Subgroups — C₁₇×#62847 #16920591

Order 4352.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3521	C₂	1	8	yes	maximal, complemented
2	C₁₇×#3520	C₂	1	8	yes	maximal, complemented
3	C₁₇×#3515	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3513	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3507	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3505	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#3492	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3491	C₂	1	4	yes	maximal, complemented
11	C₁₇×#3485	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3461	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3459	C₂	1	4	yes	maximal, complemented
14	C₁₇×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₇×#539	C₂	1	4	yes	maximal, complemented
16	C₄×C₁₇×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#559	C₂²	1	4	yes	complemented
21	C₁₇×#557	C₂²	1	4	yes	complemented
22	C₁₇×#556	C₂²	1	8	yes	complemented
23	C₁₇×#556	C₂²	1	4	yes	complemented
24	C₁₇×#554	C₂²	1	8	yes	complemented
25	C₁₇×#554	C₂²	1	8	yes	complemented
26	C₁₇×#554	C₂²	1	4	yes	complemented
27	C₁₇×#554	C₂²	1	4	yes	complemented
28	C₁₇×#553	C₂²	1	8	yes	complemented
29	C₁₇×#553	C₂²	1	16	yes	complemented
30	C₁₇×#553	C₂²	1	8	yes	complemented
31	C₁₇×#552	C₂²	1	16	yes	complemented
32	C₁₇×#552	C₂²	1	16	yes	complemented
33	C₁₇×#552	C₂²	1	8	yes	complemented
34	C₁₇×#552	C₂²	1	8	yes	complemented
35	C₁₇×#552	C₂²	1	8	yes	complemented
36	C₁₇×#551	C₂²	1	16	yes	complemented
37	C₁₇×#551	C₂²	1	16	yes	complemented
38	C₁₇×#551	C₂²	1	16	yes	complemented
39	D₄×Q₈×C₁₇	C₂²	1	4	yes	complemented
40	C₁₇×#548	C₂²	1	8	yes	complemented
41	C₁₇×#547	C₂²	1	8	yes	complemented
42	C₁₇×#547	C₂²	1	8	yes	complemented
43	C₁₇×#547	C₂²	1	8	yes	complemented
44	C₁₇×#547	C₂²	1	4	yes	complemented
45	C₁₇×#546	C₂²	1	8	yes	complemented
46	C₁₇×#546	C₂²	1	8	yes	complemented
47	C₁₇×#546	C₂²	1	8	yes	complemented
48	C₁₇×#546	C₂²	1	8	yes	complemented
49	D₄²×C₁₇	C₂²	1	4	yes	complemented
50	C₁₇×#544	C₂²	1	2	yes	complemented
51	C₁₇×#543	C₂²	1	4	yes	complemented
52	C₁₇×#542	C₂²	1	8	yes	complemented
53	C₁₇×#542	C₂²	1	4	yes	complemented
54	C₁₇×#542	C₂²	1	4	yes	complemented
55	C₁₇×#541	C₂²	1	8	yes	complemented
56	C₁₇×#541	C₂²	1	4	yes	complemented
57	C₁₇×#540	C₂²	1	4	yes	complemented
58	C₁₇×#539	C₂²	1	8	yes	complemented
59	C₁₇×#539	C₂²	1	16	yes	complemented
60	C₁₇×#539	C₂²	1	4	yes	complemented
61	C₁₇×#539	C₂²	1	8	yes	complemented
62	C₁₇×#539	C₂²	1	8	yes	complemented
63	C₁₇×#539	C₂²	1	16	yes	complemented
64	C₁₇×#539	C₂²	1	16	yes	complemented
65	C₁₇×#539	C₂²	1	4	yes	complemented
66	C₁₇×#538	C₂²	1	4	yes	complemented
67	C₁₇×#538	C₂²	1	16	yes	complemented
68	C₁₇×#538	C₂²	1	4	yes	complemented
69	C₁₇×#537	C₂²	1	2	yes	—
70	C₁₇×#536	C₂²	1	4	yes	complemented
71	C₁₇×#534	C₂²	1	4	yes	—
72	C₁₇×#534	C₂²	1	8	yes	complemented
73	C₁₇×#533	C₂²	1	8	yes	complemented
74	C₁₇×#533	C₂²	1	2	yes	complemented
75	C₁₇×#532	C₂²	1	2	yes	—
76	C₁₇×#529	C₂²	1	8	yes	complemented
77	C₁₇×#529	C₂²	1	16	yes	complemented
78	C₁₇×#529	C₂²	1	8	yes	complemented
79	C₁₇×#529	C₂²	1	8	yes	complemented
80	C₁₇×#529	C₂²	1	8	yes	complemented
81	C₁₇×#529	C₂²	1	8	yes	complemented
82	C₂×C₁₇×#126	C₂²	1	8	yes	complemented
83	C₂×C₁₇×#125	C₂²	1	8	yes	complemented
84	C₁₇×#525	C₂²	1	8	yes	complemented
85	C₁₇×#525	C₂²	1	16	yes	complemented
86	C₁₇×#525	C₂²	1	4	yes	complemented
87	C₂×C₁₇×#123	C₂²	1	8	yes	complemented
88	C₂×C₁₇×#123	C₂²	1	8	yes	complemented
89	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
90	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
91	C₂×C₁₇×#121	C₂²	1	4	yes	—
92	C₁₇×#520	C₂²	1	4	yes	complemented
93	C₁₇×#520	C₂²	1	8	yes	complemented
94	C₁₇×#520	C₂²	1	8	yes	complemented
95	C₁₇×#520	C₂²	1	8	yes	complemented
96	C₁₇×#518	C₂²	1	2	yes	—
97	C₁₇×#518	C₂²	1	8	yes	complemented
98	C₁₇×#518	C₂²	1	8	yes	complemented
99	C₄×#41×C₁₇	C₂²	1	4	yes	complemented
100	C₄×#41×C₁₇	C₂²	1	8	yes	complemented
101	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
107	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
109	C₂×C₁₇×#117	C₂²	1	2	yes	complemented
110	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
112	C₂²×C₄⋊C₄×C₁₇	C₂²	1	2	yes	complemented
113	C₁₇×H(5,𝔽₂)	—	2	16	no	—
114	C₂×#41×C₁₇	—	2	8	no	—
115	C₂×#41×C₁₇	C₂³	1	4	yes	—
116	C₂×#41×C₁₇	C₂³	1	8	yes	—
117	C₂×#41×C₁₇	C₂³	1	8	yes	—
118	C₂×#41×C₁₇	C₂³	1	8	yes	—
119	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
121	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
123	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
124	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
125	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
132	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
134	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
137	C₁₇×#127	C₂³	1	2	yes	—
138	C₁₇×#126	C₂³	1	8	yes	—
139	C₁₇×#126	C₂³	1	16	yes	—
140	C₁₇×#126	C₂³	1	16	yes	—
141	C₁₇×#126	C₂³	1	16	yes	—
142	C₁₇×#126	C₂³	1	8	yes	—
143	C₁₇×#126	C₂³	1	16	yes	—
144	C₁₇×#126	C₂³	1	8	yes	—
145	C₁₇×#126	C₂³	1	8	yes	—
146	C₁₇×#126	C₂³	1	16	yes	—
147	C₁₇×#125	C₂³	1	8	yes	—
148	C₁₇×#125	C₂³	1	16	yes	—
149	C₁₇×#125	C₂³	1	16	yes	—
150	C₁₇×#125	C₂³	1	16	yes	—
151	C₁₇×#125	C₂³	1	8	yes	—
152	C₁₇×#125	C₂³	1	8	yes	—
153	C₁₇×#125	C₂³	1	8	yes	—
154	C₁₇×#125	C₂³	1	8	yes	—
155	C₁₇×#125	C₂³	1	4	yes	—
156	C₁₇×#124	C₂³	1	8	yes	—
157	C₁₇×#124	C₂³	1	8	yes	—
158	C₁₇×#124	C₂³	1	8	yes	—
159	C₁₇×#124	C₂³	1	8	yes	—
160	C₁₇×#124	C₂³	1	8	yes	—
161	C₁₇×#124	C₂³	1	4	yes	—
162	C₁₇×#123	C₂³	1	8	yes	—
163	C₁₇×#123	C₂³	1	8	yes	—
164	C₁₇×#123	C₂³	1	16	yes	—
165	C₁₇×#123	C₂³	1	16	yes	—
166	C₁₇×#123	C₂³	1	16	yes	—
167	C₁₇×#123	C₂³	1	16	yes	—
168	C₁₇×#123	C₂³	1	16	yes	—
169	C₁₇×#123	C₂³	1	16	yes	—
170	C₁₇×#123	C₂³	1	8	yes	—
171	C₁₇×#123	C₂³	1	16	yes	—
172	C₁₇×#123	C₂³	1	16	yes	—
173	C₁₇×#123	C₂³	1	16	yes	—
174	C₁₇×#123	C₂³	1	8	yes	—
175	C₁₇×#123	C₂³	1	8	yes	—
176	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
182	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
183	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
184	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
185	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
186	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
188	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
189	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₁₇×C₂²⋊Q₈	C₂³	1	16	yes	—
191	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₁₇×#121	C₂³	1	4	yes	—
195	C₁₇×#121	C₂³	1	8	yes	—
196	C₁₇×#121	C₂³	1	8	yes	—
197	C₁₇×#121	C₂³	1	8	yes	—
198	C₁₇×#121	C₂³	1	8	yes	—
199	C₁₇×#121	C₂³	1	16	yes	—
200	C₁₇×#121	C₂³	1	8	yes	—
201	C₁₇×#121	C₂³	1	4	yes	—
202	C₁₇×#121	C₂³	1	4	yes	—
203	C₁₇×#121	C₂³	1	4	yes	—
204	C₁₇×#121	C₂³	1	16	yes	—
205	C₁₇×#121	C₂³	1	8	yes	—
206	C₁₇×#121	C₂³	1	8	yes	—
207	C₁₇×#120	C₂³	1	8	yes	—
208	C₁₇×#120	C₂³	1	16	yes	—
209	C₁₇×#120	C₂³	1	16	yes	—
210	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
211	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
212	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
213	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
214	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
215	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
216	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
217	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
218	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
219	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
220	C₄×D₄×C₁₇	C₂³	1	8	yes	—
221	C₄×D₄×C₁₇	C₂³	1	4	yes	—
222	C₄×D₄×C₁₇	C₂³	1	4	yes	—
223	C₄×D₄×C₁₇	C₂³	1	8	yes	—
224	C₄×D₄×C₁₇	C₂³	1	16	yes	—
225	C₄×D₄×C₁₇	C₂³	1	4	yes	—
226	C₄×D₄×C₁₇	C₂³	1	8	yes	—
227	C₄×D₄×C₁₇	C₂³	1	16	yes	—
228	C₄×D₄×C₁₇	C₂³	1	16	yes	—
229	C₄×D₄×C₁₇	C₂³	1	8	yes	—
230	C₄×D₄×C₁₇	C₂³	1	16	yes	—
231	C₄×D₄×C₁₇	C₂³	1	16	yes	—
232	C₄×D₄×C₁₇	C₂³	1	8	yes	—
233	C₄×D₄×C₁₇	C₂³	1	8	yes	—
234	C₄×D₄×C₁₇	C₂³	1	8	yes	—
235	C₄×D₄×C₁₇	C₂³	1	8	yes	—
236	C₄×D₄×C₁₇	C₂³	1	4	yes	—
237	C₄×D₄×C₁₇	C₂³	1	16	yes	—
238	C₄×D₄×C₁₇	C₂³	1	8	yes	—
239	C₄×D₄×C₁₇	C₂³	1	16	yes	—
240	C₄×D₄×C₁₇	C₂³	1	8	yes	—
241	C₄×D₄×C₁₇	C₂³	1	8	yes	—
242	C₄×D₄×C₁₇	C₂³	1	8	yes	—
243	C₄×D₄×C₁₇	C₂³	1	4	yes	—
244	C₄×D₄×C₁₇	C₂³	1	4	yes	—
245	C₁₇×#117	C₂³	1	4	yes	—
246	C₁₇×#117	C₂³	1	4	yes	—
247	C₁₇×#117	C₂³	1	16	yes	—
248	C₁₇×#117	C₂³	1	4	yes	—
249	C₁₇×#117	C₂³	1	8	yes	—
250	C₁₇×#117	C₂³	1	16	yes	—
251	C₁₇×#117	C₂³	1	8	yes	—
252	C₁₇×#117	C₂³	1	16	yes	—
253	C₁₇×#117	C₂³	1	8	yes	—
254	C₁₇×#117	C₂³	1	16	yes	—
255	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
262	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
263	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
264	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
266	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
267	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
268	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
269	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
270	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
271	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
272	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
277	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
278	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
279	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
280	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
281	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
282	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
285	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
286	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
287	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
288	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
289	C₂⁴×C₁₇	C₂⁴	1	8	yes	—
290	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
291	#41×C₁₇	—	2	32	no	—
292	#41×C₁₇	—	2	32	no	—
293	#41×C₁₇	—	2	16	no	—
294	#41×C₁₇	—	8	8	no	—
295	C₂×Q₈×C₁₇	—	2	4	no	—
296	C₂×Q₈×C₁₇	—	8	4	no	—
297	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₁₇	C₂⁴	1	8	yes	—
301	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
302	C₂×D₄×C₁₇	—	2	8	no	—
303	C₂×D₄×C₁₇	—	2	32	no	—
304	C₂×D₄×C₁₇	—	2	32	no	—
305	C₂×D₄×C₁₇	—	8	4	no	—
306	C₂×D₄×C₁₇	#41	1	8	yes	complemented
307	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
308	C₂×D₄×C₁₇	C₂⁴	1	16	yes	—
309	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
310	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
311	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
312	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
313	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
314	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
315	C₂×D₄×C₁₇	C₂⁴	1	8	yes	—
316	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₁₇	—	2	8	no	—
318	C₂²×C₄×C₁₇	—	2	4	no	—
319	C₂²×C₄×C₁₇	—	8	2	no	—
320	C₂²×C₄×C₁₇	—	8	8	no	—
321	C₂²×C₄×C₁₇	—	8	2	no	—
322	C₂²×C₄×C₁₇	—	8	2	no	—
323	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
325	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
328	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
329	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
333	C₂²×C₄×C₁₇	C₂⁴	1	16	yes	—
334	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
338	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
340	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
343	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
346	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
347	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
348	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
349	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
350	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
352	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
354	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
355	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
356	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
357	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
358	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
359	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
360	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
361	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
364	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₁₇	C₂⁴	1	16	yes	—
366	C₄⋊C₄×C₁₇	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
372	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
373	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
374	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
375	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
376	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
377	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
383	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₁₇	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₁₇	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₁₇	C₂⁴	1	4	yes	—
388	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
389	C₂²⋊C₄×C₁₇	C₂⁴	1	2	yes	—
390	C₂²⋊C₄×C₁₇	C₂⁴	1	8	yes	—
391	C₄²×C₁₇	C₂⁴	1	2	yes	—
392	C₄²×C₁₇	C₂⁴	1	8	yes	—
393	C₄²×C₁₇	C₂⁴	1	8	yes	—
394	C₄²×C₁₇	C₂⁴	1	8	yes	—
395	C₄²×C₁₇	C₂⁴	1	8	yes	—
396	C₄²×C₁₇	C₂⁴	1	8	yes	—
397	C₄²×C₁₇	C₂⁴	1	16	yes	—
398	C₄²×C₁₇	C₂⁴	1	2	yes	—
399	C₄²×C₁₇	C₂⁴	1	4	yes	—
400	#62847	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₁₇	—	2	2	no	—
402	C₂³×C₁₇	—	2	16	no	—
403	C₂³×C₁₇	—	4	2	no	—
404	C₂³×C₁₇	—	4	1	no	—
405	C₂³×C₁₇	—	4	2	no	—
406	C₂³×C₁₇	—	4	1	no	—
407	C₂³×C₁₇	—	4	8	no	—
408	C₂³×C₁₇	—	4	8	no	—
409	C₂³×C₁₇	C₂×#41	1	8	yes	—
410	C₂³×C₁₇	C₂⁵	1	8	yes	—
411	C₂³×C₁₇	C₂⁵	1	2	yes	—
412	C₂³×C₁₇	C₂⁵	1	4	yes	—
413	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
414	Q₈×C₁₇	—	2	8	no	—
415	Q₈×C₁₇	—	2	8	no	—
416	Q₈×C₁₇	—	4	4	no	—
417	Q₈×C₁₇	—	4	8	no	—
418	Q₈×C₁₇	—	4	4	no	—
419	D₄×C₁₇	—	2	32	no	—
420	D₄×C₁₇	—	2	16	no	—
421	D₄×C₁₇	—	2	16	no	—
422	D₄×C₁₇	—	2	8	no	—
423	D₄×C₁₇	—	4	4	no	—
424	D₄×C₁₇	—	4	8	no	—
425	D₄×C₁₇	—	4	8	no	—
426	D₄×C₁₇	—	4	4	no	—
427	D₄×C₁₇	—	4	8	no	—
428	D₄×C₁₇	C₂×#41	1	16	yes	—
429	C₂×C₄×C₁₇	—	2	2	no	—
430	C₂×C₄×C₁₇	—	2	4	no	—
431	C₂×C₄×C₁₇	—	2	16	no	—
432	C₂×C₄×C₁₇	—	2	16	no	—
433	C₂×C₄×C₁₇	—	2	8	no	—
434	C₂×C₄×C₁₇	—	2	16	no	—
435	C₂×C₄×C₁₇	—	4	1	no	—
436	C₂×C₄×C₁₇	—	4	8	no	—
437	C₂×C₄×C₁₇	—	4	2	no	—
438	C₂×C₄×C₁₇	—	4	8	no	—
439	C₂×C₄×C₁₇	—	4	1	no	—
440	C₂×C₄×C₁₇	—	4	2	no	—
441	C₂×C₄×C₁₇	—	4	4	no	—
442	C₂×C₄×C₁₇	—	4	4	no	—
443	C₂×C₄×C₁₇	—	4	8	no	—
444	C₂×C₄×C₁₇	—	4	8	no	—
445	C₂×C₄×C₁₇	—	4	16	no	—
446	C₂×C₄×C₁₇	—	4	1	no	—
447	C₂×C₄×C₁₇	—	4	8	no	—
448	C₂×C₄×C₁₇	—	4	8	no	—
449	C₂×C₄×C₁₇	—	4	1	no	—
450	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
451	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
452	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
453	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
454	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
455	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
456	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
457	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
458	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
459	C₂×C₄×C₁₇	C₂⁵	1	8	yes	—
460	C₂×C₄×C₁₇	C₂⁵	1	4	yes	—
461	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
462	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
463	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
464	#3521	C₂×C₁₇	1	8	yes	complemented
465	#3520	C₂×C₁₇	1	8	yes	complemented
466	#3515	C₂×C₁₇	1	8	yes	complemented
467	#3513	C₂×C₁₇	1	8	yes	complemented
468	#3507	C₂×C₁₇	1	2	yes	complemented
469	#3505	C₂×C₁₇	1	4	yes	complemented
470	#3501	C₂×C₁₇	1	1	yes	characteristic, complemented
471	#3496	C₂×C₁₇	1	1	yes	characteristic, complemented
472	#3492	C₂×C₁₇	1	2	yes	complemented
473	#3491	C₂×C₁₇	1	4	yes	complemented
474	#3485	C₂×C₁₇	1	2	yes	complemented
475	#3461	C₂×C₁₇	1	2	yes	complemented
476	#3459	C₂×C₁₇	1	4	yes	complemented
477	#3455	C₂×C₁₇	1	2	yes	complemented
478	C₂×#539	C₂×C₁₇	1	4	yes	complemented
479	C₄×H(5,𝔽₂)	C₂×C₁₇	1	2	yes	complemented
480	C₂×#520	C₂×C₁₇	1	1	yes	characteristic, complemented
481	C₂²×C₁₇	—	2	1	no	—
482	C₂²×C₁₇	—	2	4	no	—
483	C₂²×C₁₇	—	2	1	no	—
484	C₂²×C₁₇	—	2	4	no	—
485	C₂²×C₁₇	—	2	2	no	—
486	C₂²×C₁₇	—	2	8	no	—
487	C₂²×C₁₇	—	2	2	no	—
488	C₂²×C₁₇	—	2	8	no	—
489	C₂²×C₁₇	—	2	8	no	—
490	C₂²×C₁₇	—	2	2	no	—
491	C₂²×C₁₇	—	4	8	no	—
492	C₂²×C₁₇	—	4	4	no	—
493	C₂²×C₁₇	—	8	16	no	—
494	C₂²×C₁₇	C₂²×#41	1	8	yes	—
495	C₂²×C₁₇	C₂²×#41	1	2	yes	—
496	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
497	C₄×C₁₇	—	2	2	no	—
498	C₄×C₁₇	—	2	8	no	—
499	C₄×C₁₇	—	2	4	no	—
500	C₄×C₁₇	—	2	2	no	—
501	C₄×C₁₇	—	2	4	no	—
502	C₄×C₁₇	—	2	1	no	—
503	C₄×C₁₇	—	2	4	no	—
504	C₄×C₁₇	—	2	8	no	—
505	C₄×C₁₇	—	2	1	no	—
506	C₄×C₁₇	—	2	2	no	—
507	C₄×C₁₇	—	2	8	no	—
508	C₄×C₁₇	—	2	2	no	—
509	C₄×C₁₇	C₂²×#41	1	4	yes	—
510	C₂×H(5,𝔽₂)	C₂²×C₁₇	1	2	yes	—
511	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
512	#559	C₂²×C₁₇	1	4	yes	complemented
513	#557	C₂²×C₁₇	1	4	yes	complemented
514	#556	C₂²×C₁₇	1	8	yes	complemented
515	#556	C₂²×C₁₇	1	4	yes	complemented
516	#554	C₂²×C₁₇	1	8	yes	complemented
517	#554	C₂²×C₁₇	1	8	yes	complemented
518	#554	C₂²×C₁₇	1	4	yes	complemented
519	#554	C₂²×C₁₇	1	4	yes	complemented
520	#553	C₂²×C₁₇	1	8	yes	complemented
521	#553	C₂²×C₁₇	1	16	yes	complemented
522	#553	C₂²×C₁₇	1	8	yes	complemented
523	#552	C₂²×C₁₇	1	16	yes	complemented
524	#552	C₂²×C₁₇	1	16	yes	complemented
525	#552	C₂²×C₁₇	1	8	yes	complemented
526	#552	C₂²×C₁₇	1	8	yes	complemented
527	#552	C₂²×C₁₇	1	8	yes	complemented
528	#551	C₂²×C₁₇	1	16	yes	complemented
529	#551	C₂²×C₁₇	1	16	yes	complemented
530	#551	C₂²×C₁₇	1	16	yes	complemented
531	D₄×Q₈	C₂²×C₁₇	1	4	yes	complemented
532	#548	C₂²×C₁₇	1	8	yes	complemented
533	#547	C₂²×C₁₇	1	8	yes	complemented
534	#547	C₂²×C₁₇	1	8	yes	complemented
535	#547	C₂²×C₁₇	1	8	yes	complemented
536	#547	C₂²×C₁₇	1	4	yes	complemented
537	#546	C₂²×C₁₇	1	8	yes	complemented
538	#546	C₂²×C₁₇	1	8	yes	complemented
539	#546	C₂²×C₁₇	1	8	yes	complemented
540	#546	C₂²×C₁₇	1	8	yes	complemented
541	D₄²	C₂²×C₁₇	1	4	yes	complemented
542	#544	C₂²×C₁₇	1	2	yes	complemented
543	#543	C₂²×C₁₇	1	4	yes	complemented
544	#542	C₂²×C₁₇	1	4	yes	complemented
545	#542	C₂²×C₁₇	1	4	yes	complemented
546	#542	C₂²×C₁₇	1	8	yes	complemented
547	#541	C₂²×C₁₇	1	4	yes	complemented
548	#541	C₂²×C₁₇	1	8	yes	complemented
549	#540	C₂²×C₁₇	1	4	yes	complemented
550	#539	C₂²×C₁₇	1	4	yes	complemented
551	#539	C₂²×C₁₇	1	8	yes	complemented
552	#539	C₂²×C₁₇	1	8	yes	complemented
553	#539	C₂²×C₁₇	1	8	yes	complemented
554	#539	C₂²×C₁₇	1	16	yes	complemented
555	#539	C₂²×C₁₇	1	16	yes	complemented
556	#539	C₂²×C₁₇	1	4	yes	complemented
557	#539	C₂²×C₁₇	1	16	yes	complemented
558	#538	C₂²×C₁₇	1	4	yes	complemented
559	#538	C₂²×C₁₇	1	4	yes	complemented
560	#538	C₂²×C₁₇	1	16	yes	complemented
561	#537	C₂²×C₁₇	1	2	yes	—
562	#536	C₂²×C₁₇	1	4	yes	complemented
563	#534	C₂²×C₁₇	1	4	yes	—
564	#534	C₂²×C₁₇	1	8	yes	complemented
565	#533	C₂²×C₁₇	1	2	yes	complemented
566	#533	C₂²×C₁₇	1	8	yes	complemented
567	#532	C₂²×C₁₇	1	2	yes	—
568	#529	C₂²×C₁₇	1	8	yes	complemented
569	#529	C₂²×C₁₇	1	8	yes	complemented
570	#529	C₂²×C₁₇	1	8	yes	complemented
571	#529	C₂²×C₁₇	1	16	yes	complemented
572	#529	C₂²×C₁₇	1	8	yes	complemented
573	#529	C₂²×C₁₇	1	8	yes	complemented
574	C₂×#126	C₂²×C₁₇	1	8	yes	complemented
575	C₂×#125	C₂²×C₁₇	1	8	yes	complemented
576	#525	C₂²×C₁₇	1	4	yes	complemented
577	#525	C₂²×C₁₇	1	8	yes	complemented
578	#525	C₂²×C₁₇	1	16	yes	complemented
579	C₂×#123	C₂²×C₁₇	1	8	yes	complemented
580	C₂×#123	C₂²×C₁₇	1	8	yes	complemented
581	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	4	yes	complemented
582	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	8	yes	complemented
583	C₂×#121	C₂²×C₁₇	1	4	yes	—
584	#520	C₂²×C₁₇	1	8	yes	complemented
585	#520	C₂²×C₁₇	1	8	yes	complemented
586	#520	C₂²×C₁₇	1	4	yes	complemented
587	#520	C₂²×C₁₇	1	8	yes	complemented
588	#518	C₂²×C₁₇	1	2	yes	—
589	#518	C₂²×C₁₇	1	8	yes	complemented
590	#518	C₂²×C₁₇	1	8	yes	complemented
591	C₄×#41	C₂²×C₁₇	1	4	yes	complemented
592	C₄×#41	C₂²×C₁₇	1	8	yes	complemented
593	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
594	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
595	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
596	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
597	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	complemented
598	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	complemented
599	C₂×C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
600	C₂×C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
601	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic, complemented
602	C₂×#117	C₂²×C₁₇	1	2	yes	complemented
603	C₂²×C₄⋊C₄	C₂²×C₁₇	1	2	yes	complemented
604	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
605	C₂×C₁₇	—	2	2	no	—
606	C₂×C₁₇	—	2	8	no	—
607	C₂×C₁₇	—	4	2	no	—
608	C₂×C₁₇	—	4	8	no	—
609	C₂×C₁₇	C₂³×#41	1	1	yes	characteristic
610	C₂×C₁₇	H(7,𝔽₂)	1	1	yes	characteristic
611	C₂×C₁₇	2₋¹⁺⁶	1	1	yes	characteristic
612	H(5,𝔽₂)	—	2	16	no	—
613	C₂×#41	—	2	8	no	—
614	C₂×#41	C₂³×C₁₇	1	4	yes	—
615	C₂×#41	C₂³×C₁₇	1	8	yes	—
616	C₂×#41	C₂³×C₁₇	1	8	yes	—
617	C₂×#41	C₂³×C₁₇	1	8	yes	—
618	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
620	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
621	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
622	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
623	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
624	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
626	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
628	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
629	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
630	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
631	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
632	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
633	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
635	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
636	#127	C₂³×C₁₇	1	2	yes	—
637	#126	C₂³×C₁₇	1	8	yes	—
638	#126	C₂³×C₁₇	1	16	yes	—
639	#126	C₂³×C₁₇	1	16	yes	—
640	#126	C₂³×C₁₇	1	16	yes	—
641	#126	C₂³×C₁₇	1	8	yes	—
642	#126	C₂³×C₁₇	1	16	yes	—
643	#126	C₂³×C₁₇	1	8	yes	—
644	#126	C₂³×C₁₇	1	8	yes	—
645	#126	C₂³×C₁₇	1	16	yes	—
646	#125	C₂³×C₁₇	1	8	yes	—
647	#125	C₂³×C₁₇	1	16	yes	—
648	#125	C₂³×C₁₇	1	16	yes	—
649	#125	C₂³×C₁₇	1	16	yes	—
650	#125	C₂³×C₁₇	1	8	yes	—
651	#125	C₂³×C₁₇	1	8	yes	—
652	#125	C₂³×C₁₇	1	8	yes	—
653	#125	C₂³×C₁₇	1	8	yes	—
654	#125	C₂³×C₁₇	1	4	yes	—
655	#124	C₂³×C₁₇	1	8	yes	—
656	#124	C₂³×C₁₇	1	8	yes	—
657	#124	C₂³×C₁₇	1	8	yes	—
658	#124	C₂³×C₁₇	1	8	yes	—
659	#124	C₂³×C₁₇	1	8	yes	—
660	#124	C₂³×C₁₇	1	4	yes	—
661	#123	C₂³×C₁₇	1	8	yes	—
662	#123	C₂³×C₁₇	1	8	yes	—
663	#123	C₂³×C₁₇	1	16	yes	—
664	#123	C₂³×C₁₇	1	16	yes	—
665	#123	C₂³×C₁₇	1	16	yes	—
666	#123	C₂³×C₁₇	1	16	yes	—
667	#123	C₂³×C₁₇	1	16	yes	—
668	#123	C₂³×C₁₇	1	16	yes	—
669	#123	C₂³×C₁₇	1	8	yes	—
670	#123	C₂³×C₁₇	1	16	yes	—
671	#123	C₂³×C₁₇	1	16	yes	—
672	#123	C₂³×C₁₇	1	16	yes	—
673	#123	C₂³×C₁₇	1	8	yes	—
674	#123	C₂³×C₁₇	1	8	yes	—
675	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
676	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
677	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
678	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
679	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
680	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
681	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
682	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
683	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
685	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
686	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
687	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
688	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
689	C₂²⋊Q₈	C₂³×C₁₇	1	16	yes	—
690	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
693	#121	C₂³×C₁₇	1	4	yes	—
694	#121	C₂³×C₁₇	1	8	yes	—
695	#121	C₂³×C₁₇	1	8	yes	—
696	#121	C₂³×C₁₇	1	8	yes	—
697	#121	C₂³×C₁₇	1	8	yes	—
698	#121	C₂³×C₁₇	1	16	yes	—
699	#121	C₂³×C₁₇	1	8	yes	—
700	#121	C₂³×C₁₇	1	4	yes	—
701	#121	C₂³×C₁₇	1	4	yes	—
702	#121	C₂³×C₁₇	1	4	yes	—
703	#121	C₂³×C₁₇	1	16	yes	—
704	#121	C₂³×C₁₇	1	8	yes	—
705	#121	C₂³×C₁₇	1	8	yes	—
706	#120	C₂³×C₁₇	1	8	yes	—
707	#120	C₂³×C₁₇	1	16	yes	—
708	#120	C₂³×C₁₇	1	16	yes	—
709	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
710	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
711	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
712	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
713	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
714	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
715	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
716	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
717	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
718	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
719	C₄×D₄	C₂³×C₁₇	1	8	yes	—
720	C₄×D₄	C₂³×C₁₇	1	4	yes	—
721	C₄×D₄	C₂³×C₁₇	1	4	yes	—
722	C₄×D₄	C₂³×C₁₇	1	8	yes	—
723	C₄×D₄	C₂³×C₁₇	1	16	yes	—
724	C₄×D₄	C₂³×C₁₇	1	4	yes	—
725	C₄×D₄	C₂³×C₁₇	1	8	yes	—
726	C₄×D₄	C₂³×C₁₇	1	16	yes	—
727	C₄×D₄	C₂³×C₁₇	1	16	yes	—
728	C₄×D₄	C₂³×C₁₇	1	8	yes	—
729	C₄×D₄	C₂³×C₁₇	1	16	yes	—
730	C₄×D₄	C₂³×C₁₇	1	16	yes	—
731	C₄×D₄	C₂³×C₁₇	1	8	yes	—
732	C₄×D₄	C₂³×C₁₇	1	8	yes	—
733	C₄×D₄	C₂³×C₁₇	1	8	yes	—
734	C₄×D₄	C₂³×C₁₇	1	8	yes	—
735	C₄×D₄	C₂³×C₁₇	1	4	yes	—
736	C₄×D₄	C₂³×C₁₇	1	16	yes	—
737	C₄×D₄	C₂³×C₁₇	1	8	yes	—
738	C₄×D₄	C₂³×C₁₇	1	16	yes	—
739	C₄×D₄	C₂³×C₁₇	1	8	yes	—
740	C₄×D₄	C₂³×C₁₇	1	8	yes	—
741	C₄×D₄	C₂³×C₁₇	1	8	yes	—
742	C₄×D₄	C₂³×C₁₇	1	4	yes	—
743	C₄×D₄	C₂³×C₁₇	1	4	yes	—
744	#117	C₂³×C₁₇	1	4	yes	—
745	#117	C₂³×C₁₇	1	4	yes	—
746	#117	C₂³×C₁₇	1	16	yes	—
747	#117	C₂³×C₁₇	1	4	yes	—
748	#117	C₂³×C₁₇	1	8	yes	—
749	#117	C₂³×C₁₇	1	16	yes	—
750	#117	C₂³×C₁₇	1	8	yes	—
751	#117	C₂³×C₁₇	1	16	yes	—
752	#117	C₂³×C₁₇	1	8	yes	—
753	#117	C₂³×C₁₇	1	16	yes	—
754	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
761	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
763	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
765	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
770	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
781	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
784	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
785	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
786	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
787	C₁₇	#62847	1	1	yes	characteristic, direct product factor, Sylow
788	C₂⁴	C₂⁴×C₁₇	1	8	yes	—
789	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
791	#41	—	2	32	no	—
792	#41	—	2	32	no	—
793	#41	—	2	16	no	—
794	#41	—	8	8	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	8	4	no	—
797	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
798	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
799	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
800	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
801	C₂×Q₈	C₂⁴×C₁₇	1	8	yes	—
802	C₂×D₄	—	2	8	no	—
803	C₂×D₄	—	2	32	no	—
804	C₂×D₄	—	2	32	no	—
805	C₂×D₄	—	8	4	no	—
806	C₂×D₄	#41×C₁₇	1	8	yes	complemented
807	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
808	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
809	C₂×D₄	C₂⁴×C₁₇	1	16	yes	—
810	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
811	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
812	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
813	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
814	C₂×D₄	C₂⁴×C₁₇	1	8	yes	—
815	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
816	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
817	C₂²×C₄	—	2	8	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	8	2	no	—
820	C₂²×C₄	—	8	8	no	—
821	C₂²×C₄	—	8	2	no	—
822	C₂²×C₄	—	8	2	no	—
823	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
825	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
826	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
827	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
832	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
833	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
836	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
839	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
841	C₂²×C₄	C₂⁴×C₁₇	1	16	yes	—
842	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
843	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
844	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
845	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
846	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
850	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
851	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
852	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
853	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
855	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
856	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
857	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
859	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
864	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
865	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
866	C₄⋊C₄	C₂⁴×C₁₇	1	16	yes	—
867	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
869	C₄⋊C₄	C₂⁴×C₁₇	1	8	yes	—
870	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
871	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
872	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₁₇	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
876	C₂²⋊C₄	C₂⁴×C₁₇	1	16	yes	—
877	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
878	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
879	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₁₇	1	2	yes	—
883	C₂²⋊C₄	C₂⁴×C₁₇	1	4	yes	—
884	C₂²⋊C₄	C₂⁴×C₁₇	1	2	yes	—
885	C₂²⋊C₄	C₂⁴×C₁₇	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₁₇	1	16	yes	—
887	C₂²⋊C₄	C₂⁴×C₁₇	1	16	yes	—
888	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
889	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₁₇	1	8	yes	—
891	C₄²	C₂⁴×C₁₇	1	4	yes	—
892	C₄²	C₂⁴×C₁₇	1	8	yes	—
893	C₄²	C₂⁴×C₁₇	1	16	yes	—
894	C₄²	C₂⁴×C₁₇	1	8	yes	—
895	C₄²	C₂⁴×C₁₇	1	8	yes	—
896	C₄²	C₂⁴×C₁₇	1	8	yes	—
897	C₄²	C₂⁴×C₁₇	1	8	yes	—
898	C₄²	C₂⁴×C₁₇	1	2	yes	—
899	C₄²	C₂⁴×C₁₇	1	2	yes	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	16	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	2	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	8	no	—
908	C₂³	C₂×#41×C₁₇	1	8	yes	—
909	C₂³	C₂⁵×C₁₇	1	8	yes	—
910	C₂³	C₂⁵×C₁₇	1	2	yes	—
911	C₂³	C₂⁵×C₁₇	1	4	yes	—
912	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
913	Q₈	—	2	8	no	—
914	Q₈	—	2	8	no	—
915	Q₈	—	4	4	no	—
916	Q₈	—	4	8	no	—
917	Q₈	—	4	4	no	—
918	D₄	—	2	32	no	—
919	D₄	—	2	16	no	—
920	D₄	—	2	16	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	8	no	—
925	D₄	—	4	8	no	—
926	D₄	—	4	4	no	—
927	D₄	C₂×#41×C₁₇	1	16	yes	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	2	16	no	—
931	C₂×C₄	—	2	16	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	16	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	8	no	—
943	C₂×C₄	—	4	8	no	—
944	C₂×C₄	—	4	16	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	8	no	—
947	C₂×C₄	—	4	8	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
950	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
951	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
952	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
953	C₂×C₄	C₂⁵×C₁₇	1	4	yes	—
954	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
955	C₂×C₄	C₂⁵×C₁₇	1	4	yes	—
956	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
957	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
958	C₂×C₄	C₂⁵×C₁₇	1	8	yes	—
959	C₂×C₄	C₂⁵×C₁₇	1	4	yes	—
960	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
962	C₂×C₄	C₂⁵×C₁₇	1	2	yes	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	4	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	8	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	8	no	—
971	C₂²	—	2	8	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	4	8	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	8	16	no	—
976	C₂²	C₂²×#41×C₁₇	1	8	yes	—
977	C₂²	C₂²×#41×C₁₇	1	2	yes	—
978	C₂²	C₂⁶×C₁₇	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	8	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	4	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	4	no	—
986	C₄	—	2	8	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	8	no	—
990	C₄	—	2	2	no	—
991	C₄	C₂²×#41×C₁₇	1	4	yes	—
992	C₂	—	2	2	no	—
993	C₂	—	2	8	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	8	no	—
996	C₂	C₂³×#41×C₁₇	1	1	yes	characteristic
997	C₂	C₁₇×H(7,𝔽₂)	1	1	yes	characteristic
998	C₂	C₁₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3521	C₂	semidirect
2. C₁₇×#3520	C₂	semidirect
3. C₁₇×#3515	C₂	semidirect
4. C₁₇×#3513	C₂	semidirect
5. C₁₇×#3507	C₂	semidirect
6. C₁₇×#3505	C₂	semidirect
7. C₁₇×#3501	C₂	semidirect
8. C₁₇×#3496	C₂	semidirect
9. C₁₇×#3492	C₂	semidirect
10. C₁₇×#3491	C₂	semidirect
11. C₁₇×#3485	C₂	semidirect
12. C₁₇×#3461	C₂	semidirect
13. C₁₇×#3459	C₂	semidirect
14. C₁₇×#3455	C₂	semidirect
15. C₂×C₁₇×#539	C₂	semidirect
16. C₄×C₁₇×H(5,𝔽₂)	C₂	semidirect
17. C₂×C₁₇×#520	C₂	semidirect
20. C₁₇×#559	C₂²	semidirect
21. C₁₇×#557	C₂²	semidirect
22. C₁₇×#556	C₂²	semidirect
23. C₁₇×#556	C₂²	semidirect
24. C₁₇×#554	C₂²	semidirect
25. C₁₇×#554	C₂²	semidirect
26. C₁₇×#554	C₂²	semidirect
27. C₁₇×#554	C₂²	semidirect
28. C₁₇×#553	C₂²	semidirect
29. C₁₇×#553	C₂²	semidirect
30. C₁₇×#553	C₂²	semidirect
31. C₁₇×#552	C₂²	semidirect
32. C₁₇×#552	C₂²	semidirect
33. C₁₇×#552	C₂²	semidirect
34. C₁₇×#552	C₂²	semidirect
35. C₁₇×#552	C₂²	semidirect
36. C₁₇×#551	C₂²	semidirect
37. C₁₇×#551	C₂²	semidirect
38. C₁₇×#551	C₂²	semidirect
39. D₄×Q₈×C₁₇	C₂²	semidirect
40. C₁₇×#548	C₂²	semidirect
41. C₁₇×#547	C₂²	semidirect
42. C₁₇×#547	C₂²	semidirect
43. C₁₇×#547	C₂²	semidirect
44. C₁₇×#547	C₂²	semidirect
45. C₁₇×#546	C₂²	semidirect
46. C₁₇×#546	C₂²	semidirect
47. C₁₇×#546	C₂²	semidirect
48. C₁₇×#546	C₂²	semidirect
49. D₄²×C₁₇	C₂²	semidirect
50. C₁₇×#544	C₂²	semidirect
51. C₁₇×#543	C₂²	semidirect
52. C₁₇×#542	C₂²	semidirect
53. C₁₇×#542	C₂²	semidirect
54. C₁₇×#542	C₂²	semidirect
55. C₁₇×#541	C₂²	semidirect
56. C₁₇×#541	C₂²	semidirect
57. C₁₇×#540	C₂²	semidirect
58. C₁₇×#539	C₂²	semidirect
59. C₁₇×#539	C₂²	semidirect
60. C₁₇×#539	C₂²	semidirect
61. C₁₇×#539	C₂²	semidirect
62. C₁₇×#539	C₂²	semidirect
63. C₁₇×#539	C₂²	semidirect
64. C₁₇×#539	C₂²	semidirect
65. C₁₇×#539	C₂²	semidirect
66. C₁₇×#538	C₂²	semidirect
67. C₁₇×#538	C₂²	semidirect
68. C₁₇×#538	C₂²	semidirect
70. C₁₇×#536	C₂²	semidirect
72. C₁₇×#534	C₂²	semidirect
73. C₁₇×#533	C₂²	semidirect
74. C₁₇×#533	C₂²	semidirect
76. C₁₇×#529	C₂²	semidirect
77. C₁₇×#529	C₂²	semidirect
78. C₁₇×#529	C₂²	semidirect
79. C₁₇×#529	C₂²	semidirect
80. C₁₇×#529	C₂²	semidirect
81. C₁₇×#529	C₂²	semidirect
82. C₂×C₁₇×#126	C₂²	semidirect
83. C₂×C₁₇×#125	C₂²	semidirect
84. C₁₇×#525	C₂²	semidirect
85. C₁₇×#525	C₂²	semidirect
86. C₁₇×#525	C₂²	semidirect
87. C₂×C₁₇×#123	C₂²	semidirect
88. C₂×C₁₇×#123	C₂²	semidirect
89. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
92. C₁₇×#520	C₂²	semidirect
93. C₁₇×#520	C₂²	semidirect
94. C₁₇×#520	C₂²	semidirect
95. C₁₇×#520	C₂²	semidirect
97. C₁₇×#518	C₂²	semidirect
98. C₁₇×#518	C₂²	semidirect
99. C₄×#41×C₁₇	C₂²	semidirect
100. C₄×#41×C₁₇	C₂²	semidirect
101. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
102. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
105. C₂×C₄×D₄×C₁₇	C₂²	semidirect
106. C₂×C₄×D₄×C₁₇	C₂²	semidirect
107. C₂×C₄×D₄×C₁₇	C₂²	semidirect
108. C₂×C₄×D₄×C₁₇	C₂²	semidirect
109. C₂×C₁₇×#117	C₂²	semidirect
110. C₂×C₁₇×#117	C₂²	semidirect
111. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
112. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
306. C₂×D₄×C₁₇	#41	semidirect
400. #62847	C₁₇	direct (N × H)
464. #3521	C₂×C₁₇	semidirect
465. #3520	C₂×C₁₇	semidirect
466. #3515	C₂×C₁₇	semidirect
467. #3513	C₂×C₁₇	semidirect
468. #3507	C₂×C₁₇	semidirect
469. #3505	C₂×C₁₇	semidirect
470. #3501	C₂×C₁₇	semidirect
471. #3496	C₂×C₁₇	semidirect
472. #3492	C₂×C₁₇	semidirect
473. #3491	C₂×C₁₇	semidirect
474. #3485	C₂×C₁₇	semidirect
475. #3461	C₂×C₁₇	semidirect
476. #3459	C₂×C₁₇	semidirect
477. #3455	C₂×C₁₇	semidirect
478. C₂×#539	C₂×C₁₇	semidirect
479. C₄×H(5,𝔽₂)	C₂×C₁₇	semidirect
480. C₂×#520	C₂×C₁₇	semidirect
512. #559	C₂²×C₁₇	semidirect
513. #557	C₂²×C₁₇	semidirect
514. #556	C₂²×C₁₇	semidirect
515. #556	C₂²×C₁₇	semidirect
516. #554	C₂²×C₁₇	semidirect
517. #554	C₂²×C₁₇	semidirect
518. #554	C₂²×C₁₇	semidirect
519. #554	C₂²×C₁₇	semidirect
520. #553	C₂²×C₁₇	semidirect
521. #553	C₂²×C₁₇	semidirect
522. #553	C₂²×C₁₇	semidirect
523. #552	C₂²×C₁₇	semidirect
524. #552	C₂²×C₁₇	semidirect
525. #552	C₂²×C₁₇	semidirect
526. #552	C₂²×C₁₇	semidirect
527. #552	C₂²×C₁₇	semidirect
528. #551	C₂²×C₁₇	semidirect
529. #551	C₂²×C₁₇	semidirect
530. #551	C₂²×C₁₇	semidirect
531. D₄×Q₈	C₂²×C₁₇	semidirect
532. #548	C₂²×C₁₇	semidirect
533. #547	C₂²×C₁₇	semidirect
534. #547	C₂²×C₁₇	semidirect
535. #547	C₂²×C₁₇	semidirect
536. #547	C₂²×C₁₇	semidirect
537. #546	C₂²×C₁₇	semidirect
538. #546	C₂²×C₁₇	semidirect
539. #546	C₂²×C₁₇	semidirect
540. #546	C₂²×C₁₇	semidirect
541. D₄²	C₂²×C₁₇	semidirect
542. #544	C₂²×C₁₇	semidirect
543. #543	C₂²×C₁₇	semidirect
544. #542	C₂²×C₁₇	semidirect
545. #542	C₂²×C₁₇	semidirect
546. #542	C₂²×C₁₇	semidirect
547. #541	C₂²×C₁₇	semidirect
548. #541	C₂²×C₁₇	semidirect
549. #540	C₂²×C₁₇	semidirect
550. #539	C₂²×C₁₇	semidirect
551. #539	C₂²×C₁₇	semidirect
552. #539	C₂²×C₁₇	semidirect
553. #539	C₂²×C₁₇	semidirect
554. #539	C₂²×C₁₇	semidirect
555. #539	C₂²×C₁₇	semidirect
556. #539	C₂²×C₁₇	semidirect
557. #539	C₂²×C₁₇	semidirect
558. #538	C₂²×C₁₇	semidirect
559. #538	C₂²×C₁₇	semidirect
560. #538	C₂²×C₁₇	semidirect
562. #536	C₂²×C₁₇	semidirect
564. #534	C₂²×C₁₇	semidirect
565. #533	C₂²×C₁₇	semidirect
566. #533	C₂²×C₁₇	semidirect
568. #529	C₂²×C₁₇	semidirect
569. #529	C₂²×C₁₇	semidirect
570. #529	C₂²×C₁₇	semidirect
571. #529	C₂²×C₁₇	semidirect
572. #529	C₂²×C₁₇	semidirect
573. #529	C₂²×C₁₇	semidirect
574. C₂×#126	C₂²×C₁₇	semidirect
575. C₂×#125	C₂²×C₁₇	semidirect
576. #525	C₂²×C₁₇	semidirect
577. #525	C₂²×C₁₇	semidirect
578. #525	C₂²×C₁₇	semidirect
579. C₂×#123	C₂²×C₁₇	semidirect
580. C₂×#123	C₂²×C₁₇	semidirect
581. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
582. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
584. #520	C₂²×C₁₇	semidirect
585. #520	C₂²×C₁₇	semidirect
586. #520	C₂²×C₁₇	semidirect
587. #520	C₂²×C₁₇	semidirect
589. #518	C₂²×C₁₇	semidirect
590. #518	C₂²×C₁₇	semidirect
591. C₄×#41	C₂²×C₁₇	semidirect
592. C₄×#41	C₂²×C₁₇	semidirect
593. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
594. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
597. C₂×C₄×D₄	C₂²×C₁₇	semidirect
598. C₂×C₄×D₄	C₂²×C₁₇	semidirect
599. C₂×C₄×D₄	C₂²×C₁₇	semidirect
600. C₂×C₄×D₄	C₂²×C₁₇	semidirect
601. C₂×#117	C₂²×C₁₇	semidirect
602. C₂×#117	C₂²×C₁₇	semidirect
603. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
604. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
787. C₁₇	#62847	direct (N × H)
806. C₂×D₄	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3521	2
C₁₇×#3520	2
C₁₇×#3515	2
C₁₇×#3513	2
C₁₇×#3507	2
C₁₇×#3505	2
C₁₇×#3501	2
C₁₇×#3496	2
C₁₇×#3492	2
C₁₇×#3491	2
C₁₇×#3485	2
C₁₇×#3461	2
C₁₇×#3459	2
C₁₇×#3455	2
C₂×C₁₇×#539	2
C₄×C₁₇×H(5,𝔽₂)	2
C₂×C₁₇×#520	2
#62847	17

Subgroups — C17×#62847 #16920591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62847 #16920591