₀₃	C₂×#121
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₃ ◁ C₂³×C₄×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₁₀₃	C₂	semidirect
2. C₂²×#135×C₁₀₃	C₂	semidirect
3. C₂×#413×C₁₀₃	C₂	semidirect
4. C₂×#408×C₁₀₃	C₂	semidirect
5. C₁₀₃×#2020	C₂	semidirect
6. C₁₀₃×#2019	C₂	semidirect
7. C₁₀₃×#2018	C₂	semidirect
8. C₂×#341×C₁₀₃	C₂	semidirect
21. C₂²×Q₁₆×C₁₀₃	C₂²	semidirect
22. C₂²×SD₁₆×C₁₀₃	C₂²	semidirect
23. C₂²×D₈×C₁₀₃	C₂²	semidirect
28. C₂×#101×C₁₀₃	C₂²	semidirect
29. C₂×#100×C₁₀₃	C₂²	semidirect
34. #341×C₁₀₃	C₂²	semidirect
35. #341×C₁₀₃	C₂²	semidirect
256. #23438	C₁₀₃	direct (N × H)
264. C₂×#575	C₂×C₁₀₃	semidirect
265. C₂²×#135	C₂×C₁₀₃	semidirect
266. C₂×#413	C₂×C₁₀₃	semidirect
267. C₂×#408	C₂×C₁₀₃	semidirect
268. #2020	C₂×C₁₀₃	semidirect
269. #2019	C₂×C₁₀₃	semidirect
270. #2018	C₂×C₁₀₃	semidirect
271. C₂×#341	C₂×C₁₀₃	semidirect
272. C₁₀₃	#23438	direct (N × H)
285. C₂²×Q₁₆	C₂²×C₁₀₃	semidirect
286. C₂²×SD₁₆	C₂²×C₁₀₃	semidirect
287. C₂²×D₈	C₂²×C₁₀₃	semidirect
292. C₂×#101	C₂²×C₁₀₃	semidirect
293. C₂×#100	C₂²×C₁₀₃	semidirect
298. #341	C₂²×C₁₀₃	semidirect
299. #341	C₂²×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₁₀₃	2
C₂²×#135×C₁₀₃	2
C₂×#413×C₁₀₃	2
C₂×#408×C₁₀₃	2
C₁₀₃×#2020	2
C₁₀₃×#2019	2
C₁₀₃×#2018	2
C₂×#341×C₁₀₃	2
#23438	103

Subgroups — C103×#23438 #39928713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#23438 #39928713