Subgroups — C₁₀₃×#18818 #39924093

Order 26368.

1004 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#1641	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1640	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1620	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1555	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₁₀₃	—	2	1	no	—
13	#559×C₁₀₃	C₂²	1	2	yes	—
14	#550×C₁₀₃	—	2	1	no	—
15	#550×C₁₀₃	C₂²	1	2	yes	—
16	#546×C₁₀₃	—	2	2	no	—
17	#546×C₁₀₃	—	2	2	no	—
18	#540×C₁₀₃	—	2	2	no	—
19	#535×C₁₀₃	—	2	1	no	—
20	#533×C₁₀₃	C₂²	1	1	yes	characteristic
21	#532×C₁₀₃	—	2	1	no	—
22	#532×C₁₀₃	—	2	1	no	—
23	#532×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
25	#518×C₁₀₃	—	2	1	no	—
26	C₄×#41×C₁₀₃	C₂²	1	1	yes	characteristic
27	#497×C₁₀₃	—	2	1	no	—
28	#493×C₁₀₃	C₂²	1	2	yes	—
29	#489×C₁₀₃	—	2	1	no	—
30	#486×C₁₀₃	C₂²	1	2	yes	—
31	#482×C₁₀₃	—	2	1	no	—
32	#475×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
33	#474×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
34	#462×C₁₀₃	C₂²	1	2	yes	complemented
35	#460×C₁₀₃	C₂²	1	2	yes	complemented
36	#460×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
37	#459×C₁₀₃	—	2	2	no	—
38	#459×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
39	#452×C₁₀₃	—	2	2	no	—
40	#449×C₁₀₃	—	2	1	no	—
41	#447×C₁₀₃	—	2	2	no	—
42	#442×C₁₀₃	—	2	1	no	—
43	#440×C₁₀₃	—	2	1	no	—
44	#432×C₁₀₃	C₂²	1	1	yes	characteristic
45	#432×C₁₀₃	C₂²	1	1	yes	characteristic
46	#431×C₁₀₃	C₂²	1	1	yes	characteristic
47	#331×C₁₀₃	C₂²	1	2	yes	—
48	#331×C₁₀₃	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
50	Q₈⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
51	Q₈⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
52	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	complemented
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	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₀₃	—	2	1	no	—
58	C₂²×D₄×C₁₀₃	—	2	1	no	—
59	C₂²×D₄×C₁₀₃	D₄	1	2	yes	—
60	C₂×Q₁₆×C₁₀₃	—	2	2	no	—
61	C₂×SD₁₆×C₁₀₃	—	2	1	no	—
62	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
63	C₂×D₈×C₁₀₃	—	2	1	no	—
64	C₂×D₈×C₁₀₃	—	2	4	no	—
65	C₄⋊Q₈×C₁₀₃	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₀₃	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
68	#127×C₁₀₃	—	2	2	no	—
69	#127×C₁₀₃	—	2	1	no	—
70	#127×C₁₀₃	—	2	1	no	—
71	#127×C₁₀₃	D₄	1	2	yes	—
72	#127×C₁₀₃	C₂³	1	1	yes	characteristic
73	#127×C₁₀₃	C₂³	1	2	yes	—
74	#125×C₁₀₃	—	2	1	no	—
75	#124×C₁₀₃	—	2	2	no	—
76	#124×C₁₀₃	—	2	2	no	—
77	#124×C₁₀₃	—	2	2	no	—
78	#124×C₁₀₃	—	2	1	no	—
79	#123×C₁₀₃	—	2	4	no	—
80	#123×C₁₀₃	—	2	4	no	—
81	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
82	C₂²⋊Q₈×C₁₀₃	D₄	1	2	yes	—
83	#121×C₁₀₃	—	2	2	no	—
84	#121×C₁₀₃	—	2	2	no	—
85	#121×C₁₀₃	—	2	2	no	—
86	#121×C₁₀₃	—	2	4	no	—
87	#121×C₁₀₃	—	2	4	no	—
88	#121×C₁₀₃	—	2	2	no	—
89	#121×C₁₀₃	—	2	1	no	—
90	#121×C₁₀₃	—	2	1	no	—
91	#120×C₁₀₃	—	2	4	no	—
92	C₄×Q₈×C₁₀₃	—	2	1	no	—
93	C₄×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₀₃	C₂³	1	2	yes	—
95	C₄×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₀₃	—	2	2	no	—
97	C₄×D₄×C₁₀₃	—	2	2	no	—
98	C₄×D₄×C₁₀₃	—	2	2	no	—
99	C₄×D₄×C₁₀₃	—	2	1	no	—
100	C₄×D₄×C₁₀₃	—	2	1	no	—
101	C₄×D₄×C₁₀₃	—	2	2	no	—
102	C₄×D₄×C₁₀₃	—	2	2	no	—
103	C₄×D₄×C₁₀₃	—	2	2	no	—
104	C₄×D₄×C₁₀₃	—	2	1	no	—
105	C₄×D₄×C₁₀₃	—	2	1	no	—
106	C₄×D₄×C₁₀₃	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
108	#117×C₁₀₃	—	2	1	no	—
109	#117×C₁₀₃	—	2	1	no	—
110	#117×C₁₀₃	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₀₃	—	2	4	no	—
112	C₂×C₄²×C₁₀₃	—	2	1	no	—
113	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
114	#107×C₁₀₃	—	2	1	no	—
115	#106×C₁₀₃	—	2	1	no	—
116	C₄⋊C₈×C₁₀₃	—	2	1	no	—
117	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
119	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
120	#103×C₁₀₃	—	2	1	no	—
121	#103×C₁₀₃	—	2	2	no	—
122	#102×C₁₀₃	—	2	1	no	—
123	#102×C₁₀₃	—	2	4	no	—
124	#102×C₁₀₃	—	2	1	no	—
125	#102×C₁₀₃	—	2	1	no	—
126	#102×C₁₀₃	—	2	2	no	—
127	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
128	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
129	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
130	#97×C₁₀₃	—	2	1	no	—
131	#97×C₁₀₃	—	2	1	no	—
132	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
133	C₂⁴×C₁₀₃	—	2	2	no	—
134	#41×C₁₀₃	—	4	1	no	—
135	#41×C₁₀₃	—	4	1	no	—
136	#41×C₁₀₃	—	8	2	no	—
137	#41×C₁₀₃	—	8	2	no	—
138	#41×C₁₀₃	—	8	2	no	—
139	#41×C₁₀₃	—	8	4	no	—
140	C₂×Q₈×C₁₀₃	—	2	1	no	—
141	C₂×Q₈×C₁₀₃	—	2	1	no	—
142	C₂×Q₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₁₀₃	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₁₀₃	—	2	1	no	—
145	C₂×D₄×C₁₀₃	—	2	4	no	—
146	C₂×D₄×C₁₀₃	—	2	4	no	—
147	C₂×D₄×C₁₀₃	—	2	2	no	—
148	C₂×D₄×C₁₀₃	—	2	2	no	—
149	C₂×D₄×C₁₀₃	—	2	2	no	—
150	C₂×D₄×C₁₀₃	—	2	2	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	—	4	2	no	—
156	C₂×D₄×C₁₀₃	—	4	2	no	—
157	C₂×D₄×C₁₀₃	—	4	1	no	—
158	C₂×D₄×C₁₀₃	—	8	2	no	—
159	C₂×D₄×C₁₀₃	—	8	2	no	—
160	C₂×D₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₀₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₀₃	—	2	4	no	—
163	C₂²×C₄×C₁₀₃	—	2	4	no	—
164	C₂²×C₄×C₁₀₃	—	2	1	no	—
165	C₂²×C₄×C₁₀₃	—	2	1	no	—
166	C₂²×C₄×C₁₀₃	—	2	1	no	—
167	C₂²×C₄×C₁₀₃	—	4	1	no	—
168	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
171	Q₁₆×C₁₀₃	—	8	2	no	—
172	SD₁₆×C₁₀₃	—	4	2	no	—
173	SD₁₆×C₁₀₃	—	8	2	no	—
174	D₈×C₁₀₃	—	4	2	no	—
175	D₈×C₁₀₃	—	8	4	no	—
176	C₂×C₈×C₁₀₃	—	2	2	no	—
177	C₂×C₈×C₁₀₃	—	2	1	no	—
178	C₂×C₈×C₁₀₃	—	2	1	no	—
179	C₂×C₈×C₁₀₃	—	2	2	no	—
180	C₄⋊C₄×C₁₀₃	—	2	1	no	—
181	C₄⋊C₄×C₁₀₃	—	2	1	no	—
182	C₄⋊C₄×C₁₀₃	—	2	1	no	—
183	C₄⋊C₄×C₁₀₃	—	2	1	no	—
184	C₄⋊C₄×C₁₀₃	—	2	2	no	—
185	C₄⋊C₄×C₁₀₃	—	2	1	no	—
186	C₄⋊C₄×C₁₀₃	—	2	2	no	—
187	C₄⋊C₄×C₁₀₃	—	2	1	no	—
188	C₄⋊C₄×C₁₀₃	—	2	1	no	—
189	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
193	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
194	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
195	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
196	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
197	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
198	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
199	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
200	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
201	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
202	C₄²×C₁₀₃	—	2	1	no	—
203	C₄²×C₁₀₃	—	2	1	no	—
204	C₄²×C₁₀₃	—	2	1	no	—
205	C₄²×C₁₀₃	—	2	2	no	—
206	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₁₀₃	—	2	4	no	—
211	C₂³×C₁₀₃	—	2	1	no	—
212	C₂³×C₁₀₃	—	4	4	no	—
213	C₂³×C₁₀₃	—	4	1	no	—
214	C₂³×C₁₀₃	—	8	2	no	—
215	C₂³×C₁₀₃	—	8	2	no	—
216	C₂³×C₁₀₃	#120	1	1	yes	characteristic
217	Q₈×C₁₀₃	—	2	1	no	—
218	Q₈×C₁₀₃	—	2	1	no	—
219	Q₈×C₁₀₃	—	2	2	no	—
220	Q₈×C₁₀₃	—	2	2	no	—
221	Q₈×C₁₀₃	—	4	2	no	—
222	Q₈×C₁₀₃	—	4	2	no	—
223	D₄×C₁₀₃	—	2	1	no	—
224	D₄×C₁₀₃	—	2	1	no	—
225	D₄×C₁₀₃	—	4	4	no	—
226	D₄×C₁₀₃	—	4	4	no	—
227	D₄×C₁₀₃	—	4	4	no	—
228	D₄×C₁₀₃	—	4	2	no	—
229	D₄×C₁₀₃	—	4	2	no	—
230	D₄×C₁₀₃	—	4	2	no	—
231	D₄×C₁₀₃	—	4	2	no	—
232	D₄×C₁₀₃	—	4	1	no	—
233	D₄×C₁₀₃	—	4	1	no	—
234	D₄×C₁₀₃	—	4	2	no	—
235	D₄×C₁₀₃	—	4	2	no	—
236	D₄×C₁₀₃	—	4	2	no	—
237	D₄×C₁₀₃	—	8	2	no	—
238	D₄×C₁₀₃	—	8	4	no	—
239	D₄×C₁₀₃	—	8	4	no	—
240	D₄×C₁₀₃	—	8	2	no	—
241	C₂×C₄×C₁₀₃	—	2	1	no	—
242	C₂×C₄×C₁₀₃	—	2	1	no	—
243	C₂×C₄×C₁₀₃	—	2	2	no	—
244	C₂×C₄×C₁₀₃	—	2	1	no	—
245	C₂×C₄×C₁₀₃	—	2	1	no	—
246	C₂×C₄×C₁₀₃	—	2	1	no	—
247	C₂×C₄×C₁₀₃	—	2	2	no	—
248	C₂×C₄×C₁₀₃	—	2	2	no	—
249	C₂×C₄×C₁₀₃	—	4	1	no	—
250	C₂×C₄×C₁₀₃	—	4	2	no	—
251	C₂×C₄×C₁₀₃	—	4	2	no	—
252	C₂×C₄×C₁₀₃	—	4	2	no	—
253	C₂×C₄×C₁₀₃	—	4	1	no	—
254	C₂×C₄×C₁₀₃	—	8	2	no	—
255	C₂×C₄×C₁₀₃	—	8	4	no	—
256	C₂×C₄×C₁₀₃	—	8	4	no	—
257	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₀₃	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₁₀₃	—	4	2	no	—
264	C₈×C₁₀₃	—	4	1	no	—
265	C₈×C₁₀₃	—	4	1	no	—
266	C₈×C₁₀₃	—	4	2	no	—
267	C₂²×C₁₀₃	—	2	1	no	—
268	C₂²×C₁₀₃	—	2	1	no	—
269	C₂²×C₁₀₃	—	2	1	no	—
270	C₂²×C₁₀₃	—	4	1	no	—
271	C₂²×C₁₀₃	—	4	4	no	—
272	C₂²×C₁₀₃	—	4	1	no	—
273	C₂²×C₁₀₃	—	4	4	no	—
274	C₂²×C₁₀₃	—	4	1	no	—
275	C₂²×C₁₀₃	—	4	4	no	—
276	C₂²×C₁₀₃	—	8	1	no	—
277	C₂²×C₁₀₃	—	8	1	no	—
278	C₂²×C₁₀₃	—	8	1	no	—
279	C₂²×C₁₀₃	—	16	4	no	—
280	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
281	C₄×C₁₀₃	—	2	1	no	—
282	C₄×C₁₀₃	—	2	1	no	—
283	C₄×C₁₀₃	—	2	1	no	—
284	C₄×C₁₀₃	—	2	1	no	—
285	C₄×C₁₀₃	—	4	1	no	—
286	C₄×C₁₀₃	—	4	1	no	—
287	C₄×C₁₀₃	—	4	2	no	—
288	C₄×C₁₀₃	—	4	1	no	—
289	C₄×C₁₀₃	—	4	2	no	—
290	C₄×C₁₀₃	—	8	1	no	—
291	C₄×C₁₀₃	#575	1	1	yes	characteristic
292	C₄×C₁₀₃	#575	1	1	yes	characteristic
293	C₄×C₁₀₃	#576	1	2	yes	—
294	#18818	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂×C₁₀₃	—	4	1	no	—
296	C₂×C₁₀₃	—	8	1	no	—
297	C₂×C₁₀₃	—	8	4	no	—
298	C₂×C₁₀₃	—	16	1	no	—
299	C₂×C₁₀₃	#3005	1	1	yes	characteristic
300	C₂×C₁₀₃	#3008	1	1	yes	characteristic
301	C₂×C₁₀₃	#3019	1	1	yes	characteristic
302	#3508	C₂×C₁₀₃	1	1	yes	characteristic, complemented
303	#3216	C₂×C₁₀₃	1	1	yes	characteristic, complemented
304	#3205	C₂×C₁₀₃	1	1	yes	characteristic, complemented
305	#3115	C₂×C₁₀₃	1	1	yes	characteristic, complemented
306	#1641	C₂×C₁₀₃	1	2	yes	complemented
307	#1640	C₂×C₁₀₃	1	2	yes	complemented
308	#1621	C₂×C₁₀₃	1	2	yes	complemented
309	#1620	C₂×C₁₀₃	1	2	yes	complemented
310	#1555	C₂×C₁₀₃	1	1	yes	characteristic, complemented
311	#1497	C₂×C₁₀₃	1	1	yes	characteristic, complemented
312	#1488	C₂×C₁₀₃	1	1	yes	characteristic, complemented
313	C₁₀₃	#18818	1	1	yes	characteristic, direct product factor, Sylow
314	#559	—	2	1	no	—
315	#559	C₂²×C₁₀₃	1	2	yes	—
316	#550	—	2	1	no	—
317	#550	C₂²×C₁₀₃	1	2	yes	—
318	#546	—	2	2	no	—
319	#546	—	2	2	no	—
320	#540	—	2	2	no	—
321	#535	—	2	1	no	—
322	#533	C₂²×C₁₀₃	1	1	yes	characteristic
323	#532	—	2	1	no	—
324	#532	—	2	1	no	—
325	#532	C₂²×C₁₀₃	1	1	yes	characteristic
326	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
327	#518	—	2	1	no	—
328	C₄×#41	C₂²×C₁₀₃	1	1	yes	characteristic
329	#497	—	2	1	no	—
330	#493	C₂²×C₁₀₃	1	2	yes	—
331	#489	—	2	1	no	—
332	#486	C₂²×C₁₀₃	1	2	yes	—
333	#482	—	2	1	no	—
334	#475	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
335	#474	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
336	#462	C₂²×C₁₀₃	1	2	yes	complemented
337	#460	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
338	#460	C₂²×C₁₀₃	1	2	yes	complemented
339	#459	—	2	2	no	—
340	#459	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
341	#452	—	2	2	no	—
342	#449	—	2	1	no	—
343	#447	—	2	2	no	—
344	#442	—	2	1	no	—
345	#440	—	2	1	no	—
346	#432	C₂²×C₁₀₃	1	1	yes	characteristic
347	#432	C₂²×C₁₀₃	1	1	yes	characteristic
348	#431	C₂²×C₁₀₃	1	1	yes	characteristic
349	#331	C₂²×C₁₀₃	1	2	yes	—
350	#331	C₂²×C₁₀₃	1	2	yes	—
351	Q₈⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
352	Q₈⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
353	Q₈⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
354	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	complemented
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	D₄×C₁₀₃	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	D₄×C₁₀₃	1	2	yes	—
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	—	2	4	no	—
367	C₄⋊Q₈	D₄×C₁₀₃	1	1	yes	characteristic
368	C₄⋊Q₈	D₄×C₁₀₃	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
370	#127	—	2	2	no	—
371	#127	—	2	1	no	—
372	#127	—	2	1	no	—
373	#127	D₄×C₁₀₃	1	2	yes	—
374	#127	C₂³×C₁₀₃	1	1	yes	characteristic
375	#127	C₂³×C₁₀₃	1	2	yes	—
376	#125	—	2	1	no	—
377	#124	—	2	2	no	—
378	#124	—	2	2	no	—
379	#124	—	2	2	no	—
380	#124	—	2	1	no	—
381	#123	—	2	4	no	—
382	#123	—	2	4	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	D₄×C₁₀₃	1	2	yes	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	2	2	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#120	—	2	4	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
397	C₄×Q₈	C₂³×C₁₀₃	1	2	yes	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	D₄×C₁₀₃	1	1	yes	characteristic
409	C₄×D₄	C₂³×C₁₀₃	1	1	yes	characteristic
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	D₄×C₁₀₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	4	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
416	#107	—	2	1	no	—
417	#106	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
420	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
422	#103	—	2	1	no	—
423	#103	—	2	2	no	—
424	#102	—	2	1	no	—
425	#102	—	2	4	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	2	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	#97	—	2	1	no	—
433	#97	—	2	1	no	—
434	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
435	C₂⁴	—	2	2	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	8	2	no	—
439	#41	—	8	2	no	—
440	#41	—	8	2	no	—
441	#41	—	8	4	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₀₃	1	2	yes	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	8	2	no	—
461	C₂×D₄	—	8	2	no	—
462	C₂×D₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
463	C₂×D₄	C₂×D₄×C₁₀₃	1	4	yes	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
473	Q₁₆	—	8	2	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	8	2	no	—
476	D₈	—	4	2	no	—
477	D₈	—	8	4	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
492	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	2	no	—
508	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
511	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
512	C₂³	—	2	4	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	8	2	no	—
517	C₂³	—	8	2	no	—
518	C₂³	#120×C₁₀₃	1	1	yes	characteristic
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	4	no	—
541	D₄	—	8	4	no	—
542	D₄	—	8	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
560	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
561	C₂×C₄	#120×C₁₀₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
565	C₈	—	4	2	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	16	4	no	—
582	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	8	1	no	—
593	C₄	#575×C₁₀₃	1	1	yes	characteristic
594	C₄	#575×C₁₀₃	1	1	yes	characteristic
595	C₄	#576×C₁₀₃	1	2	yes	—
596	C₂	—	4	1	no	—
597	C₂	—	8	4	no	—
598	C₂	—	8	1	no	—
599	C₂	—	16	1	no	—
600	C₂	C₁₀₃×#3005	1	1	yes	characteristic
601	C₂	C₁₀₃×#3008	1	1	yes	characteristic
602	C₂	C₁₀₃×#3019	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×#3508	C₂	semidirect
2. C₁₀₃×#3216	C₂	semidirect
3. C₁₀₃×#3205	C₂	semidirect
4. C₁₀₃×#3115	C₂	semidirect
5. C₁₀₃×#1641	C₂	semidirect
6. C₁₀₃×#1640	C₂	semidirect
7. C₁₀₃×#1621	C₂	semidirect
8. C₁₀₃×#1620	C₂	semidirect
9. C₁₀₃×#1555	C₂	semidirect
10. C₁₀₃×#1497	C₂	semidirect
11. C₁₀₃×#1488	C₂	semidirect
32. #475×C₁₀₃	C₂²	semidirect
33. #474×C₁₀₃	C₂²	semidirect
34. #462×C₁₀₃	C₂²	semidirect
35. #460×C₁₀₃	C₂²	semidirect
36. #460×C₁₀₃	C₂²	semidirect
38. #459×C₁₀₃	C₂²	semidirect
49. Q₈⋊C₈×C₁₀₃	C₂²	semidirect
50. Q₈⋊C₈×C₁₀₃	C₂²	semidirect
51. Q₈⋊C₈×C₁₀₃	C₂²	semidirect
52. D₄⋊C₈×C₁₀₃	C₂²	semidirect
294. #18818	C₁₀₃	direct (N × H)
302. #3508	C₂×C₁₀₃	semidirect
303. #3216	C₂×C₁₀₃	semidirect
304. #3205	C₂×C₁₀₃	semidirect
305. #3115	C₂×C₁₀₃	semidirect
306. #1641	C₂×C₁₀₃	semidirect
307. #1640	C₂×C₁₀₃	semidirect
308. #1621	C₂×C₁₀₃	semidirect
309. #1620	C₂×C₁₀₃	semidirect
310. #1555	C₂×C₁₀₃	semidirect
311. #1497	C₂×C₁₀₃	semidirect
312. #1488	C₂×C₁₀₃	semidirect
313. C₁₀₃	#18818	direct (N × H)
334. #475	C₂²×C₁₀₃	semidirect
335. #474	C₂²×C₁₀₃	semidirect
336. #462	C₂²×C₁₀₃	semidirect
337. #460	C₂²×C₁₀₃	semidirect
338. #460	C₂²×C₁₀₃	semidirect
340. #459	C₂²×C₁₀₃	semidirect
351. Q₈⋊C₈	C₂²×C₁₀₃	semidirect
352. Q₈⋊C₈	C₂²×C₁₀₃	semidirect
353. Q₈⋊C₈	C₂²×C₁₀₃	semidirect
354. D₄⋊C₈	C₂²×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×#3508	2
C₁₀₃×#3216	2
C₁₀₃×#3205	2
C₁₀₃×#3115	2
C₁₀₃×#1641	2
C₁₀₃×#1640	2
C₁₀₃×#1621	2
C₁₀₃×#1620	2
C₁₀₃×#1555	2
C₁₀₃×#1497	2
C₁₀₃×#1488	2
#18818	103

Subgroups — C103×#18818 #39924093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#18818 #39924093