Subgroups — C₁₇×#61593 #16919337

Order 4352.

2148 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3320	C₂	1	4	yes	maximal, complemented
5	C₁₇×#3299	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₁₇	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3266	C₂	1	4	yes	maximal, complemented
9	C₁₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3193	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3190	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3004	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₇×#448	C₂	1	2	yes	maximal, complemented
17	C₁₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₇	C₂²	1	2	yes	complemented
19	C₂×C₁₇×#137	C₂²	1	4	yes	complemented
20	C₂²×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
21	C₁₇×#555	C₂²	1	1	yes	characteristic
22	C₁₇×#554	C₂²	1	1	yes	characteristic
23	C₁₇×#553	—	2	1	no	—
24	C₁₇×#553	C₂²	1	2	yes	—
25	C₁₇×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₇	—	2	2	no	—
27	D₄×Q₈×C₁₇	—	2	1	no	—
28	D₄×Q₈×C₁₇	—	2	1	no	—
29	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
31	D₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
32	C₁₇×#546	—	2	2	no	—
33	C₁₇×#546	C₂²	1	2	yes	—
34	D₄²×C₁₇	—	2	1	no	—
35	D₄²×C₁₇	C₂²	1	1	yes	characteristic
36	C₁₇×#540	—	2	1	no	—
37	C₁₇×#538	—	2	2	no	—
38	C₁₇×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×#529	C₂²	1	1	yes	characteristic
42	C₁₇×#525	C₂²	1	2	yes	—
43	C₂×C₁₇×C₂²⋊Q₈	—	2	2	no	—
44	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₂×C₁₇×#121	C₂²	1	2	yes	—
46	C₁₇×#518	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₁₇	—	2	1	no	—
49	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
50	C₁₇×#497	C₂²	1	2	yes	complemented
51	C₁₇×#492	C₂²	1	2	yes	complemented
52	C₁₇×#491	C₂²	1	2	yes	complemented
53	C₁₇×#487	C₂²	1	2	yes	complemented
54	C₁₇×#485	C₂²	1	4	yes	complemented
55	C₁₇×#484	C₂²	1	4	yes	complemented
56	C₁₇×#483	C₂²	1	1	yes	characteristic, complemented
57	C₁₇×#480	C₂²	1	1	yes	characteristic
58	C₁₇×#480	C₂²	1	2	yes	complemented
59	C₁₇×#479	C₂²	1	2	yes	complemented
60	C₁₇×#477	C₂²	1	2	yes	complemented
61	C₁₇×#468	C₂²	1	4	yes	complemented
62	C₁₇×#468	C₂²	1	4	yes	complemented
63	C₁₇×#467	C₂²	1	4	yes	complemented
64	C₁₇×#465	C₂²	1	4	yes	complemented
65	C₁₇×#464	C₂²	1	2	yes	complemented
66	C₁₇×#462	C₂²	1	2	yes	complemented
67	C₁₇×#461	C₂²	1	4	yes	complemented
68	C₁₇×#461	C₂²	1	2	yes	complemented
69	C₁₇×#460	C₂²	1	2	yes	complemented
70	C₁₇×#452	C₂²	1	4	yes	complemented
71	C₁₇×#451	C₂²	1	2	yes	complemented
72	C₁₇×#451	C₂²	1	1	yes	characteristic, complemented
73	C₁₇×#451	C₂²	1	4	yes	complemented
74	C₁₇×#450	C₂²	1	4	yes	complemented
75	C₁₇×#448	C₂²	1	2	yes	—
76	C₁₇×#448	C₂²	1	1	yes	characteristic
77	C₁₇×#448	C₂²	1	2	yes	complemented
78	C₁₇×#448	C₂²	1	2	yes	complemented
79	C₁₇×#448	C₂²	1	2	yes	complemented
80	C₁₇×#448	C₂²	1	4	yes	complemented
81	C₁₇×#448	C₂²	1	4	yes	complemented
82	C₁₇×#448	C₂²	1	4	yes	complemented
83	C₁₇×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
86	C₁₇×#436	C₂²	1	2	yes	complemented
87	C₁₇×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₁₇	C₂²	1	2	yes	—
89	C₁₇×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₇×#419	C₂²	1	4	yes	complemented
92	C₂×C₁₇×#103	C₂²	1	4	yes	complemented
93	C₁₇×#407	C₂²	1	2	yes	complemented
94	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂×#41×C₁₇	—	2	1	no	—
96	C₂×#41×C₁₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₇	—	2	2	no	—
98	C₂²×Q₈×C₁₇	—	2	2	no	—
99	C₂²×Q₈×C₁₇	—	2	2	no	—
100	C₂²×Q₈×C₁₇	—	4	8	no	—
101	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
103	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
104	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₇	—	2	2	no	—
106	C₂²×D₄×C₁₇	—	2	1	no	—
107	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₇	—	2	2	no	—
110	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
111	C₁₇×#137	—	4	8	no	—
112	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₁₇	—	4	8	no	—
115	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
120	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
121	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
122	C₁₇×C₄⋊Q₈	—	2	2	no	—
123	C₁₇×C₄⋊Q₈	—	2	4	no	—
124	C₁₇×C₄⋊Q₈	—	2	2	no	—
125	C₁₇×C₄⋊Q₈	—	2	1	no	—
126	C₁₇×C₄⋊Q₈	—	2	1	no	—
127	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₇×#127	—	2	1	no	—
131	C₁₇×#127	C₂³	1	1	yes	characteristic
132	C₁₇×#126	—	2	2	no	—
133	C₁₇×#126	—	2	1	no	—
134	C₁₇×#125	—	2	1	no	—
135	C₁₇×#125	C₂³	1	1	yes	characteristic
136	C₁₇×#124	—	2	2	no	—
137	C₁₇×#124	—	2	1	no	—
138	C₁₇×#124	C₂³	1	1	yes	characteristic
139	C₁₇×#123	—	2	2	no	—
140	C₁₇×#123	—	2	1	no	—
141	C₁₇×#123	—	2	2	no	—
142	C₁₇×#123	—	2	2	no	—
143	C₁₇×C₂²⋊Q₈	—	2	2	no	—
144	C₁₇×C₂²⋊Q₈	—	2	2	no	—
145	C₁₇×C₂²⋊Q₈	—	2	4	no	—
146	C₁₇×C₂²⋊Q₈	—	2	4	no	—
147	C₁₇×C₂²⋊Q₈	—	2	4	no	—
148	C₁₇×C₂²⋊Q₈	—	2	4	no	—
149	C₁₇×C₂²⋊Q₈	—	2	2	no	—
150	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₇×#121	—	2	2	no	—
155	C₁₇×#121	—	2	1	no	—
156	C₁₇×#121	—	2	2	no	—
157	C₁₇×#121	—	2	2	no	—
158	C₁₇×#121	—	2	1	no	—
159	C₁₇×#121	—	2	1	no	—
160	C₁₇×#121	—	2	2	no	—
161	C₁₇×#121	—	2	2	no	—
162	C₁₇×#121	C₂³	1	1	yes	characteristic
163	C₁₇×#121	C₂³	1	2	yes	—
164	C₁₇×#121	C₂³	1	2	yes	—
165	C₁₇×#121	C₂³	1	2	yes	—
166	C₁₇×#121	C₂³	1	2	yes	—
167	C₁₇×#120	—	2	2	no	—
168	C₁₇×#120	—	2	2	no	—
169	C₁₇×#120	—	2	2	no	—
170	C₄×Q₈×C₁₇	—	2	1	no	—
171	C₄×Q₈×C₁₇	—	2	1	no	—
172	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₁₇	—	2	2	no	—
176	C₄×D₄×C₁₇	—	2	2	no	—
177	C₄×D₄×C₁₇	—	2	4	no	—
178	C₄×D₄×C₁₇	—	2	1	no	—
179	C₄×D₄×C₁₇	—	2	2	no	—
180	C₄×D₄×C₁₇	—	2	2	no	—
181	C₄×D₄×C₁₇	—	2	1	no	—
182	C₄×D₄×C₁₇	—	2	1	no	—
183	C₄×D₄×C₁₇	—	2	2	no	—
184	C₄×D₄×C₁₇	—	2	1	no	—
185	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₇	D₄	1	2	yes	—
187	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₇	C₂³	1	2	yes	—
190	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₇	C₂³	1	2	yes	—
192	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
193	C₁₇×#117	—	2	1	no	—
194	C₁₇×#117	—	2	1	no	—
195	C₁₇×#117	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
198	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
199	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
200	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
207	C₂×C₄²×C₁₇	—	2	1	no	—
208	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
209	C₁₇×#107	C₂³	1	2	yes	—
210	C₁₇×#107	C₂³	1	4	yes	—
211	C₁₇×#106	C₂³	1	2	yes	—
212	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₇×#103	C₂³	1	4	yes	—
215	C₁₇×#103	C₂³	1	4	yes	—
216	C₁₇×#103	C₂³	1	2	yes	—
217	C₁₇×#103	C₂³	1	4	yes	—
218	C₁₇×#103	C₂³	1	4	yes	—
219	C₁₇×#103	C₂³	1	2	yes	—
220	C₁₇×#103	C₂³	1	4	yes	—
221	C₁₇×#103	C₂³	1	2	yes	—
222	C₁₇×#102	C₂³	1	2	yes	—
223	C₁₇×#102	C₂³	1	4	yes	—
224	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₇×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₁₇	C₂³	1	2	yes	—
231	C₂⁴×C₁₇	—	2	2	no	—
232	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
233	#41×C₁₇	—	4	4	no	—
234	#41×C₁₇	—	8	2	no	—
235	C₂×Q₈×C₁₇	—	2	4	no	—
236	C₂×Q₈×C₁₇	—	2	1	no	—
237	C₂×Q₈×C₁₇	—	2	4	no	—
238	C₂×Q₈×C₁₇	—	2	4	no	—
239	C₂×Q₈×C₁₇	—	2	2	no	—
240	C₂×Q₈×C₁₇	—	2	1	no	—
241	C₂×Q₈×C₁₇	—	2	8	no	—
242	C₂×Q₈×C₁₇	—	2	8	no	—
243	C₂×Q₈×C₁₇	—	4	4	no	—
244	C₂×Q₈×C₁₇	—	4	4	no	—
245	C₂×Q₈×C₁₇	—	4	4	no	—
246	C₂×Q₈×C₁₇	—	4	8	no	—
247	C₂×Q₈×C₁₇	—	4	8	no	—
248	C₂×Q₈×C₁₇	—	4	8	no	—
249	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₇	—	2	4	no	—
253	C₂×D₄×C₁₇	—	2	1	no	—
254	C₂×D₄×C₁₇	—	2	2	no	—
255	C₂×D₄×C₁₇	—	2	2	no	—
256	C₂×D₄×C₁₇	—	2	2	no	—
257	C₂×D₄×C₁₇	—	2	2	no	—
258	C₂×D₄×C₁₇	—	2	2	no	—
259	C₂×D₄×C₁₇	—	2	1	no	—
260	C₂×D₄×C₁₇	—	2	2	no	—
261	C₂×D₄×C₁₇	—	2	1	no	—
262	C₂×D₄×C₁₇	—	4	4	no	—
263	C₂×D₄×C₁₇	—	4	4	no	—
264	C₂×D₄×C₁₇	—	8	4	no	—
265	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₇	—	2	1	no	—
271	C₂²×C₄×C₁₇	—	2	4	no	—
272	C₂²×C₄×C₁₇	—	2	4	no	—
273	C₂²×C₄×C₁₇	—	2	2	no	—
274	C₂²×C₄×C₁₇	—	2	1	no	—
275	C₂²×C₄×C₁₇	—	2	2	no	—
276	C₂²×C₄×C₁₇	—	2	1	no	—
277	C₂²×C₄×C₁₇	—	2	2	no	—
278	C₂²×C₄×C₁₇	—	2	2	no	—
279	C₂²×C₄×C₁₇	—	4	4	no	—
280	C₂²×C₄×C₁₇	—	4	8	no	—
281	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
289	Q₁₆×C₁₇	—	2	4	no	—
290	Q₁₆×C₁₇	—	4	4	no	—
291	SD₁₆×C₁₇	—	2	4	no	—
292	SD₁₆×C₁₇	—	2	8	no	—
293	SD₁₆×C₁₇	—	4	4	no	—
294	SD₁₆×C₁₇	—	4	4	no	—
295	SD₁₆×C₁₇	—	4	4	no	—
296	M₁₆×C₁₇	—	4	4	no	—
297	C₂×C₈×C₁₇	—	4	4	no	—
298	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
300	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₁₇	—	2	2	no	—
302	C₄⋊C₄×C₁₇	—	2	2	no	—
303	C₄⋊C₄×C₁₇	—	2	2	no	—
304	C₄⋊C₄×C₁₇	—	2	2	no	—
305	C₄⋊C₄×C₁₇	—	2	1	no	—
306	C₄⋊C₄×C₁₇	—	2	4	no	—
307	C₄⋊C₄×C₁₇	—	2	4	no	—
308	C₄⋊C₄×C₁₇	—	2	1	no	—
309	C₄⋊C₄×C₁₇	—	2	2	no	—
310	C₄⋊C₄×C₁₇	—	2	2	no	—
311	C₄⋊C₄×C₁₇	—	2	1	no	—
312	C₄⋊C₄×C₁₇	—	2	1	no	—
313	C₄⋊C₄×C₁₇	—	2	1	no	—
314	C₄⋊C₄×C₁₇	—	2	1	no	—
315	C₄⋊C₄×C₁₇	—	2	2	no	—
316	C₄⋊C₄×C₁₇	—	2	2	no	—
317	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
324	C₂²⋊C₄×C₁₇	—	2	4	no	—
325	C₂²⋊C₄×C₁₇	—	2	4	no	—
326	C₂²⋊C₄×C₁₇	—	2	2	no	—
327	C₂²⋊C₄×C₁₇	—	2	1	no	—
328	C₂²⋊C₄×C₁₇	—	2	2	no	—
329	C₂²⋊C₄×C₁₇	—	2	1	no	—
330	C₂²⋊C₄×C₁₇	—	2	2	no	—
331	C₂²⋊C₄×C₁₇	—	2	1	no	—
332	C₂²⋊C₄×C₁₇	—	2	2	no	—
333	C₂²⋊C₄×C₁₇	—	2	2	no	—
334	C₂²⋊C₄×C₁₇	—	2	2	no	—
335	C₂²⋊C₄×C₁₇	—	2	1	no	—
336	C₂²⋊C₄×C₁₇	—	2	1	no	—
337	C₂²⋊C₄×C₁₇	—	2	2	no	—
338	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
342	C₄²×C₁₇	—	2	2	no	—
343	C₄²×C₁₇	—	2	1	no	—
344	C₄²×C₁₇	—	2	2	no	—
345	C₄²×C₁₇	—	2	2	no	—
346	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
349	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
350	#61593	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₂³×C₁₇	—	2	4	no	—
352	C₂³×C₁₇	—	2	4	no	—
353	C₂³×C₁₇	—	2	1	no	—
354	C₂³×C₁₇	—	2	2	no	—
355	C₂³×C₁₇	—	4	2	no	—
356	C₂³×C₁₇	—	4	4	no	—
357	C₂³×C₁₇	—	8	2	no	—
358	C₂³×C₁₇	—	8	2	no	—
359	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
360	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
361	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₁₇	—	2	4	no	—
363	Q₈×C₁₇	—	2	2	no	—
364	Q₈×C₁₇	—	2	4	no	—
365	Q₈×C₁₇	—	2	4	no	—
366	Q₈×C₁₇	—	2	2	no	—
367	Q₈×C₁₇	—	4	8	no	—
368	Q₈×C₁₇	—	4	8	no	—
369	Q₈×C₁₇	—	4	4	no	—
370	Q₈×C₁₇	—	8	1	no	—
371	Q₈×C₁₇	H(5,𝔽₂)	1	4	yes	—
372	D₄×C₁₇	—	2	4	no	—
373	D₄×C₁₇	—	2	2	no	—
374	D₄×C₁₇	—	2	2	no	—
375	D₄×C₁₇	—	2	4	no	—
376	D₄×C₁₇	—	4	4	no	—
377	D₄×C₁₇	—	4	2	no	—
378	D₄×C₁₇	—	4	4	no	—
379	D₄×C₁₇	—	4	2	no	—
380	D₄×C₁₇	—	8	2	no	—
381	D₄×C₁₇	—	8	1	no	—
382	D₄×C₁₇	—	8	2	no	—
383	D₄×C₁₇	—	8	2	no	—
384	D₄×C₁₇	—	8	2	no	—
385	D₄×C₁₇	#137	1	4	yes	complemented
386	C₂×C₄×C₁₇	—	2	4	no	—
387	C₂×C₄×C₁₇	—	2	2	no	—
388	C₂×C₄×C₁₇	—	2	2	no	—
389	C₂×C₄×C₁₇	—	2	2	no	—
390	C₂×C₄×C₁₇	—	2	4	no	—
391	C₂×C₄×C₁₇	—	2	4	no	—
392	C₂×C₄×C₁₇	—	2	2	no	—
393	C₂×C₄×C₁₇	—	2	1	no	—
394	C₂×C₄×C₁₇	—	2	2	no	—
395	C₂×C₄×C₁₇	—	2	1	no	—
396	C₂×C₄×C₁₇	—	2	2	no	—
397	C₂×C₄×C₁₇	—	2	1	no	—
398	C₂×C₄×C₁₇	—	2	4	no	—
399	C₂×C₄×C₁₇	—	4	2	no	—
400	C₂×C₄×C₁₇	—	4	2	no	—
401	C₂×C₄×C₁₇	—	4	2	no	—
402	C₂×C₄×C₁₇	—	4	8	no	—
403	C₂×C₄×C₁₇	—	4	8	no	—
404	C₂×C₄×C₁₇	—	4	4	no	—
405	C₂×C₄×C₁₇	—	4	2	no	—
406	C₂×C₄×C₁₇	—	4	2	no	—
407	C₂×C₄×C₁₇	—	8	2	no	—
408	C₂×C₄×C₁₇	—	8	2	no	—
409	C₂×C₄×C₁₇	—	8	2	no	—
410	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
418	C₈×C₁₇	—	2	2	no	—
419	C₈×C₁₇	—	2	4	no	—
420	C₈×C₁₇	—	2	2	no	—
421	#3519	C₂×C₁₇	1	1	yes	characteristic
422	C₂×D₄×Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
423	#3329	C₂×C₁₇	1	2	yes	complemented
424	#3320	C₂×C₁₇	1	4	yes	complemented
425	#3299	C₂×C₁₇	1	2	yes	complemented
426	D₄×SD₁₆	C₂×C₁₇	1	2	yes	complemented
427	#3278	C₂×C₁₇	1	2	yes	complemented
428	#3266	C₂×C₁₇	1	4	yes	complemented
429	#3218	C₂×C₁₇	1	1	yes	characteristic, complemented
430	#3206	C₂×C₁₇	1	1	yes	characteristic, complemented
431	#3193	C₂×C₁₇	1	2	yes	complemented
432	#3190	C₂×C₁₇	1	2	yes	complemented
433	#3112	C₂×C₁₇	1	1	yes	characteristic, complemented
434	#3108	C₂×C₁₇	1	1	yes	characteristic, complemented
435	#3004	C₂×C₁₇	1	2	yes	complemented
436	C₂×#448	C₂×C₁₇	1	2	yes	complemented
437	#2974	C₂×C₁₇	1	1	yes	characteristic, complemented
438	C₂²×C₁₇	—	2	1	no	—
439	C₂²×C₁₇	—	2	2	no	—
440	C₂²×C₁₇	—	2	1	no	—
441	C₂²×C₁₇	—	2	2	no	—
442	C₂²×C₁₇	—	2	2	no	—
443	C₂²×C₁₇	—	2	2	no	—
444	C₂²×C₁₇	—	2	2	no	—
445	C₂²×C₁₇	—	4	8	no	—
446	C₂²×C₁₇	—	4	2	no	—
447	C₂²×C₁₇	—	4	1	no	—
448	C₂²×C₁₇	—	4	1	no	—
449	C₂²×C₁₇	—	4	2	no	—
450	C₂²×C₁₇	—	4	2	no	—
451	C₂²×C₁₇	—	4	1	no	—
452	C₂²×C₁₇	—	16	4	no	—
453	C₂²×C₁₇	C₂×#137	1	4	yes	—
454	C₂²×C₁₇	#577	1	2	yes	—
455	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₁₇	—	2	4	no	—
457	C₄×C₁₇	—	2	1	no	—
458	C₄×C₁₇	—	2	2	no	—
459	C₄×C₁₇	—	2	2	no	—
460	C₄×C₁₇	—	2	1	no	—
461	C₄×C₁₇	—	2	1	no	—
462	C₄×C₁₇	—	2	1	no	—
463	C₄×C₁₇	—	4	4	no	—
464	C₄×C₁₇	—	4	1	no	—
465	C₄×C₁₇	—	4	1	no	—
466	C₄×C₁₇	—	4	2	no	—
467	C₄×C₁₇	—	4	1	no	—
468	C₄×C₁₇	—	4	2	no	—
469	C₄×C₁₇	C₂×#137	1	2	yes	—
470	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
471	C₂³×Q₈	C₂²×C₁₇	1	2	yes	complemented
472	C₂×#137	C₂²×C₁₇	1	4	yes	complemented
473	C₂²×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
474	#555	C₂²×C₁₇	1	1	yes	characteristic
475	#554	C₂²×C₁₇	1	1	yes	characteristic
476	#553	—	2	1	no	—
477	#553	C₂²×C₁₇	1	2	yes	—
478	#550	C₂²×C₁₇	1	1	yes	characteristic
479	D₄×Q₈	—	2	1	no	—
480	D₄×Q₈	—	2	2	no	—
481	D₄×Q₈	—	2	1	no	—
482	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
483	D₄×Q₈	C₂²×C₁₇	1	2	yes	complemented
484	D₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
485	#546	—	2	2	no	—
486	#546	C₂²×C₁₇	1	2	yes	—
487	D₄²	—	2	1	no	—
488	D₄²	C₂²×C₁₇	1	1	yes	characteristic
489	#540	—	2	1	no	—
490	#538	—	2	2	no	—
491	#532	C₂²×C₁₇	1	1	yes	characteristic
492	C₂×C₄⋊Q₈	—	2	1	no	—
493	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
494	#529	C₂²×C₁₇	1	1	yes	characteristic
495	#525	C₂²×C₁₇	1	2	yes	—
496	C₂×C₂²⋊Q₈	—	2	2	no	—
497	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	complemented
498	C₂×#121	C₂²×C₁₇	1	2	yes	—
499	#518	—	2	1	no	—
500	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
501	C₂×C₄×D₄	—	2	1	no	—
502	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
503	#497	C₂²×C₁₇	1	2	yes	complemented
504	#492	C₂²×C₁₇	1	2	yes	complemented
505	#491	C₂²×C₁₇	1	2	yes	complemented
506	#487	C₂²×C₁₇	1	2	yes	complemented
507	#485	C₂²×C₁₇	1	4	yes	complemented
508	#484	C₂²×C₁₇	1	4	yes	complemented
509	#483	C₂²×C₁₇	1	1	yes	characteristic, complemented
510	#480	C₂²×C₁₇	1	1	yes	characteristic
511	#480	C₂²×C₁₇	1	2	yes	complemented
512	#479	C₂²×C₁₇	1	2	yes	complemented
513	#477	C₂²×C₁₇	1	2	yes	complemented
514	#468	C₂²×C₁₇	1	4	yes	complemented
515	#468	C₂²×C₁₇	1	4	yes	complemented
516	#467	C₂²×C₁₇	1	4	yes	complemented
517	#465	C₂²×C₁₇	1	4	yes	complemented
518	#464	C₂²×C₁₇	1	2	yes	complemented
519	#462	C₂²×C₁₇	1	2	yes	complemented
520	#461	C₂²×C₁₇	1	2	yes	complemented
521	#461	C₂²×C₁₇	1	4	yes	complemented
522	#460	C₂²×C₁₇	1	2	yes	complemented
523	#452	C₂²×C₁₇	1	4	yes	complemented
524	#451	C₂²×C₁₇	1	1	yes	characteristic, complemented
525	#451	C₂²×C₁₇	1	2	yes	complemented
526	#451	C₂²×C₁₇	1	4	yes	complemented
527	#450	C₂²×C₁₇	1	4	yes	complemented
528	#448	C₂²×C₁₇	1	1	yes	characteristic
529	#448	C₂²×C₁₇	1	2	yes	—
530	#448	C₂²×C₁₇	1	4	yes	complemented
531	#448	C₂²×C₁₇	1	2	yes	complemented
532	#448	C₂²×C₁₇	1	2	yes	complemented
533	#448	C₂²×C₁₇	1	2	yes	complemented
534	#448	C₂²×C₁₇	1	4	yes	complemented
535	#448	C₂²×C₁₇	1	4	yes	complemented
536	#440	C₂²×C₁₇	1	4	yes	complemented
537	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
538	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
539	#436	C₂²×C₁₇	1	2	yes	complemented
540	#435	C₂²×C₁₇	1	4	yes	complemented
541	C₈×D₄	C₂²×C₁₇	1	2	yes	—
542	#432	C₂²×C₁₇	1	1	yes	characteristic, complemented
543	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
544	#419	C₂²×C₁₇	1	4	yes	complemented
545	C₂×#103	C₂²×C₁₇	1	4	yes	complemented
546	#407	C₂²×C₁₇	1	2	yes	complemented
547	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
548	C₂×C₁₇	—	2	2	no	—
549	C₂×C₁₇	—	2	4	no	—
550	C₂×C₁₇	—	4	2	no	—
551	C₂×C₁₇	—	8	2	no	—
552	C₂×C₁₇	—	8	1	no	—
553	C₂×C₁₇	#3484	1	1	yes	characteristic
554	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
555	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
556	C₂×#41	—	2	1	no	—
557	C₂×#41	C₂³×C₁₇	1	2	yes	—
558	C₂²×Q₈	—	2	2	no	—
559	C₂²×Q₈	—	2	2	no	—
560	C₂²×Q₈	—	2	2	no	—
561	C₂²×Q₈	—	4	8	no	—
562	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
564	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
565	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
566	C₂²×D₄	—	2	2	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
570	C₂³×C₄	—	2	2	no	—
571	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
572	#137	—	4	8	no	—
573	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
574	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
575	C₂×SD₁₆	—	4	8	no	—
576	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
577	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
581	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
582	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
583	C₄⋊Q₈	—	2	2	no	—
584	C₄⋊Q₈	—	2	2	no	—
585	C₄⋊Q₈	—	2	4	no	—
586	C₄⋊Q₈	—	2	1	no	—
587	C₄⋊Q₈	—	2	1	no	—
588	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
591	#127	—	2	1	no	—
592	#127	C₂³×C₁₇	1	1	yes	characteristic
593	#126	—	2	2	no	—
594	#126	—	2	1	no	—
595	#125	—	2	1	no	—
596	#125	C₂³×C₁₇	1	1	yes	characteristic
597	#124	—	2	2	no	—
598	#124	—	2	1	no	—
599	#124	C₂³×C₁₇	1	1	yes	characteristic
600	#123	—	2	2	no	—
601	#123	—	2	1	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	—	2	4	no	—
607	C₂²⋊Q₈	—	2	4	no	—
608	C₂²⋊Q₈	—	2	4	no	—
609	C₂²⋊Q₈	—	2	4	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
613	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
615	#121	—	2	2	no	—
616	#121	—	2	1	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	C₂³×C₁₇	1	1	yes	characteristic
624	#121	C₂³×C₁₇	1	2	yes	—
625	#121	C₂³×C₁₇	1	2	yes	—
626	#121	C₂³×C₁₇	1	2	yes	—
627	#121	C₂³×C₁₇	1	2	yes	—
628	#120	—	2	2	no	—
629	#120	—	2	2	no	—
630	#120	—	2	2	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
634	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
635	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	4	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
647	C₄×D₄	D₄×C₁₇	1	2	yes	—
648	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
649	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₁₇	1	2	yes	—
651	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₁₇	1	2	yes	—
653	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
654	#117	—	2	1	no	—
655	#117	—	2	1	no	—
656	#117	C₂³×C₁₇	1	2	yes	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	2	no	—
661	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
670	#107	C₂³×C₁₇	1	2	yes	—
671	#107	C₂³×C₁₇	1	4	yes	—
672	#106	C₂³×C₁₇	1	2	yes	—
673	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
674	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
675	#103	C₂³×C₁₇	1	2	yes	—
676	#103	C₂³×C₁₇	1	4	yes	—
677	#103	C₂³×C₁₇	1	4	yes	—
678	#103	C₂³×C₁₇	1	4	yes	—
679	#103	C₂³×C₁₇	1	2	yes	—
680	#103	C₂³×C₁₇	1	4	yes	—
681	#103	C₂³×C₁₇	1	4	yes	—
682	#103	C₂³×C₁₇	1	2	yes	—
683	#102	C₂³×C₁₇	1	2	yes	—
684	#102	C₂³×C₁₇	1	4	yes	—
685	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
686	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
687	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
689	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
690	#97	C₂³×C₁₇	1	2	yes	—
691	C₄×C₈	C₂³×C₁₇	1	2	yes	—
692	C₁₇	#61593	1	1	yes	characteristic, direct product factor, Sylow
693	C₂⁴	—	2	2	no	—
694	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
695	#41	—	4	4	no	—
696	#41	—	8	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	8	no	—
705	C₂×Q₈	—	4	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	—	4	8	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
713	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	8	4	no	—
727	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
728	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
730	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
731	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	—	4	8	no	—
743	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
747	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
751	Q₁₆	—	2	4	no	—
752	Q₁₆	—	4	4	no	—
753	SD₁₆	—	2	4	no	—
754	SD₁₆	—	2	8	no	—
755	SD₁₆	—	4	4	no	—
756	SD₁₆	—	4	4	no	—
757	SD₁₆	—	4	4	no	—
758	M₁₆	—	4	4	no	—
759	C₂×C₈	—	4	4	no	—
760	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
761	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
762	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	1	no	—
808	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
810	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
811	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	4	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
821	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
822	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	4	no	—
826	Q₈	—	2	4	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	4	8	no	—
829	Q₈	—	4	8	no	—
830	Q₈	—	4	4	no	—
831	Q₈	—	8	1	no	—
832	Q₈	C₁₇×H(5,𝔽₂)	1	4	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	1	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	2	no	—
846	D₄	C₁₇×#137	1	4	yes	complemented
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	8	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
878	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
879	C₈	—	2	2	no	—
880	C₈	—	2	4	no	—
881	C₈	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	8	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	16	4	no	—
897	C₂²	C₂×C₁₇×#137	1	4	yes	—
898	C₂²	C₁₇×#577	1	2	yes	—
899	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
900	C₄	—	2	4	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	4	4	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	C₂×C₁₇×#137	1	2	yes	—
914	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
915	C₂	—	2	2	no	—
916	C₂	—	2	4	no	—
917	C₂	—	4	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	C₁₇×#3484	1	1	yes	characteristic
921	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
922	C₂	C₂×C₁₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₁₇	C₂	semidirect
3. C₁₇×#3329	C₂	semidirect
4. C₁₇×#3320	C₂	semidirect
5. C₁₇×#3299	C₂	semidirect
6. D₄×SD₁₆×C₁₇	C₂	semidirect
7. C₁₇×#3278	C₂	semidirect
8. C₁₇×#3266	C₂	semidirect
9. C₁₇×#3218	C₂	semidirect
10. C₁₇×#3206	C₂	semidirect
11. C₁₇×#3193	C₂	semidirect
12. C₁₇×#3190	C₂	semidirect
13. C₁₇×#3112	C₂	semidirect
14. C₁₇×#3108	C₂	semidirect
15. C₁₇×#3004	C₂	semidirect
16. C₂×C₁₇×#448	C₂	semidirect
17. C₁₇×#2974	C₂	semidirect
18. C₂³×Q₈×C₁₇	C₂²	semidirect
19. C₂×C₁₇×#137	C₂²	semidirect
20. C₂²×SD₁₆×C₁₇	C₂²	semidirect
30. D₄×Q₈×C₁₇	C₂²	semidirect
31. D₄×Q₈×C₁₇	C₂²	semidirect
40. C₂×C₁₇×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
50. C₁₇×#497	C₂²	semidirect
51. C₁₇×#492	C₂²	semidirect
52. C₁₇×#491	C₂²	semidirect
53. C₁₇×#487	C₂²	semidirect
54. C₁₇×#485	C₂²	semidirect
55. C₁₇×#484	C₂²	semidirect
56. C₁₇×#483	C₂²	semidirect
58. C₁₇×#480	C₂²	semidirect
59. C₁₇×#479	C₂²	semidirect
60. C₁₇×#477	C₂²	semidirect
61. C₁₇×#468	C₂²	semidirect
62. C₁₇×#468	C₂²	semidirect
63. C₁₇×#467	C₂²	semidirect
64. C₁₇×#465	C₂²	semidirect
65. C₁₇×#464	C₂²	semidirect
66. C₁₇×#462	C₂²	semidirect
67. C₁₇×#461	C₂²	semidirect
68. C₁₇×#461	C₂²	semidirect
69. C₁₇×#460	C₂²	semidirect
70. C₁₇×#452	C₂²	semidirect
71. C₁₇×#451	C₂²	semidirect
72. C₁₇×#451	C₂²	semidirect
73. C₁₇×#451	C₂²	semidirect
74. C₁₇×#450	C₂²	semidirect
77. C₁₇×#448	C₂²	semidirect
78. C₁₇×#448	C₂²	semidirect
79. C₁₇×#448	C₂²	semidirect
80. C₁₇×#448	C₂²	semidirect
81. C₁₇×#448	C₂²	semidirect
82. C₁₇×#448	C₂²	semidirect
83. C₁₇×#440	C₂²	semidirect
84. C₄×Q₁₆×C₁₇	C₂²	semidirect
85. C₄×SD₁₆×C₁₇	C₂²	semidirect
86. C₁₇×#436	C₂²	semidirect
87. C₁₇×#435	C₂²	semidirect
89. C₁₇×#432	C₂²	semidirect
90. C₁₇×#431	C₂²	semidirect
91. C₁₇×#419	C₂²	semidirect
92. C₂×C₁₇×#103	C₂²	semidirect
93. C₁₇×#407	C₂²	semidirect
94. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
350. #61593	C₁₇	direct (N × H)
385. D₄×C₁₇	#137	semidirect
422. C₂×D₄×Q₈	C₂×C₁₇	semidirect
423. #3329	C₂×C₁₇	semidirect
424. #3320	C₂×C₁₇	semidirect
425. #3299	C₂×C₁₇	semidirect
426. D₄×SD₁₆	C₂×C₁₇	semidirect
427. #3278	C₂×C₁₇	semidirect
428. #3266	C₂×C₁₇	semidirect
429. #3218	C₂×C₁₇	semidirect
430. #3206	C₂×C₁₇	semidirect
431. #3193	C₂×C₁₇	semidirect
432. #3190	C₂×C₁₇	semidirect
433. #3112	C₂×C₁₇	semidirect
434. #3108	C₂×C₁₇	semidirect
435. #3004	C₂×C₁₇	semidirect
436. C₂×#448	C₂×C₁₇	semidirect
437. #2974	C₂×C₁₇	semidirect
471. C₂³×Q₈	C₂²×C₁₇	semidirect
472. C₂×#137	C₂²×C₁₇	semidirect
473. C₂²×SD₁₆	C₂²×C₁₇	semidirect
483. D₄×Q₈	C₂²×C₁₇	semidirect
484. D₄×Q₈	C₂²×C₁₇	semidirect
493. C₂×C₄⋊Q₈	C₂²×C₁₇	semidirect
497. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
500. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
503. #497	C₂²×C₁₇	semidirect
504. #492	C₂²×C₁₇	semidirect
505. #491	C₂²×C₁₇	semidirect
506. #487	C₂²×C₁₇	semidirect
507. #485	C₂²×C₁₇	semidirect
508. #484	C₂²×C₁₇	semidirect
509. #483	C₂²×C₁₇	semidirect
511. #480	C₂²×C₁₇	semidirect
512. #479	C₂²×C₁₇	semidirect
513. #477	C₂²×C₁₇	semidirect
514. #468	C₂²×C₁₇	semidirect
515. #468	C₂²×C₁₇	semidirect
516. #467	C₂²×C₁₇	semidirect
517. #465	C₂²×C₁₇	semidirect
518. #464	C₂²×C₁₇	semidirect
519. #462	C₂²×C₁₇	semidirect
520. #461	C₂²×C₁₇	semidirect
521. #461	C₂²×C₁₇	semidirect
522. #460	C₂²×C₁₇	semidirect
523. #452	C₂²×C₁₇	semidirect
524. #451	C₂²×C₁₇	semidirect
525. #451	C₂²×C₁₇	semidirect
526. #451	C₂²×C₁₇	semidirect
527. #450	C₂²×C₁₇	semidirect
530. #448	C₂²×C₁₇	semidirect
531. #448	C₂²×C₁₇	semidirect
532. #448	C₂²×C₁₇	semidirect
533. #448	C₂²×C₁₇	semidirect
534. #448	C₂²×C₁₇	semidirect
535. #448	C₂²×C₁₇	semidirect
536. #440	C₂²×C₁₇	semidirect
537. C₄×Q₁₆	C₂²×C₁₇	semidirect
538. C₄×SD₁₆	C₂²×C₁₇	semidirect
539. #436	C₂²×C₁₇	semidirect
540. #435	C₂²×C₁₇	semidirect
542. #432	C₂²×C₁₇	semidirect
543. #431	C₂²×C₁₇	semidirect
544. #419	C₂²×C₁₇	semidirect
545. C₂×#103	C₂²×C₁₇	semidirect
546. #407	C₂²×C₁₇	semidirect
547. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
692. C₁₇	#61593	direct (N × H)
846. D₄	C₁₇×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3519	2
C₂×D₄×Q₈×C₁₇	2
C₁₇×#3329	2
C₁₇×#3320	2
C₁₇×#3299	2
D₄×SD₁₆×C₁₇	2
C₁₇×#3278	2
C₁₇×#3266	2
C₁₇×#3218	2
C₁₇×#3206	2
C₁₇×#3193	2
C₁₇×#3190	2
C₁₇×#3112	2
C₁₇×#3108	2
C₁₇×#3004	2
C₂×C₁₇×#448	2
C₁₇×#2974	2
#61593	17

Subgroups — C17×#61593 #16919337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61593 #16919337