Subgroups — C₁₇×#34621 #16892365

Order 4352.

1918 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2651	C₂	1	4	yes	maximal, complemented
2	C₁₇×#2648	C₂	1	4	yes	maximal, complemented
3	C₁₇×#2647	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2644	C₂	1	2	yes	maximal, complemented
5	C₁₇×#2641	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2624	C₂	1	2	yes	maximal, complemented
8	C₁₇×#2619	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#2395	C₂	1	4	yes	maximal, complemented
10	C₁₇×#2392	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₇×#121	C₂	1	2	yes	maximal, complemented
14	C₁₇×#2293	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#121	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
22	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#117	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
26	C₁₇×#400	C₂²	1	4	yes	—
27	C₁₇×#399	C₂²	1	4	yes	—
28	C₁₇×#398	C₂²	1	4	yes	—
29	C₁₇×#398	C₂²	1	4	yes	—
30	C₁₇×#397	C₂²	1	4	yes	—
31	C₁₇×#397	C₂²	1	4	yes	—
32	C₁₇×#397	C₂²	1	4	yes	—
33	C₁₇×#397	C₂²	1	4	yes	—
34	C₁₇×#396	C₂²	1	4	yes	—
35	C₁₇×#396	C₂²	1	4	yes	—
36	C₁₇×#394	C₂²	1	4	yes	—
37	C₁₇×#394	C₂²	1	4	yes	—
38	C₁₇×#394	C₂²	1	4	yes	—
39	C₁₇×#394	C₂²	1	4	yes	—
40	C₁₇×#394	C₂²	1	4	yes	—
41	C₁₇×#392	C₂²	1	4	yes	—
42	C₁₇×#390	C₂²	1	2	yes	—
43	C₁₇×#390	C₂²	1	2	yes	—
44	C₁₇×#390	C₂²	1	2	yes	—
45	C₁₇×#390	C₂²	1	2	yes	—
46	C₁₇×#390	C₂²	1	4	yes	—
47	C₁₇×#389	C₂²	1	2	yes	—
48	C₁₇×#389	C₂²	1	2	yes	—
49	C₁₇×#389	C₂²	1	2	yes	—
50	C₁₇×#389	C₂²	1	2	yes	—
51	C₁₇×#388	C₂²	1	4	yes	—
52	C₁₇×#388	C₂²	1	4	yes	—
53	C₁₇×#388	C₂²	1	4	yes	—
54	C₁₇×#387	C₂²	1	4	yes	—
55	C₁₇×#386	C₂²	1	4	yes	—
56	C₁₇×#384	C₂²	1	1	yes	characteristic
57	C₁₇×#382	C₂²	1	1	yes	characteristic
58	C₁₇×#380	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₇	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
66	C₄×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
67	C₁₇×#376	C₂²	1	1	yes	characteristic
68	C₁₇×#376	C₂²	1	1	yes	characteristic
69	C₄³×C₁₇	C₂²	1	1	yes	characteristic
70	C₄³×C₁₇	C₂²	1	1	yes	characteristic
71	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
73	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₁₇×#127	—	2	4	no	—
79	C₁₇×#125	—	2	4	no	—
80	C₁₇×#121	—	2	8	no	—
81	C₄×D₄×C₁₇	—	2	8	no	—
82	C₄×D₄×C₁₇	—	4	8	no	—
83	C₄×D₄×C₁₇	—	4	8	no	—
84	C₁₇×#117	—	2	4	no	—
85	C₁₇×#117	—	2	4	no	—
86	C₁₇×#117	—	4	8	no	—
87	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₇	—	2	4	no	—
112	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
125	C₁₇×#95	C₂³	1	2	yes	—
126	C₁₇×#95	C₂³	1	2	yes	—
127	C₁₇×#95	C₂³	1	2	yes	—
128	C₁₇×#95	C₂³	1	2	yes	—
129	C₁₇×#95	C₂³	1	4	yes	—
130	C₁₇×#95	C₂³	1	4	yes	—
131	C₁₇×#95	C₂³	1	4	yes	—
132	C₁₇×#95	C₂³	1	4	yes	—
133	C₁₇×#95	C₂³	1	4	yes	—
134	C₁₇×#95	C₂³	1	4	yes	—
135	C₁₇×#95	C₂³	1	4	yes	—
136	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₇	—	2	8	no	—
139	C₂×D₄×C₁₇	—	2	8	no	—
140	C₂×D₄×C₁₇	—	2	4	no	—
141	C₂×D₄×C₁₇	—	2	4	no	—
142	C₂×D₄×C₁₇	—	2	4	no	—
143	C₂×D₄×C₁₇	—	4	4	no	—
144	C₂×D₄×C₁₇	—	4	4	no	—
145	C₂×D₄×C₁₇	—	4	4	no	—
146	C₂×D₄×C₁₇	—	4	4	no	—
147	C₂²×C₄×C₁₇	—	2	2	no	—
148	C₂²×C₄×C₁₇	—	2	2	no	—
149	C₂²×C₄×C₁₇	—	2	2	no	—
150	C₂²×C₄×C₁₇	—	2	2	no	—
151	C₂²×C₄×C₁₇	—	2	8	no	—
152	C₂²×C₄×C₁₇	—	2	8	no	—
153	C₂²×C₄×C₁₇	—	2	4	no	—
154	C₂²×C₄×C₁₇	—	2	8	no	—
155	C₂²×C₄×C₁₇	—	4	2	no	—
156	C₂²×C₄×C₁₇	#41	1	4	yes	—
157	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₁₇	—	2	8	no	—
171	C₄⋊C₄×C₁₇	—	2	4	no	—
172	C₄⋊C₄×C₁₇	—	2	4	no	—
173	C₄⋊C₄×C₁₇	—	2	4	no	—
174	C₄⋊C₄×C₁₇	—	2	4	no	—
175	C₄⋊C₄×C₁₇	—	2	4	no	—
176	C₄⋊C₄×C₁₇	—	4	4	no	—
177	C₄⋊C₄×C₁₇	—	4	4	no	—
178	C₄⋊C₄×C₁₇	—	4	4	no	—
179	C₄⋊C₄×C₁₇	—	4	4	no	—
180	C₄⋊C₄×C₁₇	—	4	4	no	—
181	C₂²⋊C₄×C₁₇	—	2	4	no	—
182	C₂²⋊C₄×C₁₇	—	2	4	no	—
183	C₂²⋊C₄×C₁₇	—	2	8	no	—
184	C₂²⋊C₄×C₁₇	—	2	8	no	—
185	C₂²⋊C₄×C₁₇	—	4	4	no	—
186	C₂²⋊C₄×C₁₇	—	4	4	no	—
187	C₂²⋊C₄×C₁₇	—	4	4	no	—
188	C₂²⋊C₄×C₁₇	—	4	4	no	—
189	C₂²⋊C₄×C₁₇	—	4	4	no	—
190	C₂²⋊C₄×C₁₇	—	4	4	no	—
191	C₂²⋊C₄×C₁₇	—	4	4	no	—
192	C₂²⋊C₄×C₁₇	—	4	4	no	—
193	C₂²⋊C₄×C₁₇	—	4	4	no	—
194	C₄²×C₁₇	—	2	2	no	—
195	C₄²×C₁₇	—	2	2	no	—
196	C₄²×C₁₇	—	2	2	no	—
197	C₄²×C₁₇	—	2	2	no	—
198	C₄²×C₁₇	—	2	2	no	—
199	C₄²×C₁₇	—	2	2	no	—
200	C₄²×C₁₇	—	2	4	no	—
201	C₄²×C₁₇	—	2	8	no	—
202	C₄²×C₁₇	—	2	4	no	—
203	C₄²×C₁₇	—	4	2	no	—
204	C₄²×C₁₇	—	4	2	no	—
205	C₄²×C₁₇	#41	1	4	yes	—
206	C₄²×C₁₇	#41	1	4	yes	—
207	#34621	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₇	—	2	1	no	—
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	2	2	no	—
211	C₂³×C₁₇	—	2	2	no	—
212	C₂³×C₁₇	—	2	4	no	—
213	C₂³×C₁₇	—	2	4	no	—
214	C₂³×C₁₇	—	2	4	no	—
215	C₂³×C₁₇	—	2	4	no	—
216	C₂³×C₁₇	—	2	4	no	—
217	C₂³×C₁₇	—	2	4	no	—
218	C₂³×C₁₇	—	2	4	no	—
219	C₂³×C₁₇	C₂×#41	1	2	yes	—
220	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
221	D₄×C₁₇	—	4	16	no	—
222	D₄×C₁₇	—	4	16	no	—
223	D₄×C₁₇	—	4	8	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	2	no	—
227	C₂×C₄×C₁₇	—	2	2	no	—
228	C₂×C₄×C₁₇	—	2	2	no	—
229	C₂×C₄×C₁₇	—	2	8	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	2	no	—
233	C₂×C₄×C₁₇	—	2	2	no	—
234	C₂×C₄×C₁₇	—	2	2	no	—
235	C₂×C₄×C₁₇	—	2	4	no	—
236	C₂×C₄×C₁₇	—	2	4	no	—
237	C₂×C₄×C₁₇	—	2	4	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	4	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	2	2	no	—
242	C₂×C₄×C₁₇	—	2	4	no	—
243	C₂×C₄×C₁₇	—	2	2	no	—
244	C₂×C₄×C₁₇	—	2	4	no	—
245	C₂×C₄×C₁₇	—	2	4	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	2	2	no	—
249	C₂×C₄×C₁₇	—	2	4	no	—
250	C₂×C₄×C₁₇	—	2	2	no	—
251	C₂×C₄×C₁₇	—	2	4	no	—
252	C₂×C₄×C₁₇	—	4	4	no	—
253	C₂×C₄×C₁₇	—	4	4	no	—
254	C₂×C₄×C₁₇	—	4	16	no	—
255	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
256	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
257	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
262	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
263	#2651	C₂×C₁₇	1	4	yes	complemented
264	#2648	C₂×C₁₇	1	4	yes	complemented
265	#2647	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#2644	C₂×C₁₇	1	2	yes	complemented
267	#2641	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#2629	C₂×C₁₇	1	1	yes	characteristic, complemented
269	#2624	C₂×C₁₇	1	2	yes	complemented
270	#2619	C₂×C₁₇	1	1	yes	characteristic
271	#2395	C₂×C₁₇	1	4	yes	complemented
272	#2392	C₂×C₁₇	1	4	yes	complemented
273	C₄×#127	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₄×#125	C₂×C₁₇	1	1	yes	characteristic, complemented
275	C₄×#121	C₂×C₁₇	1	2	yes	complemented
276	#2293	C₂×C₁₇	1	2	yes	complemented
277	C₄×#117	C₂×C₁₇	1	1	yes	characteristic, complemented
278	C₂²×C₁₇	—	2	2	no	—
279	C₂²×C₁₇	—	2	4	no	—
280	C₂²×C₁₇	—	4	1	no	—
281	C₂²×C₁₇	—	4	1	no	—
282	C₂²×C₁₇	—	4	2	no	—
283	C₂²×C₁₇	—	4	4	no	—
284	C₂²×C₁₇	—	4	4	no	—
285	C₂²×C₁₇	—	4	4	no	—
286	C₂²×C₁₇	—	4	4	no	—
287	C₂²×C₁₇	—	4	4	no	—
288	C₂²×C₁₇	—	4	4	no	—
289	C₂²×C₁₇	—	4	4	no	—
290	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
291	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
292	C₂²×C₁₇	C₂²×#41	1	1	yes	characteristic
293	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₁₇	#585	1	2	yes	—
295	C₄×C₁₇	—	2	2	no	—
296	C₄×C₁₇	—	2	2	no	—
297	C₄×C₁₇	—	2	4	no	—
298	C₄×C₁₇	—	4	1	no	—
299	C₄×C₁₇	—	4	4	no	—
300	C₄×C₁₇	—	4	1	no	—
301	C₄×C₁₇	—	4	2	no	—
302	C₄×C₁₇	—	4	4	no	—
303	C₄×C₁₇	—	4	2	no	—
304	C₄×C₁₇	—	4	2	no	—
305	C₄×C₁₇	—	4	4	no	—
306	C₄×C₁₇	#529	1	4	yes	—
307	C₄×C₁₇	#540	1	4	yes	—
308	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
309	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
310	C₂×#121	C₂²×C₁₇	1	2	yes	—
311	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
313	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
314	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
315	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
316	C₂×#117	C₂²×C₁₇	1	4	yes	—
317	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
318	#400	C₂²×C₁₇	1	4	yes	—
319	#399	C₂²×C₁₇	1	4	yes	—
320	#398	C₂²×C₁₇	1	4	yes	—
321	#398	C₂²×C₁₇	1	4	yes	—
322	#397	C₂²×C₁₇	1	4	yes	—
323	#397	C₂²×C₁₇	1	4	yes	—
324	#397	C₂²×C₁₇	1	4	yes	—
325	#397	C₂²×C₁₇	1	4	yes	—
326	#396	C₂²×C₁₇	1	4	yes	—
327	#396	C₂²×C₁₇	1	4	yes	—
328	#394	C₂²×C₁₇	1	4	yes	—
329	#394	C₂²×C₁₇	1	4	yes	—
330	#394	C₂²×C₁₇	1	4	yes	—
331	#394	C₂²×C₁₇	1	4	yes	—
332	#394	C₂²×C₁₇	1	4	yes	—
333	#392	C₂²×C₁₇	1	4	yes	—
334	#390	C₂²×C₁₇	1	2	yes	—
335	#390	C₂²×C₁₇	1	4	yes	—
336	#390	C₂²×C₁₇	1	2	yes	—
337	#390	C₂²×C₁₇	1	2	yes	—
338	#390	C₂²×C₁₇	1	2	yes	—
339	#389	C₂²×C₁₇	1	2	yes	—
340	#389	C₂²×C₁₇	1	2	yes	—
341	#389	C₂²×C₁₇	1	2	yes	—
342	#389	C₂²×C₁₇	1	2	yes	—
343	#388	C₂²×C₁₇	1	4	yes	—
344	#388	C₂²×C₁₇	1	4	yes	—
345	#388	C₂²×C₁₇	1	4	yes	—
346	#387	C₂²×C₁₇	1	4	yes	—
347	#386	C₂²×C₁₇	1	4	yes	—
348	#384	C₂²×C₁₇	1	1	yes	characteristic
349	#382	C₂²×C₁₇	1	1	yes	characteristic
350	#380	C₂²×C₁₇	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₁₇	1	4	yes	—
352	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
353	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
354	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
355	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
359	#376	C₂²×C₁₇	1	1	yes	characteristic
360	#376	C₂²×C₁₇	1	1	yes	characteristic
361	C₄³	C₂²×C₁₇	1	1	yes	characteristic
362	C₄³	C₂²×C₁₇	1	1	yes	characteristic
363	C₂×C₁₇	—	4	2	no	—
364	C₂×C₁₇	—	8	4	no	—
365	C₂×C₁₇	C₂×#529	1	1	yes	characteristic
366	C₂×C₁₇	C₂×#540	1	1	yes	characteristic
367	C₂×C₁₇	#3455	1	1	yes	characteristic
368	C₂×C₁₇	#3460	1	2	yes	—
369	C₂×C₁₇	#3460	1	2	yes	—
370	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
371	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
372	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
373	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
374	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
377	#127	—	2	4	no	—
378	#125	—	2	4	no	—
379	#121	—	2	8	no	—
380	C₄×D₄	—	2	8	no	—
381	C₄×D₄	—	4	8	no	—
382	C₄×D₄	—	4	8	no	—
383	#117	—	2	4	no	—
384	#117	—	2	4	no	—
385	#117	—	4	8	no	—
386	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
410	C₂×C₄²	—	2	4	no	—
411	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
412	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
413	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
424	#95	C₂³×C₁₇	1	2	yes	—
425	#95	C₂³×C₁₇	1	2	yes	—
426	#95	C₂³×C₁₇	1	2	yes	—
427	#95	C₂³×C₁₇	1	2	yes	—
428	#95	C₂³×C₁₇	1	4	yes	—
429	#95	C₂³×C₁₇	1	4	yes	—
430	#95	C₂³×C₁₇	1	4	yes	—
431	#95	C₂³×C₁₇	1	4	yes	—
432	#95	C₂³×C₁₇	1	4	yes	—
433	#95	C₂³×C₁₇	1	4	yes	—
434	#95	C₂³×C₁₇	1	4	yes	—
435	C₁₇	#34621	1	1	yes	characteristic, direct product factor, Sylow
436	C₂⁴	C₂⁴×C₁₇	1	4	yes	—
437	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	#41×C₁₇	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	—	4	4	no	—
480	C₄⋊C₄	—	4	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	8	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	4	2	no	—
504	C₄²	—	4	2	no	—
505	C₄²	#41×C₁₇	1	4	yes	—
506	C₄²	#41×C₁₇	1	4	yes	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	C₂×#41×C₁₇	1	2	yes	—
519	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
520	D₄	—	4	16	no	—
521	D₄	—	4	16	no	—
522	D₄	—	4	8	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	16	no	—
554	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
555	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
556	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
557	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
558	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
559	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
560	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
561	C₂×C₄	C₁₇×H(5,𝔽₂)	1	4	yes	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
575	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
576	C₂²	C₂²×#41×C₁₇	1	1	yes	characteristic
577	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
578	C₂²	C₁₇×#585	1	2	yes	—
579	C₄	—	2	4	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	4	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	1	no	—
590	C₄	C₁₇×#529	1	4	yes	—
591	C₄	C₁₇×#540	1	4	yes	—
592	C₂	—	4	2	no	—
593	C₂	—	8	4	no	—
594	C₂	C₂×C₁₇×#529	1	1	yes	characteristic
595	C₂	C₂×C₁₇×#540	1	1	yes	characteristic
596	C₂	C₁₇×#3455	1	1	yes	characteristic
597	C₂	C₁₇×#3460	1	2	yes	—
598	C₂	C₁₇×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂⁵
prime radical	C₁₇×#2619	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#2651	C₂	semidirect
2. C₁₇×#2648	C₂	semidirect
3. C₁₇×#2647	C₂	semidirect
4. C₁₇×#2644	C₂	semidirect
5. C₁₇×#2641	C₂	semidirect
6. C₁₇×#2629	C₂	semidirect
7. C₁₇×#2624	C₂	semidirect
9. C₁₇×#2395	C₂	semidirect
10. C₁₇×#2392	C₂	semidirect
11. C₄×C₁₇×#127	C₂	semidirect
12. C₄×C₁₇×#125	C₂	semidirect
13. C₄×C₁₇×#121	C₂	semidirect
14. C₁₇×#2293	C₂	semidirect
15. C₄×C₁₇×#117	C₂	semidirect
207. #34621	C₁₇	direct (N × H)
263. #2651	C₂×C₁₇	semidirect
264. #2648	C₂×C₁₇	semidirect
265. #2647	C₂×C₁₇	semidirect
266. #2644	C₂×C₁₇	semidirect
267. #2641	C₂×C₁₇	semidirect
268. #2629	C₂×C₁₇	semidirect
269. #2624	C₂×C₁₇	semidirect
271. #2395	C₂×C₁₇	semidirect
272. #2392	C₂×C₁₇	semidirect
273. C₄×#127	C₂×C₁₇	semidirect
274. C₄×#125	C₂×C₁₇	semidirect
275. C₄×#121	C₂×C₁₇	semidirect
276. #2293	C₂×C₁₇	semidirect
277. C₄×#117	C₂×C₁₇	semidirect
435. C₁₇	#34621	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#2651	2
C₁₇×#2648	2
C₁₇×#2647	2
C₁₇×#2644	2
C₁₇×#2641	2
C₁₇×#2629	2
C₁₇×#2624	2
C₁₇×#2619	2
C₁₇×#2395	2
C₁₇×#2392	2
C₄×C₁₇×#127	2
C₄×C₁₇×#125	2
C₄×C₁₇×#121	2
C₁₇×#2293	2
C₄×C₁₇×#117	2
#34621	17

Subgroups — C17×#34621 #16892365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34621 #16892365